Laboratory Simulations of Micrometeoroid Ablation

Evan Williamson Thomas

B.S., Engineering Physics, magna cum laude 2010

M.S., Physics, 2015

University of Colorado, Boulder, CO

A thesis submitted to the

Faculty of the Graduate School of the

University of Colorado in partial fulﬁllment

of the requirements for the degree of

Doctor of Philosophy

Department of Physics

2017 This thesis entitled: Laboratory Simulations of Micrometeoroid Ablation written by Evan Williamson Thomas has been approved for the Department of Physics

Prof. Tobin Munsat

Prof. Mih´alyHor´anyi

Date

The ﬁnal copy of this thesis has been examined by the signatories, and we ﬁnd that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. iii

Thomas, Evan Williamson (Ph.D., Physics)

Laboratory Simulations of Micrometeoroid Ablation

Thesis directed by Prof. Tobin Munsat

Each day, several tons of meteoric material enters Earth’s atmosphere, the majority of which consist of small dust particles (micrometeoroids) that completely ablate at high altitudes. The dust input has been suggested to play a role in a variety of phenomena including: layers of metal atoms and ions, nucleation of noctilucent clouds, eﬀects on stratospheric aerosols and ozone chemistry, and the fertilization of the ocean with bio-available iron. Furthermore, a correct understanding of the dust input to the Earth provides constraints on inner solar system dust models. Various methods are used to measure the dust input to the Earth including satellite detectors, radar, lidar, rocket-borne detectors, ice core and deep-sea sediment analysis. However, the best way to interpret each of these measurements is uncertain, which leads to large uncertainties in the total dust input.

To better understand the ablation process, and thereby reduce uncertainties in micrometeoroid ablation measurements, a facility has been developed to simulate the ablation of micrometeoroids in laboratory conditions. An electrostatic dust accelerator is used to accelerate iron particles to relevant meteoric velocities (10-70 km/s). The particles are then introduced into a chamber pressurized with a target gas, and they partially or completely ablate over a short distance. An array of diagnostics then measure, with timing and spatial resolution, the charge and light that is generated in the ablation process.

In this thesis, we present results from the newly developed ablation facility. The ionization coeﬃcient, an important parameter for interpreting meteor radar measurements, is measured for various target gases. Furthermore, experimental ablation measurements are compared to predictions from commonly used ablation models. In light of these measurements, implications to the broader context of meteor ablation are discussed. Dedication

To my parents, for oﬀering love and support in all my endeavors. v

Acknowledgements

I would like to thank my advisor, Tobin Munsat, for all of his support through this process. I would also like to acknowledge Profs. Zoltan Sternovsky and MihályHorányi for their many insights on this project. Additionally, I offer my gratitude to the entire laboratory staff at IMPACT for their assistance with running the experiments and maintaing the accelerator. This research was funded by the National Aeronautics and Space Administration and the Solar System Exploration

Research Virtual Institute. vi

Contents

Chapter

1 Introduction 1

1.1 Interplanetary Dust Particles ...... 1

1.2 Radar Measurements of Meteoroids ...... 4

1.3 Scientiﬁc Motivation & Science Questions ...... 6

1.4 Previous Laboratory Ablation Experiments ...... 9

1.5 Ablation in Laboratory Conditions ...... 11

1.6 Thesis Outline ...... 12

2 Dust Accelerator Facility 13

2.1 Dust Accelerator Overview ...... 13

2.1.1 Dust Source ...... 16

2.1.2 Accelerating Column and Focusing ...... 17

2.1.3 Beamline Dust Detectors ...... 20

2.1.4 PSU & Deﬂection Plates ...... 23

2.1.5 Accelerator Data Handling ...... 24

2.2 FPGA Particle Selection ...... 26

2.2.1 Introduction & Motivation ...... 26

2.2.2 Filter Design ...... 27

2.2.3 Algorithm Overview ...... 33 vii

2.2.4 State Machine ...... 35

2.2.5 Hardware Implementation ...... 38

2.2.6 FPGA Results ...... 39

2.3 Summary ...... 42

3 Experimental Design 43

3.1 Design Overview ...... 43

3.2 Diﬀerential Pumping ...... 45

3.3 Ablation Chamber Overview ...... 47

3.4 Charge Collection CSA Design ...... 49

3.5 Optical Setup ...... 50

3.6 Data Acquisition ...... 52

3.7 Experimental Data Examples ...... 54

3.7.1 Charge Measurements ...... 54

3.7.2 Light Measurements ...... 56

3.8 Summary ...... 58

4 Modeling Support 59

4.1 Ablation Models ...... 59

4.1.1 CM Model ...... 60

4.1.2 SECAM ...... 68

4.2 Collection Eﬃciency ...... 80

4.3 Electron Impact Ionization ...... 84

4.4 Summary ...... 87

5 Ionization Coeﬃcient Measurements 88

5.1 Methodology ...... 88

5.2 Ionization Coeﬃcient Analytical Theory ...... 92 viii

5.3 Results ...... 94

5.4 Discussion ...... 98

5.5 Summary and Future Work ...... 102

6 Ablation Model Experimental Investigation 103

6.1 Deceleration ...... 103

6.1.1 Deceleration - Methodology ...... 103

6.1.2 Deceleration - Results ...... 106

6.2 Mass Loss Via Charge Collection ...... 116

6.2.1 Mass Loss - Methodology ...... 116

6.2.2 Mass Loss - Results ...... 117

6.3 Discussion ...... 121

6.4 Summary and Future Work ...... 122

7 Conclusion 124

7.1 Ionization Coeﬃcient ...... 124

7.2 Ablation Models ...... 125

7.3 Future Work ...... 126

Bibliography 127

Appendix

A Publications 134 ix

Tables

Table

1.1 Current global IDP mass input rates to the Earth...... 8

2.1 A list of the sensitivities of the CSA circuits on the beamline dust detectors. . . . . 21

2.2 Summary of the performance diﬀerences between the FPGA system and the analog

PSU. Each system was running in parallel, but the FPGA detected many more

particles. The percent diﬀerence column gives the percentage that the respective

system missed of the other system’s dataset...... 41

4.1 Coeﬃcient values for the vapor pressure equations for the solid and liquid phase of

iron. Reproduced from [2]...... 65

4.2 Monte Carlo results of ion spreading in the ablation chamber run at 100 V bias

between the top and bottom ablation plates. The displacement is the center value

of the Gaussian, while σ is the standard deviation...... 84

5.1 The ﬁt parameters used in Figure 5.4. The coeﬃcient (b) and exponent (α) values,

and relevant velocity ranges for the power law ﬁts to the data from this experiment

for each gas are shown. The parameter c is the least-squares best ﬁt of the parameter

in the Jones [45] integral equation (Equations 5.5 and 5.8). The calculated threshold

velocity, v0 (Equation 5.9) for each gas is the lowest meteor velocity which can

produce ionization...... 97 x

6.1 Best ﬁt deceleration results of SECAM and CM for Ar. The units of aexp and amod

2 are µm/µs and aratio is deﬁned as aexp/amod...... 114

6.2 Best ﬁt deceleration results of SECAM and CM for O2. The units of aexp and amod

2 are µm/µs and aratio is deﬁned as aexp/amod...... 115 xi

Figures

Figure

1.1 A diagram showing an example temperature proﬁle of the atmosphere from 0 to 130

km, along with the associated atmospheric layers. The region where meteoroids typi-

cally ablate is labeled. Source: http://http://www.srh.noaa.gov/srh/jetstream/atmos/layers.html. 2

1.2 Mass inﬂux (per mass decade) as a function of particle mass. The huge impactors

only contribute a signiﬁcant amount of mass on geological timescales. Reproduced

from [71]...... 4

2.1 A schematic of the IMPACT dust accelerator. The accelerator contains a dust source,

Einzel lens focusing system, a high-voltage accelerating column, three dust detec-

tors, a particle selection unit (PSU), deﬂection plates, and a target chamber. The

accelerating column consists of potential rings which run down the acceleration tube

and create a uniform accelerating electric ﬁeld...... 14

2.2 A representative particle distribution from the accelerator. There is a large dynamic

range of masses (8 orders of magnitude) and velocities (2 orders of magnitude) that

the accelerator produces...... 15 xii

2.3 A schematic of the 20 kV dust source. The reservoir holds the conducting dust and

is pulsed between 0-20 kV relative to the extraction plate. The needle is held a ﬁxed

voltage, which is set to the maximum of the reservoir voltage. The dust becomes

slightly negatively charged by the pulsing reservoir and begins to levitate. The dust

becomes charged positively when it contacts the needle. The charged dust is then

accelerated by the electric ﬁeld which exists between the needle and the extraction

plate and is ejected through the pinholes. Reproduced from [81]...... 16

2.4 A schematic showing the charging mechanism for the Pelletron. The charging mech-

anism is induction-based where the inductor/supressor creates an electric ﬁeld be-

tween them and the grounded pulley. The pulley is conducting such that when a

chain metal pellet is touching the pulley, it is one grounded conductor. Looking

at the inductor side, as a pellet moves into the electric ﬁeld between the inductor

and the pulley, a charge separation occurs where negative charge is pushed onto the

pulley. Therefore, as the pellet moves oﬀ of the pulley, but is still in the electric

ﬁeld of the inductor, it gains a positive charge. The chain then transports that

chrage to the terminal where the charge is pulled oﬀ by the pickoﬀ pulleys. Source:

http://www.pelletron.com/charging.htm ...... 18

2.5 Two SIMION simulations of the dust source, Einzel lens, and accelerating tube

entrace. In the top panel (a), the Einzel lens is at 0 V, which produces a diverging

beam in the accelerating tube. In the bottom panel (b), the Einzel lens is at 10 kV,

which collimates the beam. Reproduced from [81]...... 19

2.6 A schematic of the image charge dust detectors on the accelerator beamline. The

detector consists of a conducting cylinder which is grounded through a charge sen-

sitive ampliﬁer (CSA). As the charged dust particle moves through the cylinder, it

induces an image charge on the cylinder which is ampliﬁed by the CSA...... 21 xiii

2.7 A schematic of the CSA design used on the beamline dust detectors. The circuit has

three stages: a CSA stage with a sensitivity of 1 × 1011 V/C, an ampliﬁer stage with

a 10× gain, and a unity gain buﬀer ampliﬁer stage to drive a 50 Ω load...... 22

2.8 An example signal from a beamline dust detector. The amplitude of the signal is

proporitional to the dust charge while the width of the signal is proportional to the

dust velocity...... 22

2.9 A schematic of the data acquisition system for the accelerator. The ﬁrst two beamline

detectors, PSU pulse, and ﬁnal beamline detector are digitized and sent to a Lab-

VIEW program, which reads in all four waveforms. The data is then transferred to a

LabVIEW queue, which is stored in the computer’s RAM. Next, another LabVIEW

program (DBConnection.vi) converts the LabVIEW waveforms into a compressed

HDF5 ﬁle and saves it to a MySQL database. The batch processor (Batch.vi) reads

the HDF5 ﬁle, analyzes it, marks it as “processed”, and saves the dust metadata to

the database entry corresponding to that dust event...... 26

2.10 A schematic of a cross-correlation between a square signal and a ﬁlter function. The

signal (red) is moved over the ﬁlter function (black) and the overlapping area is

integrated to generate a ﬁlter repsonse (dark red). To improve readability, the ﬁlter

repsonse is not to scale...... 28

2.11 A general schematic of the ﬁlters used in the cross-correlation calculation. Three re-

gions make up the ﬁlter (A, B, and C) with amplitudes of -1, +2, and -1 respectively.

Region B is twice the width of regions A and C such that there is equal positive and

negative area across the entire ﬁlter. The ﬁlter is indexed by the variable m and

contains a total of 3W points. The index, m, is deﬁned from 0 to −3W , where

m = −3W correpsonds to the data point that was sampled 3W samples in the past.

See text for more details...... 28 xiv

2.12 Simulation showing the eﬀectiveness of the cross-correlation calculation. The top

plot is an ideal input signal, the second is the ideal signal embedded in noise (SNR

= 0.75), the third is the ﬁlter shape (arbitrary units), and the last plot shows the

correlation response. The input signal is perfectly matched (in width) to the ﬁlter. . 31

2.13 A sensitivity plot for all 7 ﬁlters. The ﬁlters are correlated with a ideal 300 mV

square pulses. Filter 1 peaks at the lowest velocity, then Filter 2, Filter 3, etc. as

the filters progress in velocity. Each successive filter is plotted on top, but all filters

continue along the same line...... 32

2.14 The states with their transitions are shown. Also, the function of the state, along

with the boolean expression controlling the next state, is given. Unless otherwise

speciﬁed, if the boolean expression is false, the state repeats on the next clock cycle. 36

2.15 The FPGA and analog PSU particle data...... 40

2.16 A plot of the three detector signals for the particle of lowest charge (1.6 × 10−16 C)

detected by the FPGA (for this particular comparison experiment). The waveforms

are artiﬁcially oﬀset from one another for readability. The bottom waveform is the

ﬁrst detector, the middle is the second detector, and the top is the ﬁnal detector. The

left ﬁgure is the raw detector waveforms, and the markings on each signal indicate

the location of the dust particle signal as it moves down the beamline. The right

ﬁgure is a plot of the diﬀerentiated and smoothed signal from the analysis script.

The vertical black lines show the window the analysis script used to look for the

signal on the third detector (based on speed estimates from the ﬁrst two detectors).

Using the analysis script, it is clear that there is indeed a signal embedded in the

noise...... 41 xv

3.1 Schematic of the experimental setup (side view). The particles are accelerated to >

10 km/s using the accelerator facility and the ablation chamber is mounted at the

end of the beamline. A two stage diﬀerential pumping system separates the high

vacuum beamline from the pressurized ablation chamber...... 44

3.2 Simulations showing the dust heating for two particles in two diﬀerent pressures. The

pressures are the measured pressures in the second stage of the diﬀerential pumping

corresponding to ablation chamber pressures of 300 mTorr and 20 mTorr (left and

right panels, respectively)...... 47

3.3 The electronic schematic of the charge sensitive ampliﬁers used in the ablation cham-

ber. The ﬁrst and second stage have a combined sensitivity of 1 × 1013 or 2 × 1012

V/C (depending on the feedback capacitor used), and the third stage is a unity gain

buffer amplifier with a bandpass filter with cutoff frequencies 23 Hz and 21 kHz. . . 49

3.4 Schematic of the ablation chamber PMT setup (top view). Each PMT has 16 chan-

nels with each channel having an eﬀective area of 0.12 cm2. The PMT has a slit

between it and the window, which creates a pinhole image of the beamline on the

PMT face. Since the PMT face has 16 channels spread across it, this creates 16

spatial bins along the beamline axis (0.64 cm resolution). The green region shows

the view of the beamline through the slit for PMT 2, channel 1...... 51

3.5 The electronic schematic of the transimpedance amplifer circuit, which ampliﬁes each

PMT channel...... 52

3.6 A block diagram of the data acquisition system. The ablation chamber electronic

signals, along with the last beamline image charge detector, are saved by three

Joerger Model TR analog digitizers. The digitizers are triggered by the accelerator

PSU, and the data is sent to a LabView-controlled computer. The computer saves

all signals into a single ﬁle with 47 waveforms...... 53 xvi

3.7 An example of a particle ablating in the experimental chamber. The ﬁgure shows the

charge collection CSA signals vs. time. In this case, the experiment was conﬁgured

to collect ions...... 55

3.8 Ions collected by each electrode channel for the particle ablation event shown in

Figure 3.7. The 16 segmented collectors give a spatial resolution of 2.6 cm for the

charge measurements, which will allow for comparisons to ablation model predictions

in future studies...... 55

3.9 An example ablation event with both the charge and PMT signals shown. The charge

signals are color coded to match Figure 3.7. The PMT channels are artiﬁcially oﬀset

from one another, with the channels organized in chronological order from top to

bottom...... 56

3.10 The PMT pulse times from Figure 3.9 plotted as distance from the chamber en-

trance vs. time. The data was ﬁt to a linear ﬁt, which gives an average velocity of

12.21±0.29 km/s compared to a beamline measured velocity of 12.77±0.38 km/s. . . 57

4.1 Flow chart illustrating the structure and ﬂow of the CM model...... 62

4.2 Measured real (n) and imaginary (k) indices of refraction for iron. Reproduced from

[75]...... 63

4.3 Measured speciﬁc heat of iron as a function of temperature. Reproduced from [22]. . 64

4.4 Coordinate system for a suface element of the spherical particle. U is the velocity

of the dust (seen in the frame of the dust as the velocity of the impinging gas). The

coordinates are such that the x-axis is normal to the surface at the origin and the

y-axis is tangent to the surface. The angle, θ, is the angle the velocity vector makes

with the element. Reproduced from [34]...... 71 xvii

4.5 Coordinate system used for the integration over the dust surface. The x and y axes

are the same as that shown in Figure 4.4, in that they are ﬁxed with a diﬀereential

area element (red region). The normal pressure p and the tangential stress τ delivered

by the gas are labeled. The area of the annulus is 2πR2 sin αdα and integrating α

from 0 to π integrates over the entire spherical surface...... 77

4.6 Flow chart illustrating the structure and ﬂow of the SECAM model...... 80

4.7 The results from the Monte Carlo simulations. Top: The spatial distribution of

ions collected on the electrodes for vdust= 20 km/s and p = 0.2 Torr. The position

x = 0 marks the place where the atom ablated from the particle. Bottom: The

average position of collection (along the path of the dust particle, i.e. x-direction)

as a function of pressure for three diﬀerent dust velocities. The standard deviation

is shown for the 20 km/s case...... 82

4.8 The cross sections of the various types of collisions included in the secondary ionza-

tion model. See text for more details...... 85

4.9 The probability (as a function of pressure and bias voltage) that a free electron,

generated directly by the ablation process, will generate an additional ion-electron

pair before it is collected. The calculations are for N2 and a gap distance of d=3.6 cm. 86

5.1 SECAM simulations (see Section 4.1.2) showing the velocity fractional loss for iron

particles impacting N2 at pressures of 50, 100, and 200 mTorr. The mass and ve-

locity space investigated was determined based on the parameters of the majority of

particles the accelerator produces (see Figure 2.2). To simplify the simulations, all

7 −1 −1 accommodation coeﬃcients were set to 1, Cp = 0.47 ×10 erg g K , and = 1. . 89

5.2 β measurements from this experiment separated by species. The black points are β

values measured from ions, while the red are electrons...... 91

5.3 β measurements from this experiment separated by ablation chamber pressure. . . . 91 xviii

5.4 β measurements from the current experiment (black points), past experiments by

Friichtenicht, et al. [29] (green lines) and Salttery and Friichtenicht [84] (orange

line), current experimental data power law ﬁts (magenta lines), the Jones integral

equation for β(v) with a ﬁtted parameter c (blue lines), and the Jones integral for

β(v) with the parameter c from Jones [45] (gray dashed line). The dotted magenta

line is a power law ﬁt that includes data points only up to 45 km/s. The blue and

red dashed lines on the CO2 plot are also ﬁtted Jones [45] equations for β(v) but

are only ﬁt to data points from 20-30 and from 20-25 km/s, respectively. In the

second N2 plot containing the corrected β values, the green line is the same data

from Friichtenicht, et al. [29], but the blue and magenta lines are both ﬁt to the

corrected β values (black points)...... 96

5.5 β vs. velocity for the uncorrected N2 data. The β values are color coded by ab-

lation chamber pressure with the bias voltage and estimated additional ionization

precentage labeled...... 98

6.1 Ar position vs. time curves for the experimental data (black), best ﬁt model result

(red), and the model result using the parameters from Vondrak et al. [92] (blue).

The black x’s are experimental light peaks which were outliers (assumed to be noise

artifacts) and removed from the data set...... 107

6.2 Ar position vs. time curves for the experimental data (black), best ﬁt model result

(red), specular model result (green), and diﬀuse model result (blue). The black x’s

are experimental light peaks which were outliers (assumed to be noise artifacts) and

removed from the data set...... 108

6.3 O2 position vs. time curves for the experimental data (black), best ﬁt model result

(red), and the model result using the parameters from Vondrak et al. [92] (blue).

The black x’s are experimental light peaks which were outliers (assumed to be noise

artifacts) and removed from the data set...... 109 xix

6.4 O2 position vs. time curves for the experimental data (black), best ﬁt model result

(red), specular model result (green), and diﬀuse model result (blue). The black x’s

are experimental light peaks which were outliers (assumed to be noise artifacts) and

removed from the data set...... 110

6.5 The experimental deceleration vs. modeled (both CM and SECAM) deceleration for

Ar. The best ﬁts are again in red, and the special cases for each model are blue

and green. Namely, blue in the CM plot are the parameters used in Vondrak et al.

[92] and blue and green in the SECAM plots are for diﬀuse and specular reﬂection,

respectively...... 112

6.6 The experimental deceleration vs. modeled (both CM and SECAM) deceleration for

O2. The best ﬁts are again in red, and the special cases for each model are blue

and green. Namely, blue in the CM plot are the parameters used in Vondrak et al.

[92] and blue and green in the SECAM plots are for diﬀuse and specular reﬂection,

respectively...... 112

6.7 Mass vs. velocity for the best ﬁt results for Ar. The color on each point is the ratio

of the experimental deceleration to the model deceleration...... 113

6.8 Mass vs. velocity for the best ﬁt results for O2. The color on each point is the ratio

of the experimental deceleration to the model deceleration...... 113

6.9 Experimental and simulated charge proﬁles for CM. The black curve is the experi-

mental data, the red curve is the least-squares best ﬁt, the magenta line is the peak

matching best ﬁt, and the blue curve is the result with the model parameters set to

those used in Vondrak, et al. [92]...... 119

6.10 Experimental and simulated charge proﬁles for SECAM. The black curve is the

experimental data, the red curve is the least-squares best ﬁt, the magenta curve is

the peak matching best ﬁt, and the blue curve is the result with the model parameters

set to diﬀuse reﬂection...... 120 Chapter 1

Introduction

1.1 Interplanetary Dust Particles

Dust is pervasive throughout the solar system - if all of the dust in the inner solar system were to be compressed, it would form a moon 25 km in diameter [71]. This dust, also referred to as Interplanetary Dust Particles (IDPs), has a variety of origins including: asteroids, comets

(both long period Halley Type Comets and short period Jupiter Family Comets), Oort Cloud

Comets, Edeworth-Kuiper Belt Objects, and interstellar dust [87]. The main sources of the IDPs encountered by the Earth are collisions between asteroids and long-decayed cometary trails [96, 14].

These two sources produce the continuous input of sporadic meteors, which have long since lost contact with their parent bodies. In contrast, fresh dust from the sublimation of comets which crossed Earth’s orbit recently (within 100 years or so) produce the meteor showers, which account for only about one quarter of the visually observable meteors [14, 71].

The sporadic background and meteor showers produce a continual IDP input into the Earth’s atmosphere, with typical particle masses of 1-10 µg [71]. As these particles ablate in the upper atmosphere, they produce layers of metal atoms such as: iron (Fe), magnesium (Mg), calcium (Ca), potassium (K) and sodium (Na) which peak around 90 km [71]. To provide context, Figure 1.1 shows an overview of the atmospheric layers and where meteor ablation typically takes place.

The metallic atoms, produced by the ablation of IDPs in the Earth’s upper atmosphere, are responsible for a diverse range of aeronomical phenomena including: (1) the nucleation of noctilucent clouds, (2) sporadic layers of metallic ions (i.e. sporadic E layers), (3) eﬀects on the 2

Meteors Altitude[mi] Altitude[km]

Temperature [°C]

Figure 1.1: A diagram showing an example temperature proﬁle of the atmosphere from 0 to 130 km, along with the associated atmospheric layers. The region where meteoroids typically ablate is labeled. Source: http://http://www.srh.noaa.gov/srh/jetstream/atmos/layers.html.

stratospheric aerosol and O3 chemistry, and (4) ocean fertilization with bio-available Fe [71]. The following is a brief description of each phenomena. (1) Noctilucent clouds are thin (1-2 km vertical extent) clouds that occur from 80-86 km in altitude during the summer at high latitudes. These clouds, which are believed to have meteoric material as the nuclei agent, are thought to be sensitive indicators of climate change [71, 69, 74]. (2) Sporadic E layers are thin layers of metallic ions, typically 1-3 km vertical extent, which form between 90-140 km in altitude. These layers have a substantial eﬀect on radio communications in that they both allow for over-the-horizon high- frequency communication but also obscure space-to-ground communications [69]. (3) Meteoric materials have been proposed to play a role in the chlorine-catalyzed removal of ozone in the stratosphere through a variety of means [68, 69, 61]. Also, the meteoric material can act as a 3 nuclei for stratospheric aerosols and form polar stratospheric clouds, which play a major role in polar ozone depletion [69, 62, 21]. (4) Low concentrations of iron in the deep sea prevent the full utilization of macronutrients by phytoplankton in the upper ocean. Atmospheric inputs of iron into remote regions far away from continental sources, like the Southern Ocean, are required for full utilizaiton of macronutrients, and meteoric iron could play a signiﬁcant role in supplying the bio-available iron in those regions [71, 69, 44].

Apart from a better understanding of the atmospheric eﬀects, IDP measurements at Earth also provide constraints on inner solar system dust models. These models provide insight into the dust enviornment of the solar system as well as the evolution and planetary formation processes of other solar systems. For example, phenomenological (i.e. semi-dynamical) dust models describe the size, spatial, and velocity distributions of dust that are used for assessing satellite impact hazards, designing spacecraft impact experiments, and assessing extrasolar emissions such as the cosmic microwave background radiation [64, 33, 24, 85, 23]. Additionally, fully dynamical dust models, with dynamic underpinnings to sources and sinks, give more complete knowledge of dust evolution in this solar system and even provide insights into the evolution of other solar systems (e.g. debris disks) [64, 63]. Therefore, because of both the aeronomic and astrophsyical phenomena associated with IDPs, the total micrometeoroid mass input into the atmosphere is a quantity of signiﬁcant interest.

The IDP input to the Earth is measured in a variety of ways including: satellite detectors, radars, lidars, rocket-borne detectors, ice core and deep-sea sediment analysis. Figure 1.2 shows the mass inﬂux of particles as a function of their size and the associated detection methods. The smallest particles (< 10−9 g) are only detectable by impact detectors on satellites (e.g. the Long

Duration Exposure Facility (LDEF) [54]), whereas radars can detect particles with masses > 10−9 g (see for example [41, 25, 16, 55]) and meteoroids with masses ≥ 10−3 g can be detected optically

(both with spectroscopy and imaging - see for example [43, 46, 79]). Simultaneous radar and optical meteoroid measurements have also been performed recently [57, 95, 94]. While impact detectors, radars, and optical measurements measure the meteoroids either while it is still intact or actively View Article Online

particles after ejection from these sources. The model is ionize through hyperthermal collisions with air molecules.5 constrained by observations of the zodiacal cloud in the This creates a trail of electrons behind the meteoroid, which infrared at 25 mm, made by the Infrared Astronomical Satellite can be detected by radar. The mass and speed of the meteoroid (IRAS). The ZCM predicts that 85–95% of the dust in the then have to be estimated indirectly.22 Furthermore, the inner solar system comes from Jupiter family comets, which wavelength of the radar only samples a subset of the mass/ are comets with short orbital periods (typically 20 years) and velocity/altitude distribution of the meteoroids, so that some an aphelion close to the orbit of Jupiter. The remaining dust extrapolation is required to estimate the total mass input.11 comes from the asteroid belt and Halley family and Oort cloud In the past two decades, high-powered large aperture comets. Most of the dust, which drifts into the inner solar (HPLA) radars, such as the Arecibo Observatory and the system under the influence of Poynting-Robertson drag (solar EISCAT radars in the Arctic, have been able to detect by photon pressure, which causes the orbital velocities of IDPs incoherent scatter the meteor head echo (i.e. the ball of plasma with a radius larger than B1 mm to decelerate), has a mass in around the ablating particle as it descends through the atmo- the range 1–10 mg and provides a continuous input of sporadic sphere). This enables measurements of the direction of origin, meteoroids. The model predicts that these IDPs should enter velocity, deceleration and (indirectly) mass to be made.10,23–25 the terrestrial atmosphere from a near-prograde orbit with a While initially the mean entry velocity seemed to be significantly 1 1 mean speed of B14 km sÀ , producing a global mass input higher, around 40–50 km sÀ , than the velocity measured with 1 around 270 t dÀ , the highest estimate in Table 1. conventional meteor radars, it has now been realised that there The input flux of meteoroids into the atmosphere is so is a sampling bias towards high-speed meteors.26 Conventional uncertain because no single technique can observe particles meteor radars do not efficiently detect meteors which occur at 12 over the mass range from about 10À to 1 g which make up higher altitudes (>100 km), because of the rapid diffusion of the bulk of the incoming material.3 Fig. 2 shows that the the ionized trails. Since faster meteors generally occur at particle mass can vary by 30 orders of magnitude, although higher altitudes, distributions measured by meteor radars are the largest contribution of mass entering the atmosphere on biased towards the lower speeds. In fact, it has now been a daily basis comes from particles around 10 mg. Assuming a shown27 that HPLA radars observe the same population of 3 meteoroid density of B2.8 g cmÀ , these particles will have a meteors as observed by meteor radars, and in addition detect a diameter of B200 mm. There is a population of huge impac- population of faster meteors that ablate at altitudes where tors with masses greater than 1010 g which make a significant trails are not efficiently detected. However, the magnitude of contribution, but only on a geological timescale! Any single the head echo4 still depends on the meteoroid mass and measurement technique will only sample a subset of this size velocity, and each HPLA radar is sensitive to a particular ablating, lidars, rocket-bornedistribution. detectors, For instance, ice core optical and deep-sea camera networks sediment analysiswhich allmass measure range. the27 This implies that the velocity distribution of the observe visible meteors detect particles larger than about smallest particles measured by an HPLA radar will be biased remnants of meteoroids after entering the atmosphere. Lidars tuned to the optical transitions 1 mg in mass, or 1 mm in radius. Larger particles (approaching towards faster speeds: small and slow particles will not have of meteoric metals1 detect g in mass) the atomic are much metal rarer, layers so that [71, counting 53, 37], while statistics rocket-borne on a su detectorsfficient kinetic are energy to ablate, and hence will not produce time scale of months start to matter. sufficient electrons to be detected. The average entry speeds are Downloaded by University of Colorado at Boulder on 11 January 2013

Published on 07 June 2012 http://pubs.rsc.org | doi:10.1039/C2CS35132C 1 28 able to measure chargedMeteor meteoric radars smoke measure particles particles (MSPs)(formed with masses between by aggregating about meteoricnow thought metallic to be between 25 and 30 km sÀ . It should be 9 3 10À and 10À g, and therefore cover the most important mass noted that particles which originate within the solar system compounds) [73, 76, 71]. Finally, measuring the deposition of Ir, Pt, super-paramagnetic Fe and 1 range (Fig. 2). Meteor radar data was used to produce a much- must have entry velocities that range from 11.5 km sÀ for a 1 Os in ice cores andquoted deep-sea estimate sediments of 44 also t dÀ allowsfor the for global an estimation input, although of the IDP this inputparticle (see [71] in and the same prograde orbit as the Earth (i.e. orbiting in 1 involved artificially increasing the size distribution to match visual the same direction), to 72 km sÀ for a particle in a retrograde references therein).meteor observations.11 The evaporating atoms, particularly metals, orbit.2 9 The population of IDPs smaller than 10À g can only be measured by impact detectors on satellites. An important estimate of the IDP input was provided by the Long Duration Exposure Facility (LDEF), an orbital impact detector placed on a spacecraft for several years, which yielded an estimate of 1 9 110 t dÀ . However, the LDEF experiment measured crater size, which was treated as a proxy for particle kinetic energy. Hence, the particle velocity distribution had to be assumed in order to determine the mass distribution. If the average velocity 1 is higher (see above) than the value of only 18 km sÀ that was employed in the LDEF analysis, then the corresponding mass distribution would be shifted down by more than an order of magnitude.10 Because of their very high entry velocities, meteoroids undergo rapid frictional heating by collision with air molecules. If the particles reach melting point (B1800 K), their constituent minerals will then rapidly vaporize – the process termed Fig. 2 Mass influx (per decade of mass) plotted against particle mass meteoric ablation. Ablation tends to occur where the atmo- Figure 1.2: Mass influx (per mass decade) as a function of particle mass. The huge impactors only [data taken from Flynn21]. spheric pressure is around 1 mbar. In the case of the Earth, contribute a significant amount of mass on geological timescales. Reproduced from [71].

