Interstellar Helium Pickup Ion Flux Variations Observed with SOHO

University of New Hampshire University of New Hampshire Scholars' Repository

Doctoral Dissertations Student Scholarship

Spring 2005

Interstellar helium pickup ion flux ariationsv observed with SOHO/ CELIAS

Lukas A. Saul University of New Hampshire, Durham

Follow this and additional works at: https://scholars.unh.edu/dissertation

Recommended Citation Saul, Lukas A., "Interstellar helium pickup ion flux ariationsv observed with SOHO/CELIAS" (2005). Doctoral Dissertations. 272. https://scholars.unh.edu/dissertation/272

This Dissertation is brought to you for free and open access by the Student Scholarship at University of New Hampshire Scholars' Repository. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of University of New Hampshire Scholars' Repository. For more information, please contact [email protected]. NOTE TO USERS

Page(s) not included in the original manuscript and are unavailable from the author or university. The manuscript was scanned as received.

4, 6, 9, 28, 40, 42, 49, 51, 55, 56, 63, 64, 67, 78-80, 86, 90-92, 107, 709-110, and 112

This reproduction is the best copy available.

® UMI

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. INTERSTELLAR HELIUM PICKUP ION FLUX VARIATIONS

OBSERVED WITH SOHO/CELIAS

LUKAS A. SAUL

BS Yale University, 1997

Submitted to the University of New Hampshire In Partial Fulfillment o f

The Requirements for the Degree of

Doctor of Philosophy In

Physics

May, 2005

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3169089

INFORMATION TO USERS

The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.

® UMI

UMI Microform 3169089 Copyright 2005 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code.

ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This dissertation has been examined and approved.

Dr. Eberhard Mobius, Dissertation Director Professor of Physics and Earth, Oceans, and Space

•r. John F. Dawson, Professor of Physics

Dr. Philip A. Isenberg, Research Profe:SgOTOf Physics and Earth, Oceans, and Space

P_JL- Dr. Martin A. Lee, Professor of Physics and Earth, Oceans, and Space

Dr. Charles W. Smith HI, Research Professor o f

Physics and Earth, Oceans, and Space

Date

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. DEDICATION

To Rachel

111

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ACKNOWLEDGEMENTS

Graciously acknowledged is the support of National Aeronautics and Space

Administration through the Graduate Student Research Program, Grant NGT5-

50381, for three years. This work was also partially supported by NASA grants

NAG5-10890 and NNG04GA24G.

The hospitality and instruction of Maciej Bzowski and Daniel Rucinski of the

Space Research Centre of the Polish Academy of Sciences in Warsaw over the

summer of 2000 are acknowledged, and were important for initiating this work.

The investigators of the SOHO spacecraft project, in particular the CELIAS

instrument package, as well as investigators of WIND spacecraft and the MFI

instrument, are acknowledged for their hard work obtaining the observations on

which this dissertation is based.

The International Space Science Institute in Bern, and the Swiss National

Foundation are acknowledged for their collaboration and support.

The tutelage of the Experimental Space Plasma Group at UNH, and the

departments of Physics and of Earth, Oceans and Space at UNH, have greatly

assisted this author and made this work possible.

Most importantly, the committee members, John Dawson, Phil Isenberg, Marty

Lee, Chuck Smith, and especially Eberhard Mobius, are acknowledged for the

ideas, advice, and expertise which have so improved this thesis and its author.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS

DEDICATION...... iii

ACKNOWLEDGEMENTS...... iv

LIST OF TABLES...... viii

LIST OF FIGURES...... ix

ABSTRACT...... xi

CHAPTER PAGE

INTRODUCTION...... 1

1. THE HELIOSPHERE IN THE LOCAL INTERSTELLAR MEDIUM...3

Stellar Winds and the Solar Wind ...... 5

The Outer Heliosphere ...... 7

Interstellar Neutrals in the Heliosphere ...... 10

Ionization Interactions ...... 12

Helium ...... 14

2. PICK-UP ION TRANSPORT...... 16

Gyrotropy...... 16

Charged Particle Distributions ...... 19

Convection and Cooling ...... 22

The Diffusive Approximation ...... 24

Transport Coefficients and Resonance ...... 26

Timescales...... 29

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3. INTERPLANETARY MAGNETIC FIELD FLUCTUATIONS...... 30

Power Spectrum Distribution in Frequency Space ...... 33

Single Spacecraft Observations ...... 34

4. INSTRUMENTATION...... 36

SOHO/CELIAS/CTOF...... 37

WIND/MFI and Data Extrapolation ...... 39

Computational Methodology, Data Preparation and Techniques ...... 42

5. COMPRESSION REGIONS AND SOLAR WIND BULK EFFECTS...46

Co-rotating and Stream Interaction Regions ...... 46

Pickup Ion Variations - Statistical Analysis ...... 47

Interpretation ...... 52

Individual Compression Events ...... 53

Cutoff Shift at Magnetic Discontinuities ...... 57

Upwind Cutoff Shift ...... 61

Detrending PUI Variations with SW Correlations ...... 64

Conclusions ...... 70

6. PUI WAVE-PARTICLE INTERACTIONS ...... 72

Pitch Angle Scattering by Waves...... 72

Wave Parameters...... 73

PUI Parameters...... 74

Observations ...... 76

Superposed Epoch Analysis ...... 78

Statistical Correlations ...... 81

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Preliminary Conclusions ...... 84

Hemispheric Model of Pitch Angle Diffusion ...... 85

Conclusions ...... 93

7. ENERGY SPACE DIFFUSION ...... 95

2nd Order Fermi Acceleration ...... 95

Observations of Accelerated PUIs ...... 96

Individual Acceleration Events ...... 99

Acceleration by IMF Fluctuations and Waves ...... 106

Conclusions ...... 113

8. RESULTS AND CONCLUSIONS...... 115

Review of Results ...... 115

Open Questions for Further Research ...... 117

REFERENCES...... 118

APPENDIX A ...... 133

Vll

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF TABLES

Table 2.1 Major Transport Processes for Helium PUIs...... 29

Table 6.1 Wave/PUI parameter correlation coefficients ...... 82

Table 7.1 Largest He+ acceleration events observed by SOHO/CTOF 101

Table A.l Ancillary Data Parameters ...... 135

viii

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES

Figure 1.1 Working Map of LISM...... 4

Figure 1.2 Parker Spiral and Interplanetary Magnetic Field ...... 6

Figure 1.3 Heliosphere and LISM Interface with Voyager Spacecraft.. .9

Figure 2.1 Ring Distribution in Velocity Space (Perpendicular Field)... 17

Figure 2.2 Ring Distribution in Velocity Space (Oblique Field) ...... 18

Figure 2.3 Particle Trajectory and IMF Fluctuations Cartoon ...... 28

Figure 3.1 IMF Frequency Spectrum Example ...... 31

Figure 4.1 CTOF Sensor Diagram...... 37

Figure 4.2 Data convection technique diagram ...... 40

Figure 4.2 WIND Orbit Plot (Earth Orbiting)...... 41

Figure 4.3 WIND Orbit Plot (LI Point) ...... 42

Figure 5.1 CIR overview figure...... 47

Figure 5.2 PUI energy spectra sorted by SW proton density ...... 49

Figure 5.3 Histogram of PUI cutoff flux vs. SW proton density ...... 50

Figure 5.4 PUI energy spectra sorted by IMF magnitude ...... 51

Figure 5.5 PUI energy spectra sorted by |B| in radial fields ...... 52

Figure 5.6 Stream interaction observed on DOY 170 ...... 55

Figure 5.7 Magnetic cloud interaction observed on DOY 149 ...... 56

Figure 5.8 Energy spectra illustrating cutoff shift on DOY 170 ...... 58

Figure 5.9 Model predictions vs. observations for cutoff shift ...... 60

Figure 5.10 Injected PUI distribution w/ upwind cutoff shift ...... 62

Figure 5.11 Example of upwind cutoff shift fitting procedure ...... 63

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 5.12 Upwind cutoff shift vs. Keplerian model ...... 64