This journal is c The Royal Society of Chemistry 2012 Chem. Soc. Rev., 2012, 41,6507–6518 6509

1.2 Radar Measurements of Meteoroids

Radar measurements play a particularly important role in the observation of the incoming

extraterrestrial particles, as this technique is (1) sensitive to the size range where most of the mass

input occurs [71]; and (2) easily provide large statistical datasets (e.g. in a day radars can detect

thousands of events). Particles entering the atmosphere with velocities >11 km/s produce trails

of ionized gas (i.e. plasma) that allow for the detection and characterization of individual meteors 5 if the plasma is dense enough for the radio frequencies transmitted by the radar to bounce oﬀ of them, producing detectable echoes [65, 18, 39, 25]. Radar observations of meteors are sensitive to particles with masses between 10−9 − 10−3 g.

There are three types of radar echoes that can be used to measure meteor properties: specular reflection from the plasma trail, non-specular reflection from the trail, and head echoes. Specular reflection is a phenomena observed by all-sky VHF meteor radars, whereas non-specular reflection and head echoes are more commonly detected by high power large aperture (HPLA) radars.

Classical meteor radars, which began to be used to study meteors shortly after the second world war [14], operate in the high frequency/very high frequency (HF/VHF) range and detect meteors through specular reflection off of the meteor trail. Specifically, classical meteor radars measure the velocity of the meteor by a detection of the Fresnel diffraction pattern off of the meteor trail

[40] and require the meteor trail to be perpendicular to the radar beam (see [56] and [14] for an overview of classical meteor physics). Non-specular reflection is a phenomenon observed by HPLA radars, and have been attributed to coherent radio scatter from magnetic field aligned irregularities in electron density [26]. Finally, head echoes (also detected by HPLA radars) are radar reflections off of a layer of plasma surrounding the meteoroid as it ablates [40]. Head echo detections allow for the measurement of the instantaneous meteoroid velocity using the Doppler shift of the returned echo, which is markedly different from the techniques used by classical meteor radars.

There are several important biases in the interpretation of both classical meteor radars and

HPLA measurements. Firstly, the Fresnel diffraction intensity is very sensitive to the orientation of the meteor trail and requires that the meteor trail be perpendicular to the radar beam, as mentioned above [40]. Secondly, the height ceiling effect refers to a tendency of the highest velocity meteors to ablate and form trails at higher altitudes where the trails rapidly diffuse. The rapid diffusion does not allow for the trail to form over a Fresnel zone so that while the trails produce reflections, velocity measurements cannot be made. However, the height ceiling effect can be compensated for by using ultra low frequencies. Studies at 2 MHz, which moves the height ceiling to 140 km, show peak meteor rates at ∼104 km, which agrees with HPLA distributions [40]. Additionally, there is a 6 mass bias in the classical meteor radar techniques in that the more massive meteors produce trails at lower altitudes where they are more easily detectable [40].

The biases of HPLA measurements were recently investigated [41, 42], and involved the development of a probabilistic approach to radar detectability as a function of meteor parameters.

The probability of detection depends on mass, velocity, and entry angle with respect to the beam.

The analysis particularly focused on the eﬀect of low velocity meteors (∼11 km/s) not reaching high enough temperatures to vaporize the less volatile meteoric elements like Fe, Mg, or Si and thus only releasing alkalis like Na and K. The release of alkalis will occur very rapidly and in a very narrow altitude range. Since the detection eﬃciency depends on where in the radar beam the plasma is produced, and since this scenario would also produce less total electrons which further constrains where in the beam the plasma must be generated, this introduces a complicated bias which needs to be accounted for when reconstructing velocity or mass distributions from HPLA data.

1.3 Scientiﬁc Motivation & Science Questions

The research presented here is motivated by uncertainties in the interpretation of IDP measurements, particularly radar measurements, and the resulting uncertainty in the total IDP mass input to the Earth. IDP measurements can be approximately categorized as space-based measurements, atmospheric measurements, and terrestrial measurements (see Section 1.1). All of the measurements, however, have biases that introduce uncertainties in their interpretation leading to diﬀerences in the ﬁnal value of the total IDP mass input. A review of IDP measurements was published in 2012 [71] and Table 1.1 gives an overview of the current estimates and their uncertainties. Table 1.1 indicates that the estimates for the total IDP mass input range from 3-300 t/d

(metric tons/day). However, in a more recent review (2015) [72] the author indicates that when an atmospheric circulation model is used to interpret results obtained from the ice core measurements in Greenland (see [30, 50]) and Antarctica (see [51, 31]), those measurements instead indicate a global input rate of 75-100 t/d. The ice core measurements in Table 1.1 that indicate a much 7 higher rate are most likely overestimated due to an assumption of dry deposition, instead of wet deposition (i.e. snow). Therefore, the current best estimates for the IDP input mass rate are closer to 5-100 t/d [72].

The factor of 20 uncertainty in the incoming meteoric mass is in part due to the wide range of particle masses/sizes and the lack of a single technique that provides measurement of the ﬂux over the entire mass range (see Figure 1.2). The bulk of the incoming material is from particles in the range of 10−10 − 1 g with a peak at around 10−5 g (∼100 µm in radius [14]). The wide range of incoming velocities, 11-72 km/s [6], further complicates the situation as some measurement methods for inferring ﬂux depend strongly on both the mass and the velocity of the particles.

The interpretation of meteor observation using radar techniques is subject to a number of biases, as the ablation and ionization are functions of the particles’ mass, density and incoming velocity and angle. Such biases also depend on the scattering mechanisms being considered (see

Section 1.2). The ionization coefficient, β, is a critical parameter in these measurements in that it relates the physical ablation of the meteor to the intensity of the radar return. However, there remain significant uncertainties in the β values for the various chemical components of micrometeoroids and atmospheric gases due to the historical lack of measurements. Furthermore, the physical models describing the ablation process, including the differential ablation of the various chemical components, have not yet been fully validated in laboratory experiments. This introduces various biases in the radar measurements with velocity, size and composition [39, 41].

Recently, Janches, et al. [41] described the diﬃculty of reconciling meteor head echo observations using the Arecibo 430 MHz radar with the Zodiacal Dust Cloud (ZDC) model (see [64, 63]).

The ZDC model predicts that most of the IDP mass reaching the Earth are particles from Jupiter

Family Comets (JFCs) in the 1-10 µg range with an average velocity of 14 km/s [10]; however, this population is missing from the radar measurements, which raises the question whether the lack of detection is due to their inexistence or an inability of the radars to detect them. Given these inconsistencies, it was suggested that lowering β from its commonly used values by one or two orders of magnitude would bring the radar measurements into better agreement with the ZDC 8 Technique IDP Input Reference Potential Meas. Type [t/d] Problem Micrometeorites in 4 ± 1 [89] Lower limit, since Terrestrial polar ice most IDPs ablate HPLA radars 5 ± 2 [55] Possible velocity Atmosphere bias/selective mass range Fe in Antarctice ice 15 ± 5 [51] Very little wet depo- Terrestrial core sition by snow Na layer modeling 20 ± 10 [70] Sensitive to vertical Atmosphere eddy diﬀusion Fe/Mg strato- 22-104 [21] Limited geographi- Atmosphere spheric aerosols cally Iridium aerosols at 27 [90] Limited geographi- Atmosphere South Pole cally Vostok ice core in 24-50 [51] Potentially inaccu- Terrestrial Antarctica rate model of deposition Optical extinction 40 [35] Uncertainty in re- Atmosphere measurements fractive indices Zodiacal cloud ob- 37 [63] Needs to be con- Space-based servations and mod- strained by radars eling Conventional me- 44 [38] Extrapolation and Atmosphere teor radars velocity/mass bias Os in deep-sea sedi- 101 ± 36 [66] Focusing by ocean Terrestrial ments currents Long Duration 110 ± 55 [54] Sensitive to velocity Space-based Exposure Facility distribution (LDEF) Fe in Greenland ice 175 ± 68 [50] Assumed dry depo- Terrestrial core sition, when likely wet deposition is important Ir and Pt in Green- 214 ± 82 [30] Assumed dry depo- Terrestrial land ice core sition, when likely wet deposition is important Ir in deep-sea sedi- 214 [93] Focusing by ocean Terrestrial ments currents

Table 1.1: Current global IDP mass input rates to the Earth.

model.

The motivation of this work is therefore to simulate the entire ablation process in a laboratory 9 setting, because every one of the IDP influx measurement methods measure some outcome of this process (ionization, release of Na, Fe, etc.). A laboratory simulation of the ablation process allows for direct validation of ablation models which are critical to the interpreation of the various methods of measuring IDPs. Given the uncertainties in the ionization coefficient (β), as well as the overall physical ablation process, this work will address two main scientific questions:

(1) Are the currently used values of the ionization coeﬃcient (β) correct? Since β

directly relates the intensity of the radar return and the physical parameters of the meteor

(e.g. mass), understanding the velocity dependence of β for particles with a known mass

is critical to correctly interpreting radar measurements.

(2) How well do the physical ablation models describe the ablation process? Abla-

tion models are used to model the deceleration, heating, and evaporation of micrometeors.

The evaporation of the various chemical constituents, and therefore the generation of the

plasma, must be modeled correctly in order to interpret radar measurements.

1.4 Previous Laboratory Ablation Experiments

Much of the previous laboratory ablation research has focused on measuring particular ablation parameters, such as the ionization coefficient. There are two types of experimental methods for determining the ionization coefficient of the various elements present in meteoric material. In the first, high-velocity neutral metal atoms are introduced into a collision chamber filled with the target gas and the ionizing collision cross section is measured (where β is the ratio of the ionization cross section to the total cross section). Out of the materials relevant for meteoroid composition, this method has been applied only to alkali metals. Early measurements, performed by Bydin and

Bukhteev [12] focused on Na and K atoms colliding with N2 and O2 molecules over a velocity range of 35 - 130 km/s. Moutinho, et al. [60] measured the ionization cross section of Na and K atoms with O2 molecules in the velocity range of 5-13 km/s. Cuderman [20] performed a more rigorous experimental study of ionizing collisions between K and various gases, including O2 and N2, over a 10 velocity range of 15-70 km/s. The results are reasonably similar to that of Bydin and Bukhteev [12] and the ionization cross section with O2 is roughly an order of magnitude larger than that with N2 throughout the range investigated. Kleyn, et al. [49] also measured the ionization cross sections of alkali atoms with oxygen over an extended range of velocities. In the overlapping range the results are similar to that by Moutinho, et al. [60], however, no meaningful comparison is provided to the data by Cuderman [20].

The second experimental method, which includes the experimental facility described in this work, uses a dust accelerator that generates small particles with high velocities. The accelerated particles enter a pressurized chamber, where the partial or complete ablation occurs over a short distance. With the assumption that individual atoms evaporate off of the surface of the particle and collide with the background gas, the ionization coefficient can be directly measured by collecting the number of ion-electron pairs produced in the case of complete ablation. The ionization coefficient is then simply the total number of ion-electron pairs divided by the total number of atoms in the particle. Slattery and Friichtenicht [84] measured β for iron particles ablating in argon gas and air in the velocity range of 20 - 40 km/s. Friichtenicht, et al. [29] extended the measurements for a wider range of background gases, including N2 and O2. Friichtenicht and Becker [28] used air as the target gas and dust particles made of Cu and LaB6.

The current understanding of β and its variation with velocity is based on these experimental results, which are limited for non-alkali metals. The results reported in Chapter 5 address this limitation and provide experimental parameters for the commonly used Jones [45] analytical β model. They also demonstrate that the model eﬀectively describes the velocity variation of β for iron particles impacting N2 and air with atmospherically relevant speeds with the exception of high-speed impacts (> 70 km/s).

The ablation facility described here, as well as the recently developed Meteoric Ablation Sim- ulator (MASI) [10], are the first laboratory experiments capable of measuring the ablation process and not limited to measuring particular ablation parameters. The MASI instrument simulates ablation after assuming a particular heating temporal profile. In particular, it uses a heating filament 11 to replicate the heating profile predicted from ablation models. However, the temperature profile must be calculated from meteor physics equations and assume values for parameters like the free molecular drag coefficient and the free molecular heat transfer coefficient [10].

1.5 Ablation in Laboratory Conditions

The experimental setup described here makes it possible to simulate the ablation process and benchmark ablation models against well-defined laboratory data and obtain important physical parameters. The typical size of micrometeoroids in Earth’s atmosphere is 100 µm, the atmospheric pressure at 90 km is ∼ 1 mTorr, and the ablation takes place over many kilometers. This process is simulated in the laboratory accelerator setup with both the particle size and ablation path scaled down significantly. The typical size of the particles used in the accelerator are ∼0.05 µm and the ablation chamber is 41 cm long, requiring higher pressures (15-500 mTorr) to achieve complete ablation. The relevant physical parameters, however, are similar in the two conditions. First, the ablation in both cases occurs in the free molecular regime, where the dust size is much smaller than the mean free path between atomic or molecular collisions (R/λ 1, where R is the particle radius and λ is the mean free path). Second, based on the value of the Biot number being Bi < 0.1 up to high temperatures, Vondrak, et al. [92] argued that typical (e.g. olivine) micrometeoroids will remain isothermal during the ablation process. For a spherical object, the Biot number is defined as

hR Bi = 3k , where h is the heat transfer coeﬃcient, R is the radius, and k is the thermal conductivity. Since the Biot number is proportional to the radius of the particle and inversely proportional to the thermal conductivity, the isothermal condition is valid for the smaller iron particles typically used in the laboratory experiments.

The composition of the meteoroids entering the atmosphere can be complex, which may lead to the interesting phenomena of diﬀerential ablation (see, for example, [39]). The volatile elements

(Na, K, e.g.) are evaporated first at lower temperatures and higher altitudes, while more heating and higher temperatures are needed for the evaporation of the refractory elements. The differential ablation of Na, Fe, and Ca has already been observed using the MASI [10]. Iron dust is used in the 12 initial measurements described in this work, which provides the benefit of direct comparison with earlier measurements and models. Measurements of dust particles with different compositions is left for future studies.

1.6 Thesis Outline

This thesis is divided into four main sections:

• A description of the experimental setup. Chapter 2 describes the accelerator fa-

cility, which provides the hypervelocity dust particles for the experiment. It begins with

a description of the dust source and the linear electrostatic acceleration system. Next,

the accelerator beamline components are described with an emphasis on the particle se-

lection unit (PSU). Chapter 3 describes the dust ablation facility, which is the particular

experimental setup designed for this work.

• Modeling support. Chapter 4 is devoted to describing the ablation models that are used

in the meteor community to model the physical ablation process. These models are critical

to the interpretation of the various IDP measurement techniques. Chapter 4 also describes

two supporting models, which are used to correctly interpret the experimental results from

the dust ablation facility.

• β measurements. Chapter 5 presents measurements of the ionization coeﬃcient (β) for

iron particles impacting N2, air, CO2, and He. A discussion is presented which places these

measurements into the larger context of the meteor community.

• Ablation model experimental investigation. Chapter 6 presents an analysis of exper-

imental ablation data in comparison to predictions from ablation models. Chapter 2

Dust Accelerator Facility

The enabling facility for this research is the 3 MV hypervelocity dust accelerator at the

Institute for Modeling Plasma, Atmospheres, and Cosmic Dust (IMPACT) at the Univesity of

Colorado. The dust accelerator is capable of accelerating conducting micron and sub-micron sized particles from 1-100 km/s and can detect accelerated particles with charges of > 0.08 fC. The dust is loaded into a dust source and is accelerated, one particle at a time, through the electrostatic high- voltage column and moves through two image charge dust detectors. A particle selection unit (PSU) then analyzes (in real time) the detector signals and measures the velocity and charge of the dust and sends a signal to a pair of electrostatic deflection plates to either allow the particle to continue or deflect it out of the beamline. Lastly, the dust moves through a final detector just before entering the experimental apparatus. This chapter describes the components of the accelerator facility, and the description of the particular experimental setup for ablation measurements is given in Chapter

2.1 Dust Accelerator Overview

The dust accelerator facility at IMPACT (see Shu et al. [81]), which is based on the Max-

Planck-Institut f¨urKernphysik accelerator [59], is shown schematically in Figure 2.1, and the following is a walkthrough of the components. The high voltage is generated by a National Electro- statics brand Pelletron generator. The dust source, Einzel focusing lens, and acceleration column are housed inside the Pelletron shell which is kept at a pressure of 6 atm of SF6 to reduce sparking. 14

The dust (micron and sub-micron sized conducting particles) is placed inside the dust source, which charges the particles and gives them a small (∼ 15 kV) initial pre-acceleration. The acceleration column, which can be charged to 3 MV, then further accelerates the charged dust particles down the beamline. The acceleration column consists of an acceleration tube lined with metallic potential rings, which create a uniform electric field. Next, the dust moves through two image charge dust detectors, separated by 30 cm, which measure the particles’ velocity and charge as they move through the detectors. The detector signals are fed into the particle selection unit (PSU), which uses logic programmed on a field-programmable gate array (FPGA) to measure the particles’ properties (see Section 2.2) and decide whether the particle meets the user-defined criteria (i.e. mass, speed, or charge range) for the particular experiment that is using the accelerator. A signal is then sent to a pair of electrostatic deflection plates which open to allow a particle through, or stay closed if the particle has not met the criteria. A final detector measures the dust just before entering the target chamber to verify the particle selection process.

Pelletron Shell Acceleration Target Tube Deflection Final Chamber Detectors Plates Detector

Dust Source PSU & Einzel Lens

Figure 2.1: A schematic of the IMPACT dust accelerator. The accelerator contains a dust source, Einzel lens focusing system, a high-voltage accelerating column, three dust detectors, a particle selection unit (PSU), deﬂection plates, and a target chamber. The accelerating column consists of potential rings which run down the acceleration tube and create a uniform accelerating electric ﬁeld.

The accelerator provides a characteristic mass vs. velocity distribution of the accelerated particles, shown in Figure 2.2. The amplitude and timing of the detector signals is measured by 15 the PSU, which measures the value of the dust charge, QD, and the velocity vD and in turn allows for the mass calculation,

2QDUA m = 2 , (2.1) vD where UA is the accelerating voltage. QD is imparted to the dust by the dust source (see Section

2.1.1) and so the velocity of the dust is then determined by its mass and the Pelletron voltage.

Furthermore, the particles used in this work are spherical iron particles, so that the particles with relevant meteoric velocities (10-70 km/s) have radii that range from 20-100 nm. in general, the accelerator is capable of producing dust particles from 0.5-100 km/s with radii of 20 nm - 5µm.

120

10-12

10-13 100

10-14 80

10-15

60 10-16 Mass [kg]

10-17 40 NumberParticlesof

10-18

20 10-19

10-20 1 20 40 60 80100 Velocity [km/s]

Figure 2.2: A representative particle distribution from the accelerator. There is a large dynamic range of masses (8 orders of magnitude) and velocities (2 orders of magnitude) that the accelerator produces. 16

2.1.1 Dust Source

A schematic of the dust source, which is based on the MPI-K design [86], is shown in Figure

2.3. The dust source sits inside the Pelletron shell and contains the dust that the accelerator will accelerate. It is therefore the ﬁrst element in the dust beamline. The dust source contains a dust reservoir, needle, pinhole apertures, and an extraction plate. The reservoir holds approximately 1 g of dust and is pulsed by the electrode between 0-20 kV relative to the extraction plate, which is electrically grounded. The needle is held at a ﬁxed voltage by the DC electrode, which is equal to the maximum voltage of the reservoir. Pinhole apertures allow the dust to exit the source ideally in a collimated “beam”. It is important to note that the dust is accelerated one particle at a time and is therefore not a true beam, but one may use the term loosely to describe the dust beam in an aggregate sense of075108-3 many particles Shu et over al. time. Rev. Sci. Instrum. 83,075108(2012)

Figure 2.3: A schematicFIG. 3. of 20 the kV 20 dust kV source. dust The source. reservoir The holds reservoir dust and is holds pulsed the between conducting dust and is 0–20 kV relative to the extraction plate. The needle is held at the maximum pulsed between 0-20potential kV relative of the reservoir. to the extraction Dust particles plate. that come The in contactneedle with is held the needle a fixed voltage, which is set to the maximumare of ejected. the reservoir voltage. The dust becomes slightly negativelyFIG. charged 4. (a) by Simulation the of dust beam from source entrance of accelerator cal- pulsing reservoir and begins to levitate. The dust becomes charged positively whenculated it contacts in SIMION. the Red lines are equipotenial lines spaced 2 kV apart. The needle. The charged dust is then accelerated by the electric field which exists betweenEinzel the lens needleis off resulting in a beam in the inset that is diverging. (b) Same and the extraction plateneedle. and Whenever is ejected a dust through particle the contacts pinholes. the Reproduced tip of the needle, from [81].simulation with Einzel lens at optimal voltage. Inset shows resulting beam to the particle becomes charged positively by contact or electron be collimated. Beams as small as 1 mm in diameter can be achieved. emission and is ejected by the electric field between the needle and the extraction plate.4 This charging process is some- The entrance of this potential drop strongly focuses the As stated above,what the random reservoir and thus pulses the betweencharge and 0-20 mass kV, of whilethe particles the needle be- ischarged kept at particlea fixed beam, whereas the exit does not. This is due ing ejected is not well controlled. The dust then exits through to the fact that particles are traveling slowly near the entrance three concentric pinhole apertures in the reservoir, extraction and fast near the exit. This strong focusing leads to a highly plate, and outer shell, which collimates the pre-accelerated divergent beam at the exit of the acceleration tube. To colli- beam. mate this beam, an Einzel electrostatic focusing lens is placed The magnitude of particle charging has several limits. between the dust source and acceleration tube. The lens is First of all, a particle can only be charged to the ion field used to prefocus the beam so that a divergent beam enters the emission limit of the dust material, which can be in excess of accelerating tube and is then collimated by the entrance of the 1010 V/m for some metals.3 In fact, the choice to launch pos- acceleration tube. itively charged particles is due to the higher field emission The Einzel lens consists of three concentric inline cylin- limit of positive vs. negative charge. Particles also cannot be drical electrodes, only the center of which is charged to high- charged to a surface potential beyond the potential of the nee- voltage. The outer two cylinders are kept grounded. This dle. This places constraints on the total charge-to-mass ratio forms a saddle-shaped potential causing charged particles to any single particle can have, thereby limiting the performance be focused. SIMION, a charged particle optics simulation of the accelerator. The resulting impact on the operating space software package, is used to model the collective charac- of the accelerator is discussed in Sec. III. teristics of the dust beam under different voltage conditions and determine the appropriate focusing voltage. As shown in Fig. 4(a),thesourceproducesabeamthatbecomesfocused C. Focusing and high voltage by the entrance of the acceleration tube. At the exit, this beam is diverging as seen in the inset. In Fig. 4(b),theEinzellensis The Pelletron charging system is similar to a Van de set to the optimal voltage and the beam becomes prefocused Graaf generator, which uses a moving belt to physically trans- so a diverging beam enters the acceleration tube entrance. The port charge to a high-voltage terminal. The primary differ- focusing of the entrance collimates the beam as seen in the ences are that a chain of metal pellets connected by insulat- inset. These simulations have shown that the theoretical dust ing links is used instead of a belt, and an inductive charge- beam diameter minimum is on the order of 1 mm. separation system is used to charge the chain instead of a brush. The metal chain is more durable and does not gener- D. Detectors and particle selection ate any belt dust in the system. Furthermore, the metal can be charged to higher voltage enabling systems of 25 MV or Particle properties are detected in flight using a series of greater.15 This system is housed inside a metal vessel which is three image charge detectors, constructed from the MPI-K de- 13 filled with 6 atmospheres of SF6 to prevent arcing. The charg- tector design. Each detector is composed of two grounded ing system is used to create a linearly falling potential dif- shielding cylinders and a central detection cylinder as shown ference across a series of metallic rings separated by ceramic in Fig. 5. When a particle enters the central cylinder, an image blocks called the acceleration tube. charge is induced onto the cylinder. The cylinder is narrow 17 voltage. When the reservoir is at a voltage that is less than the needle voltage, the conducting dust gains a slightly negative charge. The pulsing of the reservoir (and the resulting electric field between the reservoir and the needle) levitates the dust, and if a dust particle touches the needle it gains a positive charge through contact charging or electron emission [81]. Once charged, the dust particle is accelerated out of the reservoir due to the electric field between the needle and the extraction plate. This charging mechanism is somewhat random, which produces a distribution of particles with varying charges. This is evident in Figure 2.2 as there is a spread of dust velocities for a given particle mass due to the varying charges, QD. Furthermore, the rate of particle ejection is somewhat random and can only be controlled coarsely by varying the reservoir pulse width, voltage, and frequency. Typical operating parameters are 3 ms (pulse width), 14 kV (reservoir/needle voltage), and 20 Hz (pulse frequency). However, these parameters can be adjusted from 0-4 ms,

0-20 kV, and 0-30 Hz.

The total charge acquired by a dust particle is limited by several factors. Firstly, a dust particle cannot be charged above the ion ﬁeld emission limit, which can be 1010 V/m for some materials [81]. Secondly, particles cannot be charged to a potential larger than the needle voltage.

The limit for the lowest charge a particle can have is an engineering limit based on the detection limits of the beamline dust detectors. The detectors are capable of detecting particles with charges

> 0.08 fC.

2.1.2 Accelerating Column and Focusing

The Pelletron charging system is shown as a schematic in Figure 2.4. The charging system is similar to Van de Graaff generators, which use a belt to physically transport charge to the high- voltage terminal. The main difference between the two is that the Pelletron system uses metal pellets connected by insulating nylon links instead of a belt, and the metal pellets are charged by induction instead of a brush. Specifically, there is an inductor and a suppressor, which are charged up to 50 kV and between them is a grounded pulley (left side of Figure 2.4). Therefore, there is an electric field between the pulley and the inductor/suppressor. The pulley is electrically conducting 18 such that when a metal pellet is in contact with the pulley, it acts as a single conductor. As a metal pellet moves into the electric field between the inductor and the pulley, a charge separation occurs. As the metal moves off of the pulley, but is still in the electric field of the inductor, it gains a positive charge. This charge is then transported to the high-voltage terminal where a portion of the charge is pulled off by the pickoff pulleys to supply charge to the opposite inductor, which repeats the process except it brings negative charge from the terminal onto the chain. A suppressor over the terminal pulley pushes all remaining positive charge from the chain onto the terminal pulley.

The terminal pulley is connected through a series of large resistors, which run along the potential rings, to ground. This generates the accelerating electric ﬁeld. This charging mechanism does not produce belt dust and produces greater terminal stability than Van de Graaﬀ generators [27]. The

Pelletron shell is kept at 6 atmospheres of SF6, because SF6 has about 2.5 times higher dielectric strength compared to air and this reduces arcing inside the Pelletron (even more so then evacuting the chamber; the vacuum level required to suppress arcing at several megavolts would be diﬃcult to achieve) [80].

Figure 2.4: A schematic showing the charging mechanism for the Pelletron. The charging mechanism is induction-based where the inductor/supressor creates an electric field between them and the grounded pulley. The pulley is conducting such that when a chain metal pellet is touching the pulley, it is one grounded conductor. Looking at the inductor side, as a pellet moves into the electric field between the inductor and the pulley, a charge separation occurs where negative charge is pushed onto the pulley. Therefore, as the pellet moves off of the pulley, but is still in the electric field of the inductor, it gains a positive charge. The chain then transports that chrage to the terminal where the charge is pulled off by the pickoff pulleys. Source: http://www.pelletron.com/charging.htm

The acceleration tube is a series of metallic rings separated by ceramic blocks. The voltage is 19

stepped down from the terminal pulley along these rings through a series of resistors, which creates

a linearly decreasing potential (uniform axial electric ﬁeld). The entrance to the acceleration tube

strongly focuses the dust particles due to their relatively low velocities, which creates a divergent

beam at the exit of the tube. To account for this, there is an Einzel lens placed before the 075108-3 Shu et al. Rev. Sci. Instrum. 83,075108(2012) acceleration tube.

Dust Beam

FIG. 3. 20 kV dust source. The reservoir holds dust and is pulsed between 0–20 kV relative to the extraction plate. The needle is held at the maximum potential of the reservoir. Dust particles that come in contact with the needle are ejected. Figure 2.5: Two SIMIONFIG. 4. (a) simulations Simulation of of dust the beam dust from source, source Einzel entrance lens, of accelerator and accelerating cal- tube entrace. culated in SIMION. Red lines are equipotenial lines spaced 2 kV apart. The In the top panel (a),Einzel the lens Einzel is off lens resulting is at in 0 a V, beam which in the produces inset that is adiverging. diverging (b) beam Same in the accelerating needle. Whenever a dust particle contacts the tiptube. of the In needle, the bottomsimulation panel (b), with the Einzel Einzel lens at lens optimal is at voltage. 10 kV, Inset which shows collimates resulting beam the to beam. Reproduced the particle becomes charged positively by contactfrom or [81]. electron be collimated. Beams as small as 1 mm in diameter can be achieved. emission and is ejected by the electric field between the needle and the extraction plate.4 This charging process is some- The entrance of this potential drop strongly focuses the what random and thus the charge and mass of the particlesThe be- Einzel lenscharged is an particle electrostatic beam, focusing whereas element, the exit does which not. is Thisused is to due produce a collimated ing ejected is not well controlled. The dust then exits through to the fact that particles are traveling slowly near the entrance three concentric pinhole apertures in the reservoir,dust extraction beam at the endand of fast the near acceleration the exit. tube. This strong The Einzel focusing lens leads prefocuses to a highly the dust beam so that a divergent beam at the exit of the acceleration tube. To colli- plate, and outer shell, which collimates the pre-accelerateddivergent beam enters the acceleration tube, and the entrance of the acceleration tube then focuses beam. mate this beam, an Einzel electrostatic focusing lens is placed The magnitude of particle charging has severalthe beam limits. such thatbetween it is collimated the dust upon source exiting and acceleration the tube. The tube. lens The is lenscomprised is of three inline First of all, a particle can only be charged to the ion field used to prefocus the beam so that a divergent beam enters the emission limit of the dust material, which can beand in concentricexcess of cylinders,accelerating where tube the and center is then cylinder collimated is biased by the to aentrance high-voltage of the and the outer two 1010 V/m for some metals.3 In fact, the choice to launch pos- acceleration tube. cylinders are grounded. Figure 2.5 shows results from two simulations of the dust beam performed itively charged particles is due to the higher field emission The Einzel lens consists of three concentric inline cylindrical electrodes, only the center of which is charged to high- limit of positive vs. negative charge. Particles alsowith cannot SIMION, be a charged particle optics simulation program. The simulations contained the dust charged to a surface potential beyond the potential of the nee- voltage. The outer two cylinders are kept grounded. This dle. This places constraints on the total charge-to-mass ratio forms a saddle-shaped potential causing charged particles to any single particle can have, thereby limiting the performance be focused. SIMION, a charged particle optics simulation of the accelerator. The resulting impact on the operating space software package, is used to model the collective charac- of the accelerator is discussed in Sec. III. teristics of the dust beam under different voltage conditions and determine the appropriate focusing voltage. As shown in Fig. 4(a),thesourceproducesabeamthatbecomesfocused C. Focusing and high voltage by the entrance of the acceleration tube. At the exit, this beam is diverging as seen in the inset. In Fig. 4(b),theEinzellensis The Pelletron charging system is similar to a Van de set to the optimal voltage and the beam becomes prefocused Graaf generator, which uses a moving belt to physically trans- so a diverging beam enters the acceleration tube entrance. The port charge to a high-voltage terminal. The primary differ- focusing of the entrance collimates the beam as seen in the ences are that a chain of metal pellets connected by insulat- inset. These simulations have shown that the theoretical dust ing links is used instead of a belt, and an inductive charge- beam diameter minimum is on the order of 1 mm. separation system is used to charge the chain instead of a brush. The metal chain is more durable and does not gener- D. Detectors and particle selection ate any belt dust in the system. Furthermore, the metal can be charged to higher voltage enabling systems of 25 MV or Particle properties are detected in flight using a series of greater.15 This system is housed inside a metal vessel which is three image charge detectors, constructed from the MPI-K de- 13 filled with 6 atmospheres of SF6 to prevent arcing. The charg- tector design. Each detector is composed of two grounded ing system is used to create a linearly falling potential dif- shielding cylinders and a central detection cylinder as shown ference across a series of metallic rings separated by ceramic in Fig. 5. When a particle enters the central cylinder, an image blocks called the acceleration tube. charge is induced onto the cylinder. The cylinder is narrow 20 source, Einzel lens, and the acceleration tube. The top panel (a) shows the simulation with the

Einzel lens set to 0 V, while the bottom panel (b) shows the Einzel lens at 7.8 kV. It is evident that with no focusing the beam diverges in the accleration tube, whereas with the Einzel lens ﬁxed at

7.8 kV, the dust beam is collimated. When operating the accelerator, the Einzel lens is typically biased from 7-15 kV depending on the needle voltage and the Pelletron voltage.

2.1.3 Beamline Dust Detectors

Once in the beamline, the dust particle moves through two image charge detectors. Figure

2.6 shows a schematic of the detectors, which consist of an inner conducting cylinder connected to a charge sensitive amplifier (CSA), outer grounded cylinders which provide electronic shielding, and a vacuum feedthrough with electrical connections. The inner cylinder has an inner diameter of 0.9 cm and is 20 cm long, while the entire detector (from flange to flange) is 30 cm long. A CSA probe electrically connects the inner cylinder to the input of the CSA circuit, which amplifies the generated image charge. There is a grounded cylinder which separates the inner cylinder from the electronics, and there is another cylinder which isolates the electronics from the detector chassis.

The vacuum feedthrough houses power cables (+/- 6 V), a test input signal, and an output signal.

The detectors, along with the rest of the beamline, are maintained at < 10−7 Torr by magnetically levitated turbomolecular pumps with dry backing pumps.

The CSA schematic is shown in Figure 2.7. The circuit consists of three stages: (1) a CSA stage, (2) a voltage amplifier stage, (3) and a buffer amplifier stage. The CSA stage, which uses an Amptek A250 CSA, has a sensitivity of 2.5×1012 V/C, while the second stage has a 10× gain.

The buffer amplifier stage has unity gain and is used to provide enough current to drive a 50 Ω load. Altogether, the CSA circuit has a sensitivity of approximately 2.5×1013 V/C. The sensitivity of each detector was calibrated using a well-defined calibration capacitor, to provide charge to the input of the CSA circuit, and measuring the output voltage. Table 2.1 gives a list of the exact sensitivities of the three detectors on the beamline. The errors on the sensitivity are due to the errors in the calibration of the capacitor as well as small measurement errors in the input/output 075108-4 Shu et al. Rev. Sci. Instrum. 83,075108(2012)

FIG. 6. Typical signals from image charge detectors and gate output along Figure 2.6:FIG. A schematic 5. Image of charge the image detector. charge Image dust charge detectors is deposited on the on accelerator the inner con-beamline. The beamline. Particle charge is proportional to signal height and velocity is de- detector consistsductor of when a conducting a charged cylinder particle enters. which isThis grounded charge is through detected a usingcharge a sensitive charge amplifier termined by time-of-flight between the first and third detectors. The TTL gate (CSA). As thesensitive charged amplifier dust particle and can moves be used through to determine the cylinder, particle it induces charge. an Velocity image charge is on the pulse shows where the electrostatic deflection plates are turned on and off, be- cylinder whichdetermined is amplified through by the time CSA. of flight, which can be done by a single detector or fore the particle arrives and after the particle leaves. Each vertical black line multiple detectors. signifies where the particle has reached in time. voltage measurements.and very long compared to the end openings such that nearly has entered the target chamber and will hit the target. These all of the chargeDetector on the particleSensitivity is induced (V/C) onto the cylinder. points are depicted in Fig. 6 by the black lines. The time scale The induced charge is1 detected2.34 using± 0.09 a× charge1013 sensitive ampli- for acoustic noise is large enough that the signals appear to fier (CSA) connected2 to the central2.54 ± 0.03 cylinder×1013 through the CSA 3 (final) 2.47 ± 0.03 ×1013 sit on a dc offset (which have been removed in Fig. 6). This probe in Fig. 5.Theamplitudeofthesignalisproportional changing baseline still contributes to the noise floor as a sim- Table 2.1:to the A list charge of the of sensitivities the particle of the by CSA a calibrated circuits on the constant, beamline and dust thedetectors.ple threshold will still trigger from a changing baseline. velocity of the particle can be determined using time-of-flight The fastest particles tend to have the smallest signals. A The dustbetween detectors two produce detectors. square Ashaped single signals detector as a dust can particle also enters be used and tothen exitsparticle’s the charging efficiency follows: detect velocity, determined using time-of-flight from when it inner cylinder of the detector. The image charge forms on the cylinder and stays on the cylinder q r2, (2) enters and exits the detector, and is used only as a check with ∝ until the dustthe particle final detector exits the todetector. ensure Therefore, particles the entering amplitude the of target the signal cham- and the widthwhile the mass follows: ber are the desired particles. From this information, the mass of the pulse are directly proportional to the particle’s charge and inverse of velocity, respectively. m r3. (3) of the particle can be derived using the equation ∝ Figure 2.8 shows an example of a beamline detector signal. The signal in Figure 2.8 is fast enoughFrom Eqs. (1)–(3) it is clear that 1 2 such that the voltage level is constant whilemv the dustQU isp in, the detector. For slower(1) particles, the 2 = q 1 1 signals begin to decay based on the time constant of the Amptek A250 chip (250 µs). Therefore, v r− 2 . (4) ∝ m ∝ r ∝ where m is the particle mass, v is the particle velocity, Q is the ! ! the initial amplitude of the signal corresponds to the dust charge. particle charge, and Up is the accelerating potential of the Pel- This means that the fastest particles are the smallest, but also letron. The detectors are very sensitive to acoustic noise, and have the lowest charge, making them the most difficult to de- resonant vibrations can be excited in the detectors whenever tect. For example, a 100 nm diameter iron particle that has vibrational energy is provided. Because of this, magnetically been charged to 1 kV potential will have 5.6 fC of charge and levitated turbo pumps and other vibration-damping hardware will be accelerated to 90 km/s. On the other hand, a 1 µm are used on the beamline to reduce vibrations. Since particle diameter iron particle that has also been charged to 1 kV po- charge is related to signal height from the CSAs, particle de- tential will have 56 fC of charge and will be accelerated to tection is done through simple thresholding. If the output of only 9 km/s. Notice that the charge is increased by an or- the CSA reaches a certain level, a particle is detected. This der of magnitude but the velocity is decreased by an order of level must be set above the acoustic and other noise sources magnitude. in order to prevent false triggers. As the charge and mass distribution of particles from the AtypicalsignalisshowninFig.6,andshowshowthe source are broad, a PSU is used to analyze detector signals in charge and velocity are measured. When the square pulse on real time to donwnselect individual particles before they reach the first detector trace passes the threshold, it has entered the the target. In this way, only particles within a user-selectable first detector tube. When the square pulse on the third detector range of mass, energy, or velocity enters the target chamber. trace passes the threshold, the particle has entered the third de- Figure 7 shows a block diagram of the PSU. Signals from detector tube. By measuring the delay between these two times, tectors 1 and 3 are fed into a thresholding Schmitt trigger and the velocity is determined by time of flight. Once the veloc- the outputs are then sent as start and stop pulses to a com- ity is known, the delay required to reach the beginning and bined time to amplitude converter with single channel ana- the end of the PSU deflection plates is known, so the time re- lyzer (TAC/SCA). The TAC/SCA converts the delay between quired to open and close the PSU gate is known. Finally, the the start and stop signals into a voltage which it then compares particle reaches the final detector signifying that the particle to a user selected voltage window. If the voltage is within the 22

LMH6714

Stage 1 Stage 2 Stage 3

Figure 2.7: A schematic of the CSA design used on the beamline dust detectors. The circuit has three stages: a CSA stage with a sensitivity of 1 × 1011 V/C, an amplifier stage with a 10× gain, and a unity gain buffer amplifier stage to drive a 50 Ω load. 1/2/2017 4:04:55 PM f=0.90 Y:\Circuits\Shu Eagle Circuits\detector boards\detector CSA.sch (Sheet: 1/1) . 7

6 Velocity: 13.6 km/s 5 Mass: 4.8 x 10-18 kg

Charge [fC] 1

-1

-2

-3 0.2 0.25 0.3 0.35 0.4 Time [ms]

Figure 2.8: An example signal from a beamline dust detector. The amplitude of the signal is proporitional to the dust charge while the width of the signal is proportional to the dust velocity. 23

2.1.4 PSU & Deﬂection Plates

The beamline detector signals are input into the particle selection unit (PSU), which measures each particle’s velocity and charge, and uses these (with the Pelletron voltage) to calculate mass. The PSU decides in real time whether or not the particle meets the criteria for the current experiment and will either allow the particle into the experimental chamber or deflect it. The reason for deflecting the particles is because some experiments do not want certain particles entering the experiment (e.g. impact experiments) and also to decrease data volume. The PSU logic is written on a field-programmable gate array (FPGA), which is described in detail in Section 2.2. In order to allow a particle through, the PSU sends a TTL pulse to a pair of rectangular electrostatic deflection plates (see Figure 2.1).

The deﬂection plates deﬂect incoming particles out of the beamline with a strong electric

field oriented vertically with respect to the beamline. When the PSU decides to allow a particle through, it sends a TTL pulse to the deflection plates. The TTL pulse triggers a circuit which grounds the plates, thereby eliminating the electric field, and the particle then passes through the region unaffected. The plates have dimensions of 7.6 x 20 cm, are separated by 3.8 cm, and are charged to 6 kV. The electric field generated by the plates is

Ep = Vp/s, (2.2) where Vp is the deﬂection plates voltage (6 kV) and s is the separation distance (3.8 cm). The time the particles are in the electric ﬁeld is given by

t = l/vD, (2.3) where l is the length of the plates (20 cm) and vD is the velocity of the particle. The acceleration of the particle due to the electric ﬁeld is given by

Q E Q V p a = D p = D (2.4) y m sm 24 where QD and m are the particle’s charge and mass, respectively. Therefore, the particle is deﬂected in the transverse direction and given a velocity in the y-direction, vy, of

QDVpl VplvD vy = ayt = = , (2.5) smvD 2sUA where m was replaced with Equation 2.1. Finally, the particle leaves the deﬂection plates at an angle given by

v V l tan θ = y = p . (2.6) vD 2sUA

It is clear from Equation 2.6 that the amount of deﬂection is only dependent on the voltage of the plates (6 kV), the length of the plates (20 cm), the plate separation (3.8 cm), and the

Pelletron voltage (maximum of 3 MV), none of which are particle properties. Using Equation 2.6, one can calculate the amount of deflection the particle undergoes before entering the final beamline detector, which is 1.3 m down the beamline. The deflection is given by tan θ × 1.3 m = 0.0068 m

= 0.68 cm. A steel annulus surrounding the entrance to the inner cylinder of the third detector was installed so that no particles outside of the 0.9 cm diameter beam will be able to enter the third detector. Therefore, a particle deﬂected outside of the center of the beam by 0.68 cm will not be able to enter the third detector. For a more typical Pelletron operating voltage of 2.2 MV, the deﬂection is even larger (0.93 cm).

2.1.5 Accelerator Data Handling

The deﬂection plate PSU TTL signal is sent not just to the deﬂection plates but also into a data acquisition system, which saves the dust detector waveforms and the PSU pulse for each particle detected by the PSU. The data acquisition system consists of a National Instruments (NI)

PXI-1042 crate which contains two NI PXI-5124 12-bit, 200 MS/s digitizer cards. For each PSU signal, the cards save all four waveforms (the ﬁrst and second detectors, the PSU pulse, and the

final detector) to a database with an automatic batch processing system. The batch processor 25 automatically analyzes the waveforms and measures the velocity and charge of each particle. From these measurements, it calculates the mass and radius (assuming a spherical particle) and populates a metadata file for that experiment. Therefore, for every experiment on the accelerator there is a metadata file with the properties of every particle selected, as well as the raw waveforms from each particle. This metadata file also includes a timestamp for each particle, so one can then match up experimental data with accelerator data after the fact.

The data acquisition system is written in LabVIEW and IDL and uses the NI-PXI 5124 digitizer cards as input. Figure 2.9 is a schematic of the accelerator data ﬂow. The PSU pulse triggers the LabVIEW program (DataAcquisition.vi), which then saves the waveforms to a local memory queue in the computer’s RAM and creates an empty dust event entry in the database. A local memory queue is used because writing to the hard disk would be too slow, and the program could potentially miss particles. Therefore, the rate of the acclerator must be controlled so that the queue does not become full. A separate LabVIEW program (DBConnection.vi) pulls waveforms from this queue and writes them to the database in an HDF5 ﬁle format. Next, the batch processor

(Batch.vi), which is a combination of LabVIEW code and IDL code, reads in the saved waveforms and analyzes them. The analysis is done using an IDL routine which uses a series of cross-correlation

filters to measure the velocity and charge of the dust grains, even for dust with very low signal-to- noise ratios. The cross-correlation method is similar to that used by the PSU, which is described in detail in Section 2.2, with the main difference being that the batch processor is a software solution and therefore not real-time. After the analysis, the batch processor marks the HDF5 files as “processed” and writes the dust metadata to the database entry. The database, which is a

MySQL database, is searchable through a variety of parameters such as particular experiments, particular dust event numbers, timestamps, velocity, charge, mass, and radius. Typically, once an experiment has completed, the users are provided with the experiment metadata ﬁle as well as the experiment HDF5 ﬁle containing all of the raw accelerator waveforms. 26 Data Signals Main LabVIEW Comp. Database Batch LabVIEW Comp.

NI PXI Crate Detector 1 DataAcquisition.vi HDF5 File Batch.vi

5124 Digitizer Metadata Detector 2 PCI LabVIEW Queue

PSU Pulse 5124 Digitizer Ethernet

Detector 3 DBConnection.vi

Figure 2.9: A schematic of the data acquisition system for the accelerator. The first two beamline detectors, PSU pulse, and final beamline detector are digitized and sent to a LabVIEW program, which reads in all four waveforms. The data is then transferred to a LabVIEW queue, which is stored in the computer’s RAM. Next, another LabVIEW program (DBConnection.vi) converts the LabVIEW waveforms into a compressed HDF5 file and saves it to a MySQL database. The batch processor (Batch.vi) reads the HDF5 file, analyzes it, marks it as “processed”, and saves the dust metadata to the database entry corresponding to that dust event.

2.2 FPGA Particle Selection

2.2.1 Introduction & Motivation

The charges on the dust particles can vary by several orders of magnitude. For example, the mass vs. velocity distribution of the accelerator (Figure 2.2) shows particles with the same velocity but with masses that vary by as much as four orders of magnitude. By Equation 2.1, this leads to four orders of magnitude diﬀerence in charge. Therefore, the smallest particles (e.g. < 100 nm) can have charges < 0.1 fC, but Figure 2.8 shows a dust detector waveform with a noise level of approximately 1 fC. Clearly a simple analog threshold trigger on the PSU would miss particles and also have a large number of false triggers depending on the threshold value.

To address the problem of detecting particles with very low charge, the PSU system was designed around a digital filtration system which filters the waveforms in real time to extract signals with low signal-to-noise ratios (SNRs). The filters take advantage of the fact that the signals are of a known family of shapes (i.e. square pulses) and use a cross-correlation to produce 27 an easily triggerable output signal when a dust particle passes through the detectors. The filtration scheme was tested on the beamline and was able to detect particles with SNRs as low as 0.25.

The PSU must detect and measure the properties of a dust particle in real time in order to decide if that particular particle should be allowed through to the experimental chamber. The process of detection, measurement, and the decision logic must be completed in the time it takes for the particle to move from the second beamline detector to the deflection plates. For the fastest particles, the PSU has only 14 µs before the particle reaches the deflection plates. If the PSU took longer than that to execute, the particle would enter the deflection region and be lost even if it met the criteria for the experiment. Therefore, the PSU execution time is critical. To meet the timing demand, the logic was written on a field-programmable gate array (FPGA).

2.2.2 Filter Design

The primary calculation performed by the FPGA algorithm is a discreet, running cross- correlation of the detector output with a set of digital ﬁlters corresponding to the expected signal shape. In general, cross-correlations are used to measure the similarity between two functions. A discreet, running cross-correlation refers to the fact that the algorithm is being calculated in real time, sample by sample, as the FPGA analog-to-digital converters (ADCs) sample the beamline dust detectors (in this case, the ADCs are clocked at 26 MHz, which is discussed in detail in

Section 2.2.5). Figure 2.10 shows a schematic of the process. A signal (red) is convolved over a

filter function (black) and the overlapping area is integrated to create a large filter response (dark red). The result is that the maximum of the filter response occurs when there is maximum overlap between the two functions. The filter response is typically orders of magnitude larger than the original signal, and it is important to note that to improve readability, the filter repsonse in Figure

2.10 is not to scale.

The ﬁlter design is based on the design in Auer, et al. [4], which used triangular shaped

ﬁlters. In contrast, the beamline dust detector signals are approximately a square pulse (see Figure

2.8), which led to the use of an array of seven triple square ﬁlters. Figure 2.11 shows a general 28

Signal & Filter Filter Response

Figure 2.10: A schematic of a cross-correlation between a square signal and a filter function. The signal (red) is moved over the filter function (black) and the overlapping area is integrated to generate a filter repsonse (dark red). To improve readability, the filter repsonse is not to scale.

schematic of the filter shape. The filters contain three regions (A, B, and C), where region A is negative, region B is positive, and region C is also negative. Regions A and C have an amplitude of -1, whereas region B has an amplitude of +2 such that the there is equal positive and negative area in the entire filter. The reason for having equal positive and negative area is that the integral over the filter will always return back to zero and never generate an offset. Furthermore, splitting up the negative portions so that they are symmetric across the filter mitigates the effect of a signal on a slope (e.g. a square pulse superimposed on a sine wave).

Figure 2.11: A general schematic of the filters used in the cross-correlation calculation. Three regions make up the filter (A, B, and C) with amplitudes of -1, +2, and -1 respectively. Region B is twice the width of regions A and C such that there is equal positive and negative area across the entire filter. The filter is indexed by the variable m and contains a total of 3W points. The index, m, is defined from 0 to −3W , where m = −3W correpsonds to the data point that was sampled 3W samples in the past. See text for more details.

Each ﬁlter has a nominal width given (in units of integer samples) by

W = (l/v) ∗ f (2.7) where l is the detector length, v is the nominal filter velocity (the dust velocity that the filter is 29 designed to be most sensitive to), and f is the sampling rate of the data acquisition. The way one should conceptually read Figure 2.11 is that the left side (with m = 0) is where the signal begins to move over the filter function, thereby creating the correlation response. As the signal is sampled in real time, the data points move through the filter (from left to right), and the most recently sampled data point is always at m = 0. This means that the negative indices indicate the number of samples, in the past, when that data point was sampled. Therefore, data that is currently overlapping the part of the filter with an index of m = −3W was sampled 3W samples

(or 3W/f s) in the past. Furthermore, the value of the correlation response at any given time is equal to the overlapping area of the signal and ﬁlter functions at that moment.

In general, a discrete cross-correlation is deﬁned as:

∞ X y(n) = f(m)s(n + m) (2.8) m=−∞

In equation 2.8, n is the data point index, m is the variable used to move the signal over the filter, y(n) is the correlation response, f(m) is the filter function, and s(n) is the signal function. With the triple square filter function, equation 2.8 can be rewritten as:

"−W ∆t #  −2W ∆t   −3W ∆t  X X X y(t) = − s(t + τ) + 2  s(t + τ) −  s(t + τ) . (2.9) τ=0 τ=(−W −1)∆t τ=(−2W −1)∆t

In equation 2.9, ∆t = 1/f is the sampling period, and we have switched to discrete time variables, instead of index variables, in order to emphasize the fact that this calculation is done in real time. By comparing the expanded forms of y(t = 0) and y(t = −∆t) (which correspond to the current time point and the previous time point, respectively), it can be shown that the correlation response is:

y(0) = y(−1) − s(0) + 3s(−W − 1) − 3s(−2W − 1) + s(−3W − 1), (2.10) where we have suppressed factors of ∆t for convenience. In equation 2.10, we are calculating the current value of the correlation response by using the previous value. The terms s(−W − 1), 30 s(−2W − 1), and s(−3W − 1) are the data points which were previously in the rightmost filter positions of sections A, B, and C of the filter (see Figure 2.11), respectively. In the case of s(−W −1) and s(−2W − 1), the data points are moving from a negative area to a positive area (or vice versa), and therefore need to be added/subtracted 3 times (to make up for the difference from a −1 valued

filter area to a +2 valued filter area). For s(−3W − 1), the data point is moving from a −1 valued area to a 0 valued area and so only needs to be added once. This form allows the correlation value at each time point to be quickly calculated from the previous correlation value with minimal additional computational cost. Specifically, this form involves 5 additions/subtractions and two bit shifts, whereas a brute force cross-correlation would involve 3W additions/subtractions and W bit shifts.

The expected SNR of the filter can be calculated in the following manner. First, the filter implementation is a finite impulse response (FIR) filter in that the response will always return back to zero in a finite amount of time. For FIR filters, the signal and noise levels can be calculated directly from the filter coefficients. The maximum filter response will occur when a perfectly matched dust signal is overlapped with region B of the filter. The response at that point will be equal to the integrated overlapping area, and the noise for an FIR filter can be calculated as the root sum square of the filter coefficients [4]. Therefore, the expected maximum SNR of the filter response is given by,

P 2Qpk √ B 2QpkW Qpk W SNRmax = r = √ = , (2.11) σ P 22 σ 4W σ B where Qpk and σ are the signal charge level and noise standard deviation, respectively, and the summations are summing over region B (which has W samples).

The accelerator is capable of producing dust with velocities ranging from 0.5-100 km/s, and in practice the ﬁlters are responsive to dust signals wider than a factor of two apart in width.

Therefore, seven ﬁlters covering the relevant velocities are used in the implementation. The speciﬁc widths used are 4101, 2053, 1029, 517, 261, 133, and 69 samples, which correspond to velocities 31 of 1.3, 2.6, 5.2, 10.3, 20.4, 40.1, 77.3 km/s (with a 26 MHz ADC). These widths were used due to hardware limitations (see Section 2.2.5) and are assigned within the algorithm to particles with velocities of < 2, 2-4, 4-8, 8-16, 16-32, 32-64, and > 64 km/s, respectively. The maximum expected

SNR for these ﬁlters can be calculated by converting Equation 2.11 into a function depending on velocity, rather than ﬁlter width. Using Equation 2.7 to replace W , Equation 2.11 becomes

q l Qpk v f Q 2280 SNR = = pk √ , (2.12) max σ σ v where l = 0.2 m and f = 26 MHz was used, and v is in units of m/s. As an example, we can use

ﬁlter 6, which corresponds to a particle with a velocity of 40.1 km/s, and assume that σ = 1 fC and Qpk = 0.2 fC. This is a low-charge particle, but still a realistic example (see Figure 2.2). In this scenario, SNRmax = 2.3 compared to the orginal ratio of Qpk / σ = 0.2.

1 Input Signal

V 0

-1

2 Input Signal + Noise

V 0 -2

2 Filter 0 Arb.

-2

500 Filter Response

V 0

-500 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 Time [ms]

Figure 2.12: Simulation showing the effectiveness of the cross-correlation calculation. The top plot is an ideal input signal, the second is the ideal signal embedded in noise (SNR = 0.75), the third is the filter shape (arbitrary units), and the last plot shows the correlation response. The input signal is perfectly matched (in width) to the filter.

To further demonstrate the effectiveness of the filter design, Figure 2.12 shows an example of a cross-correlation calculation applied to an artificially-generated noisy signal. The top of the 32

figure shows a clean input signal with noise being added to that signal in the next pane. The third pane shows the triple square filter function with which the noisy signal is correlated with. The input signal is perfectly matched (in width) to the filter. The final pane shows the result of the correlation: an easily triggerable signal.

Filter 1 Filter 2 103 Filter 3 Filter 4 Filter 5 Filter 6 Filter 7

102 Max Filter Response [V]

101 0 20 40 60 80 100 Velocity [km/s]

Figure 2.13: A sensitivity plot for all 7 filters. The filters are correlated with a ideal 300 mV square pulses. Filter 1 peaks at the lowest velocity, then Filter 2, Filter 3, etc. as the filters progress in velocity. Each successive filter is plotted on top, but all filters continue along the same line.