Figure 5.13 Example of real vs. corrected PUI flux data ...... 67

Figure 5.14 Example of real vs. corrected PUI flux data incl. IMF ...... 69

Figure 6.1 PUI spectra sorted by IMF orientation ...... 76

Figure 6.2 Dynamic PUI spectra and SW data for DOY 82-84 ...... 77

Figure 6.3 Distribution of observed wave-powers in IMF ...... 78

Figure 6.4 PUI spectra sorted by transverse wave-power, radial IMF... 79

Figure 6.5 PUI spectra sorted by transverse wave-power, perp. IMF....75

Figure 6.6 Trend plot of PUI flux vs. wave-power (radial IMF) 83

Figure 6.7 Trend plot of PUI flux vs. wave-power (perp. IMF) ...... 83

Figure 6.8 Alfven wave dispersion relations and resonance ...... 86

Figure 6.9 Hemispheric fit in radial IMF with high wave-power 90

Figure 6.10 Hemispheric fit in radial IMF with low wave-power 91

Figure 6.11 Hemispheric model: mean free path vs. wave-power 92

Figure 7.1 PUI spectra with maximum acceleration spectrum ...... 97

Figure 7.2 PUI flux spectra showing the effect of shocks ...... 98

Figure 7.3 PUI flux spectra without shocks ...... 99

Figure 7,4 PUI acceleration events on DOY 94 ...... 103

Figure 7.5 PUI acceleration events on DOY 99 ...... 104

Figure 7.6 PUI acceleration events on DOY 210 ...... 105

Figure 7.7 PUI spectra sorted by fluctuation index tj...... 107

Figure 7.8 PUI spectra sorted by resonant transverse wave-power 109

Figure 7.9 PUI spectra sorted by resonant parallel wave-power 110

Figure 7.10 PUI spectra sorted by pitch angle diffusion index ...... 112

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABSTRACT

INTERSTELLAR HELIUM PICKUP ION FLUX VARIATIONS

OBSERVED WITH SOHO/CELIAS

Lukas A. Saul

University of New Hampshire, May, 2005

Interstellar pickup ions are formed when neutral atoms freely enter the

heliosphere and are subsequently ionized. Once these particles are charged they

become a component of the interplanetary plasma and are transported outward

with the solar wind (SW). Measurements of these particles give information

about the local interstellar gas in which our sun resides. However, fluxes of

pickup ions in the solar wind are observed to vary substantially in both magnitude

and energy spectrum.

Hypothesized is that the main causes of these variations are transport

phenomenon in the solar wind, determined by the solar wind and the

interplanetary magnetic field. If so, solar wind conditions can be used to predict

pickup ion fluxes, and pickup ion fluxes can be used to indicate solar wind

transport conditions. To prove the feasibility of this hypothesis, in situ

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. measurements of helium pickup ions from the CTOF instrument on the SOHO

spacecraft are used to characterize transport parameters.

Results are presented which show the effect of solar wind structures on pickup

ions. Compression regions are shown to strongly affect measured fluxes of

pickup ions. Observations show that compression regions can also cause an

adiabatic heating or a shift in the pickup ion velocity distribution.

Also investigated is the effect of interplanetary magnetic field fluctuations and

waves on pickup ions. These fluctuations can scatter pickup ions, in both pitch

angle and energy. Comparison with WIND/MFI magnetic field measurements

show that the pitch angle scattering rate is correlated with the wave-power. A

hemispheric model for the pickup ion distribution is used to determine pitch angle

diffusion coefficients from observed spectra. We find that the observed scattering

rate differs from the predictions of simple diffusion models, especially in low

wave-powers. Energy diffusion or particle acceleration is also observed in the

pickup ion velocity distribution, most notably in the passage of solar wind

disturbances such as shocks but also during quiet times. However, suprathermal

pickup ions are not found to be well correlated with resonant wave-power.

Finally, measurements of SW parameters are used to de-trend the pickup ion data,

reducing the variability of the dataset.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. INTRODUCTION

Interstellar Pickup Ion Flux Variations

We live in the heliosphere. We are protected from much of the high energy

radiation present throughout the heliosphere by the Earth’s atmosphere and

magnetic field, but we cannot deny our place as residents of the extended Sun. In

fact, almost all energy used on Earth comes from the Sun. Without it, not only

would life on Earth be impossible, but Earth itself would not have formed. For

these reasons, we must study the sun and its surroundings! Its variations, its

travels through our galaxy, and its interaction with its surroundings, all give key

evidence into our place in the universe, our past, and our future.

Our knowledge of the heliosphere has tremendously increased over the last 50

years, with the advent of the space age. We can now leave our protected

sanctuary, and sample the heliosphere elsewhere, measuring its particle energies

and composition and electromagnetic properties in amazing detail. Interstellar

material measured in the solar wind acts as a messenger from outside the borders

of the heliosphere, and as a tracer to heliospheric processes. These particles tell

us of the conditions from where they come, i.e. the great voids and clouds of

interstellar space. They also tell us of their journey through the heliosphere,

where they become ionized, and what happens to them in the solar wind.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In this thesis this last aspect of the interstellar pickup ions is pursued in detail,

in which interstellar pickup ions can act as tracers of solar wind particle transport.

Large variations of pickup ion flux are classified based on ideas of solar wind

transport, in the process explaining many of the variations. Interstellar pickup

ions provide a valuable tool for studying space plasma physics, and only some of

their potential is included here. It is my hope that this effort will be continued,

using some of the basics included here, to use interstellar pickup ions to better

understand space plasma, heliospheric physics, and our place in the universe.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 1

THE HELIOSPHERE IN THE LOCAL INTERSTELLAR MEDIUM

In which the stage is set for the arrival o f the interstellar pickup ion at our home, the heliosphere.

Absorption lines in stellar spectra were a first clear indicator that the space

between the stars is not empty and indeed contains a diffuse gas or plasma. As

observations of interstellar matter improved, the importance of this material, the

interstellar medium, became more clear. In fact, clouds of interstellar hydrogen

form the seed and the growth conditions for stars such as our sun, and can shape

the evolution of astrospheres and stellar systems such as our solar system.

Interstellar material contains the building blocks of stars, planets, and even life

[for review see Shklovskii, 1975],

However, the details and composition of interstellar matter are difficult to

ascertain. No spacecraft has sampled the material directly, and it is not usually

self-illuminating. Studies of absorption of light from background stars must

model both the original spectrum of the light source and the geometry of the

material along the line of sight. By measuring absorption lines in all areas of the

spectrum, with telescopes both under and above the Earth’s atmosphere, much

progress has been made in mapping the interstellar gas in the Milky Way and

around the Sun [e.g. Trumpler, 1930], The use of the fine structure radio

emission line of Hydrogen at 21cm for finding interstellar H clouds was an

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Once we know of the existence of this interstellar medium, the question arises

of how the sun interacts with its environment, the LISM. A key aspect to this

interaction is the unstable solar atmosphere or the solar wind.

Stellar Winds and the Solar Wind

One early clue that material streams away from the sun came from the

correlation between observed sunspots and aurora on Earth, discovered in 1744 by

Jean Jacque Dortous de Mairan. Further insight into this phenomenon came from

its effect on comets, whose tails always stream away from the sun [. Hoffmeister,

1943], The comet tails showed that material was always coming from the sun, not

only during flares or from sunspots. That the atmosphere of the sun could not be

at equilibrium was pointed out by [Parker, 1960], who used magneto-

hydrodynamic equations to model the plasma in the solar atmosphere and corona

[for review see Hundhausen, 1968].

The advent of the space age enabled in situ measurements of the solar wind,

confirming that a hot plasma is emitted from the sun and moves at supersonic

(and super-AlfVenic) speeds through interplanetary space. The solar wind has

been sampled from high and low heliospheric latitudes and as far as 80 AU from

the sun. The solar wind is mostly protons, at densities on the order of 10 cm'3

near Earth, and has a small percentage of fully ionized helium and an array of

trace heavy elements, representing largely the composition of the solar

atmosphere. It is not homogenous, and shows structures with a wide variety of

spatial scales, compositions, densities and magnetic fields. Because of the ionized

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V x (u x B) = 0 (1.1)

When combined with the divergence free nature of magnetic fields (V B = 0)

and the boundary condition at the surface of the rotating sun, the components of

the heliospheric magnetic field or Parker spiral can be written:

f r \ 2 Br =B0 r0 v y (1.2) B _ U,P rC0o B

The important features of this heliospheric magnetic field structure are that the

azimuthal component is inversely proportional to the heliocentric distance, while

the radial component is inversely proportional to the square of this distance.

Hence, the field is primarily azimuthal in the outer heliosphere. The 27 day

period of solar rotation and solar wind speed are such that this field is at nearly a

45 degree angle at 1AU.

The Outer Heliosphere

As the solar wind expands around the sun, it becomes cooler and less dense.

Eventually, the wind reaches the outside pressure of the interstellar medium.

Because of the supersonic and super-Alfvenic motion of the wind, a shock forms

at the interface known as the termination shock. It is here that the solar wind

becomes sub-sonic and enters the heliopause. Depending on the magnetic field in

the LISM, a bow shock may form, analogous to the Earth’s bow shock. The

position and properties of the heliosphere-LISM interface are very dependent on

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the LISM parameters (such as density, magnetic field, and temperature), as well

as the solar wind parameters in the outer heliosphere [see e.g. Baranov et al., 1981,

Pauls et al., 1995; Izmondenov et al., 2003; Zank & Muller, 2003].

The positions of the boundaries of our heliosphere are believed to move with

solar activity, as the solar wind pressure and field strength are altered.