Figure 2.13 shows a theoretical sensitivity plot for all filters. Each filter was run through a cross-correlation with an array of artificial (ideal) signals corresponding to particles of differing velocities. For each velocity, the curve represents the maximum of the convolved signal from each

filter. There are two notable features of the plot: the velocity dependence of each filter, as well as the relative maximum response of each filter. The velocity dependence is as described above, with the maximum response of each filter occurring at the signal velocity that corresponds to the nominal width, W , of the filter. The maximum response of each filter decreases as the filter width decreases (or equivalently, goes up in signal velocity sensitivity). One should notice that the maximum response of filter 1 is at least as large (or larger) as the maximum response of all other filters. Therefore, it is not immediately obvious why one would not just use filter 1 for all velocities. Judging from filter response alone, the higher velocity filters offer no benefit. The reason 33 for multiple filters is based on the timing implications for the large range of velocities the accelerator produces, which are discussed in more detail below.

2.2.3 Algorithm Overview

On the FPGA hardware, Equation 2.10 is implemented by constructing each filter out of three queues (sections A, B, and C in Figure 2.11), which together make up the triple square filter shape. As is evident from Figure 2.11, each queue has a length of W , with the back of the queue being to the left and the front being to the right. A queue data structure allows for the data to be put into the back of a queue, and then move through the queue as data is taken out of the front of the queue. This is analogous to the signal moving through the filter from left to right, as discussed perviously. The sequence for each clock cycle of the FPGA’s analog-to-digital converters (ADCs) is as follows:

(1) ADC pushes the new data value onto the back of queue A and the algorithm subtracts the

data’s value from the running correlation total (ﬁrst two terms in Equation 2.10).

(2) The front value in queue A is added three times (third term of Equation 2.10) and pushed

onto the back of queue B .

(3) The front value in queue B is subtracted three times (fourth term of Equation 2.10) and

pushed onto the back of queue C.

(4) The front value of queue C is added once (last term of Equation 2.10) and dequeued from

queue C.

(5) Logic is performed on the running correlation total (described in section 2.2.4).

Each detector output is fed into an ADC on the FPGA board and runs through its own set of

7 filters with each of the filters having its own filter response threshold value. In order to effectively determine the appropriate trigger threshold values, each filter has a threshold value which equals a 34 user-defined coefficient multiplied by the highest correlation response that particular filter reached by detector noise alone (measured immediately preceding the dust source being turned on).

Having multiple detectors on the beamline allows for a precise velocity measurement as the dust moves down the beamline. Within each ﬁltered signal, the zero-crossings represent reliable, well-deﬁned reference time points, and are therefore used to calculate particle velocity as follows.

After a ﬁlter has reached its threshold value, the FPGA looks for the associated zero crossing. At the zero crossing, the FPGA starts a timer and counts the number of clock cycles until the same zero crossing is recorded at the second detector. The zero crossing that is used for this application is the second zero crossing of the correlation response, which can be seen in Figure 2.12 at approximately t = 0.075 ms. This time diﬀerence determines velocity.

The zero crossing is the crux of the timing issue that was alluded to in reference to the filter sensitivity plot (Figure 2.13). For a filter that perfectly matches an ideal signal, the second zero crossing is delayed and occurs when the particle has reached a distance of exactly 1 and 2/3 detector lengths from the exit of the detector (for real particles with noise, this is only approximate). This effect can be seen in Figure 2.12. As the input signal moves through the filter, it creates the response shown in the last panel. The second zero crossing lines up with a point which is 2/3 into section C of the filter. This is understood to be 1 and 2/3 detector lengths away for the following reason: as the front edge of the (perfectly matched) signal moves from section A to section B, the dust is leaving the detector. The data then moves through section B, at which point the dust is one detector length away (in terms of real beamline distance). Once it moves 2/3 into section C, it is then 1 and 2/3 detector lengths away.

The rest of the algorithm proceeds as follows. With the zero crossing distance known (1 and

2/3 detector lengths down the beamline), the time it takes for the particle to reach the deflection plates is a known multiplicative factor of the time used to measure velocity. A significant amount of buffer distance (15 cm) is added into the multiplicative factor to account for the fact that the signal may not be perfectly matched to the fitler. However, with multiple filters, there is a reduction in the uncertainty of where a particle is in the beamline at that zero crossing as long as the algorithm 35 uses the filter which is closest to the particle velocity. The exact procedure for this is described in

Section 2.2.4. In order to measure charge, any DC oﬀset of the detector signal is subtracted from the measured peak of the second detector’s raw signal. This gives the amplitude of the detector signal, and therefore the charge of the dust grain. A detailed description of this is also given in

Section 2.2.4.

2.2.4 State Machine

The logic in Step 5 in the previous section involves the execution of a state machine, which is checked and updated at each clock cycle. There is a separate instance of the state machine for each filter. Running in parallel to the state machine are two running averages. One is an average, with a window size of 37 samples, used to measure the amplitude of the signal from the second detector (called amplitude average). The other, with a window size of 10 samples, is used to measure any baseline offset on the second detector’s signal (called offset average). These averages are always running, and the state machine checks and holds their values when appropriate throughout execution. Figure 2.14 shows a diagram of the state machine with the state transitions.

Each block in the diagram describes what the state does, and also contains a boolean expression which controls the next state. If the expression is true, the correct arrows are followed. If it is false, that state repeats on the next clock cycle unless otherwise speciﬁed. Also, if an action is performed on the state transition, it is labeled next to the arrow. 36 State 0

Corr 1 > Threshold? Yes, Hold the Offset Avg. State 1 Sample/Hold Amp. Avg. Corr. 1 < -Threshold? Yes A B State 2

Sample/Hold Amp. Avg Corr. 2 < -Threshold? (A) Or Corr.1 > 0? (B) State 3 State 4 Sample/Hold Amp. Avg. Corr. 1 > 0? Start Velocity Count Corr. 2 < -Threshold? Yes Yes State 5 State 6 Start Velocity Count Continue Velocity Count Corr. 2 > 0? Yes Yes Corr. 2 > 0?

State 7 Calculate Wait Count Does Velocity Count Fit Filter? No, Restart at Yes State 0 State 8 Charge = Amp. Avg. - Offset Charge & Velocity in Range? No, Restart at Yes State 0 State 9 Count Down Wait Count Wait Count = 0? Yes State 10 Yes, Set TTL Low and Restart at Set TTL High State 0 Count Down TTL Count TTL Count = 0?

Figure 2.14: The states with their transitions are shown. Also, the function of the state, along with the boolean expression controlling the next state, is given. Unless otherwise speciﬁed, if the boolean expression is false, the state repeats on the next clock cycle.

• State 0: The beginning or restarted state. The FPGA checks to see if the ﬁrst detector’s

correlation response (Corr. 1) is greater than the the ﬁlter threshold. This corresponds to

the ﬁrst positive peak of the correlation response in Figure 2.12.

• State 1: The amplitude average is sampled each clock cycle and the most negative value

is held. This sample and hold is looking for the dust signal on the second detector, because 37

correlation 1 has indicated there might be a particle coming (state 0). In addition, the

FPGA looks for a negative threshold from correlation 1 (larger, negative portion of the

correlation response in Figure 2.12).

• State 2: The FPGA continues the sample and hold of the amplitude average in State 2.

It also simultaneously checks for a zero crossing of correlation 1 or the negative threshold

of correlation 2.

• State 3: The FPGA checks for the zero crossing of correlation 1. Correlation 2 has hit the

negative threshold, so it is no longer necessary to check the amplitude average (the dust

has already gone through the second detector).

• State 4: The sample and hold of the amplitude average continues, and the FPGA starts

counting clock pulses. This count (called velocity count from here on) will give the velocity

of the particle. It also checks for the negative threshold of correlation 2.

• State 5: The FPGA starts counting clock pulses (the velocity count), and checks if corre-

lation 2 passes zero.

• State 6: The FPGA keeps counting clock pulses (velocity count) and checks for the cor-

relation 2 zero crossing.

• State 7: The FPGA compares the velocity count, which counted the clock pulses between

the zero crossings of correlation 1 and 2, to the range that is appropriate for that particular

ﬁlter. In addition, the FPGA calculates a wait count, which is the number of clock pulses

to wait until it sends out a TTL pulse to the deﬂection plates.

• State 8: The FPGA subtracts the detector signal oﬀset (which was sampled and held

from the oﬀset average in state 0) from the held amplitude average value. This gives the

measured charge of the grain. It then compares the particle’s velocity and charge to the

parameters set by the user. If the particle properties fall outside the user-deﬁned range 38

(i.e. the dust properties the user wants for the current experiment), the FPGA restarts at

state 0.

• State 9: The FPGA waits for the speciﬁed number of clock pulses calculated in state 7.

• State 10: Finally, in State 10, the FPGA outputs a high TTL value to the deﬂection

plates, which opens them. The length of time the TTL pulse is high was determined in

state 9, and the particle moves through the deﬂection plates undisturbed. Once the TTL

pulse is completed, the state machine restarts at State 0.

It should be noted that there is a velocity range dependent timeout count that is checked in states 1-5. If the state machine waits for longer than would be possible for the velocity range currently being used, the state machine reverts back to state 0. The longest timeout allowable is

3.5 ms.

2.2.5 Hardware Implementation

The code was written in LabVIEW FPGA module and runs on a National Instruments PXI-

7954R FPGA (Xilinx Virtex-5 LX110 based board) with a National Instruments 5781R adapter module. The 5781R contains two 14-bit ADCs capable of clock rates up to 100 Ms/s. Also, the

5781R has a 9 pin, multi-purpose digital I/O auxiliary connector used for the TTL pulse.

As mentioned previously, each filter is broken up into 3 queues. In hardware, these are implemented using first-in first-out (FIFO) data structures. The size of the FIFO data structures on the FPGA was very limited, which was the reason for the particular widths chosen in this implementation. In particular, the FIFO widths were limited to sizes corresponding to 2n + 5, with n being an integer. The FIFOs are first filled up with size-1 zero elements before allowing the

ADC to start inputting data. This ensures that each data point is in each queue for the proper number of clock cycles. The FPGA resources are clocked to the ADC clock (set to 26 Mhz for this implementation), which guarantees the calculations and logic are run once for each new data point 39 acquired. The reason the FPGA resources are not clocked to the full capability of the ADCs (100

MHz) is because the logic gates on the FPGA cannot execute fast enough.

2.2.6 FPGA Results

The FPGA system was compared to an analog PSU solution with particle signals from the accelerator. The analog PSU system (see Shu et al. [81] for a detailed discussion of this system) looks for simple analog threshold crossings of the raw detector signals and counts clock pulses between these thresholds on the ﬁrst and second detector. The threshold at the time of this experiment was set to 5 × 10−16 C, and is purely a function of the noise level of the detectors.

The particle selection for the comparison runs discussed here was based on velocity, with both the

FPGA and the analog PSU inputting TTL pulses to the deﬂection plates. These digital signals were fed into a boolean OR gate, which allowed for either system to detect and select a particle.

Two waveform sets were saved: one set containing all three detector signals plus the FPGA gate pulse, and the other set containing all three detector signals with the analog PSU gate pulse. Both sets were triggered from their respective gate pulses. Therefore, the data sets collected showed the particle signals which each system detected individually. These systems were running in parallel, so one would expect that most of the data would be duplicated across both data sets. If one system detected far more particles, or particles with higher velocities/lower charges, this would mean that one system is outperforming the other.

The detector waveforms were analyzed with an analysis script to give a velocity, charge, radius, and mass for each particle waveform set. By demanding that all three detector signals be present in the analysis, faulty signals are easily thrown out and a high degree of accuracy in the analysis of particle parameters was possible through detector coincidence checking. The velocity and charge are meassured directly from the detector and the mass is solved for (Equation 2.1).

With the mass found, the radius is approximated with the equation,

4 m = ρ πr3. (2.13) 3 40

In equation 2.13, the particles are treated as spheres with a density of ρ and a radius of r. For the iron particles used in this experiment, this is a very good approximation. FPGA and PSU Particle Data −12 10

−14 10

−16 10 Mass[kg] Mass (kg) FPGA Data −18 10 PSU Data FPGA lowest charge/highest velocity PSU lowest charge/highest velocity

−20

10 2 3 4 5 10 10 10 10 Velocity [km/s](m/s)

Figure 2.15: The FPGA and analog PSU particle data.

Figure 2.15 shows a plot of mass vs. velocity for the FPGA and analog PSU datasets. There are 3627 FPGA triggers shown vs. 1637 analog PSU triggers. Of those 3627 FPGA points, 2194 of them (60%) were missed by the analog PSU. Conversely, of the 1637 analog PSU triggers, only

216 of them (13%) were missed by the FPGA (it is not determined how many of these were false triggers). Additionally, the highest velocity/lowest charge detected are shown by the solid and dotted lines. The vertical lines show the highest velocity of this data set, while the lines with negative slope are lines of constant charge. The FPGA detected both a higher velocity (53 km/s) and lower charge (1.6 × 10−16 C) compared to the analog PSU (48 km/s and 5.7 × 10−16 C). Table

2.2 shows a summary of these results. Notice that the lowest charge for the analog PSU is very close to the theoretical minimum expected based on the analog threshold of 5 × 10−16 C.

Figure 2.16 shows the three detector signals for the particle with the lowest charge detected by the FPGA. The plot on the left shows the raw detector waveforms, while the plot on the right shows 41 System Number Detected Percent Missed Highest Velocity Lowest Charge FPGA 3627 13 53 km/s 1.6 × 10−16C Analog PSU 1637 60 48 km/s 5.7 × 10−16C

Table 2.2: Summary of the performance diﬀerences between the FPGA system and the analog PSU. Each system was running in parallel, but the FPGA detected many more particles. The percent diﬀerence column gives the percentage that the respective system missed of the other system’s dataset.

Figure 2.16: A plot of the three detector signals for the particle of lowest charge (1.6 × 10−16 C) detected by the FPGA (for this particular comparison experiment). The waveforms are artificially offset from one another for readability. The bottom waveform is the first detector, the middle is the second detector, and the top is the final detector. The left figure is the raw detector waveforms, and the markings on each signal indicate the location of the dust particle signal as it moves down the beamline. The right figure is a plot of the differentiated and smoothed signal from the analysis script. The vertical black lines show the window the analysis script used to look for the signal on the third detector (based on speed estimates from the first two detectors). Using the analysis script, it is clear that there is indeed a signal embedded in the noise.

the differentiated/smoothed waveforms from the analysis script. The signals are offset artificially for readability and go (from bottom to top) as the first, second, and third detectors respectively.

In the first two raw detector waveforms, the signal (whose location is given by the markings on the signals) is almost entirely buried in the detector noise. The FPGA detection uses these first two detector signals for its decision making, and therefore these signals would be impossible to use for a simple analog threshold (indeed, the analog PSU missed this signal). The FPGA, however, was able to detect this signal and trigger the deflection plates correctly. As is evident from the plot on the right, the analysis script was able to detect this signal, but only after a software algorithm of 42 smoothing, differentiating and coincidence checking of all three detectors. As stated earlier, this kind of algorithm is far too slow to be implemented in real-time, but the FPGA algorithm is both fast enough and accurate enough to achieve this kind of detection in real-time.

It is evident from Figure 2.15 that the FPGA is detecting many more particles which fall below the minimum threshold for the analog PSU. This alone is reason enough to use the FPGA instead of the analog PSU, but the FPGA also detects more particles in general. This is likely due to a rate limitation of a reset stage in the analog PSU, which is not present in the FPGA.

2.3 Summary

The hypervelocity dust accelerator at the Institute for Modeling Plasma and Cosmic Dust

(IMPACT) is the enabling facility for this work. It provides micron and sub-micron sized dust particles from 0.5-100 km/s with radii of 20 nm - 5 µm. Beamline dust detectors and an associated batch processing system automatically analyzes the accelerated particles and the facility provides experiments with metadata, including a timestamp, and raw waveforms for every particle. The

PSU, which is implemented on an FPGA, detects particles in real-time and decides whether or not to allow particles through a deﬂection region and into the target chamber.

The FPGA system described here provides a new method of dust detection. Using a family of

ﬁlter shapes in a cross-correlation algorithm, the system can accurately measure velocity and charge of in-ﬂight dust particles with signals buried in detector noise. The FPGA system outperformed the current analog PSU in terms of number of detections, highest velocity, and lowest charge. The highest velocity detected by the FPGA was 53 km/s, while the analog PSU detected a particle with a velocity of 48 km/s. The FPGA’s lowest charge was 1.6 × 10−16 C, compared to 5.7 × 10−16 C for the analog PSU. These results show that it is now possible to detect very small, low-SNR dust signals in dust accelerators thereby allowing for the study of nano-sized grains in the laboratory.

Since the FPGA comparison, which was performed in 2013, the FPGA has detected even faster and lower charged particles. For example, the FPGA has detected particles with velocities

> 100 km/s and with charges as low as 0.07 fC. Chapter 3

Experimental Design

A new experimental facility was designed to utilize the accelerator facility and simulate micrometeoroid ablation in laboratory conditions. The facility is a combination of a pressurized ablation chamber and a diﬀerential pumping system, which allows the dust particles to move from the high vacuum beamline into the pressurized experimental chamber. The experimental setup is attached at the end of the main beamline, behind the target chamber (see Figure 2.1). The experimental chamber contains a suite of electronics which is capable of measuring the plasma and light production as the particle ablates. These measurements allow for measurements of the ionization coeﬃcient, β, as well as for comparisons between the experimental ablation and predictions from ablation models. This chapter describes the experimental facility, which was used for the ablation studies described in Chapters 5 and 6.

3.1 Design Overview

A dust particle’s path through the experimental setup at the end of the main beamline (see

Figure 3.1 for a schematic) is as follows. Before entering the experimental setup, the particle moves through an image charge detector (the third beamline dust detector), which provides a velocity and mass measurement. The particle then moves through a narrow tube (5 mm diameter) into the

ﬁrst stage of diﬀerential pumping, which is designed to separate the high vacuum beamline (10−7

Torr) from the pressurized ablation chamber (0.01-0.5 Torr). Next, the particle moves through a skimmer cone that protrudes into the second stage of diﬀerential pumping before entering the 44 Shielding and segmented Differential pumping collectors Accelerator beamline Stage 1 Stage 2 Ablation chamber 10-7 10-5 10-3 0.01-0.5 Torr Incoming dust Torr Torr Torr Electronic signals Impact detector Skimmer cone Gas inlet Rough Image charge Vacuum Vacuum Vacuum pump Pressure detector pump pump pump (650 l/s) (300 l/s) (300 l/s) Windows gauge

Figure 3.1: Schematic of the experimental setup (side view). The particles are accelerated to > 10 km/s using the accelerator facility and the ablation chamber is mounted at the end of the beamline. A two stage diﬀerential pumping system separates the high vacuum beamline from the pressurized ablation chamber.

ablation chamber through a 3 mm aperture. Inside the ablation chamber, the particle collides with the target gas and begins to heat, melt, and ablate (evaporate). The ablated dust atoms collide with molecules of the target gas and ionize with a certain probability given by the ionization coeﬃcient, β. This process generates a trail of plasma as the particle moves through the 41 cm ablation chamber.

The ablation chamber diagnostics allow for the observation of the ablation process in two ways: biased electrodes above and below the ablation path collect the generated plasma, and four windows evenly spaced along the ablation path allow for optical measurements. The electrodes are segmented, with each segment connected to a separate charge sensitive ampliﬁer (CSA) in order to resolve the ionization as a function of distance. An impact detector (described in detail in Section

3.3) is placed at the end of the chamber to measure the impact charge generated by the remaining particle, if any. The amplitude of the impact charge signal provides the mass of the remaining particle. 45

3.2 Diﬀerential Pumping

A differential pumping system (shown in Figure 3.1) separates the high vacuum beamline from the pressurized ablation chamber. In order to observe all of the ablation physics, the differential pumping must have low enough pressures so that the dust particle’s temperature does not increase significantly (< 100 K) before entering the ablation chamber. To achieve this, there are two stages of differential pumping, each 20 cm in length. The first stage (10−5 Torr) of the differential pumping is separated from the beamline (10−7 Torr) through a cylindrical tube 5 mm in diameter and 8 cm long, and is pumped by a 300 l/s turbomolecular pump with a dry scroll forepump. In the molecular flow regime, the conductance (l/s) through the tube is given by

v πd3 C = t (3.1) 12l where vt is the thermal speed of the gas, d is the diameter of the tube, and l is the length of the

◦ d3 tube. For air at 20 C, the conductance is only C = 12.1 l = 0.19 l/s. This has no eﬀect on the pressure in the main beamline, which is maintained by a 650 l/s turbomolecular pump.

The second stage (10−3 Torr) contains a concentric skimmer cone with the larger end welded onto the chamber wall and is also pumped by a 300 l/s turbomolecular pump. The skimmer cone extends the effective length of the first stage by protruding into the second stage until the cone terminates 3 cm before the ablation chamber. Therefore, the particle is in the lower pressure environment of the first stage until just before entering the ablation chamber. Both the end of the cone and the entrance to the ablation chamber have adjustable apertures. The preliminary experiments were performed with 3 mm apertures for both the cone and the ablation chamber. In the molecular flow regime, the conductance of an aperture is given by [91]

v A C = t (3.2) 4 where A is the area of the aperture opening. For air at 20◦ C, C = 11.6A = 0.82 l/s. However, in the pressure regime of the ablation chamber (up to 0.5 Torr), the Knudsen number (λ/L, where λ 46 is the mean free path and L is a representative distance in the system - in this case 3 mm) is 1 at

23 mTorr and < 1 at higher pressures. This means that for pressures > 23 mTorr, the ﬂow through the ablation chamber aperture is viscous.

For viscous ﬂow, the conductance through an aperture is given by [91]

20A C = (3.3) 1 − δ

p2 where δ = p1 is the ratio of the pressure in the second stage of diﬀerential pumping (p2) to the pressure in the ablation chamber (p1). This equation is correct when δ ≤ 0.528 (for air at 20◦

C). The pressures in both the ablation chamber and the second stage of diﬀerential pumping were measured across the entire range of operating pressures and it was found that δ ≈ 0.004 for the entire parameter range. Therefore, the conductance through the aperture is approximately 1.4 l/s for all of the ablation chamber pressures. This is well below the pumping speed of the vacuum pumps and allows for the system to reach an equilibrium pressure in each chamber. The second stage also uses a 300 l/s turbomolecular pump, but due to the higher pressures involved in the second stage, a higher throughput forepump is used.

As stated previously, the goal of the diﬀerential pumping is to keep dust heating to < 100

K before entering the ablation chamber, and therefore the pressures in both stages were measured for the entire operating pressure range of the ablation chamber (0.01-0.5 Torr). In the case of the highest ablation chamber pressure used in this work (0.3 Torr), the pressure in the second differential pumping stage was measured to be 1 mTorr. Therefore, 1 mTorr was used as the pressure in an ablation simulation to ascertain if the differential pumping system succeeds in limiting dust heating to < 100 K. Additionally, a simulation was done for a low pressure ablation chamber of 0.02 Torr, where the pressure in the second stage of differential pumping was found to be 0.08 mTorr. The two situations correspond to two different velocity ranges, with the high pressure case being used for particles with low velocities (15 km/s in this case), and the low pressure case being used for high- speed particles (60 km/s in this case). The simulation code used is a thermodynamic code described in Hood and Horányi [36] and Kalashnikova, et al. [47]. The code assumes diffuse reflection of gas 47 particles off of the dust surface and calculates drag and heating coefficients for the particle along its trajectory. It accounts for phase transitions and calculates the mass loss due to evaporation. Figure

3.2 shows the results of the two simulations. In both cases, the particle’s temperature increases by < 100 K in 3 cm, which is the distance from the end of the skimmer cone to the entrance of the ablation chamber. Therefore, since the pressure in the first stage of the differential pumping is about two orders of magnitude lower than the second stage, and the fact that the simulations show the particle will not heat significantly in the second stage, we concluded that the particles do not undergo significant heating before entering the ablation chamber.

400 400 Velocity: 15 km/s Velocity: 60 km/s Mass: 10 fg Mass: 0.7 fg Pressure: 1 mTorr (N ) Pressure: 0.08 mTorr (N ) 380 2 380 2

360 360

340 340

Dust Temperature [K] 320 Dust Temperature [K] 320

300 300 0 5 10 15 20 0 2 4 6 Distance [cm] Distance [cm]

Figure 3.2: Simulations showing the dust heating for two particles in two diﬀerent pressures. The pressures are the measured pressures in the second stage of the diﬀerential pumping corresponding to ablation chamber pressures of 300 mTorr and 20 mTorr (left and right panels, respectively).

3.3 Ablation Chamber Overview

The ablation chamber is ﬁrst evacuated and then back-ﬁlled with the target gas using an

Alicat MC-200SCCM mass ﬂow controller. The pressure in the chamber is monitored using a

Baratron 622C gauge for a gas-independent, absolute pressure measurement with a resolution of

0.1 mTorr. By adjusting the mass ﬂow controller, the user is able to select the desired fate of the particle from modest heating to complete ablation. The approximate mean free path in the chamber is 0.1 - 5 mm for neutral-neutral and ion-neutral momentum exchange collisions. 48

The plasma generated from the ablation is collected on 16 segmented charge collection plates above and below the ablation path (see Figure 3.1). Each plate is connected to a charge sensitive ampliﬁer (CSA) circuit which converts the collected charge to a measurable voltage. The top and bottom plates are separated by 3.6 cm, and each plate is 8 cm long (transverse to the beamline) and

2.6 cm wide (along the beamline axis). This gives a spatial resolution of 2.6 cm. One side of the plates is biased by +/- 70-90 V, creating an electric ﬁeld oriented vertically in the chamber which separates the ions and electrons, so that each species is collected separately. The bias voltage is well below the Paschen breakdown voltage limit and creates an electric ﬁeld which dominates over the initial kinetic energy of the ions/electrons after a few collisions with molecules of the background gas. Therefore, the ions/electrons are collected close to where they were generated. See section 4.2 for a full discussion of this point.

If the particle does not fully ablate, whatever mass is left over will strike an impact detector at the end of the ablation chamber (see Figure 3.1) and generate a charge signal from which the remaining mass can be calculated. An impact detector is a common way of detecting dust particles through impact ionization (see, for example, Auer [3] and Collette, et al. [19]). The impact detector consists of a tungsten coated charge collection plate (also connected to a CSA) with a biased high- throughput grid in front of it. The tungsten target is grounded, while the grid is biased at the same potential as the plates. When a particle impacts the tungsten target, ions and electrons are generated through impact ionization. Those ions and electrons are then separated by the electric

ﬁeld (generated by the biased grid) and collected on the tungsten target. The impact charge signal allows for the measurement of the remaining mass of the particle that did not ablate. This can be used simply as a way of noting whether the particle fully ablated, or it can be used quantitatively for comparisons to predictions from ablation models.

Four windows evenly spaced along the ablation path allow for optical measurements of the ablation process. The windows are 3.6 cm diameter quartz windows mounted on 7 cm ﬂanges. The

ﬂanges allow for mounting photomultiplier tubes (PMTs) that can be used for light measurements.

A full description of the PMT setup can be found in Section 3.5. 49

3.4 Charge Collection CSA Design

The design of the electronics for collecting the charge on the segmented electrodes is critical, as it sets the limit of sensitivity. Figure 3.3 shows the schematic of the CSA. The CSA circuit consists of three stages: a charge sensitive ampliﬁer stage with a sensitivity of 5 × 1011 or 1 × 1011

V/C depending on the feedback capacitor, an op-amp stage with a 20x gain, and a unity gain buffer amplifier. The buffer amplifier stage has a bandpass filter formed from a high-pass filter and a low-pass filter with cutoff frequencies of 23 Hz and 21 kHz, respectively. The high-pass filter in front of the buffer amplifier eliminates any DC bias from the second stage, whereas the low-pass

ﬁlter reduces high frequency noise.

2 or 10 pF

500 ΜΩ 10 kΩ Input − 500 Ω − 50 Ω − 0.68 µF Output + + 0.15 F 2.2 µF + µ OPA656 10.2 kΩ OPA4820 AD8005

Figure 3.3: The electronic schematic of the charge sensitive amplifiers used in the ablation chamber. The first and second stage have a combined sensitivity of 1 × 1013 or 2 × 1012 V/C (depending on the feedback capacitor used), and the third stage is a unity gain buffer amplifier with a bandpass filter with cutoff frequencies 23 Hz and 21 kHz.

The CSA circuits were carefully characterized and have an equivalent noise level of about

3 × 103 e− rms. The CSA circuit is on a printed circuit board with the copper electrode on the opposite side of the board and a via connecting the electrode to the CSA input. There is a grounded plane separating the circuitry layer of the board from the electrode. Also, there is a thin (0.9 mm) grounded strip on the edge of each board’s electrode that mitigates crosstalk between two adjacent electrodes/CSAs such that it is negligible. To reduce noise pickup, there is a cylindrical shield surrounding the plates (see component labled shielding in Figure 3.1), which also acts as a large ground bus. 50

3.5 Optical Setup

Measuring the light emission from an ablating particle is useful for a number of reasons:

(1) real meteors are often observed through optical measurements [13] and using two techniques simultaneously (such as radar and optical measurements) is more eﬀective at constraining the properties of the meteors [57], and (2) one of the goals of this facility is to follow the particle’s position as it moves through the ablation chamber to obtain velocity/deceleration measurements.

The ability to measure the particle’s velocity as it ablates allows for low-velocity β measurements

(when the particle might be slowing down) and it allows for the validation of ablation model predictions.

The four windows on the ablation chamber (see Figure 3.1) allow for the measurement of the light produced by the ablation. A PMT setup was tested on the chamber, consisting of four

Hamamatsu R5900U-16-L20 16-channel PMTs. Each channel on the PMTs has a rectangular eﬀective area with dimensions of 0.076 x 1.6 cm (0.12 cm2). The rectangular channels were oriented such that the larger dimension was vertical with respect to the dust trajectory. The advantage of this setup is that by placing a vertical slit in front of the PMT, it is possible to segment the ablation path into 64 distinct bins (16 bins per window) at a cost of reduced light. The slit and PMT act as a pinhole imager, so that a reversed image of the beamline falls onto the PMT face. Since the

PMT face is divided into 16 channels, this segments the beamline into 16 separate spatial bins.

This segmentation gives a spatial resolution of 0.64 cm along the beamline for each PMT channel.

Figure 3.4 shows a schematic of the ablation chamber PMT setup from a top-down perspective with only two out of the four window/PMT assemblies shown (charge collection plates not shown).

There are 5.08 cm apertures cut out of the inner CSA shielding, which ensures the shielding will not obstruct the view of the beamline, and the PMTs are oﬀset from the window to achieve the spatial binning. Figure 3.4 also shows the slit and the view of one of the PMT channels (green region). Speciﬁcally, the view of PMT 2, channel 16 is projected through the slit and onto the beamline axis with a 0.64 cm resolution. 51 Ablation chamber CSA shielding

Total PMT field of Optical channel spacing = Incoming dust view = 10.41 cm 10.41/16 = 0.64 cm

Interior 6.35 cm aperture 5.08 cm 10.16 cm Window aperture 3.56 cm 2.24 cm 1.91 cm Slit

PMT face PMT 1 PMT 2 Light intersecting (16 Channels) PMT 2, channel 16

Figure 3.4: Schematic of the ablation chamber PMT setup (top view). Each PMT has 16 channels with each channel having an eﬀective area of 0.12 cm2. The PMT has a slit between it and the window, which creates a pinhole image of the beamline on the PMT face. Since the PMT face has 16 channels spread across it, this creates 16 spatial bins along the beamline axis (0.64 cm resolution). The green region shows the view of the beamline through the slit for PMT 2, channel 1.

With a real slit of ﬁnite width, there is a small uncertainty introduced in the measured position of the particle. The light from a point source particle along the beamline axis going through a real slit produces a spreading, δs, on the PMT face given by

H δs = w , (3.4) h where w is the slit width (0.17 cm), H is the distance from the beamline to the PMT (14.3 cm), and h is the distance from the beamline to the slit (12.4 cm). This error must be accounted for when imaging the particle.

Each PMT channel is amplified by a transimpedance amplifier, shown in Figure 3.5. The amplifiers have a time constant of 90 ns, which is equivalent to the transit time across a bin of a 71 km/s particle. Therefore, the PMT signals are fast enough to clearly capture a transiting particle entering and exiting a channel’s field of view. Furthermore, the amplification is sufficient to observe 52 3 pF

30 kΩ 3 kΩ

Input − − 3 kΩ Output

+ 0.1 µF + 50 Ω LMH6644 LMH6644

Figure 3.5: The electronic schematic of the transimpedance amplifer circuit, which ampliﬁes each PMT channel.

single photon events.

3.6 Data Acquisition

The data acquisition system used in the experiment is a multichannel system which saves all charge, impact, and light signals simultaneously with a timestamp that can be compared to the particle data that the accelerator facility produces (see Shu, et al. [81] for a full description of the capabilities of the accelerator facility). For example, every particle shot by the accelerator is measured by the particle selection unit (PSU), which outputs a mass and velocity and is saved with a timestamp. This mass and velocity data is critical to all experiments which use the accelerator, as it provides the parameters for each particle that enters the experiment. The dust ablation facility matches (using timpestamps) its dataset with the particle parameters from the accelerator, so that each ablation event is associated with a known particle mass and velocity.

Figure 3.6 shows a block diagram of the data acquisition system, and the details are as follows.

This setup allows for 47 channels saved for each ablation event: 16 charge signals, 1 impact signal,

1 beamline image charge detector signal, and 29 light signals. In principle, one could use all 47 channels for light collection, but in this work the ionization signals, impact signal, and 1 beamline detector signal were saved in order to help with identifying the light signals as well as matching them to particles in the beamline database. The beamline detector signal assists with matching each ablation event to the correct particle from the accelerator’s measurements. A Computer-Aided

Measurement and Control (CAMAC) crate is used as the data bus (LeCroy 1434 CAMAC crate), 53 and the electronic signals are digitized by three Jorger Model TR analog digitizer cards (16 channels per card with one dead channel on one of the cards, 40 MHz, 12 bits). The data is sent over a

LeCroy 8901A GPIB interface to a LabVIEW-controlled computer, where it is saved as a comma separated value (csv) ﬁle.

PSU Trigger

Data Signals

Ablation Chamber CAMAC Crate ~1.4 MB csv ﬁle 16 Charge 16 Ch. . . of data 47 waveforms Signals . . Joerger digitizer LabVIEW Computer

. 16 Ch. GPIB Ablation.vi 1 Impact Signal . Joerger digitizer

. 29 Light . . 16 Ch. Signals . Joerger digitizer .

Beamline Detector

Figure 3.6: A block diagram of the data acquisition system. The ablation chamber electronic signals, along with the last beamline image charge detector, are saved by three Joerger Model TR analog digitizers. The digitizers are triggered by the accelerator PSU, and the data is sent to a LabView-controlled computer. The computer saves all signals into a single ﬁle with 47 waveforms.

The Joerger cards are triggered by a carefully timed digital pulse from the PSU. As a particle moves down the beamline, the PSU detects the particle and measures its parameters, as stated previously. After it has measured the particle’s velocity, it then waits the correct amount of time for the particle to reach the last beamline detector. Once it does, the PSU sends a pulse to the

Joerger cards and triggers them. Due to the timing restrictions of the various signals, each ablation event must be saved with the maximum sampling frequency (40 MHz) and contain ∼ 20,000 data points per channel. Therefore, each ablation event contains ∼ 1.4 MB of raw data, and with a GPIB interface maximum data transfer rate of 450 KB/s, this produces a download time of several seconds for each ablation event. Faster, more modern, data acquisition interfaces are being investigated to reduce download time in the future. 54

3.7 Experimental Data Examples

Examples of experimental data are shown below in order to demonstrate the capabilities of the facility. Charge and light measurements with spatial resolution, a ﬁrst for laboratory experiments, are shown along with a basic analysis which calculates β and measures the velocity of an ablating particle.

3.7.1 Charge Measurements

Figure 3.7 shows an example of the charge data (ions in this case) collected by the experiment.

In this example, the iron particle had a velocity of 45.6 km/s and the ablation chamber was pressurized with air to 15 mTorr. The CSAs have a much longer time constant than the time it takes to collect the charges, and so the CSAs integrate the charge that each electrode collects.

Therefore, the peak of each signal gives the total charge collected by that electrode. Five peaks are labeled in Figure 3.7 (channels 4-8) that show the gradual increase and decrease of ionization as the particle travels down the ablation chamber.

Figure 3.8 shows the total number of ions collected on each channel (i.e. the peak voltage on each channel converted to charge). The ionization coeﬃcient is the ratio of elementary charges produced to the total number of atoms ablated. Therefore, for an ablation event where the particle completely ablates (such as this example), the ionization coeﬃcient can be calculated as β =

Nq/NF e, where Nq is the total number of elementary charges collected across all channels (3.5 million for this particle) and NF e is the total number of atoms in the dust particle (8.5 million).

For this particle, β was found to be 0.41. This procedure was done for a variety of target gases (N2, air, CO2, and He) and across a wide range of velocities (20-90 km/s). The results of that study are presented in Chapter 5.

One important distinction between this facility and previous experimental ablation facilities

(see for example Friichtenicht, et al. [29] and Slattery and Friichtenicht [84]), is that this facility has 16 charge collection plates. The plates give spatially-resolved measurements over the entire 55 0.5 Velocity: 45.6 km/s Channel Number Mass: 7.9 x 10-19 kg (iron) 0.45 7 1 6 Pressure: 15 mTorr (air) 0.4 2 3 8 5 0.35 4 5 0.3 6 7 0.25 8 9 4 0.2 10 11 CSA Signals [V] 0.15 12 13 0.1 14 15 16 0.05

0 0 0.05 0.1 0.15 0.2 Time [ms]

Figure 3.7: An example of a particle ablating in the experimental chamber. The ﬁgure shows the charge collection CSA signals vs. time. In this case, the experiment was conﬁgured to collect ions.

0.5

0.4

0.3

0.2

0.1

Elementary Charges Collected [Millions] 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Channel Number

Figure 3.8: Ions collected by each electrode channel for the particle ablation event shown in Figure 3.7. The 16 segmented collectors give a spatial resolution of 2.6 cm for the charge measurements, which will allow for comparisons to ablation model predictions in future studies.

ablation profile, and this allows for the comparison between experimental ablation profiles and the predicted profiles from ablation models. 56

3.7.2 Light Measurements

An example of an ablation event with both the charge and the PMT signals is shown in Figure

3.9. The PMT channels are arranged chronologically from top to bottom, and in this example, the channels are separated by 0.64 cm (i.e. every other PMT channel was recorded) and channels prior to the first light signal are not shown. Specifically, due to the limited light channels the data acquisition is able to record with the current setup (29), the light signals which were saved for the event in Figure 3.9 were arranged in the following way. The first channel was saved, followed by the third, fifth, etc. all the way to channel 55. Channel 56 was also saved such that the total was 29.

For this event, the PMTs detected mostly single photon events, which is due to a combination of the light production eﬃciency and the geometry of the PMT setup. The transimpedance ampliﬁers are capable of amplifying single photon events well above the noise (as is evident in Figure 3.9).

Charge signals 0.03 Velocity: 12.8 km/s 0.02 Mass: 7.3 x 10 -19 kg 0.01 Pressure: 175 mTorr (air) 0

CSA Signals [V] -0.01 250 300 350 400 Time [µs]

PMT signals 0

-0.5

PMT Signals [V] -1 250 300 350 400

-0.5

PMT Signals [V] -1 290 295 300 305 310 315 Time [µs]

Figure 3.9: An example ablation event with both the charge and PMT signals shown. The charge signals are color coded to match Figure 3.7. The PMT channels are artiﬁcially oﬀset from one another, with the channels organized in chronological order from top to bottom.

In order to measure the dust velocity from the PMT signals, the times for the start of each 57 pulse were measured and are shown in Figure 3.10. Care must be taken when selecting PMT pulses for Figure 3.10. Each PMT channel may have multiple pulses and it is possible a pulse may be caused by background photons or PMT dark current, rather than from a direct viewing of the particle itself. Furthermore, there is a position error on each data point that is a combination of

PMT pulse rise time (∼ 100 ns), the size of the PMT bins (0.64 cm), and the slit width error (δs, see

Equation 3.4). The calculation of the total error is as follows. First, the PMT pulse rise time error was converted to a position error based on the particle velocity (provided from the accelerator).

Next, the sum of the PMT bin size error and δs was added in quadrature to the PMT pulse rise time error to obtain a total error for each data point (±0.85 cm). These are the vertical error bars shown in Figure 3.10.

PMT Data 25 Linear Fit

5 Distance From Chamber Entrance [cm]

0 285 290 295 300 305 310 Time [µs]

Figure 3.10: The PMT pulse times from Figure 3.9 plotted as distance from the chamber entrance vs. time. The data was ﬁt to a linear ﬁt, which gives an average velocity of 12.21±0.29 km/s compared to a beamline measured velocity of 12.77±0.38 km/s.

After carefully selecting PMT pulses, a least-squares linear fit was made to the data (black line in Figure 3.10) which gave a velocity of 12.21±0.29 km/s, compared to 12.77±0.38 km/s measured from the beamline detectors. The total error on the fit was found by first calculating the root mean squared error (rmse). The rmse is given by[88] 58

v u N u 1 X σ = t (y − A − Bx )2, (3.5) y N − 2 i i i=1 where σy is the rmse on the linear function y = A + Bx, N is the number of data points in the ﬁt

(13), and A and B are the best estimates of the coeﬃcients. The error on the slope (i.e. velocity) is then [88]

r N σ = σ , (3.6) B y ∆ where ∆ = N P x2 − (P x)2.

The novelty of these light measurements is that it is now possible to track the dust particle as it moves through a laboratory ablation chamber. This capability is used in the experimental investigation of ablation models, described in Chapter 6.

3.8 Summary

A new dust ablation facility was developed for this work. The facility includes an ablation chamber and a diﬀerential pumping system which attaches to the end of the IMPACT dust accelerator at the University of Colorado.

The ablation chamber contains a suite of electronics which collect the generated plasma from an ablated dust particle over two sets of 16 segmented collectors. The collectors allow for a spatial resolution of 2.6 cm and allow for the comparison between experimental ablation profiles and profiles generated by ablation models. The charge measurements also allow for β measurements for a variety of dust and gas types (see Chapter 5 for the first β results of the facility).

In addition to charge measurements, the ablation facility is conﬁgured to enable the measurement of light production as a particle ablates. The chamber has four windows evenly spaced along the ablation path that allow for the placement of PMTs to measure the dust velocity as it ablates.

Velocity and charge generation measurements are used to constrain ablation models in Chapter 6. Chapter 4

Modeling Support

There are a total of four models used in this work. The first two, described in Section 4.1, are physical ablation models which describe the heating, melting, evaporation, and ionization which occurs as a micrometeoroid ablates. These models are used in the meteor community to interpret the various methods of IDP detection, and one of the goals of this work is to investigate how well these models describe real meteor ablation (see the second science question in Section 1.3). The last two models, described in Sections 4.2 and 4.3, are models used in the interpretation of the experimental data from the dust ablation facility. Specifically, the collection efficiency model takes into account the forward velocity of ablated meteoric atoms and calculates the axial spread of collected ions.

The second model, electron impact ionization, models the motion of accelerated electrons in the ablation chamber electric ﬁeld and takes into account impact ionization cross sections (among other types of cross sections) with N2 in order to calculate the probability of additional ionization beyond that predicted by the ionization coeﬃcient, β. This chapter describes all four models.

4.1 Ablation Models

The ablation models investigated in this work include a simpliﬁed version of the The Chemical

Ablation Model (CABMOD) and a model described in Hood and Hor´anyi [36]. The version of

CABMOD which is used in this work does not include code which models the differentiation of the molten meteor since the particles in this work are all purely iron. Also, this version neglects the effects of gravity, which are negligible in the accelerator experiments. To differentiate between 60

CABMOD (described in Vondrak, et al. [92]) and the version used here, we will refer to it as CM from hereon.

The model described in Hood and Horányi [36] was originally developed to describe dust particles in a comet coma, but describes equally well micrometeors ablating in a planetary atmosphere. It is a fully self-consistent ablation model, in that the equations use three accommodation coefficients, which describe the microphysics of the gas-dust interaction, to calculate model quan- tities such as the drag coefficient and heat transfer. Therefore, it is called the SElf-Consistent

Ablation Model (SECAM) from hereon. In contrast, the CM model allows for model parameters to be varied in any way. Both models assume the molecular ﬂow regime and the isothermal condition.

Both models also calculate particle heating, account for phase transitions, and model the particle evaporation. However, there are several important diﬀerences. The details of the models, including their diﬀerences, are described in Sections 4.1.1 and 4.1.2.

4.1.1 CM Model

The CM model can be broken down into four interrelated components: the deceleration of the particle, the energy balance equation for the dust particle, the thermal mass loss due to

Langmuir evaporation, and the non-thermal mass loss due to sputtering. The code takes a particle, characterized by position, velocity, temperature, and mass, and progresses through a sequence of small, discrete timesteps. At each timestep, the particle’s characteristics are incrementally adjusted by the physics descriptions of deceleration, heat transfer, thermal mass loss, and sputtering. Based on the evolved velocity, the temporal evolution of the particle is mapped to a spatial evolution.

Figure 4.1 shows the structure and ﬂow of the model.

4.1.1.1 Deceleration

The deceleration of the spherical particle can be calculated in the free molecular regime by assuming that the momentum of the impinging gas molecules is transferred to the particle with an eﬃciency given by the “free-molecular drag coeﬃcient”, Γ. This assumption can be written as 61

∆(mdvd) = −Γmgvd (4.1) where md and vd are the mass and velocity of the dust particle, respectively, and mg is the mass of the impinging gas. In some time, ∆t, the dust particle intercepts a cylindrical volume of gas. The volume of the cylinder is given by

2 2 V = πR L = πR vd∆t (4.2) where R is the dust radius and L is the length of the cylinder which the dust sweeps out. By substituting ρgV for mg (where ρg is the gas mass density), Equation 4.1 becomes

∆(mdvd) = −Γmgvd

md(vdf − vdi) = −ΓρgV vd (4.3) 2 = −ΓρgπR vd∆tvd

2 2 = −ΓρgπR vd∆t.

In Equation 4.3, vdf is the ﬁnal dust velocity after intercepting the gas, and vdi is the inital dust

4 3 velocity. Dividing Equation 4.3 by ∆t, substituting md = 3 πR ρd, and letting ∆t → 0, Equation 4.3 can be rewritten as

dV 2 3ρg = −Γvd . (4.4) dt 4ρdR where ρd is the dust mass density. Typically, Γ is set from 0.5-1 [92].

4.1.1.2 Energy Balance

As the dust particle impacts the gas molecules, the frictional heating is balanced by the following mechanisms: radiative heat loss, heat lost due to mass ablation (i.e. sputtering and sublimation or evaporation depending on the phase), dust temperature increase, and phase transitions.

Therefore, the energy balance equation can be written as [92] 62 Solid Solid/Liquid Liquid

Frictional heating Frictional heating Mass loss by sputtering Radiative heat loss Radiative heat loss Mass loss by Langmuir Heat loss by mass ablation Heat loss by mass ablation evaporation Melting phase transition (dT/dt = 0)

Mass loss by sputtering Deceleration of particle Mass loss by Langmuir evaporation Mass loss by sputtering Mass loss by Langmuir evaporation

No Deceleration of particle m < mmin?

Deceleration of particle

Yes No

T > Tmp? Code terminates Fully No Yes Melted?

Yes

Frictional heating Radiative heat loss Heat loss by mass ablation

Figure 4.1: Flow chart illustrating the structure and ﬂow of the CM model.

1 4 dT dm πR2v3ρ Λ = 4πR2σ(T 4 − T 4 ) + πR3ρ C + L . (4.5) 2 d g env 3 d p dt dt

In Equation 4.5, the terms represent the following. The ﬁrst term (left hand side) corresponds to the frictional heating with the dimensionless parameter Λ being the “free-molecular heat transfer coeﬃcient”. Λ is the fraction of incident kinetic energy of the gas which is transferred to the particle.

The frictional heating term is calculated in an analogous way to the deceleration equation (Equation

4.4) in that the dust particle sweeps through a volume of gas in a time, ∆t, and that kinetic energy is transferred to the particle with the efficiency given by Λ. The three terms on the right hand side represent where the frictional heat energy is partitioned. Specifically, the first term on the right is the radiative heat loss with and σ being the dust emissivity and the Stefan-Boltzmann constant, respectively. The two temperatures, T and Tenv, are the dust temperature and gas temperature, 63 respectively. The next term describes the dust temperature increase and is simply the dust particle

dT mass multiplied by the speciﬁc heat, Cp, and the change in temperature dt . The ﬁnal term is the heat loss due to mass ablation with L being the latent heat (either of sublimation or vaporization

dT depending on the dust phase). During phase transitions, dt = 0 and the net heat goes into the phase transition rather than in raising the dust temperature.

40 Iron

Imaginary Real 20

Real and Imaginary Indices of Refraction 0 10-4 10-3 Wavelength [cm]

Figure 4.2: Measured real (n) and imaginary (k) indices of refraction for iron. Reproduced from [75].

The emissivity in Equation 4.5 is set to 1.0 in Vondrak, et al. [92], but for small micrometer- sized (or smaller) particles, the emissivity is more complicated. Due to their small size, the particles are ineﬃcient radiators in the infrared. In the ﬁrst-order theory of Mie spheres, the emissivity can be calculated in the limit 2πR/λ < 1 (i.e. spheres smaller than the wavelength) as a function of emitted wavelength to be [75]

48πnk R = , (4.6) (n2 − k2 + 2)2 + 4n2k2 λ where the index of refraction is n+ik. Figure 4.2 shows the real and imaginary indices of refraction for iron as a function of wavelength (from lab measurements). To simplify the radiative term in

Equation 4.5, the emissivity is calculated (using Equation 4.6) at the peak wavelength of the 64 blackbody emission for a given temperature.

The specific heat used in Vondrak, et al. [92] was 1 × 103 J kg−1 K−1; however, the specific heat for iron is a function of temperature. Therefore, Figure 4.3 shows the specific heat as a function of temperature (Cp(T )) given by Desai [22], which is used in the model equations in this work.

80 -1

K 70 -1

50 Liquid

40 Specific Heat, J mol 30

20 500 1000 1500 2000 Temperature [K]

Figure 4.3: Measured speciﬁc heat of iron as a function of temperature. Reproduced from [22].

The thermal mass loss is modeled as Langmuir evaporation, which assumes that the rate of evaporation in a vacuum is balanced by the rate of uptake for a particular species. The Langmuir evaporation is given by [92]

T r dm µi = −γpiS (4.7) dt 2πkBT where γ is the uptake (or sticking) coeﬃcient, pi is the vapor pressure of species i, S is the particle area, and µi is the molecular weight. The value of γ is set to a sigmoid function in Vondrak, et al.

[92], such that it is 0 below 1700 K, 0.5 at the melting point, and 1 at 1900 K. This has the eﬀect of mostly eliminating Langmuir evaporation before the particle melts, but is a smooth transition around the melting point. The vapor pressures of iron, pF e, are in the functional form of [2]

−1 −3 log10(pF e) = 5.006 + A + BT + C log10 T + DT . (4.8) 65

The pressure in Equation 4.8 is in units of Pascals. The coeﬃcients A, B, C, and D in Equation

4.8 for both the solid and liquid phase are given in Table 4.1 [2].

Coeﬃcient Solid Liquid A 7.1 6.347 B -21723 -19574 C 0.4536 0 D 0.5846 0

Table 4.1: Coeﬃcient values for the vapor pressure equations for the solid and liquid phase of iron. Reproduced from [2].

4.1.1.3 Sputtering

The sputtering yields used in the CM model are for ions such as H+, He+, and D+ instead of neutral atmospheric gases like N2. However, experimental studies have shown that the sputtering yields for ions and neutrals are largley the same [58]. Therefore, Vondrak, et al. [92] uses these methods for the sputtering component, as does the CM model described here.

The physical mechanism for sputtering is described as a cascade of binary collisions between recoiling atoms oﬀ of the surface of the material. As a gas molecule with energy E collides with the dust particle, a fraction of the atoms in this cascade of collisions will acquire an energy greater than the surface binding energy, U0, and be liberated from the material as a sputtered atom. That fraction at normal incidence, Y (E, θ = 0), is given by Vondrak, et al. [92] as

αS (E) Y (E, θ = 0) = 4.2 × 1014 n . (4.9) U0

In Equation 4.9, E is in erg, U0 is in eV, and α is a ratio between the target and projectile masses

(dust atom and gas molecule, respectively). Sn(E) is the nuclear stopping cross-section of the target material (erg cm2) and is given by [92]

2 Mp Sn(E) = 4.2πaZpZte sn(pt), (4.10) Mp + Mt 66 where e is the electron charge (1 esu), a is the screening length of the Coulomb interaction (in cm),

Zp is the atomic number of a projectile, Zt is the atomic number of a target atom, and sn(pt) is a dimensionless, universal sputtering function given by [92]

√ 3.411 pt ln pt + 2.718 sn(pt) = √ √ (4.11) 1 + 6.35 pt + pt(−1.708 + 6.882 pt)

As stated previously, α relates to the mass ratio of a target atom to a projectile atom. For a mass ratio of 0.5 < Mt/Mp < 5, α can be taken as [92]

2 M 3 α = 0.3 t . (4.12) Mp

The dust particles used in this work are all pure iron (Mt, 55 amu). The most massive gas molecules used are CO2 (Mp, 44 amu), and the lighest is He (Mp, 4 amu). Therefore, there are instances where the ratio, Mt/Mp, is greater than 5. In those cases, α is reduced by multiplying by the ratio of the average projected range of an incident particle, Rproj, to the average path length, R [8]:

R M proj = (K t + 1)−1. (4.13) R Mp

In Equation 4.13, K depends on the target material. For the case of the mass ratio exceeding 5,

Equation 4.13 would be multiplied by Equation 4.12 to modify α. For completeness, one should mention that for mass ratios of Mt/MP < 0.5, α is a constant value of 0.2. However, for the model analysis in this work, only gases which fall into the range 0.5 < Mt/Mp < 5 are used. Therefore,

Equation 4.12, without any modiﬁcation, is used for α. This is the case for the most important atmospheric gases, such as N2 and O2.

Returning back to Equation 4.10, the screening length of the Coulomb interaction between nuclei, a, is given by [92]

2 2 1 3 3 − 2 a = 0.885a0 Zp + Zt (4.14) 67 where a0 is the Bohr radius (in cm). The parameter, pt, in Equations 4.10 and 4.11 incorporates the projectile energy, E, in such a way that it is dimensionless and makes sn(pt) a universal function of sputtering for all combinations of targets and projectiles. pt is given by [92]

Mt a pt = 2 E. (4.15) Mp + Mt ZpZte

In order for a target atom to leave the surface, it must gain enough energy to overcome the binding energy, U0. In sputtering theory, near the threshold, it is assumed that the ejection of surface target atoms is entirely due to recoiling projectile atoms. In that case, the threshold projectile energy is calculated to be [9]

U0 Mp Eth = for ≤ 0.3 (a) G(1 − G) Mt (4.16) 5 Mp 2 Mp Eth = 8U0 for ≥ 0.3 (b). Mt Mt

The parameter G is given as [9]

4MpMt G = 2 . (4.17) (Mp + Mt)

When calculating the sputtering yield, there is a special case for low energy projectiles (E

20Eth), where a large collision cascade is absent and only a small fraction of the recoiling atoms have kinetic energy above U0. In that case, Sn in Equation 4.10 is replaced with [92]

2 2 E 3 E S0 = S 1 − th 1 − th . (4.18) n n E E

The total sputtering yield is taken in Vondrak, et al. [92] as an angle-averaged sputtering yield for low energy impacts, such that the total yield is 2Y (E, θ = 0). Therefore, the total mass loss rate for a spherical particle averaged over 0 to π/2 is given as [92]

dmS X = −2πR2VM n Y (E, θ = 0), (4.19) dt t i i i 68 where the superscript S refers to sputtering, the index i refers to the atmospheric components, V is the velocity of the dust, and ni refers to the number density of the i-th atmospheric component.

The sputtering mass loss rate is then added to the thermal mass loss rate to get a total rate of

dm dmT dmS = + . (4.20) dt dt dt

4.1.2 SECAM

SECAM, as described in Hood and Hor´anyi [36], is similar to the CM model in that it accounts for heat transfer from the impinging gas to the dust, radiative heat loss, deceleration of the particle, and evaporative mass loss. However, there are several important diﬀerences. First,

SECAM models the gas-dust interaction as a gas molecule contacting the dust particle, thermally accommodating to some extent, and then the gas molecule being emitted from the dust particle.

The impinging gas is modeled as a shifted (by the dust velocity) Maxwellian distribution, and the re-emitted particles as a non-shifted Maxwellian distribution. From these distributions, the pressure on the dust particle (and thereby the drag coeﬃcient) can be calculated, as well as the total heat transfer. In this way, the model self-consistently calculates momentum and heat transfer to the dust particle. Second, the evaporative mass loss is not modeled as Langmuir evaporation, but rather is the net heat divided by the latent heat of vaporization after the dust particle has reached the vaporization temperature.

Hood and Horányi [36], and earlier Gombosi, et al. [32], describe the ablation of dust in the free molecular regime with the gas-dust interactions being completely diffusive. Diffuse reflections of gas molecules off of the dust surface means that the gas molecules completely thermally accommodate and leave the dust particle with a Maxwellian distribution which has the same temperature as the dust. In this work, we derive model equations which do not assume completely diffuse reflection and thereby allow for a potentially more realistic scenario of reflections which partially accommodate. 69

4.1.2.1 Accommodation Coeﬃcients

When a gas molecule impinges on the dust particle, there is a transfer of both momentum and energy to the dust particle. The efficiency with which these transfers take place are described by accommodation coefficients. For example, a completely diffuse reflection is when the gas molecule completely accommodates and is released from the dust particle at the same temperature as the dust. A completely specular reflection is when the gas molecule is reflected from the dust surface with the same temperature it came in with. Therefore, a thermal accommodation coefficient can be defined as [34]

Ei − Er ae = , (4.21) Ei − Ed where Ei is the incident energy per unit area per second of a stream of impinging gas molecules.

Similarly, Er is the energy of the reflected (or re-emitted) particles, and Ed is the energy of the particles if they were the same temperature as the dust particle. Therefore, for a diffuse reflection, since the particles are re-emitted with the same temperature as the dust, Er = Ed and ae = 1. In constrast, in a specular refelction, there is no energy exchange and the reflected particles have the same energy as they came in with, Ei = Er, which leads to ae = 0.