Unfortunately the material is too tenuous and not energetic enough to remotely

sense the presence of these regions from Earth. However, as Voyager 1 moves

closer to the termination shock (Figure 1.3) all eyes are on it’s measurements,

which have indicated hints of heliosphere-LISM interaction [MacDonald et al.,

2003; Krimigis et al., 2003]. Also, efforts are underway to build a dedicated

neutral sensor in Earth orbit, the Interstellar Boundary Explorer (IBEX) which

will detect interstellar neutral atoms and neutral products of the heliosphere-LISM

interface [McComas et al., 2004],

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Interstellar Neutrals in the Heliosphere

Before the neutrals are ionized to become pickup ions, they are already

detectable and can also be used as probes of the interstellar medium. Detection

can be done in situ with modem instrumentation [Witte et al., 1993], and remotely

via resonant back scattering of solar UV radiation [e.g. Flynn et al, 1998; Paresce

& Bowyer, 1973], This detection is of great importance in constraining our

knowledge of the very local interstellar medium. However, it is a later product of

these neutrals, the more easily measurable population of pickup ions (PUIs) which

this thesis is concerned with. We will find that PUIs are important not only in

shaping the heliosphere and learning of its boundaries but also in diagnosing

transport processes in the solar wind.

The LISM neutrals, immune to the effects of magnetic fields, are still affected

by the gravitational field of the sun. Indeed, they follow hyperbolic Keplerian

trajectories as they effectively enter the gravitational well of the sun from an

infinite distance. They move only in the plane determined by their initial velocity

vector and the position of the sun, and their distance from the sun can be solved as

a function of the angle swept out by the particle 9-0':

* o - g2) 1 + ecos(f?— 0 )

where e (the eccentricity which is greater than one for interstellar neutrals on

hyperbolic orbits), and a are determined by the particles angular momentum and

total energy which are conserved in the motion [e.g. Danby & Camm, 1957; Fahr,

1978; Wu& Judge, 1979],

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. One simple way to model the heliosphere - neutral LISM interaction is to

assume the neutrals are a flowing gas without appreciable thermal motion of the

interstellar neutrals, i.e. the cold model. The only forces on the neutrals as they

approach the heliosphere are solar; the gravitational force and any radiation

pressure due to solar photons. For the case of helium, the radiation pressure is

negligible, while for hydrogen the strong Lyman alpha radiation pressure almost

exactly cancels the gravitational pull [e.g. Wu & Judge , 1979]. For helium, the

effect of the sun’s gravity on the inflowing gas acts to focus the gas on the

downwind side forming the interstellar neutral focusing cone [Fahr, 1991;

Mobius et al., 1995; Bzowski et al., 1997]. In the cold model, there are two

possible trajectories of interstellar neutrals at any point in the heliosphere, one

coming from out of the heliosphere and going in (direct trajectory), and the other

on a return voyage from the point of closest approach (indirect trajectory).

Despite the complication of the direct and indirect trajectories, the cold model

is much simpler than a more complete hot or statistical approach. In the hot

model, the interstellar neutrals take on a range of velocities, distributed about the

mean velocity of the cold model with a Gaussian or Maxwellian distribution given

by a characteristic temperature. The distribution function is given by:

'f m \ ' 3/2 m\v-u\2 fL IS M (V) — n exp (1.4) 2nkT 2kT

where « is the motion of the LISM with respect to the sun, T is the temperature

and n the density of the LISM, m is the mass of the neutral particle under

consideration, and k is Boltzmann’s constant. The addition of the thermal

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. velocity becomes important in the detail of the focusing cone on the downwind

side [e.g. Bzowski et al., 1997].

Ionization Interactions

As the interstellar neutrals penetrate the heliosphere, they are subject to

ionization processes. These can be identified as three main contributions [see e.g.

Rucinski andFahr, 1989; Rucinski et al., 1996]. The most important ionization

process for interstellar helium is ionization by solar UV radiation. Any UV

photon above the ionization potential of helium can eject an electron from an

interstellar neutral. The intensity of this radiation is inversely proportional to the

square of the heliospheric distance, and the intensity has recently been well

measured by UV monitors on SOHO [McMullin et al., 2002],

Another important ionization mechanism is charge exchange. When two

atoms are close enough, an electronic interaction can take place in which an

electron is transferred from one to the other. Charge exchange interactions are

important for ionizing hydrogen and other species with high charge exchange

cross sections with solar wind particles. For these species, a knowledge of the

SW flux is crucial to calculating the ionization rate, and variable SW speeds and

densities make this calculation more difficult. For this reason, the interaction of

interstellar hydrogen with the heliosphere is particularly complex, and a good

model must take into account latitudinal asymmetries (e.g. faster solar wind in the

polar regions) and time dependences. In the case of helium, a noble gas, charge

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. exchange interaction are negligible, contributing to about four percent of the

helium ionization rate [e.g. Rucinski et al., 1996],

A third ionization mechanism is direct electron impact ionization. A neutral

particle bombarded with a solar wind electron can lose one of its own electrons,

leaving behind an ion. The cross section for electron impact ionization is

dependent on the velocity of the electrons, and so the electron temperature as well

as electron density is important for determining the relative importance of

electron impact ionization. For this reason electron impact ionization will be

enhanced in interplanetary shocks [Isenberg & Feldman, 1995], due to the

turbulent heating of electrons in these regions. Because the electrons are hotter

close to the sun, the electron impact ionization rate does not diminish with

heliocentric radius squared, as the UV ionization rate does. This means electron

impact ionization takes on a higher relative role close to the sun. This effect has

been invoked to describe measurements of the focusing cone near the sun by the

UVCS imager on SOHO [Michels et al., 2002; Lallement et al., 2004], where hot

electrons, especially during solar maximum, can erode the neutral population.

The distribution of neutrals given by (1.3) & (1.4) can be integrated over

velocity space to yield the density of neutrals anywhere in the heliosphere.

However, their loss due to ionization must be included. Remarkably, one of the

velocity integrals can be solved analytically using Bessel’s functions (assuming

the ionization rate is proportional to the inverse square of heliocentric radius),

leaving only two dimensions to integrate numerically [see e.g. Wu & Judge, 1979].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Helium

The discussion thus far has been general, in that interstellar atoms of all

species can be described. However, there are numerous differences in the details

of the interaction that make pickup ions of different species behave differently.

For a number of reasons, this work focuses on helium pickup ions despite the fact

that hydrogen is the dominant species.

One reason to consider helium is that its high ionization potential (as a noble

gas) allows the neutrals to penetrate deep into the heliosphere. Other species,

such as the dominant hydrogen component, do not penetrate in sufficient number

to be detected at 1AU, and much less data is available. Another potential

advantage of helium is that it is more easily identified as a pickup ion component.

Solar wind helium, coming from the hot corona, is almost all fully stripped or

doubly charged, whereas interstellar pickup helium is singly charged.

One final reason to focus on measurements of helium PUIs is the minor role of

charge exchange in their creation. Because the charge exchange rate depends on

solar wind properties, the dynamic solar wind can have a complex effect on

pickup ion distributions. The small charge exchange cross section for helium

makes the heliosphere - LISM interaction far easier to model. Essentially,

interstellar helium is unaffected by the heliospheric boundary, and therefore

enables sampling of pristine interstellar conditions from 1 AU.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Once the neutral material is ionized and picked up by the solar wind, the

evolution becomes much more complex, as magnetic and electric fields become

the dominant forces acting on the particle, which change far more rapidly than the

constant gravitational force that has been the main player in describing the

physics in this chapter.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 2

PICK-UP ION TRANSPORT

In which the newly picked up ions are pushed and prodded by the solar wind

Gyrotropy

As soon as interstellar neutral atoms are ionized, they are affected by the

magnetic field in the solar wind. This is due to the Lorentz force F = q(v x B), or

the electric field seen because the new ions are at motion with respect to the rest

frame of the plasma and its magnetic field. In the rest frame of the solar wind, the

ion is moving at the solar wind speed - towards the sun or in the x direction.

Thus, the velocity of a pickup ion takes the form (for the special case of a

perpendicular magnetic field):

v* = vsw cos(&t) vz = ' vsw sin(«aO

where at is the gyrofrequency and here the magnetic field is taken in the +y direction.

When viewed in the spacecraft frame or the heliospheric rest frame, the motion

of the solar wind is simply added (the motion is non-relativistic):

vx=vsw cos(a)t) + vsw = -vw sin(tyr)

Here it can be seen that the radial velocity of a pickup ion vx varies from a

minimum of zero to a maximum of twice the solar wind speed. This cycloidal

motion is the same as that of a pebble embedded in a wheel of a moving vehicle -

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. whose instantaneous velocity is zero as it touches the ground but is twice the

vehicle speed when it is on top of the wheel. The signature of this motion is

important for detecting pickup ions in any plasma.