It should be noted that in Equation 4.21, it is assumed that all of the energies associated with the molecular degrees of freedom (vibrational, rotational, translational, etc.), which interact with the surface, are all accommodated to the same degree. There is evidence that the translational and rotational accommodation coefficients are approximately the same, but the vibrational energy should require a longer adjustment time. Therefore, the assumption of a single coefficient is probably incorrect, but nevertheless we shall use a single coefficient (as is done in Hayes and Probstein

[34]). The greater adjustment time required for some forms of energy - an “absorption relaxtion eﬀect” - should show a dependence on the temperature of the body and therefore should manifest as a temperature dependence on αe [34]. Fits of αe(T ) with various functional forms could be done in future studies to investigate this eﬀect and possibly improve model performance. 70

Similar to the thermal accommodation coefficient, the difference between the incoming and outgoing normal and tangential force components of the gas are specified by their own accommodation coefficients. For the normal force components, it is completely analogous to the thermal accommodation coefficient and is given by [34]

pi − pr fn = . (4.22) pi − pd

In Equation 4.22, pi is the momentum flux from the incident gas, pr is the momentum carried away by the reflected gas, and pd is the momentum carried away by the reflected gas if it were fully accommodated. The formulation for the tangential coefficient is similar except for the fact that for fully a accommodated gas, the gas molecules are emitted from the dust particle in all directions. Therefore, the fully accommodated gas does not have any net tangential force, and the accommodation coefficient is defined as

τi − τr ft = , (4.23) τi where τ is the tangential force, or shear, on the dust particle. In this case, for a fully accommodated gas, τd = 0 and therefore it does not appear in Equation 4.23. For diffuse reflections, τr = τd = 0 and so ft = 1. Additionally, for specular reflection the tangential velocity component of the gas molecules is conserved such that τr = τi, and therefore ft = 0.

4.1.2.2 Momentum and Energy Transfer

We will now deﬁne the particle distributions which are used in the calculation of the momentum and heat transfer. Figure 4.4 shows the coordinate system for the problem. A macroscopic velocity vector, U impinges (in the dust particle frame) on the dust with the velocity of the dust particle (from the lab frame). It makes an angle θ with respect to a surface element, dA, and the x-axis is situated such that it is normal to the surface at the origin, while the y-axis is tangential to the surface element. 71

Figure 4.4: Coordinate system for a suface element of the spherical particle. U is the velocity of the dust (seen in the frame of the dust as the velocity of the impinging gas). The coordinates are such that the x-axis is normal to the surface at the origin and the y-axis is tangent to the surface. The angle, θ, is the angle the velocity vector makes with the element. Reproduced from [34].

With the coordinate system deﬁned, we next introduce the particle distribution for the impinging gas. The distribution is a Maxwellian distribution of gas particle velocities (cx, cy, and cz), such that fdcxdcydcz is the number of particles per unit volume with velocities between cx + dcx, cy + dcy, and cz + dcz. The distribution is given by [34]

n (c − U sin θ)2 + (c + U cos θ)2 + c2 f(c , c , c ) = g exp − x y z (4.24) x y z 3/2 (2πkBTg/m) 2kBTg/m where ng is the total number of incident molecules per unit volume, Tg is the gas temperature, m is the mass of a gas molecule, and kB is Boltzmann’s constant. With the distribution deﬁned, we can solve for the various “moments” of the distribution to obtain particle ﬂux, pressure, and incidient kinetic energy.

The particle ﬂux on the surface element can be calculated by integrating cxfdcxdcydcz across all available velocities. The incident ﬂux is given by 72

Z ∞ Z ∞ Z ∞ Ni = cxfdcxdcydcz. (4.25) −∞ −∞ 0

The lower limit of 0 for the integral over cx is due to the fact that no particles with a negative x velocity can strike the front of the surface element. Evaluating the integral gives

r k T 2 √ N = n B g [e−(sa sin θ) + π(s sin θ)[1 + erf(s sin θ)]], (4.26) i g 2πm a a where n is the number of incident molecules per unit volume, erf is the error function and sa is the

U speed ratio, sa = √ . 2kB Tg/m Similarly, the incident momentum ﬂux in the normal direction is calculated by integrating

2 mcxfdcxdcydcz,

Z ∞ Z ∞ Z ∞ 2 pi = m cxfdcxdcydcz −∞ −∞ 0 (4.27) 2 ρU 2 √ 1 √ −(sa sin θ) 2 = 2 (sa sin θ)e + π + (sa sin θ) 1 + erf(sa sin θ) 2 πsa 2 where ρ is the mass density of the incoming gas. The total normal pressure on the dust can be calculated from the deﬁnition of the normal accommodation coeﬃcient (Equation 4.22), such that

p = pi + pr = (2 − fn)pi + fnpd. (4.28)

The pressure pd is the pressure exerted on the dust from particles leaving the surface with a distribution at the same temperature as the dust (i.e. the pressure from a fully accommodated gas). To calculate this, we use the same distribution function but with U = 0, ng → nd, and

Tg → Td. The integral over the now stationary Maxwellian gives

Z ∞ Z ∞ Z 0 2 pd = m cxf(U = 0)dcxdcydcz −∞ −∞ −∞ (4.29) 1 = n k T 2 d B d 73 where nd is the density of reflected gas with the same temperature as the dust, Td is the dust temperature, and the integral over cx was done from −∞ to 0 because the dust is leaving the surface and therefore has no positive x velocity. In Equation 4.29, the density nd can be solved for by considering a hypothetical stationary gas which is impacting the opposite side of the dust particle. The flux of this hypothetical gas is equivalent to Ni except that sa = 0, Tg → Td, and ng → nd. Furthermore, the flux of this gas is identical to the flux of the particles reflecting off of the front surface with the same temperature as the dust, Nd. Therefore, we use Equation 4.25 to calculate the flux as

r k T N = n B d . (4.30) d d 2πm

In a steady state, the incoming flux of gas molecules must equal the reflected flux (Ni = Nd), which means that

r 2πm nd = Ni . (4.31) kBTd

Substituting the expression for nd into the equation for pd (Equation 4.29) gives

1 r 2πm pd = Ni kBTd 2 kBTd r k T πm = N B d (4.32) i 2 n 2 √ = g k pT T e−(sa sin θ) + π(s sin θ) 1 + erf(s sin θ) . 2 B d g a a

With expressions for pi and pd, we can calculate the total normal pressure on the dust, p, as

p = (2 − fn)pi + fnpd

2 s ρU (2 − f ) f T 2 √ n n d −(sa sin θ) = 2 sa sin θ + e (4.33) 2sa π 2 Tg s 2 fn √ Td + (2 − fn)(1/2 + (sa sin θ) ) + π sa sin θ (1 + erf(sa sin θ)) . 2 Tg 74

We next calculate the shear acting on the surface of the dust particle. Incident gas molecules having velocities between cx and cx + dcx transport a tangential component of momentum equal to −mcy per molecule to the dust surface. Therefore, the total incident tangential momentum transfered to the dust is equal to

Z ∞ Z ∞ Z ∞ τi = −m cxcyfdcxdcydcz −∞ −∞ 0 (4.34) 2 2 √ ρu cos θ −(sa sin θ) = √ [e + π(sa sin θ)[1 + erf(sa sin θ)]]. 2 πsa The total shear on the particle can be calculated using the tangential accommodation coeﬃcient

(Equation 4.23) as,

τ = τi − τr = ftτi. (4.35)

In Equation 4.35, one can check the limiting cases of specular and diffuse reflection (where ft = 0 and ft = 1, respectively). For specular, τ = 0, since no tangential momentum is transfered in a specular reflection. For diffuse, τ = τi, which is also correct since the incident tangential momentum is fully absorbed, and there is no net tangential momentum in the reflected molecules.

Finally, we must calculate the heat transfer to the particle. Hayes and Probstein [34] deﬁne the heat transfered per unit time per unit area to the body as

q˙ = Ei − Er (4.36)

= ae(Ei − Ed), where Ei and Er are the incident and reflected energies of the gas molecules. In Equation 4.36, the definition of the thermal accommodation coefficient (Equation 4.21) was used to rewrite the heat transfer in terms of a reflected gas distribution with the same temperature as the dust (i.e. Ed).

In order to calculate the total incident energy, we ﬁrst calculate the total translational energy of

1 2 2 2 the incident gas. Each gas molecule has a translational energy of 2 m(cx + cy + cz), and the total translational energy ﬂux can be calculated as 75

Z ∞ Z ∞ Z ∞ m 2 2 2 Ei,tr = cx(cx + cy + cz)fdcxdcydcz 2 −∞ −∞ 0 r k T 2 = n k T B g (s2 + 2)e−(sa sin θ) (4.37) g B g 2πm a √ 2 + π(sa + 5/2)(sa sin θ)[1 + erf(sa sin θ)] .

This is suﬃcient for monatomic gases, but for more general cases (such as diatomic gases), we will use the assumption of classical equipartition of energy. Each of the molecules carries an

1 additional amount of energy equal to 2 jintkBTg of energy, where jint is the number of internal degrees of freedom [34]. With three translational degrees of freedom, the total number of degrees of freedom for the gas is j = 3 + jint. For a perfect gas, the total number of degrees of freedom is related to the speciﬁc heat ratio, γ, by j = 2/(γ − 1). Therefore, the internal degrees of freedom can be written as jint = (5 − 3γ)/(γ − 1). Given these considerations, the total incident internal energy can be written as

5 − 3γ k T E = B g N , (4.38) i,int γ − 1 2m i where Ni is the incident ﬂux of gas molecules. In order to complete the calculation of the heat transfer, we must have expressions for the energy of the reﬂected gas which has fully accommodated

(Ed,tr and Ed,int). The translational energy can be found by setting sa → 0, ng → nd, and Tg → Td in the expression for Ei,tr (Equation 4.37) such that

r k T E = 2n k T g d d,tr d B d 2πm r r 2πm kTd (4.39) = 2Ni kTd kTd 2πm

= 2kTdNi where Equation 4.31 was used to substitute nd. Furthermore, Ed,int is found by 76

kT E = j d N d,int int 2 d 5 − 3γ kT = d N γ − 1 2 d r 5 − 3γ kT kT = d n d (4.40) γ − 1 2 d 2πm r r 5 − 3γ kTd kTd 2πm = Ni γ − 1 2 2πm kTd 5 − 3γ kT = d N . γ − 1 2 i The total reﬂected energy is then

Ed = Ed,tr + Ed,int

5 − 3γ kTd = 2kTdNi + Ni (4.41) γ − 1 2 N kT γ + 1 = i d . 2 γ − 1 Putting Equations 4.36, 4.41, 4.37, 4.38, and 4.26 together, we calculate the total heat transfer to the surface of the dust per unit area per unit time as

q˙ = ae(Ei − Ed) r kBTg 2 γ γ + 1 Td = aepg sa + − × (4.42) 2πm γ − 1 2(γ − 1) Tg 2 √ 1 2 (e−(sa sin θ) + π(s sin θ)[1 + erf(s sin θ)]) − e−(sa sin θ) . a a 2 where pg = ngkBTg is the pressure of the gas.

With expressions for the normal pressure (p), tagential stress (τ), and heat transfer (q ˙) to the particle in hand, we can calculate the total drag force and total heat transfer (per unit time) to the particle by integrating over the surface of the particle. Figure 4.5 shows a diagram of a spherical dust particle with the x and y axes from Figure 4.4 labeled, which are ﬁxed with the diﬀerential area element (red region). An annulus is constructed over the surface of the sphere with an area of (2πR sin α)(Rdα) = 2πR2 sin αdα. The angle θ is the same angle from the y-axis to the gas 77

π velocity vector (U) as in Figure 4.4, and it relates to α by θ = 2 − α. The normal pressure, p, and tangential stress, τ, from the incident gas are also labeled (blue arrows).

Figure 4.5: Coordinate system used for the integration over the dust surface. The x and y axes are the same as that shown in Figure 4.4, in that they are ﬁxed with a diﬀereential area element (red region). The normal pressure p and the tangential stress τ delivered by the gas are labeled. The area of the annulus is 2πR2 sin αdα and integrating α from 0 to π integrates over the entire spherical surface.

To calculate the total drag force, one must add together the projections of the normal pressure and stress onto an axis parallel to the incident gas. Given the geometry shown in Figure 4.5, the pressure projected into the correct direction is

pdrag = p(θ) cos α + τ(θ) cos θ = p(θ) sin θ + τ(θ) cos θ. (4.43)

Equation 4.43 is then integrated over the surface of the sphere by integrating over the angle α from

0 to π. As stated above, the area of the annulus is 2πR2 sin αdα = −2πR2 cos θdθ. Therefore, the total drag force is 78

Z π/2 2 FD = 2πR [p(θ) sin θ + τ(θ) cos θ] cos θdθ. (4.44) −π/2

For the purposes of this work, we calculate the integral in terms of the drag coeﬃcient, CD, so that the deceleration of the particle is written in the form of the standard drag equation

1 F = ρ A C U 2. (4.45) D 2 g proj D

In Equation 4.45, ρg is the mass density of the gas and Aproj is the projected area of the sphere.

In this form, the drag coeﬃcient is

4 Z π/2 CD = 2 [p(θ) sin θ + τ(θ) cos θ] cos θdθ ρgU −π/2 2 s 1 6e−sa (2 − f + f )s (2s2 + 1) √ T n √ t a a 3 d 4 2 = 4 + 8fn πsa + 3(2 − fn + ft)(4(sa + sa) − 1)erf(sa) 12sa π Tg (4.46)

To check the calculation, one will notice that for the cases of specular (fn = ft = 0) and diﬀuse reﬂection (fn = ft = 1), Equation 4.46 reduces to the cases presented in Hayes and Probstein [34] and Gombosi, et al. [32]

2 4 2 2s + 1 2 4s + 4s − 1 √a −sa a a CDspec = 3 e + 4 erf(sa) (4.47) πsa 2sa √ s 2 π Td CDdiff = CDspec + (4.48) 3sa Tg

The total energy transfer to the particle is also calculated by integratingq ˙ over the surface of the dust particle. The total energy is given by

Z π/2 2 qd = 2πR q˙(θ) cos θdθ −π/2 (4.49) 2 = 4πR aeρgU(Trec − Td)CH , 79 where the total heat transfer has been written in the form of the recovery temperature, Trec, and the heat trasnfer function, CH , given by [32, 48]

T 1 T = g 2γ + 2(γ − 1)s2 − (4.50) rec a 2 −0.5 2 −1 γ + 1 0.5 + sa + saπ exp(−sa)erf (sa)

γ + 1 kB −0.5 2 2 CH = 2 [π saexp(−sa) + (0.5 + sa)erf(sa)]. (4.51) γ − 1 8msa The recovery temperature is deﬁned as the dust temperature where the heat transfer is zero.

4.1.2.3 Model Equations

With the expressions for the drag coeﬃcient and heat transfer rate, the energy balance and deceleration equations for the dust particle are straight forward. The particle energy balance is given by

S 4π 3 dTd 2 4 4 dm ρdR Cp = qd − 4πR σ(Td − Tenv) + L where T 6= Tmelt , Tevap 3 dt dt (4.52)

= Qnet where Cp is the speciﬁc heat of the dust, σ is the Stefan-Boltzmann constant, is given by Equation

dmS 4.6, and L dt is the energy from the sputtered particles. The sputtering mass loss is the same as given in the CM model. The deceleration of the particle is given by the standard drag equation

4π dU 1 ρ R3 = − πR2C ρ U 2. (4.53) 3 d dt 2 D g The mass loss is simply

dm Qnet = − where T = Tevap, (4.54) dt Lv where Lv is the latent heat of vaporization. Equations 4.52, 4.53, and 4.54 model the entire ablation process.

Figure 4.6 shows the progression and structure of the model. The model calculates the deceleration of the particle, sputtering mass loss, and heat transfer/losses to the particle as it 80 progresses through melting and vaporization phase transitions. The vaporization temperature is deﬁned such that the partial pressure of iron equals the pressure of the ablation chamber (see

Equation 4.8). Once evaporating, sputtering is neglected as the thermal evaporation dominates the mass loss.

Deceleration of Particle Deceleration of Particle Deceleration of Particle Deceleration of Particle

Heat Transfer to Particle Mass Loss by Sputtering Mass Loss by Sputtering Mass Loss by Sputtering Radiative Heat Loss

Heat Transfer to Particle Heat Transfer to Particle Heat Transfer to Particle Evaporative Mass Loss Radiative Heat Loss Radiative Heat Loss Radiative Heat Loss dT/dt = 0 Melting Phase Transition Heat Loss by Mass Loss Heat Loss by Mass Loss (dT/dt = 0) Heat Loss by Mass Loss

No No No m < mmin? T > Tmp? T > Tvap? No Fully Melted? Yes Yes Yes Yes Code Terminates

Figure 4.6: Flow chart illustrating the structure and ﬂow of the SECAM model.

4.2 Collection Eﬃciency

In order for the ablation chamber and its diagnostics to be useful as a scientific instrument, it is important to characterize the behavior of the generated ions/electrons in the presence of the electric field. To this end, Monte Carlo simulation codes were developed to investigate the motion of the ions in the electric field and to determine the extent to which the ions spread in the chamber

(the electron spread is much less due to the ﬁve orders of magnitude smaller mass). This section describes the model and presents model results.

The collisions between the ablated atoms and the molecules of the background gas are most easily described in the center-of-mass (COM) system. Since the ablated atoms leave the surface with a thermal speed (e.g. 532 m/s for a 1900 K Fe atom) that is much smaller than the velocity 81 of the parent dust particle (typically > 10 km/s), we assume that the ablated atom moves with the same velocity in the same direction as the parent particle. Similarly, we can neglect the thermal speed of molecules of the ambient gas and thus assume it is initially at rest in the lab frame. Let vr,0 be the relative velocity before the collision, which equals the speed of the dust particle at the time of ablation (based on the assumptions above). The velocities of the ablated atom with mass

M m and the gas molecule with mass M, respectively, in the COM frame are then v0 = vr,0( m+M ) m and V0 = vr,0( m+M ). The energy conservation before and after the collision can be written in the COM frame as

1 1 µv2 = µv2 + ∆W, (4.55) 2 r,0 2 r,1 where µ = mM/(m + M) is the reduced mass, vr,1 is the relative speed after the collision, and

∆W > 0 is the energy absorbed in inelastic collisions. For elastic collisions, ∆W = 0 and vr,0 = vr,1.

Now let us assume that ionization occurs in the collision, thus ∆W equals the ionization potential jIP and thus the relative speed after the collision is

2j v2 = v2 − IP . (4.56) r,1 r,0 µ

The minimum initial speed needed for ionization is calculated for the condition vr,1 = 0 and thus the minimum corresponding dust particle velocity is

2j v2 = IP . (4.57) D,min µ

The ionization potentials of 7.87 eV for Fe atoms and 15.58 eV for N2 molecules yields 9.0 km/s and 12.7 km/s minimum dust speed, respectively. It is clear that at low velocities, the ionization of Fe atoms will dominate over N2.

A collisional Monte Carlo code is developed after Robertson and Sternovsky [77] that follows the particles from the ionizing collision and produces a spatial distribution of the generated ions when collected on one of the electrodes. The following simplifying assumptions are made in the 82 calculations. (1) Since the size of the dust particle (e.g. 50 nm) is much smaller than the mean free path between collisions (e.g. 143 µm at 0.5 Torr), presence of the dust particle is neglected on all subsequent processes. (2) The ionization occurs in the ﬁrst collision and all subsequent collisions

−10 are elastic. (3) Hard sphere collisions with velocity-independent radii rF e = 1.4 × 10 m [83], and

−10 rN2 = 1.58 × 10 m [1] are assumed. In each collision, the relative speed of the ion is randomly reoriented and in between collisions the ion is accelerated by the electric ﬁeld (see Robertson and Sternovsky [77]). (4) The collision partner is selected randomly from a Maxwell-Botzmann distribution.

Figure 4.7: The results from the Monte Carlo simulations. Top: The spatial distribution of ions collected on the electrodes for vdust= 20 km/s and p = 0.2 Torr. The position x = 0 marks the place where the atom ablated from the particle. Bottom: The average position of collection (along the path of the dust particle, i.e. x-direction) as a function of pressure for three diﬀerent dust velocities. The standard deviation is shown for the 20 km/s case.

Figure 4.7 shows the spatial distribution of collected ions. Location x = 0 refers to the location where the atom is ablated from the particle, and the results show an offset distribution 83 that is relatively symmetric. This can be explained in that the initial velocity of the particle is in the positive x-direction (going with the dust particle), and after the first collision the velocity is randomly distributed. The bias between the plates was fixed at 100 V for these simulations, the velocities investigated were 10, 20 and 40 km/s and the pressure was varied between 0.02 - 0.5 Torr, which corresponds to collision mean free paths on the order of 0.22 - 5.5 mm. The distributions resemble a Gaussian distribution for all cases investigated. The average distance traveled along the dust’s path before collection is decreasing with increasing pressure and shows only a weak variation with velocity. The average value of x is typically 2 - 4 times the collision mean free path. The simulations show that for pressures ≥ 0.2 Torr, the ions from each ablating atom will typically be collected by the plate directly beneath the ablation event, while at the lowest pressures, the ions are likely to be collected on the next plate. The standard deviations in the x and z directions are similar and roughly equal to the average of x.

This model gives the displacement (x0) and the standard deviation (σ) of a Gaussian function given by

2 1 − (x−x0) f(x|x0, σ) = √ e 2σ2 . (4.58) σ 2π The Gaussian parameters from the Monte Carlo simulation are shown in Table 4.2, so that given any pressure and velocity, one can interpolate correct x0 and σ values. For the instrument geometry described in section 3.3, we can conclude that the applied bias voltage is suﬃcient to collect all ions on the plates. Even for the lowest pressure and highest velocity investigated, the collection eﬃciency is about 95%.

When comparing the ablation models to the experimental charge data, the Gaussian (Equa- tion 4.58) is convolved with simulated ablation proﬁles, which has the eﬀect of spreading the ions to better match experimental conditions. This is done in Chapter 6 when comparing the two ablation models in Section 4.1 to the experimental data. 84 Displacement (x0,mm) Pressure (Torr) 10 km/s 20 km/s 40 km/s σ(mm) 0.0200 11.0 13.0 14.0 12.0 0.0300 8.70 9.70 11.0 9.70 0.0500 6.10 6.60 7.00 6.80 0.0700 4.83 4.60 5.36 5.50 0.100 3.75 3.39 3.62 4.40 0.150 2.57 2.45 2.48 3.33 0.200 1.97 1.83 1.81 2.84 0.300 1.43 1.14 1.19 2.17 0.500 0.98 0.77 0.85 1.59

Table 4.2: Monte Carlo results of ion spreading in the ablation chamber run at 100 V bias between the top and bottom ablation plates. The displacement is the center value of the Gaussian, while σ is the standard deviation.

4.3 Electron Impact Ionization

The other supporting model is also a Monte Carlo simulation used to investigate secondary ionization effects and its contribution to the total collected charge. The bias voltage applied between the collecting plates is on the order of 100 V. This means that free electrons generated in between the plates may gain sufficient energy to produce additional ion-electron pairs. These generated secondary charges would contribute to the total collected charge and inflate the β measurements.

The simulation eﬀort described below follows the motion of electrons accelerated towards the positive collection plates and collisions with the background gas are modeled in a Monte Carlo fashion. The calculations presented are for N2, since that is the most relevant constituent of Earth’s atmosphere. In the simulations, the electrons start with zero kinetic energy half way in between the biased collector plates. The accelerating electric ﬁeld is E = U/d, where U is the potential applied across the collecting plates separted by d = 3.6 cm. The accelerated electrons undergo collisions with a total cross section of

σTOT = σion + σexcit + σelast (4.59) where σion is the ionization cross section, σexcit is the excitation cross section, and σelast is the elastic cross section. Figure 4.8 shows the cross section model derived from Phelps and Pitchford 85

[67], however, simpliﬁcations are made because of the large number of ongoing processes. The elastic (or momentum transfer cross section) is the largest with a strong resonant feature at around

2 eV electron energy. One possible channel for the inelastic collisions is the rotational excitation of the molecules, in which the electrons only loose a relatively small amount of energy (0.02 eV).

Electrons can lose between 0.29 and 2.35 eV over a range of possible vibrational excitation collisions

[67]. For simplicity, the model assumes that the weighted average of 1 eV is lost in each collision and the cross sections are summed up over all possibilities. There are multiple channels for electron excitation collisions as well. These collisions were separated into two categories (number 1 and 2 in

Figure 4.8) with an average energy loss of 8 and 12 eV, respectively. Electrons gaining energy larger than 15.6 eV are capable of ionizing the nitrogen molecules with a cross section increasing with increasing electron energy. The model assumes that each collision results in a random isotropic reorientation of the primary electrons’ velocities.

Figure 4.8: The cross sections of the various types of collisions included in the secondary ionzation model. See text for more details.

Figure 4.9 shows the results of the numerical model, which is the probability that an electron starting in the middle of the ablation chamber will produce an additional ion-electron pair on its way towards the collecting electrode. This probability depends on both the bias voltage applied 86 across the electrodes, as well as the pressure of the background gas. For the parameters investigated, the maximum occurs at a pressure of about 0.1 Torr, which corresponds to a pressure-gap length of pd = 0.36 Torr·cm. This value is comparable to the position of the minimum in the breakdown voltage on the Paschen curve [52], suggesting that the mechanism for the maximum is similar. For example, the ionization probability decreases for lower pressures because there are fewer collisions between electrons and neutrals and decreases for larger pressures because electrons do not gain suﬃcient energy in between collisions for ionization to occur. The more detailed analysis of the collision processes reveals that electron excitation collisions play an eﬀective role in limiting the attainable electron energy and thus reducing the probability of ionization. The roughly 40% ionization probability for the investigated parameter range also means that the cascading breakdown of the gas can be neglected. This is not surprising, given that the maximum applied bias voltage is far below the Paschen discharge voltage (> 300 V [52]).

Figure 4.9: The probability (as a function of pressure and bias voltage) that a free electron, generated directly by the ablation process, will generate an additional ion-electron pair before it is collected. The calculations are for N2 and a gap distance of d=3.6 cm.

The results of this model are applied to the ionization coeﬃcient measurements in Chapter

5 by adjusting the total amount of charge collected on each channel. In general, the effect can be 87 mitigated by using a bias voltage of 70 V, unless the pressure used in the experiment is sufficiently low or high for the effect to be negligible.

4.4 Summary

There are four models used in this work. Two ablation models (CM and SECAM) are used to simulate the full ablation process, and two supporting models (Collection Eﬃciency and

Electron Impact Ionization) are used to better interpret the experimental data. The CM model calculates the frictional heat transfer by assuming a certain percentage of the incident kinetic energy of the background gas is transfered to the particle (given by Λ). The difference between this frictional energy and the heat lost due to radiation and Langmuir evaporation goes into raising the temperature of the dust. The calculation of the deceleration of the particle uses a drag coefficient which is a free parameter in the model. In contrast, the SECAM model uses a self-consistent calculation of the energy and momentum transfer based on Maxwellian incident and reflected gas molecule distributions. The particle distributions allow for the calculation of the heat transfer to the dust particle as well as a calculation for the drag coefficient. The Collection Efficiency model models the movement of the generated ions in the ablation chamber electric field and provides an ion spread distribution, which can be correlated with mass loss curves calculated from the ablation models. This spreads the predicted mass loss along the ablation chamber so that the ablation models better represent the experimental data. The Electron Impact Ionization model predicts the probability for additional ionization created by electrons accelerated by the electric field and colliding with the background gas. Chapter 5

Ionization Coeﬃcient Measurements

To address the first science question (presented in Section 1.3), the ionization coefficient (β) was measured for iron particles impacting N2, air, CO2, He, and O2 gases. This experiment used the charge collection capability of the ablation facility, described in Chapter 3. The new dataset is compared to previous laboratory data, where it is found to agree except for He, air, and O2 impacts > 30 km/s. A commonly used analytical model of β, the Jones model [45], is calibrated and the analysis provides fit parameters to this model for these gases. Agreement is found between the dataset and the Jones model for all gases except CO2 and high-speed air and O2 impacts

where βair > 1 is observed for velocities > 70 km/s, and βO2 > 1 is observed for velocities > 60 km/s. Therefore, this dataset demonstrates that β is probably not contributing signiﬁcantly to the deviation of the predicted HPLA meteor rates, which are based on the Zodiacal Cloud Model

[64, 63]), and the actual radar observations, as presented in Janches, et al. [41]. However, this data demonstrates potential problems with using the Jones model for CO2 atmospheres as well as for high-speed meteors on Earth.

5.1 Methodology

For this experiment, Fe particles incident on N2, air, CO2, He, and O2 gas were used, and the data analysis below is limited to a dust velocity range of 20-90 km/s and background gas pressures

≥ 10 mTorr (for a description of the accelerator/experimental setup, see Chapters 2 and 3). In this parameter range, the particles are completely ablated within the chamber, and their velocity does 89 not change by more than ∼10%. The former is conﬁrmed by analyzing the (lack of) impact signal at the end of the chamber and the latter was checked through numerical simulations using SECAM, since there was no optical data for these measurements (see Section 4.1.2 for a description of the

SECAM model). Figure 5.1 shows the results of those simulations for iron particles impacting N2 at 50, 100, and 200 mTorr. The simulations predicted that particles with velocities < 20 km/s will signiﬁcantly decelerate within the ablation chamber. In particular, for the pressures of 100 and 200 mTorr, some particles are predicted to decelerate by 20-40%. In order for slower speed particles (i.e. < 20 km/s) to ablate fully in the ablation chamber, higher pressures are needed (up to 200 mTorr for the slowest particles). By restricting the particles to > 20 km/s, the pressures used are typically < 100 mTorr, which mitigates the deceleration. Since β is a function of velocity, the velocity must be roughly constant in the ablation chamber to ensure a correct β measurement.

0.25 0.45 50 mTorr N 100 mTorr N 200 mTorr N 2 0.14 2 2 0.4

0.2 10-16 0.12 10-16 10-16 0.35

0.3 0.1 0.15 0.25 10-17 0.08 10-17 10-17

Mass [kg] 0.2

0.06 0.1 0.15 Velocity Fractional Loss 10-18 10-18 10-18 0.04 0.1 0.05

0.02 0.05

20 40 60 80 20 40 60 80 20 40 60 80 Initial Velocity [km/s]

Figure 5.1: SECAM simulations (see Section 4.1.2) showing the velocity fractional loss for iron particles impacting N2 at pressures of 50, 100, and 200 mTorr. The mass and velocity space investigated was determined based on the parameters of the majority of particles the accelerator produces (see Figure 2.2). To simplify the simulations, all accommodation coeﬃcients were set to 7 −1 −1 1, Cp = 0.47 ×10 erg g K , and = 1. 90

With the conditions of complete ablation and minimum deceleration satisﬁed, β is simply

Q β = tot (5.1) NF e where Qtot is the total charge generated by the ablation (the sum of the signals from all charge collector plates), and NF e is the number of Fe atoms in the particle calculated from its mass.

It was confirmed that the β measurements presented below were independent of both the polarity of the electric field (i.e. species collected) and the pressures used. The former was confirmed by plotting β vs. velocity for experiments with both electrode polarities and color coding ions and electrons, which is shown in Figure 5.2. This confirmed that the same number of electrons and ions are generated in the ablation process, and are collected with full efficiency. The latter was confirmed by once again plotting β vs. velocity, color coding the pressures, and observing that there is no pressure dependence on the β values (shown in Figure 5.3). In principle, this would eliminate the possibility of extra ionization as electrons are accelerated by the electric field and collide with the background gas. The possibility of additional ionization due to electron impacts is discussed and modeled in Section 4.3 for N2 only. These model results are applied below to the

N2 data and are found to be a relatively small eﬀect - in agreement with the lack of β pressure dependence.

To ensure the ablation chamber diagnostics were not missing any charge production due to the particle ablating early, we disregarded any particles with an ablation proﬁle (e.g. Figure 3.8, showing the charges collected across all 16 charge collection plates) that clearly indicated either early or incomplete ablation. If the proﬁle did not have a clear rise in charge production, a peak, and a decline, it was discarded. Furthermore, we investigated whether there was any pattern in the β values that was correlated with the position in the chamber where the ablation took place.

For the case of air and CO2, almost all of the ablation events had signals on the ﬁrst channel. This may imply that the ablation was taking place before the particle entered the chamber and therefore artiﬁcially lowered the measured β. However, for the case of N2 and He, the ablation events had an 91

N Air CO He O 2 2 2

100 100 100 100 100

10-1 10-1 10-1 10-1 10-1 β

10-2 10-2 10-2 10-2 10-2

10-3 10-3 10-3 10-3 10-3 20 40 60 80 20 40 60 80 20 40 60 80 20 40 60 80 20 40 60 80 Velocity [km/s]

Figure 5.2: β measurements from this experiment separated by species. The black points are β values measured from ions, while the red are electrons.

N Air CO He O 2 2 2

100 100 100 100 100

10-1 10-1 10-1 10-1 10-1 β

-2 -2 -2 -2 -2 10 93.8 mTorr 10 10 10 10 85 mTorr 25 mTorr 93.1 mTorr 85 mTorr 65 mTorr 181.4 mTorr 23 mTorr 17 mTorr 21.3 mTorr 23.7 mTorr 70 mTorr 71 mTorr 15 mTorr 50 mTorr 210 mTorr 15 mTorr 48.9 mTorr 15.2 mTorr 100 mTorr 150 mTorr 9.8 mTorr 10-3 10-3 10-3 10-3 10-3 20 40 60 80 20 40 60 80 20 40 60 80 20 40 60 80 20 40 60 80 Velocity [km/s]

Figure 5.3: β measurements from this experiment separated by ablation chamber pressure. 92 equal mixture of particles ablating near the entrance, the middle, and the end of the chamber. For these gases, there is no discernible pattern in the β values between the diﬀerent categories. Since there was no pattern, and the diﬀerential pumping was tested to have a pressure of no more than 1 mTorr in the second stage (for the pressures used in these experiments), this suggests that ablation was occurring entirely within the ablation chamber.

5.2 Ionization Coeﬃcient Analytical Theory

A commonly used analytical theory of the ionization coeﬃcient, developed by Jones [45], is compared to the experimental results presented here, and the following is a brief description of the model. For an atom that has just ablated from the surface of the dust particle at speed v, the probability that the atom will ionize on its ﬁrst collision with a background gas molecule is given by [45]

σi β0 = , (5.2) σt where β0 is the probability for ionization after the ﬁrst collision, σi is the ionization cross section of an iron atom ionizing in a collision with a gas molecule, and σt is the total cross section. Jones then uses the general approximation of σt = σel + σi, where σel is the elastic cross section. Jones takes the expression from Bronshten [11] for σel as

0.8 σel = cel/v , (5.3) where cel is a constant and v is the velocity. Earlier work by Sida [82] gave an expression for the ionization cross section as

n σi = ci(v − v0) + ..., (5.4) where ci is a constant, v0 is the minimum threshold velocity a dust atom can have and still ionize in a collision, and n > 0. Only the ﬁrst term is shown on the right-hand side, and Jones uses the 93

ﬁrst term of this equation with n = 2 such that β0 is given by [45]

σi β0(v) = σt σi = σel + σi c (v − v )2 = i 0 cel 2 (5.5) v0.8 + ci(v − v0) 2 0.8 ci(v − v0) v = 2 0.8 cel + ci(v − v0) v 2 0.8 c(v − v0) v = 2 0.8 , 1 + c(v − v0) v where c is a constant that must be calibrated with experimental data.

Equaion 5.5 gives the probability for ionizaion after the ﬁrst collision, but for atoms with velocities well above the threshold velocity, v0, subsequent collisions could also result in ionization.

To account for this, Jones deﬁnes the total probability, β(v) as [45]

β(v) = β0 + (1 − β0) < β >v, (5.6)

0 0 where < β >v is the average β(v ) over all possible ﬁnal velocities v after an elastic collision at the initial velocity, v. Jones derives < β >v as [45]

2 Z v (1 + µ) 0 0 0 < β >v= 2 β(v )v dv , (5.7) 2v µ v0 where µ is the ratio of the mass of a meteor atom to the mass of a gas molecule, and v0 (the minimum velocity a meteor atom can have and still ionize) has been used as the lower bound on the integral since β(v0) = 0. Therefore, the total β is [45]

2 Z v (1 + µ) 0 0 0 β(v) = β0(v) + (1 − β0(v)) 2 β(v )v dv . (5.8) 2v µ v0 Equation 5.8 is an integral equation which can be converted into a standard ordinary differential equation (ODE) through the substitution u = R v β(v0)v0dv0. It can then be solved using v0 94

du 1 ODE methods and transformed back using β(v) = dv v . For this work, the integral equation was solved using a 5th order Runge-Kutta variable step size solver.

Finally, the threshold velocity can be derived through conservation of energy and is given by

[45]

2 2(1 + µ)φ v0 = , (5.9) µma where φ is the ionization energy of the meteor atom (7.9 eV for Fe) and ma is the mass of a gas molecule. Note that this is identical to the minimum threshold velocity derived in Section 4.2

(Equation 4.57).

5.3 Results

Figure 5.4 shows the measured ionization coeﬃcient for individual iron particles impacting

N2, air, CO2, He, and O2. There are two plots of N2, where the ﬁrst, labeled simply as N2, shows the β values ignoring any possibility of additional ionization due to accelerated electrons impacting

N2 (discussed in Section 4.3). The second, however, contains corrected β values based on the model results from Section 4.3. The β values from this experiment (black points) are compared to two other experimental measurements of β for Fe particles (green lines from Friichtenicht, et al. [29] and the orange line in the air plot from Slattery and Friichtenicht [84]). The β measurements are also compared to the commonly used Jones [45] integral expressions (Equation 5.8) for β(v) (blue and gray lines). The blue lines are the integral expressions with parameters which ﬁt this dataset

(explained in detail below), while the gray dashed line is the integral equation taken directly from

Jones [45]. The blue and red dashed lines on the CO2 plot are also ﬁtted Jones [45] curves but are

fit to data in the velocity ranges of 20-30 (blue) and 20-25 (red) km/s. This is discussed in detail in the Discussion section. The data from this experiment was also fit to a power law (magenta lines) of the form β(v) = bvα. There are two power law fits for air. The solid line is a fit of the whole velocity range of collected data (20-90 km/s), while the dashed line is only fit to data from 20-45 95 km/s. This is done to directly compare this dataset with previous datasets which did not exceed

45 km/s. The power law ﬁts have little physical meaning but are intended to make it easier to use these results. Finally, it should be noted that the green line in the corrected N2 plot is the same data from Friichtenicht, et al. [29] as the uncorrected N2 plot, but the blue and magenta lines on the corrected plot are ﬁt to the corrected β values. All of these results are summarized in Table

5.1.

The Jones [45] integral expressions were fit to this dataset with the parameter c as the free parameter. The parameter c is a constant in the expression for β0 (Equation 5.5) and requires a calibrating dataset. In the original work by Jones [45], c was found (for air) by forcing the expression for β(v) (Equation 5.8) to give the same value as the Slattery and Friichtenicht [84] data evaluated at 40 km/s. The gray curve in the air panel of Figure 5.4 is the integral equation with this value of c (34.5×106), and the orange line is the calibrating dataset. In contrast, the blue β(v) curves in Figure 5.4 were created by performing a least-squares fit of Equation 5.8 with the data from this experiment (black points) to find new values of c. We therefore used an entire dataset to fit c instead of just one value. The same technique was performed to create the blue and red dashed lines on the CO2 plot, but the data points used in the fit were limited to 20-30 and 20-25 km/s, respectively. The fitted values of c for this dataset and the value used in Jones [45] are listed in Table 5.1 along with the coefficient and exponent values from the power law fits and threshold

velocity, v0. It should be noted that our calculated value of v0air = 8.91 km/s is diﬀerent than the value of 9.4 km/s reported in Jones [45]. This new value is used in the gray dashed curve in Figure

5.4.

The error bars in Figure 5.4 include contributions from a 3 mV estimated systematic error on each channel due to a small bias on the CSA channels, and a calculated error on the number of atoms in each particle. The number of atoms is given by the mass of each particle, which is a function of the measured charge on the dust particle (estimated 20% error), velocity (1% error), and the accelerating potential (1% error). The total error on each data is ∼22%. 96 N N - Electron Impact Ionization Corrected 2 0 2 100 10

10-1 10-1 β β

10-2 10-2

10-3 10-3 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90

CO Air 2 100 100

10-1 10-1 β β

10-2 10-2

-3 10 10-3 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90

O He 2 100 100

10-1 β β

-2 10 10-2

10-3 20 30 40 50 60 70 80 90 20 30 40 50 60 70 80 90 Velocity [km/s] Velocity [km/s]

Figure 5.4: β measurements from the current experiment (black points), past experiments by Friichtenicht, et al. [29] (green lines) and Salttery and Friichtenicht [84] (orange line), current experimental data power law fits (magenta lines), the Jones integral equation for β(v) with a fitted parameter c (blue lines), and the Jones integral for β(v) with the parameter c from Jones [45] (gray dashed line). The dotted magenta line is a power law fit that includes data points only up to 45 km/s. The blue and red dashed lines on the CO2 plot are also fitted Jones [45] equations for β(v) but are only fit to data points from 20-30 and from 20-25 km/s, respectively. In the second N2 plot containing the corrected β values, the green line is the same data from Friichtenicht, et al. [29], but the blue and magenta lines are both fit to the corrected β values (black points). 97 (km/s) 0 v 9.06 9.06 8.91 9.40 (Jones [45]) 7.89 20.2 8.68 (Equation 5.9) for each gas is the lowest meteor 0 v ) values, and relevant velocity ranges for the power 6 is the least-squares best fit of the parameter in the α c 10 × c 20.38 (uncorr.) 14.52 (corr.) 19.65 34.50 (Jones [45]) 18.60 13.12 (20-30 km/s, blue dashed) 11.99 (20-25 km/s,dashed) red 0.8800 71.15 ) and exponent ( b Power Law Velocity(km/s) Range 20-40 20-40 20-45 (dashed) 20-90 (solid) 20-40 30-45 20-75 α 3.843 (uncorr.) 3.796 (corr.) 3.003 (dashed) 2.068 (solid) 4.340 8.280 2.221 (solid) 7 7 6 4 8 15 4 − − − − − − − 10 10 10 10 10 10 10 × × × × × × × b 3.372 (uncorr.) 3.037 (corr.) 6.224 (dashed) 1.629 5.201 1.791 1.816 2 2 2 N He O Air Gas CO Table 5.1: The fitlaw parameters fits used to in the FigureJones data [45] 5.4. integral from The equation this coefficient (Equationsvelocity experiment ( 5.5 which and for can 5.8). produce each The ionization. gas calculated are threshold shown. velocity, The parameter 98

In order to generate the corrected N2 β values, the biases and pressures used in each experiment were recorded and then compared to the modeling results from Section 4.3. Figure 5.5 shows the uncorrected β values of iron impacting N2 (the same as the N2 panel in Figure 5.4). The β values are labeled by the ablation chamber pressure and the bias voltage used, and each data set has an estimated percentage of additional ionization based on the model results (see Figure 4.9).

The bias voltages were between 70-90 V and were used in conjuction with the pressure to determine the percentage. The percentage was subtracted from each β value and the error was recalculated to give the data in the corrected N2 panel of Figure 5.4.

100

N 2

10-1

β 93.8 mTorr, 70 V: 15%

93.1 mTorr, 70 V: 15%

181.4 mTorr, 83 V: 20%

21.3 mTorr, 83 V: 9%

71.0 mTorr, 83 V: 26% 10-2 48.9 mTorr, 90 V: 25%

20 30 40 Velocity [km/s]

Figure 5.5: β vs. velocity for the uncorrected N2 data. The β values are color coded by ablation chamber pressure with the bias voltage and estimated additional ionization precentage labeled.

5.4 Discussion

Friichtenicht et al. [29] (green lines in Figure 5.4) estimated their errors to be ∼20%, which could account for small discrepancies between that dataset and this experiment except for the air and O2 data for v > 30 km/s and the He data. This can partially be explained in that the

Friichtenicht et al. [29] air and O2 data did not exceed 40 km/s, while this current experiment 99 contains data up to 90 km/s. However, this does not explain the discrepancy in the velocity range

30-40 km/s or the He data. One explanation could be that the Friichtenicht et al. [29] ﬁts were hand drawn, which adds a diﬃcult to quantify uncertainty. Interestingly, the earlier air results of

Slattery and Friichtenicht [84] match this current experiment better. In fact, the dashed power law

fit in the air panel in Figure 5.4 (power law fit to this newest dataset from 20 < v < 45 km/s) is nearly parallel to the Slattery and Friichtenicht [84] dataset. Friichtenicht et al. [29] noted that ion escape (generated ions that overcome the potential difference and are collected on the positive side instead of the negative) could have been an underestimated problem in Slattery and Friichtenicht

[84]. However, both the chamber design and the potentials used in this experiment more closely resemble the setup described in Friichtenicht et al. [29] than Slattery and Friichtenicht [84]. The exact pressures used are not stated in either paper, but Friichtenicht et al. [29] states a range of

50-200 mTorr, which is consistent with the current experiment (10-200 mTorr). The pressures in this experiment were such that the particle fully ablated within the chamber boundaries (similar to Friichtenicht et al. [29]) and the potentials used were large (70-90 V). Furthermore, the electric

fields used in Slattery and Friichtenicht [84] were larger than both Friichtenicht et al. [29] and this current experiment due to the much smaller plate separation. Therefore, it is difficult to see how ion escape would be a problem for this experiment but not for Friichtenicht et al. [29]. The differences most likely stem from some other unknown systematic error (e.g. possible unaccounted for electron impact ionization in the Friichtenicht et al. [29] data).

The slopes of the analytical Jones [45] curves ﬁt the experimental data well except in two ways. Firstly, the Jones [45] curve asymptotes to 1 for air and O2 (by design) while the current experimental data goes above 1 at high speeds. In fact, β goes as high as 3 for O2 at 73 km/s.

This is not surprising given that there is no physical reason to assume β ≤ 1, but it highlights the potential limitations of the Jones [45] model at high speeds and is evidence that secondary ionization is occurring. Secondly, there is a notable diﬀerence between the slope of the Jones [45]

curve and the CO2 data. At 20 km/s, the Jones [45] curve produces a βCO2 ∼60% larger than the power law ﬁt, while at 40 km/s it is ∼24% smaller than the ﬁt. Given that the slopes of the Jones 100

[45] curves ﬁt the data well for N2, air (excluding high speed), O2 (again excluding high speed), and

He, two additional Jones [45] curves were fit to the CO2 data at different velocity ranges. The blue and red dashed curves were fit to data in the velocity ranges of 20-30 and 20-25 km/s, respectively, and both fit the data within error. One possible explanation for the Jones curve not fitting the entire velocity range of CO2, could be that CO2 has a larger contribution of secondary ionization

at v > 30 km/s. Another possibility is that βCO2 is suppressed at low speeds in a way that N2/air is not. It should be noted that βHe is an order of magnitude smaller than the other gases because of its low atomic weight, which leads to a higher v0, not because of any anomalous suppression.

The diﬀerence between the two Jones [45] curves for air plotted in Figure 5.4 (blue and gray) also varies with velocity. For example, at 20 km/s the original Fe-air Jones [45] curve (gray) is

∼70% larger than the new fit, while at 80 km/s it is only ∼5% larger since both curves asymptote to 1. The outliers in Figure 5.4 passed the screening process described in Section 5.1. Therefore, they are most likely due to an unknown inefficiency other than early or late ablation. Since we could not conclusively identify the inefficiency, the data points were not removed from Figure 5.4 and both the Jones [45] and power law fits include the outliers.

The eﬀect of additional ionization due to electron impact is probably a relatively small eﬀect.

As stated previously in reference to Figure 5.3, it is not obvious from the β values that there is a significant pressure effect. Due to the bias voltages used, the electron impact effect was relatively mitigated except perhaps for the 71 and 48.9 mTorr data shown in Figure 5.5. Overall, the effect reduced the value of the fitted c parameter by 28.8% (see Table 5.1) for the corrected N2 data. Since this effect is relatively small for the N2 data, it is reasonable to assume it is also a small effect for the other gases. Currently, the model only contains the cross sections for N2, and so future studies could add other gases (e.g. O2) to the model. However, the effect can most likely be mitigated in future studies by using a bias voltage of 70 V, unless the pressure used in the experiment is sufficiently low or high for the effect to be negligible.

This new data has several implications to the broader context of meteor ablation. The new

Jones [45] curve ﬁt for Fe-air is signiﬁcantly lower than the previous (gray) curve at lower speeds. 101

Since it is assumed that the physics are the same at lower velocities, this is an indication that the previously used β values for low velocity (< 20 km/s) meteors were too large. However, even at

15 km/s, the previous curve is still only ∼74% larger than the new ﬁt, which is not a large enough diﬀerence to account for discrepancies between the ZDC model and radar measurements [41, 42].

Specifically, the revised β values in Janches, et al. [41] appear to be too small by an order of magnitude, and therefore these results suggest that the ionization coefficient is not contributing significantly to the deviation of the modelled meteor rates and radar observations. Janches et al.

[41] also discussed O2-enhanced ionization (observed for potassium), as a way of re-estimating β in meteor radar observations. The Fe-O2 data in this experiment is larger than the Fe-N2 data by about 300% (at 20 km/s) down to 50% (at 40 km/s), but it does not exhibit the extreme order of magnitude ionization enhancement observed with K-O2 impacts [41, 20]. Furthermore, the data where βair > 1 has implications for radar measurements which use the plasma density to determine the meteor mass [17]. A βair value derived from the Jones [45] curve would overestimate the mass at those velocities. Although it is true that meteors with velocities > 70 km/s are a relatively small population, these meteors do exist as interstellar meteors that allow for probing the interstellar medium [5, 15]. Lastly, these are new Fe-CO2 and Fe-He laboratory β measurements, and while these gases do not play an important role in Earth’s atmosphere, they are important for other planets such as Mars and Jupiter. For example, when the comet Siding Spring encountered Mars,

Fe ions generated from dust ablation were detected with the Neutral Gas and Ion Mass Spectrometer

[7] and the Imaging Ultraviolet Spectrograph onboard the Mars Atmosphere and Volatile Evolution

Mission (MAVEN) spacecraft [78]. The comet passed Mars with a relative velocity of 56 km/s, which would place the dust particles above the Jones [45] curve in Figure 5.4 by extrapolating the power law ﬁt. The contribution of secondary ionization is uncertain at those speeds, but if it is similar

to air, βCO2 would be somewhere between the Jones [45] curve and the power law ﬁt. Therefore, one would have to use an alternative model for β to derive dust/comet properties from the Fe measurements. 102

5.5 Summary and Future Work

We present new measurements of the ionization coeﬃcient for Fe particles impacting N2, air, CO2, He, and O2 at velocities > 20 km/s. We have compared these results with the other available experimental data along with the theoretical expectations. Our experimental data agrees with, within errors, the past experimental results reported by Slattery and Friichtenicht [84] and

Friichtenicht, et al. [29] except that our data does not agree with Friichtenicht et al. [29] for He, air, and O2 at velocities > 30 km/s. This could be due to the fact that their ﬁts were hand drawn, but this is diﬃcult to quantify.

Our experimental data also agrees with the Jones [45] analytical model of β for Fe-N2, Fe-O2, and Fe-air in the range of speeds that are atmospherically relevant with the exception of high-speed meteors (> 70 km/s for air and > 60 km/s for O2). This gives some confidence in extrapolating the Jones [45] model towards the range of velocities that dominates the distribution of the most abundant meteors (∼14 km/s). In the case of Fe-CO2, the Jones [45] model fits the lower speed data (20-30 km/s), but the slope of the model differs from the data when the entire experimental velocity range is included in the fit. This could be an indication of a larger contribution of secondary ionization for CO2 compared to that of N2/air.

Future studies will focus on the much needed measurement of β for a variety of meteoric elements and target gases at velocities < 20 km/s. These studies will use a combined modeling and experimental approach and could also test cosmic dust analogues to simulate electron density proﬁles for atmospheric entry. However, before these studies are performed, the ablation models must be veriﬁed. Chapter 6

Ablation Model Experimental Investigation

To address the second science question (presented in Section 1.3), the deceleration and mass loss of iron particles was measured and compared to predictions from the ablation models CM and SECAM. This experiment used both the light collection and charge collection capabilities of the ablation facility, which are described in detail in Chapter 3. For the deceleration study, dust particles impacted Ar and O2 at 300 mTorr and 286 mTorr, respectively, while for the mass loss study the dust particles impacted N2 at 48.9 and 93.1 mTorr. The results indicate that CM better matches the experimental data for both deceleration and mass loss, but this is most likely due to the larger potential variability of its parameters. Furthermore, the results indicate that the models are missing at least one piece of physics in their desription of the ablation process. One possibility is that the dust particle, once molten, is no longer spherical.

6.1 Deceleration

6.1.1 Deceleration - Methodology

To investigate the deceleration of the particles in the ablation chamber, and to compare that deceleration to predictions from ablation models, iron particles were sent into the ablation chamber which was pressurized with Ar and O2 at 300 mTorr and 286 mTorr, respectively. All particles investigated were between 10-14 km/s, which were predicted to give the maximum deceleration (see

Figure 5.1). As the particles impacted the gas, light was produced and was measured by the PMT system described in Section 3.5. 104

The PMT signals measure the position of the particle relative to the entrance of the ablation chamber. With PMT signals across multiple channels, the particle’s position as a function of time can be directly measured. The PMT peaks included in the position data set for each particle were determined ﬁrst by a threshold trigger. If a PMT signal peak had a magnitude larger than 13 mV, it was included in the data set. It should be noted that the light levels were generally low, and a single PMT peak could be just a single photon. Next, the analysis code cycled through each threshold crossing and found pairs of PMT signals (p1 and p2) such that p2 occured later in time than p1. This pair matching helps to ensure that the PMT peaks are not random noise spikes, but rather correspond to a particle moving through the ablation chamber. The PMT peaks were then down-selected manually to exclude any clear outlier peaks due to stray photons or PMT dark current. If it was not clear that a peak was an outlier, it was left in the data set. The exception to this is if an outlier peak was on the earliest PMT channel in the data set. In this case, that entire

PMT channel was removed from the data set to ensure that the ﬁrst PMT channel had a reliable peak. For this analysis, all of the particle events were required to have 12 or more PMT peaks in the data set. Events with less peaks produced undersampled position vs. time curves and were not used. The position error on each PMT peak is described in Section 3.7.2 and includes errors from the PMT pulse rise time (∼ 100 ns), the size of the PMT bins (0.64 cm), and the slit width error,

δs. Additionally, every particle event included in this analysis was required to have a signal on the third beamline detector, which further ensures that the PMT peaks were caused by a particle.

For every particle event in this analysis (8 for Ar and 6 for O2), both CM and SECAM were used to simulate the particle for a variety of model parameters (see Section 4.1 for a description of the models and their parameters). The SECAM model parameter values (the normal accommodation coefficient fn, the tangential accommodation coefficient ft, and the thermal accommodation coefficient ae) used were 0, 0.33, 0.67, and 1. The thermal accommodation coefficient, ae, had a lower bound of 0.1 (instead of 0) due to the fact that with ae = 0 there is no ablation, and the model tended to have numerical errors. Varying these parameters from 0 to 1 explores the parameter space between fully specular reflection (0) and fully diffuse reflection (1). 105

The CM parameters (the drag coefficient Γ, the heat transfer coefficient Λ, and the uptake coefficient γ) were varied in two ways. First, Γ had values of 0.5, 0.65, 0.85, 1, 1.25, 1.5, 2.0, 2.5,

2.75, and 3.0. Vondrak, et al. [92] states that the value of Γ is typically between 0.5-1; however, for a sphere in free molecular ﬂow, Γ can be larger than 1 [34]. The decision to go as high as 3 was made so that the deceleration would not be limited in the simulations. The other two parameters,

Λ and γ, had values of 0.5, 0.65, 0.85, and 1. The reason for those parameters stopping at 1 is because Λ is defined as the fraction of kinetic energy from the incident gas that is absorbed by the particle, and γ is defined as the probability that the molecule is retained on the surface after a collision. Both of these definitions preclude values above 1. A lower bound of 0.5 was used because values lower than that reduces the mass loss considerably, and the simulation is no longer relevant to the experiments.

In order to compare the simulated decelerations to the experimental data, several steps were needed. First, for each simulation (i.e. one set of parameter combinations) the experimental data was offset in time such that the first PMT signal was anchored to the model position vs. time curve. This was necessary because the experimental data was triggered by the accelerator PSU such that the waveforms would also include the third beamline detector signal. This stipulation resulted in experimental data which was not referenced to the moment when the particle entered the ablation chamber. Second, polynomial fits of degree 2 were made to both the model results and the experimental data. In order for the experimental data to be fit properly, a point was added at the origin, so that the experimental polynomial fit was required to start at the chamber entrance.

The polynomial ﬁts were of the form

1 x(t) = x + v t + at2, (6.1) 0 0 2 where x(t) is the particle position as a function of time, x0 is the initial position (0 in this case), v0 is the initial velocity, and a is the average deceleration of the particle.

Once the decelerations were computed from the fits, the model decelerations were compared 106 to the experimental decelerations for each parameter combination. A best fit parameter combination was found by minimizing the difference between the model decelerations and the shifted experimental decelerations, and an error was computed for both the model and experimental fits equal to 1 standard deviation. The result of this fitting procedure was that there was a best fit model, in terms of average deceleration, and an associated experimental fit which had been shifted in time in the manner described above.

6.1.2 Deceleration - Results

The results of the ﬁts are presented in three ways. First, position vs. time curves for the models and experimental data are shown along with the best ﬁt parameters. Second, a plot of experimental vs. model decelerations is shown with the same model parameter combinations.

Third, a mass vs. velocity plot investigates any potential mass and velocity dependence on the model performance.

Figures 6.1 and 6.2 show the CM and SECAM position vs. time curves for iron particles impacting Ar. The experimental data is black, with the black points being the individual light peaks and the black line being the experimental ﬁt associated with the best ﬁt model result, which is shown as the red line. The black x’s are outlier light peaks which were removed from the data set.

The blue lines are a special case of the model results and correspond to the values used in Vondrak et al. [92] for CM (Γ = Λ = γ = 1) and to diffuse reflection for SECAM (fn = ft = ae = 1). The green lines on the SECAM plots are another special case of the model results and correspond to specular reflection (fn = ft = ae = 0).