(CTOF aperture)

Sunward

a=rc/2

Injected Ring Distribution of PUIs

Fig 2.1. One half of the ring distribution of newly injected PUIs is seen as the thick shaded line in a velocity space diagram. The other half of the ring appears behind the sphere. The origin represents particles at rest in a heliospheric or spacecraft rest frame. The particles which can enter the CTOF instrument are shown with velocities between the dashed lines.

Because PUIs are created continuously from the source population of

interstellar neutrals, the injected distribution forms a ring in velocity space, filled

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. by PUIs at all phases of the Larmor gyration. The resulting ring distribution for

the case of a perpendicular IMF is shown in Figure 2.1.

Injected Ring Distribution of PUIs

(CTOF aperture)

Sunward

Fig 2.2. The initial ring distribution in an oblique magnetic field. One half of the ring distribution o f newly injected PUIs is seen as the thick shaded line in a velocity space diagram. The other half of the ring appears behind the sphere. The origin represents particles at rest in a heliospheric or spacecraft rest frame.

In a collisionless plasma, charges are free to move and so the conductance is

effectively infinite. In such a system, the electric field will vanish. However,

magnetic fields remain and the Lorentz force is the dominant force acting on

plasma evolution.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. If the magnetic field is at an oblique angle, a similar ring distribution results,

although without the symmetry present in Figure 2.1. Instead, the ring

distribution will have a smaller radius and will be present on one side of the

sphere, as shown in Figure 2.2.

Because the phase angle in a particle’s rotation about the field is not important,

one degree of freedom can be eliminated from the system. This aspect is known

as gyrotropy, and a gyrotropic distribution is one which is equally distributed in

cycloidal phase of Larmor gyration. The three dimensional velocity space is

reduced to two dimensions, which are usually referred to as particle speed v and

pitch angle a , where the pitch angle is the angle from the field vector to a

particle’s velocity vector.

Charged Particle Distributions

The solar wind is a nearly fully ionized gas, and the evolution of this gas and

the pickup ions contained therein is properly described by the techniques of

plasma physics. Treatment of every particle in a plasma, its motion and the forces

on it due to all other particles, quickly becomes tedious or impossible. It

behooves us to use a statistical interpretation, in a kinetic theory. In such a theory,

the plasma’s constituents are described with distribution functions, which keep

track of the relative amounts of particles with different velocities and locations.

Probabilistic distributions of the particles are considered, in both physical space

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (particle positions) and in velocity space (particle velocities). The total phase

space density describes the relative amounts of particles at different velocities and

at different positions in space at a given time. Each particle species a can be

fully described by a seven dimensional distribution function/ which gives the

phase space density of particles at a given location, velocity, and time:

fa = fa(*’V;t) (2.1)

Kinetic theories have been enormously successful in describing systems with

many constituents, including gases and plasmas [for reviews see Wu, 1966; Liboff,

1969]. The Liouiville theorem, which states that the total phase space density is

conserved in the absence of collisions, gives a starting point for the derivation of a

system of kinetic equations to describe the evolution of a system under any

external forces. For the case of a plasma where only electric and magnetic fields

act on the constituent particles, these derivations lead to the Vlasov equation,

which describes the evolution of a charged particle distribution:

f +fv,+f ^ ,+wA) = 0 (2.2) ot ox. ov: m

H ere/is the distribution function of a constituent particle, q and m are the

charge and mass of the particle, and E, B are the electric and magnetic fields,

functions of space and time alone. Repeated indices in (2.2) are to be summed

over all their possible values, and eijk is the fully anti-symmetric unit tensor

which generates the cross product, and its usage in (2.2) is in the Lorentz force

term. Equation (2.2) can be multiplied by powers and combinations of velocities

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and integrated over velocity space to obtain the moment equations that form the

heart of magneto-hydrodynamics (MHD). For a review of the power and utility

of the Vlasov equation in plasma physics, see the texts [Chen, 1984; Ichimaru,

1992], It is important to note that the right hand side of this equation is zero,

whereas for a gas with frequent collisions between constituent particles there will

be a collision term here. The solar wind is so diffuse that the mean free path to

Coulomb collisions is on the order of the size of the heliosphere, and so the

plasma is effectively collisionless. For the larger volumes of interstellar space,

the collision terms will need to be taken into account, but for analyzing transport

of an ion from its injection (ionization) inside of 1 AU to a spacecraft near the

Earth, this term can be safely neglected.

The problem of PUI transport in the solar wind can be described as the

application of the Vlasov equation to the PUI population, although in practice

many assumptions must be made to proceed. This problem was addressed as

early as the 1970s [Vasilyunas & Siscoe, 1976], before the first confirmation of

the existence of this population [Mobius et al., 1985]. The problem of ion

transport is also of great interest in other aspects of plasma and fluid dynamics, as

various approximations of (2.2) such as MHD and diffusion models have

limitations which make the evolution difficult to predict.

The first step in tracing the motion of the PUIs is the determination of the

injection population, or the initial distribution from which the evolution is to be

calculated. In the simplest model, the interstellar neutrals are ionized with zero

velocity (in a heliocentric rest frame). Because the inflow velocities and thermal

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. velocities are small compared with the solar wind speed, this cold model

approximation is justified, and more detailed models will include a thermal or

even non-Maxwellian spread about this initial distribution.

Convection and Cooling

As the solar wind moves out in the heliosphere, the magnetic field changes.

Some of these changes are due to the global heliospheric magnetic field, and some

are due to waves or turbulence present in interplanetary space. It behooves us to

consider these two portions of the IMF separately. The global or “bulk” field is

described by the Parker spiral, and takes (on average) the form given in equation

( 1.2).

. This change in the magnetic field strength is an electric field according to

Faraday’s law, which slows the particles in their gyration. Such a process can be

viewed as the conservation of an adiabatic invariant, and is therefore known as

adiabatic cooling. A similar process occurs in the expansion of an ordinary gas,

as the temperature is reduced when volume is expanded due to collisions with

expanding walls of the container. For the solar wind plasma, there are no walls of

the container to cool the plasma. The cooling is accomplished by the magnetic

field which controls and contains the plasma.

The precise amount of cooling of the PUI distribution depends on the pitch

angle distribution of the PUIs, as well as the heliospheric magnetic field. An

2 adiabatic invariant for a single particle gyrating about a magnetic field is B '

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This means that a particle moving with zero pitch angle (no perpendicular

velocity) will not be affected by the changing magnetic field, as can be shown by

noting that such a particle sees no Lorentz force and so is unaffected by the

magnetic field of any magnitude. For a Parker spiral field with |B| ~ Mr this

implies the perpendicular velocity will decrease as r l/2.

If the particles are scattered in pitch angle quickly, specifically more quickly

than the adiabatic expansion of the solar wind or the decrease of the magnetic

field, then a spherical distribution is formed in place of the ring distribution. In

effect, the magnetic field of the expanding solar wind acts as an opening piston

does on a volume of gas, and the PUIs behave as an ideal gas in their cooling

characteristics. The speed of a pickup ion (in the solar wind frame) at a position

r0 can then be written as

r v3/2 “ = (2-3) vsw y r )

where r is the radius at which the PUI was injected and vsiv is the solar wind

speed [e.g. Vasilyunas & Siscoe, 1976; Mobius et al., 1995], This relation enables

the PUI velocity spectrum to be interpreted as a radial injection spectrum, where a

given velocity maps to a given injection radius.

However, neither the spherical distribution nor the ring distribution describes

the cooling process precisely. This issue will be returned to when the effects of

magnetic discontinuities on the PUI distribution are discussed in Chapter 5. To

proceed in the case of less efficient pitch angle scattering we must consider the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. entire distribution of pickup ions, and how many of these ions are at different

pitch angles, calculating the cooling for each pitch angle from the adiabatic

invariant. To do so requires treatment of magnetic field fluctuations which can

scatter particles to different pitch angles, or cause pitch angle diffusion.

The Diffusive Approximation

The lack of collisions due to the low density of the SW plasma and the lack of

electric fields due to its high conductance suggest that the system described by

(2.2) should be easy to solve, describing the subsequent motion of the PUIs.

However, this is not the case as the magnetic field is not known everywhere in the

heliosphere, and fluctuates over a variety of timescales. Such behavior in theory

makes the system intractable. However, there is a way to proceed, as the

fluctuations of the magnetic field can be treated statistically as effectively random,

allowing these effects to be treated as a Markov process or a “random walk”. A

similar effect occurs in a normal gas, when collisions happen often enough to be

effectively random in time and space, forcing concentrations to diffuse away from

the area of concentration. This is known as the diffusive approximation.

To proceed from (2.2), the total magnetic field is written as the sum of a bulk

term Bj, which is stationary or constant in time, and a fluctuating term SBj,

which is composed of MHD waves and turbulence present in the solar wind:

Ei -^E i + SEi Bl ^ B i +SBi

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. . The Vlasov system now can be written as a Boltzmann equation [see e.g.