Figures 6.3 and 6.4 show the CM and SECAM position vs. time curves for iron particles impacting O2. The experimental data is again black, the red lines are the best ﬁt results, and the blue and green lines are once again the special cases. 107 s] s] µ µ Time [ Time [ : 0.5 : 0.5 : 2 : 1.25 : 0.65 : 0.85 Γ Λ γ Vel: 11.3 km/s Mass: 52.6 fg Γ Λ γ Vel: 11.1 km/s Mass: 63.9 fg 0 20 40 0 20 40 0 0 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 s] s] µ µ Time [ Time [ : 1 : 1 : 2 : 2 : 1 : 0.85 Vel: 10.1 km/s Mass: 46.5 fg Γ Λ γ Vel: 13.1 km/s Mass: 66.6 fg Γ Λ γ 0 10 20 30 40 0 10 20 30 40 0 0 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 s] s] Argon - 300 mTorr CM µ µ Time [ Time [ : 0.85 : 1 : 1.5 : 1.5 : 0.85 : 1 Vel: 10.1 km/s Mass: 25.4 fg Γ Λ γ Γ Λ γ Vel: 11.7 km/s Mass: 32.7 fg 0 20 40 0 20 40 0 0 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 s] s] µ µ Time [ Time [ : 1 : 1.5 : 1 : 1 : 1.5 : 1 Γ Λ γ Vel: 11.1 km/s Mass: 32 fg Vel: 10.1 km/s Mass: 25.7 fg Γ Λ γ Blue: Vondrak 0 20 40 0 20 40 0 0

0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 Distance From Chamber Entrance [m] Entrance Chamber From Distance [m] Entrance Chamber From Distance Figure 6.1: Arparameters position from Vondrak vs. et al.and time removed [92] curves from (blue). for the The data the black set. x’s experimental are data experimental (black), light peaks best which ﬁt were outliers model (assumed result to (red), be noise and artifacts) the model result using the 108 s] s] µ µ Time [ Time [ Vel: 11.3 km/s Mass: 52.6 fg fn: 0 ft: 1 ae: 1 Vel: 11.1 km/s Mass: 63.9 fg fn: 0.33 ft: 0.67 ae: 0.67 0 20 40 0 20 40 0 0 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 s] s] µ µ Time [ Time [ fn: 0 ft: 1 ae: 1 Vel: 10.1 km/s Mass: 46.5 fg Vel: 13.1 km/s Mass: 66.6 fg fn: 0 ft: 1 ae: 1 0 10 20 30 40 0 10 20 30 40 0 0 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 s] s] µ µ Argon - 300 mTorr SECAM Time [ Time [ Vel: 11.7 km/s Mass: 32.7 fg fn: 0 ft: 1 ae: 1 fn: 0 ft: 1 ae: 1 Vel: 10.1 km/s Mass: 25.4 fg 0 20 40 0 20 40 0 0 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 s] s] µ µ Time [ Time [ Vel: 11.1 km/s Mass: 32 fg fn: 0 ft: 1 ae: 1 Vel: 10.1 km/s Mass: 25.7 fg fn: 0 ft: 1 ae: 1 Green: Specular Blue: Diffuse 0 20 40 0 20 40 0 0

0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 Distance From Chamber Entrance [m] Entrance Chamber From Distance [m] Entrance Chamber From Distance Figure 6.2: Ar positiondiffuse vs. model result time (blue). curvesfrom for the The the data black experimental set. x’s data are (black), experimental best light fit peaks model which result were (red), outliers specular (assumed model to result be (green), noise and artifacts) and removed 109 s] s] µ µ Time [ Time [ : 0.5 : 2 : 1 : 0.5 : 3 : 0.65 Vel: 11.1 km/s Mass: 63 fg Γ Λ γ Vel: 11 km/s Mass: 10.5 fg Γ Λ γ 0 10 20 30 40 0 10 20 30 40 0 0 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 s] s] µ µ Time [ Time [ - 285 mTorr CM 2 O : 0.5 : 1.25 : 1 : 0.85 : 3 : 1 Γ Λ γ Vel: 10.2 km/s Mass: 17.8 fg Vel: 11.9 km/s Mass: 38.7 fg Γ Λ γ 0 10 20 30 40 0 10 20 30 40 0 0 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 : 0.5 : 2 : 1 s] s] Γ Λ γ Blue: Vondrak Vel: 12.8 km/s Mass: 45 fg µ µ Time [ Time [ : 0.5 position vs. time curves for the experimental data (black), best fit model result (red), and the model result using the : 2.5 : 0.65 Γ Λ γ Vel: 13 km/s Mass: 42.7 fg 2 0 10 20 30 40 0 10 20 30 40 0 0

0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 Distance From Chamber Entrance [m] Entrance Chamber From Distance [m] Entrance Chamber From Distance Figure 6.3: O parameters from Vondrak et al.and removed [92] from (blue). the The data black set. x’s are experimental light peaks which were outliers (assumed to be noise artifacts) 110 s] s] µ µ Time [ Time [ fn: 0 ft: 1 ae: 1 Vel: 11 km/s Mass: 10.5 fg fn: 0 ft: 1 ae: 1 Vel: 11.1 km/s Mass: 63 fg 0 10 20 30 40 0 10 20 30 40 0 0 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 s] s] µ µ Time [ Time [ - 286 mTorr SECAM 2 O Vel: 10.2 km/s Mass: 17.8 fg fn: 0.33 ft: 0.67 ae: 0.67 fn: 0 ft: 1 ae: 1 Vel: 11.9 km/s Mass: 38.7 fg 0 10 20 30 40 0 10 20 30 40 0 0 0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 s] s] fn: 0 ft: 1 ae: 1 µ µ Vel: 12.8 km/s Mass: 45 fg Green: Specular Blue: Diffuse Time [ Time [ position vs. time curves for the experimental data (black), best ﬁt model result (red), specular model result (green), and fn: 0 ft: 1 ae: 1 Vel: 13 km/s Mass: 42.7 fg 2 0 10 20 30 40 0 10 20 30 40 0 0

0.4 0.3 0.2 0.1 0.4 0.3 0.2 0.1 Distance From Chamber Entrance [m] Entrance Chamber From Distance [m] Entrance Chamber From Distance diﬀuse model result (blue).from the The data black set. x’s are experimental light peaks which were outliers (assumed to be noise artifacts) and removed Figure 6.4: O 111

The position vs. time curves show at least one obvious feature - the CM curves reproduce the experimental results much better than SECAM. This could be due to the greater freedom the

CM parameters allow. Specifically, the drag coefficient in CM (Γ) is a free parameter which can be set arbitrarily high, whereas in SECAM it is a calculated quantity. The fact that the SECAM plots almost universally do not have enough deceleration suggests this is the case. Furthermore, the most common best fit free parameters for SECAM (fn = 0 and ft = 1) provide the largest drag force. One can see this in Figure 4.5, in the description of the SECAM model (Section 4.1.2).

To provide the largest component of force in the direction of the gas (i.e. drag force), fn = 0 and ft = 1. This suggests SECAM is reaching some limit on the amount of deceleration it can provide, which apparently is not enough to match the experimental data.

To show how well the two models perform in terms of average deceleration, Figures 6.5 and

6.6 show the experimental deceleration vs. the model deceleration for both gases. The red points are the best ﬁt models, the blue data points in the CM plots are the parameters used in Vondrak, et al. [92] (Γ = Λ = γ = 1), and in the SECAM plots the blue and green points are the diﬀuse

(fn = ft = ae = 1) and specular (fn = ft = ae = 0) reﬂection cases, respectively (see Section 4.1.2).

The black line designates a perfect match between experiment and model. The vertical error bars are 1 standard deviation (the model error is arbitrarily low).

One may notice from Figures 6.5 and 6.6 that the experimental decelerations are diﬀerent between the two models. This is due to the fact that the experimental data is time shifted, as described above in Section 6.1.1. The experimental decelerations will vary somewhat depending on the model and the combination of model parameters. However, it is clear from Figures 6.5 and 6.6 that the CM model (using best-ﬁt parameters) performs better in terms of average deceleration. 112 0 0 Argon - 300 mTorr - CM Argon - 300 mTorr - SECAM SECAM - Best Fit CM - Best Fit SECAM - Diffuse CM - Vondrak SECAM - Specular ] -50 Exp. = Mod. Line ] -50 2 2 Exp. = Mod. Line s s µ µ m / m / µ µ -100 -100

-150 -150

Experimental Deceleration [ -200 Experimental Deceleration [ -200

-250 -250 -160 -140 -120 -100 -80 -60 -40 -160 -140 -120 -100 -80 -60 -40 Model Deceleration [ µm / µs2] Model Deceleration [ µm / µs2]

Figure 6.5: The experimental deceleration vs. modeled (both CM and SECAM) deceleration for Ar. The best fits are again in red, and the special cases for each model are blue and green. Namely, blue in the CM plot are the parameters used in Vondrak et al. [92] and blue and green in the SECAM plots are for diffuse and specular reflection, respectively.

0 0 O - 286 mTorr - CM O - 286 mTorr - SECAM 2 2 CM - Best Fit SECAM - Best Fit -50 CM - Vondrak -50 SECAM - Diffuse ] ] 2 Exp. = Mod. Line SECAM - Specular 2 s s µ Exp. = Mod. Line µ m / m / µ -100 -100 µ

-150 -150

-200 -200 Experimental Deceleration [ Experimental Deceleration [ -250 -250

-300 -160 -140 -120 -100 -80 -60 -40 -300 -160 -140 -120 -100 -80 -60 -40 Model Deceleration [ µm / µs2] Model Deceleration [ µm / µs2]

Figure 6.6: The experimental deceleration vs. modeled (both CM and SECAM) deceleration for O2. The best fits are again in red, and the special cases for each model are blue and green. Namely, blue in the CM plot are the parameters used in Vondrak et al. [92] and blue and green in the SECAM plots are for diffuse and specular reflection, respectively.

To investigate if there was any mass and/or velocity bias in the performance of the model, 113

Figures 6.7 and 6.8 show the ratio of experimental deceleration to model deceleration as a function of both mass and velocity. Again, the plots showcase the better performance of CM, but there is no apparent mass or velocity trend. Tables 6.1 and 6.2 summarize the results of the deceleration study.

70 70

Argon - 300 mTorr - CM 1.35 Argon - 300 mTorr - SECAM 1.35 65 65

1.3 1.3 60 60

55 1.25 55 1.25

50 1.2 mod 50 1.2 mod /a /a exp exp a

Mass [fg] 45 1.15 Mass [fg] 45 1.15 a

40 1.1 40 1.1

35 35 1.05 1.05

30 30 1 1

25 25 10 10.5 11 11.5 12 12.5 13 13.5 10 10.5 11 11.5 12 12.5 13 13.5 Velocity [km/s] Velocity [km/s]

Figure 6.7: Mass vs. velocity for the best ﬁt results for Ar. The color on each point is the ratio of the experimental deceleration to the model deceleration.

70 70 O - 286 mTorr - CM O - 286 mTorr - SECAM 2 2 2 2

60 60

1.8 1.8

50 50

1.6 mod 1.6 mod /a

40 40 /a exp a exp Mass [fg] Mass [fg] 1.4 1.4 a

30 30

1.2 1.2

20 20

1 1

10 10 10 10.5 11 11.5 12 12.5 13 13.5 10 10.5 11 11.5 12 12.5 13 13.5 Velocity [km/s] Velocity [km/s]

Figure 6.8: Mass vs. velocity for the best fit results for O2. The color on each point is the ratio of the experimental deceleration to the model deceleration. 114 . mod /a exp a ratio a mod is defined as a ratio a exp and CM 2 γ a µm/µs are mod a ΓΛ 1.50 1.001.50 1.00 0.852.00 0.85 -89.13 1.001.25 1.00 -84.05 0.501.50 -86.14 0.85 -90.85 1.001.50 -83.37 1.03 1.00 -62.80 1.002.00 -87.20 1.01 -102.05 1.00 1.002.00 -63.83 1.04 -114.95 -99.23 0.85 0.50 0.98 -113.85 -150.18 0.65 1.03 -146.75 1.01 -96.54 1.02 -98.02 0.98 and exp a ratio a mod a exp a SECAM e a t f n f 0.00 1.000.00 1.00 1.000.00 1.00 -89.17 1.000.33 1.00 -83.80 0.670.00 -86.21 -100.29 0.67 1.000.00 -86.55 1.03 -72.64 1.00 -63.95 1.000.00 0.96 -101.77 1.00 1.000.00 1.38 -63.34 -100.80 -144.62 1.00 1.00 1.01 -115.52 1.01 -163.81 1.00 -123.14 0.99 -105.90 1.33 -90.87 1.17 Dust 10.1 25.7 10.110.111.111.1 25.4 11.7 46.5 13.1 63.9 11.3 32.0 32.7 66.6 66.6 Vel. (km/s) Mass (fg) Table 6.1: Best fit deceleration results of SECAM and CM for Ar. The units of 115 is defined as ratio a ratio a mod a and 2 exp µm/µs CM are γ a mod a and exp a ΓΛ 2.00 0.501.25 1.00 0.503.00 -109.09 0.85 1.002.50 -108.75 0.65 -60.19 0.503.00 1.00 -152.25 0.65 1.002.00 -61.06 -143.74 -127.88 1.00 0.50 0.99 -132.95 1.06 -154.89 0.50 -138.69 0.96 -67.91 1.12 -74.27 0.91 ratio a . The units of mod 2 a exp a SECAM e a t f n f 0.00 1.000.33 1.00 0.670.00 -117.23 0.67 1.000.00 -99.64 1.00 -61.12 1.000.00 -168.81 1.00 1.000.00 1.18 -61.02 -107.62 -147.49 1.00 1.00 1.00 -106.81 1.57 -185.35 1.00 1.38 -88.14 -73.80 -63.17 2.1 1.17 Dust 12.8 45.0 10.211.013.011.9 17.8 11.1 10.5 42.7 38.7 63.0 Vel. (km/s) Mass (fg) . mod /a exp a Table 6.2: Best fit deceleration results of SECAM and CM for O 116

6.2 Mass Loss Via Charge Collection

6.2.1 Mass Loss - Methodology

To investigate the mass loss performance of CM and SECAM, iron particles were accelerated into the ablation chamber pressurized with N2 at 48.9 mTorr and 93.1 mTorr. The bias voltage used in the ablation chamber was 90 V for the 48.9 mTorr data and 70 V for 93.1 mTorr data. All particles in this data set were between 20-40 km/s. There was no light collection for this data, but with the velocity and pressure ranges used, decleration was expected to be minimal (see Figure

5.1). The reason for using N2 is because it is the only gas for which the appropriate cross sections have been implemented in the electron impact ionization model (described in Section 4.3), which is used in this analysis.

As the particles ablated, the produced charge was collected on the charge collection plates.

The charge production is directly related to the mass loss of the particle by the ionization coeﬃcient,

β(v). β(v) for N2 was measured in Chapter 5, and those measurements are used here to relate the collected charge to the mass loss. While charge production is an indirect method of measuring mass loss, with a well defined β(v) it is directly proportional to the mass loss. For example, a charge profile (collected charge vs. charge collection channel number) like that shown in Figure 3.8, is equivalent to a mass loss profile of a particle (after accounting for ion spreading) by dividing the charge by β.

Both CM and SECAM simulated the particles in this data set with the same parameter ranges as described in Section 6.1.1. The simulations produced a particle mass vs. distance curve, which was used to calculate the expected amount of measured charge in the following way. First, the mass vs. distance curve was convolved with the correct ion spreading Gaussian, which depends on pressure, bias voltage and initial dust velocity (described in Section 4.2). This convolution spreads the mass loss in the direction of the dust trajectory, which is an eﬀect which must be accounted for when comparing experimental charge proﬁles to those predicted by ablation models. Next, the convolved mass loss curve was then binned into 16 spatial bins corresponding to the positions of the 117

16 charge collection plates. Each bin was then assigned an average velocity by using the velocity predicted by the ablation model at the center of the bin. After binning the mass and converting to atoms, each bin was multiplied by β(v) evaluated at the assigned bin velocity. The β(v) curve used here was the ionization corrected curve from Chapter 5.

Two best fits were made between the simulated charge profiles and the experimental charge profiles. The first was a least-squares fit between all 16 channels, where the sum of the differences in charges for each channel squared was minimized. This fit treats each channel equally and does not place any importance on any particular channel. In contrast, the second fit method was a peak matching method which preferenced the channel with the largest charge. Specifically, it selects the model result which had its peak charge closest to the channel number with the peak charge in the experimental data. If there were multiple model results with matching peak channels, it selected the model result where the peak charge was most similar in magnitude to the peak charge of the experimental data.

6.2.2 Mass Loss - Results

Comparisons between the experimental and simulated charge proﬁles are presented in Figures

6.9 and 6.10. The experimental charge profile is the black curve, the least-squares best fit is the red curve, the peak matching best fit is the magneta curve, and the blue curve is the special case for each model (parameters set to Vondrak, et al. [92] for CM and diffuse reflection for SECAM).

There is no specular reﬂection case for SECAM due to the fact that there is no heat transfer when ae = 0, and therefore no thermal ablation. The error bars on the simulated curves correspond to the error on the β measurements which were used to convert the simulated mass loss into charge.

The uncertainty in the data points in the β(v) curves in Chapter 5 were ∼22%, and so this was used as the error on the simulated charge values. The error on the experimental data was negligibly small (∼ 5000 electrons) and is therefore not shown.

In general, CM more accurately reproduces the experimental data for these particles. Fur- thermore, the peak matching method better captures the shape of the experimental data in every 118 instance. The least-squares method tends to select model results with a flatter profile, such that the difference in charge values is minimized across the entire profile at a cost of poorly reproducing the shape of the experimental data.

For both CM and SECAM, the model is predicting early ablation, in that the models consistently have the peak charge 2-3 channels upstream compared to the experimental data. This suggests a problem with the models’ heating of the dust particle. Interestingly, in the case of CM, lowering the value of the heat transfer coefficient, Λ, does not appear to be the solution. The least-squares best fit results have lower values of Λ, and that does shift the curve in the appropriate direction, but it also has the effect of flattening the profile and losing the shape of the experimental data. 119 : 1 : 1 : 1 Γ Λ γ : 1 : 1 : 1 Γ Λ γ : 48.9 mTorr 2 : 0.85 : 0.85 : 0.5 : 48.9 mTorr N Vel: 32.9 km/s Mass: 2.5 fg Γ Λ γ 2 : 0.85 : 0.85 : 0.5 N Vel: 38.1 km/s Mass: 1.6 fg Γ Λ γ Channel Number 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 2 1 0 1 0 2.5 1.5 0.5 1.5 0.5 : 1 : 1 : 1 Γ Λ γ : 1 : 1 : 1 Γ Λ γ : 48.9 mTorr 2 : 0.85 : 93.1 mTorr : 0.85 : 0.5 2 : 0.85 : 0.85 N Vel: 25.9 km/s Mass: 2.2 fg : 0.5 Γ Λ γ N Vel: 21.4 km/s Mass: 3.8 fg Γ Λ γ Channel Number 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 0 0 0.3 0.2 0.1 0.4 0.3 0.2 0.1 0.35 0.25 0.15 0.05 CM : 1 : 1 : 1 Γ Λ γ : 0.85 : 0.85 : 1 Γ Λ γ : 48.9 mTorr : 93.1 mTorr 2 : 0.85 : 0.85 2 : 0.65 : 0.65 : 0.5 : 0.5 N Vel: 31.5 km/s Mass: 4.1 fg Γ Λ γ N Vel: 20.6 km/s Mass: 8.8 fg Γ Λ γ Channel Number 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 0 2 1 0 0.5 0.4 0.3 0.2 0.1 1.5 0.5 : 1 : 1 : 1 Γ Λ γ : 1 : 1 : 0.85 Γ Λ γ : 48.9 mTorr : 93.1 mTorr 2 : 0.85 : 0.85 : 0.5 2 : 0.85 : 0.85 : 0.5 N Vel: 27.9 km/s Mass: 5.5 fg Γ Λ γ Blue: Vondrak N Vel: 21.5 km/s Mass: 5.1 fg Γ Λ γ Channel Number 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 0 1 0

0.5 0.4 0.3 0.2 0.1 1.2 0.8 0.6 0.4 0.2 Elementary Charges Collected [millions] Collected Charges Elementary [millions] Collected Charges Elementary Figure 6.9: Experimental andbest simulated charge fit, profiles the for CM. magentaVondrak, The line et black al. is curve is the [92]. the peak experimental data, matching the best red fit, curve is and the the least-squares blue curve is the result with the model parameters set to those used in 120 fn: 1 ft: 1 ae: 1 fn: 1 ft: 1 ae: 1 : 48.9 mTorr 2 fn: 1 ft: 0 ae: 0.67 Vel: 32.9 km/s Mass: 2.5 fg N : 48.9 mTorr 2 fn: 1 ft: 0 ae: 0.67 N Vel: 38.1 km/s Mass: 1.6 fg Channel Number 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 2 1 0 2 1 0 2.5 1.5 0.5 1.5 0.5 fn: 1 ft: 1 ae: 1 fn: 1 ft: 1 ae: 1 : 48.9 mTorr 2 fn: 1 ft: 0 ae: 0.67 Vel: 25.9 km/s Mass: 2.2 fg N : 93.1 mTorr 2 Vel: 21.4 km/s Mass: 3.8 fg N fn: 1 ft: 0 ae: 0.67 Channel Number 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 0 0 0.3 0.2 0.1 0.4 0.3 0.2 0.1 0.35 0.25 0.15 0.05 SECAM fn: 1 ft: 1 ae: 1 fn: 1 ft: 1 ae: 0.67 : 48.9 mTorr 2 fn: 1 ft: 0 ae: 0.67 N Vel: 31.5 km/s Mass: 4.1 fg : 93.1 mTorr 2 N Vel: 20.6 km/s Mass: 8.8 fg fn: 1 ft: 0 ae: 0.33 Channel Number 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 0 2 1 0 0.6 0.5 0.4 0.3 0.2 0.1 1.5 0.5 fn: 1 ft: 1 ae: 1 fn: 1 ft: 1 ae: 1 : 48.9 mTorr 2 fn: 1 ft: 0 ae: 0.67 Vel: 27.9 km/s Mass: 5.5 fg N : 93.1 mTorr 2 fn: 1 ft: 0 ae: 0.67 Blue: Diffuse Vel: 21.5 km/s Mass: 5.1 fg N Channel Number 1 3 5 7 9 11 13 15 1 3 5 7 9 11 13 15 0 1 0

0.5 0.4 0.3 0.2 0.1 1.2 0.8 0.6 0.4 0.2 Elementary Charges Collected [millions] Collected Charges Elementary [millions] Collected Charges Elementary Figure 6.10: Experimentalleast-squares and best fit, simulated the chargediffuse magenta profiles reflection. curve for is the SECAM. peak The matching black best curve fit, is and the the blue experimental curve data, is the the result red with curve the model is parameters the set to 121

6.3 Discussion

When comparing CM and SECAM, CM better matches both the experimental position vs. time curves (i.e. deceleration) and the charge proﬁles when the model parameters are varied.

However, CM is not as consistent in the values of the best fit parameters. For instance, the average Γ value for the Ar study is 1.7, while for the O2 study it is 2.3 and for the mass loss it is 1. Additionally, the best fit Γ varies somewhat within both the Ar and O2 study. The other parameters, Λ and γ, vary between 0.5-1 for the deceleration studies and are mostly fixed at 1 for the mass loss study. In contrast, the best parameters for SECAM are ft = ae = 1 for both the deceleration and mass loss studies, while the best value for fn is 0 for the deceleration study and

1 for the mass loss study.

The large value for the best fit Γ in CM is particularly interesting due to the fact that the drag coefficient for a sphere in free molecular flow is 1 for specular reflection and only slightly >

1 for diffuse reflection (the SECAM model description in Section 4.1.2 derives this, but note that there is a factor of 2 difference between the drag coefficient definitions in SECAM and in CM). This is how the drag coefficient is implemented in SECAM, but it is clear that SECAM underpredicts the deceleration. This could be evidence that the dust particle, once molten, is no longer spherical.

The best fit peak matching parameters for the SECAM mass loss indicates that it is best modeled through diffuse reflection, and this is consistent across both models. For example, the drag coefficient in SECAM for diffuse reflection is given by Equation 4.48 and is equal to 2. After accounting for the factor of 2 difference in definitions, this is the same as the best fit Γ for the CM mass loss (Γ = 1). The fact that the CM drag coefficient must be ∼ 2 to match the decleration, but at the same time must be ∼ 1 to match the mass loss, is further evidence that some piece of physics is missing. 122

6.4 Summary and Future Work

In this study, we compared the experimental deceleration and mass loss curves of iron particles to those predicted by two ablation models. The deceleration study was performed using Ar and O2 at 300 and 286 mTorr, respectively. The PMT setup measured the light produced as the particles ablated, and the peaks of the PMT data were converted to positions in the ablation chamber. With these positions, we constructed a position vs. time curve for each ablation event and measured the deceleration of the particle. The particles were modeled with CM and SECAM and the modeled declerations were compared to the experimental data. The mass loss study was performed using N2 at 48.9 and 93.1 mTorr. The bias voltages for the N2 data was 90 V for the 48.9 mTorr data and

70 V for the 93.1 mTorr data. The particles were again modeled with CM and SECAM, and the predicted mass loss curves were convovled with an ion spreading Gaussian, binned into 16 charge collection bins, and compared to the experimental data.

The results indicate that CM is better able to match both the deceleration and mass loss of the experimental data, but this is a consequence of the ability to set the drag coefficient to arbitrarily large values. The best fit CM drag coefficient is larger than what is expected for a sphere in free molecular flow, which could be evidence that the molten particle is not actually a perfect sphere. Additionally, the mass loss results indicate that it should be modeled as diffuse reflection. This is consistent across both models, but the best fit Γ for the CM mass loss is about a factor of 2 smaller than for the deceleration, which further indicates missing physics.

Future studies could investigate this by varying the shape of the molten dust particle, integrating the pressure and stress terms over the new shape (as is done in Section 4.1.2), and simulating the particle. Depending on the chosen shape, this could also aﬀect the mass loss. Speciﬁcally, the

Langmuir evaporation equation, which governs the mass loss in CM, is proportional to the surface area of the dust particle.

Another factor to consider in these studies is the issue of fragmentation. The models assume that the particle remains a perfect sphere throughout the ablation process and does not fragment. 123

If fragmentation did occur, the smaller fragments would decelerate more and ablate earlier in the ablation chamber. The experimental data would therefore show more total deceleration and the mass loss would occur earlier in the chamber (compared to a particle which did not fragment).

The experimental data does show signiﬁcantly more deceleration than expected, but it also shows mass loss occuring later in the chamber (opposed to earlier, which would indicate fragmentation).

Therefore, it is not clear if there is any fragmentation occuring. Chapter 7

Conclusion

This thesis described a new laboratory micrometeoroid ablation facility and presented measurements of the ionization coeﬃcient as well as comparisons between experimental ablation data and predictions from ablation models. This work was motivated by the following two science questions (presented in Section 1.3):

(1) Are the currently used values of the ionization coeﬃcient (β) correct?

(2) How well do the physical ablation models describe the ablation process?

7.1 Ionization Coeﬃcient

To address question 1, iron particles were accelerated into the ablation chamber where they impacted the target gases N2, air, CO2, He and O2. The generated charge was measured by the charge collecting plates as the particle ablated. To calculate β from these measurements, there were two requirements that the ablation event must meet: the particle does not slow down by more than 10 % while ablating, and the particle completely ablates within the 41 cm ablation chamber. The ﬁrst requirement was met by restricting the dust velocities to > 20 km/s, such that the deceleration was expected to be minimal. The second requirement was met by rejecting any ablation event which had an impact signal and did not have a charge proﬁle which showed a clear rise, peak, and decline along the ablation path. With these requirements met, β was calculated by summing all 16 charge collection channels together and dividing by the total number of atoms in the particle. 125

The β values were compared to previous experimental results, as well as a commonly used analytical theory of β (described in Jones [45]). The measurements agreed with previous experimental β measurements except for Fe-He, Fe-air, and Fe-O2 at velocities > 30 km/s. This could be due to the fact that the previous experimental ﬁts were hand drawn, but this is diﬃcult to quantify.

The β values also agreed with the Jones [45] analytical model of β for Fe-N2, Fe-O2, and Fe-air in the range of speeds that are atmospherically relevant with the exception of high-speed meteors

(> 70 km/s for air and > 60 km/s for O2). This gives confidence for using the Jones model with velocities < 20 km/s, which corresponds to the most abundant source of meteors [64]. Furthermore, it suggests that β is not contributing significantly to the deviation of the modeled meteor rates and radar observations (reported in Janches, et al. [41]). However, the Jones model did not fit the entire velocity range for the Fe-CO2 data, which could be an indication of a larger contribution of secondary ionization for CO2 compared to that of N2/air.

7.2 Ablation Models

To address question 2, the deceleration and mass loss of iron particles were measured in the ablation chamber. The experimental data was then compared to predictions from two ablation models, designated as CM and SECAM. Both models contain three parameters which were varied in an attempt to match the deceleration and mass loss experimental data. In CM, the drag coeﬃcient

(Γ), the heat transfer coefficient (Λ), and the uptake coefficient (γ) were varied. For SECAM, the three accommodation coefficients (fn, ft, and ae) were varied between specular and diffuse reflection.

The results showed that CM better matches the experimental data for both deceleration and mass loss. Additionally, SECAM underpredicts the deceleration of the particle. Both models, however, predicted mass loss curves which ablate too early compared to experimental data.

In order for CM to correctly model the deceleration, the drag coefficient had to be set to larger than expected values (> 2 in some instances). In the case of SECAM, the drag coefficient is a calculated quantity, and therefore could not be set to a large enough value to match the 126 experimental deceleration. Furthermore, the CM parameter values which best fit the deceleration did not match with the best fit parameters for the mass loss. These results indicate that the models are missing at least one piece of physics. One possibility could be that the molten particle does not remain spherical.

7.3 Future Work

Future studies using the ablation facility could investigate several important questions. First, the ionization coeﬃcient for velocities < 20 km/s could be directly measured. With the current

PMT setup, it is possible to directly measure the position and speed of the particle as it is ablating.

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Publications

• Thomas, E., Simolka, J., DeLuca, M., Hor´anyi, M., Janches, D., Marshall, R., Munsat,

T., Plane, J. M. C., and Sternovsky, Z., Experimental setup for the laboratory investigation

of micrometeoroid ablation using a dust accelerator, RSI, 88, 034501 (2017).

• Thomas, E., Hor´anyi, M., Janches, D., Munsat, T., Simolka, J., and Sternovsky, Z.,

Measurements of the ionization coeﬃcient of simulated iron micrometeoroids, Geophys.

Res. Lett., 43, 8, (2016).

• Thomas, E., Auer, S., Drake, K., Hor´anyi, M., Munsat, T., and Shu, A., FPGA cross-

correlation ﬁlters for real-time dust detection and selection, Planet. Space. Sci., 89, 71,

(2013).

• Shu, A., Collette, A., Drake, K., Gr¨un,E., Hor´anyi, M., Kempf, S., Mocker, A., Munsat,

T., Northway, P., Srama, R., Sternovsky, Z., and Thomas, E., 3 MV hypervelocity dust

accelerator at the Colorado Center for Lunar Dust and Atmospheric Studies, RSI, 83,

075108, (2012).