Ichimaru, 1992]:

S f S f^d fq — +— v,. + (ejk VjBk) = S f dt dx. dv. m (2.4)

where the scattering operator contains the action of the fluctuating fields on the

distribution, and in the diffusive approximation can be written:

d f ]_d_ D + - d d-L V D £ (2.5) S f = MM W /-s dfj.v dMj djuv v2dv[ MVdju + v 2 dv dv

Here the diffusion coefficients are taken to be gyrotropic, and written in terms of

the particle speed v and the cosine of the pitch angle //, as well as being position

and possibly time dependent.

The basic idea behind (2.5) is that the essentially random collisions which

make up the scattering operator will act to push the distribution toward isotropy.

We say that the physical process of scattering is a Markov process, similar to a

random walk. The rate at which the distribution diffuses is proportional to the

gradient of the distribution, or the anisotropy. The constants of proportionality

are the components of the diffusion tensor, which are written in terms of pitch

angle and energy space in (2.5). These terms represent the amount by which a

gradient of the distribution in pitch angle space will affect the energy space

evolution, and in which a gradient of the distribution in energy space will affect

the pitch angle space evolution. In general they can be calculated in terms of the

power in fluctuations of the IMF [see e.g. Bogdan et al., 1991].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PUIs are subject to pitch angle scattering processes after their initial injection,

such as magnetic field fluctuations which will be considered in more detail

Chapter 3. The scattering due to a pure magnetic fluctuation does not change the

energy of the particles (as only an electric field can do that), but spreads their

distribution out onto the spherical shell visible in Figure 2.1.

Such a system of only pitch angle scattering can be described to evolve as:

S f d f d f q . - d ( n d p D ^ot p uXj V'+ 7 dvj T m (^*vA ) = i dfi r dp (2.6)

The scattering agents which underlie the diffusion coefficients are contained in

the magnetic and electric fields found in the third term of Equation 2.2.

As the solar wind travels outward, the magnetic field decreases and the wind

cools adiabatically, as described above. The PUIs see the decreasing magnetic

field as an electric field and are thus decelerated, cooling with the solar wind.

This adiabatic cooling is described by the convection terms of the Vlasov

equation. The gyrophase averaged form of this equation has been expressed in

[Isenberg, 1987; see also Skilling, 1971],

Transport Coefficients and Resonance

Much work has gone into determination of the transport coefficients of (2.5)

from the types of magnetic fluctuations that exist [see e.g. Jokipii, 1972 & 1974;

Bogdan et al., 1992; Schlickeiser, 1998, Isenberg et al., 2003], We will not

review the quasi-linear methods here, as that is beyond the scope of this thesis.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. However, we must review that the major contribution to the pitch angle diffusion

term is usually taken to be resonance with MHD waves.

When a particle gyrates about the magnetic field with such a frequency that its

phase is precisely matched by that of a magnetic field wave, we say the particle is

in resonance with the wave. This condition can be expressed mathematically (in

the non-relativistic limit) by writing the frequency of the wave, Doppler shifted to

the particle’s center of motoin:

co-kjv^=-r£l (2.7)

Here a> is the frequency of the wave, is the component of the wave vector

parallel to the magnetic field, and v|( and Q are the velocity parallel to the

magnetic field and the gyro-frequency (respectively) of the particle. The integer n

is the degree of harmonic of the resonance, with lower harmonics usually

representing a stronger coupling between particle and wave motion. In the solar

wind, a spectrum of MHD waves is present, representing a range of frequencies

and wave numbers, such that waves are moving both in many different directions

and with different frequencies. However, the conditions at 1 AU and closer are

such that most of the sources for these waves are sunward, i.e. the waves

propagate anti-sunward. The presence of Alfven waves and other turbulent

disturbances in the solar wind is well established by in situ measurements.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Timescales

Although our discussion of pickup ion transport in the solar wind is in some ways just

beginning, it behooves us to review the major processes involved to help as a guide with

comparison to observations and more detailed modeling later in this thesis. One natural

way to order the transport processes is by their timescale, i.e. the rate at which they effect

the pickup ion distribution. These processes and their associated timescales are listed

below in Table 2.1.

TABLE #2.1. Major Transport Processes acting on Helium Pickup Ions in the Solar Wind at 1AU Process Name Description Relevant Timescale Lorentz Force Leads to gyration about magnetic -10 sec. - 30 field. sec. Pitch angle Forms isotropic distribution (due to -lOhrs.- 100 Diffusion magnetic fluctuations). hrs. Adiabatic Cooling Expanding solar wind and decreasing IMF cools pickup ions. -100 hrs.

Energy Diffusion Statistical acceleration by waves will scale with Alfven speed over -1000 hrs. solar wind speed, squared.

Coulomb scattering SW density decreases as r'2; mean free path becomes on order of size -5000 hrs. of the heliosphere.

Further details of pitch angle scattering and energy diffusion will be discussed later in

this thesis, in Chapters 6 & 7 respectively, where models of these processes are used to

compare transport theory with in situ observations of pickup ion velocity distributions.

This table orders the transport processes for average solar wind conditions, however

extenuating circumstances discussed in later chapters can change the timescales given

significantly. It is important to note that the time scales associated with pitch angle

diffusion and with adiabatic cooling can be similar. This makes transport modeling

difficult as time ordering approximations fail.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 3

INTERPLANETARY MAGNETIC FIELD FLUCTUATIONS

In which our pickup ions are jostled and scattered by oscillations o f the IMF

The Parker spiral and the IMF configuration described in Chapter 1 are an

idealized solution. In reality, there are large fluctuations from this field over a

variety of time and length scales. Measurements of the IMF have been taken in

situ to very high time resolution and in many different locations in the heliosphere.

For example, Ulysses took a near polar orbit via a Jupiter swing-by, Helios I & II

took an elliptical orbit in the inner heliosphere, and Voyager executed a grand

tour of the planets finally leaving Neptune on an escape trajectory. Although the

details are very different, fluctuations in the solar magnetic field are observed in

all locations of the solar wind. Many changes can be ascribed to “global”

heliospheric changes, for example movement of the current sheet or

superstructures on the sun.

In addition to global heliospheric IMF changes, which combine to create the

switch in polarity over the eleven year solar cycle, there are rapid fluctuations

which come more under the category of waves or turbulence. To discuss in detail

the causes and effects of these fluctuations it is useful to Fourier analyze the fields,

or to refer to the power of the oscillations in frequency space. An example of the

resultant fluctuation spectra as observed by the WIND spacecraft is shown in

Figure 3.1.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. _N

*JL c

Q in EL

Fig 3.1. The frequency (x-axis) spectrum o f IMF fluctuations is shown for one half hour interval (DOY 99.43-99.45) as an example. The frequency in Hertz is on the x axis, while the power is on the y axis. The frequency spectrum of the X, Y, and Z components of the field, as well as the frequency spectrum o f the magnitude and trace of spectral tensor are shown. Spacecraft spin harmonics can be seen as spikes in the higher frequency portion of the spectrum, and power law fits are shown for comparison, [plot from Charles W. Smith and WIND/MFI team]

The discovery of waves and fluctuations in the IMF was not a surprise. The

physical forces which appear in a plasma, including the magnetic field and the

kinetic pressure of individual particle populations, act as restoring forces and

enable a variety of wave modes to propagate in the plasma from any disturbances.

The details of the zoo of plasma wave modes and their interplay are beyond the

scope of this thesis. However, it will be important for us to recognize the

differences between modes that can be observed via spacecraft measurements,

and that are likely to affect ion distributions.

AlfVen waves are named for Hannes AlfVen who first hypothesized their

existence, solving for linear propagation modes coupling particle motion and

magnetic fields. They result from disturbances in which the field fluctuates

perpendicular to the mean field. These disturbances are analogous to waves on

strings, where in this case the field lines are represented as strings, resistant to

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. change in direction. Alfvenic fluctuations in the solar wind were detected by the

Helios spacecraft [.Belcher & Davis , 1971; Neubauer et al., 1977].

Magnetosonic waves are analogous to sound waves, except that the magnetic

field pressure gives an additional boost to the restoring force for the wave. There

are two main types of magnetosonic waves, the fast and slow modes, named for

the relation of their phase speeds. For derivations and dispersion relations

related to these waves (and other wave modes) see texts e.g. [Ichimaru, 1992;

Chen, 1984; Kallenrode, 1998]. It is expected that the effects of these wave

modes will change the evolution of the pickup ion distribution [e.g. Ragot &

Schlickeiser, 1998; Michalek et al., 1999], however because more energy is in

AlfVen mode oscillations those are expected to have stronger effects on the PUI

distribution.

The character of IMF fluctuations from the point of view of an experimentalist

is somewhat different from that of a theoretical physicist analyzing behavior of

single wave modes. When measuring the magnetic field on a spacecraft, a three

dimensional field vector is determined for each measurement, via a fluxgate

magnetometer or other magnetic field vector measurement. The fluctuating

portion of these measurements is determined by choosing a time scale to average

over, for which the average field or mean field becomes the background to any

fluctuations. After subtracting this background, the fluctuating component is left,

and spectral analysis can begin.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Power Spectrum Distribution in Frequency Space

The fluctuations of each vector component are important, as are fluctuations in

combinations of the components. When analyzing these fluctuations it is

important to use a coordinate system sympathetic to the mean field direction. The

z axis is usually chosen parallel to the mean field, and the solar wind velocity

vector is used to choose the x andy axes [e.g. Belcher & Davis, 1971], Once the

fluctuating field components have been expressed in mean field coordinates,

Fourier or spectral analysis can begin.

For example, the Fourier transform of a magnetic field component Bt(t) in

frequency space is given by Bi(ctf) = Bt (t)e~m d t . In practice, the field

strength components are measured as a time series, and so a discrete Fourier

transform is used (see Chapter 6 for more details).

The power distribution of the IMF fluctuations can be taken from any

combination of components, such as a single component, the magnitude of the

magnetic field vector, or more complicated quantities. In general, all the

quadratic quantities which can be analyzed form the spectral matrix i f , whose

components are defined as

SBJB^ SB,SB, SB,SB, 8Bx8By 8By8By 8Bz8By 8BX8BZ 8By8Bz 8BZ8BZ

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where the tilde indicates a Fourier transform of the quantity below it. From this

matrix one can construct the trace, giving the power in the magnitude squared of

the field vector. Of immediate interest are the diagonal components of the

spectral matrix. Pa is the power in the magnitude of fluctuations parallel to the

mean field, and the transverse components Pxx and P give power in fluctuations

perpendicular to the mean field. The cross terms are also important, e.g. for

measurements of helicity [Smith, 2003], but they will not be used in the analysis

of pickup ion - wave power correlations that is presented in this thesis.

Single Spacecraft Observations

Although the IMF measurements and spectral analysis techniques are powerful,

they are limited in that they represent a time-series obtained from a single

spacecraft, from only a single point in space at any one time. Any spatial

variations of the magnetic field other than the radial motion of the plasma past the

spacecraft are not observable. In fact, if the spacecraft moves so quickly with

respect to the bulk plasma, the time series measurements taken by a spacecraft

magnetometer can be seen as a spatial distribution of magnetic field vectors, and

the measured spectrum and its components can be interpreted as a wave-number

(k) spectrum:

Pj (

, where k is the wave number and Vsw is the plasma flow velocity past the

spacecraft.

The determination of wave power in all four dimensions (three of wave

number and one of frequency) cannot be made with single spacecraft observations.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. To compensate for this techniques are available that use time series of particle

measurements as well, and that rely on estimates of spatial gradients using e.g. the

frozen in condition [see e.g. Matthaeus & Smith, 1981; Smith, 2003], For the

purpose of comparing wave power to the pickup ion distribution observed in the

solar wind, we use Fourier time series of magnetic field data alone, using the

frequencies near gyro-resonance as a proxy for waves satisfying the resonance

condition.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 4

INSTRUMENTATION

In which the solar wind speaks to us directly, via in situ particle and field measurements.

The remarkable advances over the last century in technology are paralleled by

modem space measurement instruments. For this research we rely on two basic

groups of instruments, particle spectrometers and magnetic field sensors, each on

board spacecraft outside of the Earth’s magnetosphere, in the solar wind. The

primary particle instrument used for the data in this thesis is the

SOHO/CELIAS/CTOF time of flight spectrometer. The fluxgate magnetometers

on board WIND served as magnetic field measurements for this survey [Lepping

et al., 1995], as SOHO did not have a magnetometer. The procedure used to

determine field conditions at SOHO via these WIND wave measurements, as well

as a brief discussion of the instruments, are included in this chapter.

A full review of the many techniques that have been used to measure the

particles in the solar wind is well beyond the scope of this thesis. However,

because the bulk of our material comes from a specific instrument on board

SOHO, capable of identifying helium PUIs and measuring their energy and flux

density, we give some background into this instrument here. The bulk solar wind

measurements (i.e. proton density and temperature) are also used in this thesis,

and these are provided from SOHO by the proton monitor MTOF/PM [Ipavich et

al., 1998],

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SOHO/CELIAS/CTOF

The CTOF instrument, in the CELIAS package on board SOHO, produced 150

days of data in the upwind region of the interstellar flow. The large geometric

factor of the instrument makes high time resolution observations of PUI velocity

spectra possible [Hovestadt et al., 1995]. Furthermore, its location at the

Lagrangian point and 3-axis stabilized platform gives continuous sampling of the

solar wind near 1 AU. This makes the dataset interesting for studying short term

variations in both total flux and velocity distribution of interstellar He+ PUIs as

caused by interplanetary disturbances.

CtOF-SENSOR SOHO CELIAS INTERMH TO DPU CLECTMNKS

m o coaptER

ltr.cLKiimcs

QlUDRUPtitE 1

STOP MCp 5M.ID STATE DETECTOR START HCP ClEtTROSfATIC .

CAHHCN IW L HV-FEED1HRQUGH avAoatipoLE t

RMTH VOLTAGE IK N E R A T M t'

Figure 4.1 Schematic of the Charge Time of Flight (CTOF) sensor in the CELIAS package on board SOHO. Diagram from [Aellig & Bochsler, 1998],

The instrument (see Figure 4.1) consists of an entrance collimator (which faces

sunward), an electrostatic analyzer (hemispherical analyzer), a time of flight (TOF)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. spectrometer, and a solid state detector (SSD) that can measure the final energy of

a particle. These three components enable measurement respectively of the

energy per charge of the particle E/Q, the TOF across a known distance, and the

final energy ESsd- The hemispherical analyzer, along with the quadrupole focus

and the entrance to the instrument, only allows an ion with a certain range of

energy per charge to continue to the TOF portion of the instrument (Figure 4.1).

The TOF system then uses an acceleration system with a negative voltage of

typically 23 kV. After the post-acceleration the ions pass through a thin carbon

foil. Electrons emitted as the ion passes through the foil trigger a multi-channel

plate detector (MCP), providing a start signal. When the ion passes through the

TOF section and enters the solid state detector, additional electrons are produced

that trigger the MCPs, providing a stop signal. Fast electronics determines a

digital value for the time of flight.

This allows determination of the mass per charge of the particle:

m/q = 2{T/d)2(Uacc+E/qyp (4.1)

Here d is the distance traveled by the particle between start and stop signals in the

applied potential Uacc, and T is the time of flight. E/q is determined by the

electrostatic analyzer, and /? is a number between zero and one due to loss in the

carbon foil and depends on the energy and species.

The SSD then provides the energy Essd, as well as a third timing signal for

triple coincidence. This allows determination of the mass:

m = 2(T / d )2 E ssd ■ fj. (4.2)

Here // is greater than one and due to energy loss in SSD. The energy losses in

the foil and the SSD are significant and energy dependent, and the instrument

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. must be carefully calibrated accordingly to determine the form of f3 and p

[Aellig & Bochsler, 1998; Hefti, 1997],

The electrostatic analyzer selects ions based on their energy per charge, and

this energy per charge is stepped logarithmically to allow sequential measurement

of ions over the energy range of the instrument, from 0.1 to 55 keV per charge.

The ions enter through a 50 degree opening centered in the sunward direction, i.e.

antisunward particles enter the instrument.

Further details of instrument calibration and operation procedures can be found

in the CELIAS Dataphase Manual [Wurz et al., 1997],

WIND/MFI and Data Extrapolation

SOHO was unfortunately not equipped with a magnetometer, so interplanetary

magnetic field (IMF) measurements from the fluxgate magnetometers from the

Magnetic Field Investigation (MFI) on the WIND spacecraft were used [Lepping

et al., 1995], These IMF measurements were used both to determine the

orientation and magnitude of the magnetic field and to determine the level of

fluctuations or turbulence present in the solar wind.

During the time period considered (DOY 80-230, 1996) WIND passed through

the Earth’s magnetosphere 3 times, and was always within 250Re of SOHO. The

position of the spacecraft is shown in Figures 4.3 and 4.4. We ignored data from

well before to well after the magnetosphere crossings to avoid terrestrial effects

(DOY 86-89, 109-111, 130-133). The IMF measurements were shifted in time to

correspond to SOHO’s location, using the measured solar wind speed and IMF

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The amount of ancillary data was also large, including not only the average

magnetic field vectors from WIND/MFI and proton parameters from

SOHO/MTOF/PM but also three second magnetic field vectors from which SW

turbulence levels could be determined. The software used and the libraries

created in this work are catalogued in Appendix A.

While the software details will not be discussed in detail here, there are two

components of the analysis that merit discussion in this context, as much of the

results relied on these aspects, and they are relatively unique to pickup ion data

analysis techniques. The first is the normalization of spectra by the solar wind

speed, and the second is the use of energy flux density as the unit of choice over

the flux density or the distribution function that are more closely related to the

measurement and commonly discussed in particle measurements.

The measured energy spectra of pickup ions need to be normalized to the solar

wind speed if they are to be compared during times of different solar wind speeds.

Due to the nature of the pickup process as described in Chapter 1 & 2, a cutoff

velocity is expected at twice the solar wind speed. This cutoff will not be clear if

the spectra are averaged over times of different solar wind speed, unless a proper

normalization procedure is carried out when forming a spectrum or energy

histogram.

To create a normalized spectrum, a histogram is created in v/Vsw• An

individual helium event, which has a possible range of velocities, is translated to a

range in v/Vsw using the MTOF/PM data from the same time period. The

individual helium event is not put wholly into the most applicable bin in v/Vsw,

rather it is treated as a fraction of an event in the v/Vsw bins straddled by the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. velocity range determined by the instrument. This avoids the so-called “fencepost

effect”, in which certain v/Vsw bins collect more counts by virtue of their

placement in the original spacecraft energy bins. This also enables a final

normalized histogram with a different number of bins than the energy bins of the

instrument.

The energy flux density is tabulated in this histogram, by multiplying the

calibrated number fluxes J, from the count rates by the midpoint energy in the

energy bin:

EFluxi = J iEi (4.3)

where the subscript i indicates the ith energy bin and Et is the energy of particles

in that bin. The number flux is determined from the count rate with the

instrument geometric factor and calibrated energy efficiency [see Aellig &

Bochsler, 1998; Hefti, 1997], In terms of the PUI distribution function / , the

number flux can be written as:

J(£,Q,r) = — /(F,v) m (44)

where the instrument then integrates this over the solid angle ^ and energy range

AE dictated by the aperture and electrostatic analyzer [e.g. Kallenrode, 1998],

The energy flux density is used here because this quantity is predicted to be

independent of the solar wind speed, in contrast with other quantities which could

be used [Mobius et al., 1995], This can be seen by examining the form of f (r, v)

for an isotropic model [e.g. Vasilyunas & Siscoe, 1976]. This PUI distribution

has as its source the interstellar neutral distribution multiplied by the ionization

rate, neither of which depends on the solar wind speed. However, a parcel of

solar wind which spends more time in the inner heliosphere (lower SW speed) has

more time to accumulate PUIs. This implies an inverse dependence of the pickup 44

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ion density on the SW speed. Also, in the solar wind frame the ions are injected

at the solar wind speed. Assuming that they fill a sphere in velocity space

isotropically implies this volume of phase space is ~ Vsw3, and so the distribution

function contains an additional factor of Vsw~3 . This means that the phase space

density / (r, v) is inversely proportional to fourth power of the solar wind speed.

From the definition of the energy flux density in terms of the velocity

distribution, using (4.4):

EFlux = J*E- £ / ( v ,r) ~ (wV^ 1 4 . (4.5) ^ ^ y S W

Here the EFlux is expressed in terms of the normalized velocity, w = v/V sw, and

the distribution function ffw). The solar wind velocity dependence of (4.5)

cancels.

In a fast solar wind, the PUIs are swept out quickly and do not accumulate to

as high a density, hence their density is inversely proportional to the SW speed.

The number flux of PUIs also exhibits this inverse dependence. However, the

energy flux, which includes the speed of the ions as they move with the solar

wind, does not include a term proportional to the solar wind speed, for simple

models of pickup ion generation and transport. For this reason, energy flux

density, as measured in cm 'V sr'1 is appropriate when comparing pickup ion

spectra from different solar wind conditions. In actuality some dependence on the

solar wind speed may still be observed, as PUI transport parameters vary with

different SW conditions, and the distribution is not always isotropic.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 5

COMPRESSION REGIONS AND SOLAR WIND BULK EFFECTS

In which the solar wind pushes itself and its constituents, causing variations in magnetic fields, solar wind bulk parameters, and pickup ions.

Co-rotating and Stream Interaction Regions

It is a necessary consequence of a variable speed solar wind that compression

regions will form. Convection of a faster flow into a region of slower flow

compresses the fluid ahead. Because such compression also affects the SW

magnetic field, the pickup ions in the SW are also affected. Indeed, many of the

features in the dynamic pickup velocity spectrum can be explained as results of

SW compression or rarefaction [Schwadron et al., 1996; Klecker et al., 2001].

Presented in this chapter are results that concentrate on the effects of SW

compressions on PUI fluxes.

When such a fast wind flows from a coronal hole, the structure appears from

Earth to repeat, with the frequency of the solar rotation. This is called a co-

rotating interaction region (CIR), and is depicted in a cartoon in Figure 5.1. As

the fast wind continues to push the slow wind ahead, very high densities can form,

and due to the supersonic and super-Alfvenic flow speeds involved, a shock can

form. Often such a region will have a forward and reverse shock on either side of

the compression region. Such a shock often does not form until the region moves

further out in the heliosphere (2 or more AU), where the pressure has had more

time to build up in the interaction region and the magnetic field lines become

more perpendicular to the fluid flow enabling further compression.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Such a compression region can be formed in other circumstances as well. A

fast moving CME will have a compression region ahead of it, which may or may

not steepen to form a shock. Smaller changes in the solar wind, or those more

variable or transitory than a full solar rotation, are also common and have earned

the moniker “transient interaction region”, or TIRs. Such structures were also

found to have strong effects on PUI distributions.

■Stream

Bmttwt'm

Amiteat Setsjr Wind

Figure 5.1. A co-rotating or stream interaction region. The Parker spiral is shown in magnetic field lines, and the solar wind velocity is depicted with arrows. A high speed stream emission is represented by the dark shaded region, with a compression region ahead of it and rarefaction region behind it. A possible shock front is indicated with dashed line. Figure taken from [Forsyth, 2002],

Pickup Ion Variations - Statistical Analysis

That compression regions play a role in PUI dynamics is not a surprise.

ULYSSES measurements [Gloeckler et al., 1994] showed that enhancements in

pickup helium were mirrored by pickup hydrogen, a result consistent with solar

wind transport processes playing a role. Strongly accelerated PUIs were also

found to coincide with CIRs and interplanetary shocks from ACE SEPICA

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. measurements [Mobius et al., 2002; Kucharek et al., 2003], and at lower energies

from SOHO STOF measurements [Klecker et al., 2001]. We concentrate here on

the effect of compression regions on the bulk PUI population, as pitch angle and

energy diffusion by compressions and shocks will be discussed later.

One goal of this work is to determine the causes of the large variations in PUI

fluxes. To do so we examine individual events of pickup ion variations, and we

perform a statistical analysis searching for correlations between various solar

wind parameters and the PUI fluxes. While individual event analysis is

compelling, the statistical results are unambiguous in their determination of

compression region effects on PUI distributions and so are presented first. By

combining time periods of similar solar wind density in a superposed epoch

analysis, PUI spectra were made for different ranges of SW parameters. Spectra

were combined with respect to the normalized velocity, as described in Chapter 4.

Pickup ion spectra were obtained by accumulating different ranges of the

parameters which included IMF as well as proton density, velocity, and

temperature (see Appendix A for complete list of parameters considered).

A strong trend emerged when this technique was employed with proton density

as measured by MTOF/PM, to produce e.g. Figure 5.2.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. magnetic moment decreases the pitch angle of particles, enabling them to escape

more quickly from a compression region.

Because the PUI fluxes showed correlations with both IMF strength and proton

density, we then looked in more detail at individual times of solar wind

compression, which have both enhanced IMF and proton density. The unique

nature of each compression region (due to different conditions at its formation)

will be washed out in the statistical analysis, but should be clear from looking at

individual events.

Individual Compression Events

SOHO saw several solar wind compression events during 1996. Some CIRs

and transient stream interaction regions have also been observed over this time

period with other instruments on SOHO [Klecker et al., 2001]. Two events are

shown in detail here; the interested reader is directed to the catalog of events that

was produced along with this dissertation research and described in Appendix A.

These two figures (5.6 & 5.7) are shown as examples of compression regions

in the solar wind and the resulting disturbances in the PUIs in three energy ranges.

They show the data from three instruments, SOHO/MTOF/PM in the top three

plots (proton data), WIND/MFI in the next two plots (IMF), and SOHO/CTOF in

the lower three plots (Helium PUIs).

We observed a strong transient stream interaction on DOY 170 (Figure 5.6),

with a clear jump in the solar wind speed driving the compression. The proton

density jumped to the highest level in the dataset, approaching 50 cm'3. A

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. simultaneous compression of pickup ions was also observed during this time

(lower three panels of Figure 5.6), though their larger gyro-radii and more diffuse

density made the width of the PUI compression region wider than the narrow

proton peak. The PUIs in the range 1.8 < v/Vsw <2.0 (second PUI panel) are

seen to be enhanced for four times longer than the protons.

Acceleration of the PUIs is also visible in the higher energy ranges in the

bottom two panels of Figure 5.6, which will be discussed later in Chapter 7. In

particular, note the apparent strong enhancement of the high energy PUIs (with

speeds greater than the cutoff velocity) in a single data point coincident with the

largest magnetic field discontinuity. It will be shown later that this is not true

acceleration but is indicative of an adiabatic shift of the PUI distribution.

A magnetic cloud CME around DOY 149 (Figure 5.7) was also observed.

This cloud displayed compression of the solar wind and He+ before and after its

passage, with stronger compression trailing the region. As the cloud arrived, a

strong jump in magnetic field magnitude was observed, and a smaller spike in

proton density and in the PUI density. Again, the close correlation of the PUIs to

the SW conditions can be observed despite the collisionless and diffuse nature of

the interaction. It can also be seen from this compression region that the PUIs are

most affected in the range of 1.8 < Vsw < 2.0, near the injection or cutoff velocity.

This corresponds to the statistical observations (Figures 5.2 - 5.5) and lends

credence to the explanation that compression regions are behind this effect. It

could be that these recently injected particles are more susceptible to compression

due to their more anisotropic distribution or to their larger gyroradii; however the

exact reasons for the preferred enhancement near the cutoff velocity are not

known at this time.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Cutoff Shift at Magnetic Discontinuities

To determine hot the pickup ion distribution changed during these events, we

plotted one hour spectra and overlaid them to see the change, as in Figure 5.8. In

some cases, the PUI spectra showed a shift in the cutoff velocity right at the onset

of compression regions. This shift can be seen in the velocity spectra shown in

Figure 5.8., where the PUI spectra at the discontinuity looks just like the normal

PUI spectra shifted in normalized velocity space. The data are taken from the

time period shown in detail in Figure 5.6., where the cutoff shift appears as the

strongest peak in the lowest panel showing supra-thermal PUIs. In Figure 5.6 it

can be seen that this peak in higher energy PUIs coincides with the jump in IMF

magnitude (4th panel). Although these PUIs do have energies exceeding the

nominal cutoff (2V/Vsw), they are not actually a supra-thermal tail, as can be seen

by the velocity distribution in Figure 5.8. A supra-thermal distribution would

show an extended tail, or a hard spectrum, whereas the observed spectral

characteristics show only a shift in energy space. The cutoff shift is most clearly

visible around a magnetic field discontinuity in the compression region on DOY

170, and the spectra just before, during, and just after the magnetic field jump are

shown in Figure 5.8.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10

I 4 o 10' W 7 £ u

LU + 0) X 1000 DOY 170.85 -170.915 P DOY 170.915 - 170.955 --❖ --DO Y 170.955 - 171.000

100 2.5 V /V sw

Figure 5.8. Logarithmic PUI differential energy flux spectra corresponding to three one hour time periods right at the magnetic discontinuity visible in Figure 5.4. The spectrum shifts to the right and returns to its original position in velocity space. The downward arrows show expected cutoff position before and after magnetic discontinuity using an isotropic model of the PUI distribution (see text).

We hypothesized that this phenomenon was due to conservation of the

adiabatic moment v2 l\B\ as the PUI distribution entered a compression region

with enhanced IMF. Consistent with this explanation, such a short term shift was

only observed close to a jump in magnetic field magnitude.

We consider two models of this effect based on the hypothesis, one for a ring

distribution of pickup ions (e.g. the injected population, unmodified), and one for

a distribution isotropic in pitch angle (e.g. assuming efficient pitch angle

scattering). The ring distribution is the simpler model. If the shift is due to

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. conservation of the adiabatic moment it will only affect perpendicular velocity.

Therefore, the maximum PUI velocity shift is predicted for a ring distribution, for

which the shift is: v2 = v, ^ B 2 / 5, .

To find the shift for an isotropic distribution we can integrate the velocity shift

over all pitch angles, where the shift in velocity magnitude for pitch angle a is

given by:

(5.1)

The average shift for the isotropic distribution is thus:

(5.2)

This can be approximated numerically as v 2 ~ v, (B21 B{ )°'4.

The injection speed (in the SW frame) is taken as the solar wind speed [e.g.

Vasilyunas & Siscoe, 1976], The isotropic approximation of adiabatic cooling

from that paper, as described in Equation (2.3), describes the change of PUI speed

as a function of radius. Here we have described the velocity change as a function

of magnetic field magnitude. The isotropic adiabatic cooling rate due the the

expanding volume of the solar wind is recovered from the above analysis only if

the IMF magnitude has inverse cubed or slower dependence on the distance from

the sun. This is a lower power of radius than is expected from the Parker spiral

model of the IMF, however we note that the model described here treats only the

change of PUI velocity due to changing field, and does not include effects due to

the expanding volume of the solar wind or other forces that isotropize the

distribution.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The model described above for heating by magnetic discontinuity of an

isotropic distribution predicts the relative variation between the initial and

compressed (final) cutoff velocities based on the change in field magnitude. The

determination of the initial cutoff velocity reflects the non-zero injection speed of

the PUIs due to the LISM flow, which will be discussed in the next subsection,

while the determination of the final cutoff velocity is taken to be that which

exhibits the same decrease in flux as the initial distribution did at its cutoff.

1.5

1.4

1.3

1.2

1.1

1 1 1.2 1.4 1.6 1.8 2 B2/B1

Figure 5.9. Predicted velocity shift ratios for isotropic (dashed line) and ring distributions (solid line) are shown vs. the corresponding magnetic field compression ratio observed at four compression events (crosses). The magnetic field data is from WIND/MFI and the PUI cutoff shift is observed with SOHO/CELIAS/CTOF. The estimated shifts in 4 observed distributions are shown.

To further test the interpretation the cutoff shift phenomenon at IMF

discontinuities the ratio v^/v; was estimated for four observed magnetic field

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. discontinuities and PUI distribution shifts using the inflection points of

polynomial fits to the spectra (in linear representation). The results are shown for

four compression events (Figure 5.9), including the one shown here at DOY 170,

the trailing edge of the event at DOY 149, and two smaller compressions on DOY

99. The results suggest the isotropic distribution model is more accurate than the

ring distribution, i.e. the distributions are mostly isotropized before the passage of

the discontinuity.

When measuring small shifts in velocity space of the interstellar PUI

distribution, one effect arises that must be taken into account, especially when

comparing data over time scales approaching a year. There can be a PUI

distribution shift due to non-zero injection velocity of the interstellar neutrals.

Upwind Cutoff Shift

The neutral interstellar atoms that are the seed for the pickup ion population

are moving much slower than the solar wind speed. For this reason most simple

models take the injection speed of PUIs to be zero relative to the sun (see

Chapters 1 and 2). However, the non-zero injection velocity of PUIs can be

observable, notably in the upwind portion of the heliosphere. The interstellar

neutral velocity is also enhanced by the gain in speed as the neutral particles fall

into the gravitational potential well of the sun; the resulting speed of a cold

interstellar neutral at 1AU is near 50km/s. This changes the injected ring

distribution of PUIs by making it a larger ring, extending it slightly in the

sunward direction and slightly past the nominal cutoff of V/Vsw=2.0, as shown in

Figure 5.10. As viewed from the solar wind frame and on the upwind side of the

LISM flow, the incoming neutrals have a slightly higher speed than the solar wind

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. speed, therefore the initial ring distribution is wider and goes above the nominal

cutoff.

Sunward

V injection SW

Injected Ring Distribution of PUIs

Figure 5.10. The injected ring distribution of pickup ions is shown for a small but nonzero injection velocity corresponding to the interstellar flow speed. PUIs are present at speeds greater that twice the solar wind speed due to the shift in the distribution.

Despite the small ratio of interstellar neutral velocity to solar wind velocity, the

resulting shift in the pickup ion distribution is visible in in-situ measurements

with SOHO/CTOF especially when the solar wind speed is low [see Mobius et al.,

1999]. Here we extend the analysis by [Mobius et al., 1999] to the entire data set.

To measure the cutoff shift, we compared PUI distributions during time periods of

near perpendicular field to an isotropic model of the pickup ion distribution.

Despite many variations due to changing magnetic field strengths, compression

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. precision measurements of heliospheric and interstellar parameters. This chapter

has emphasized the importance of solar wind compression regions in creating PUI

flux variations. Here our knowledge of compression regions is used to attempt a

detrending of the PUI dataset. While the outcome is far from our goal of an

invariant energy flux dataset, the procedure does reduce variability. A simple

model was used to give a first order measurement of the efficacy of PUI

smoothing based on statistical correlations with solar wind data, and this was

extended to include field orientation and wave power.

We used the solar wind proton density as measured onboard SOHO as a proxy

for the overall compression of the plasma, and compared this to the energy flux of

singly charged helium near the cutoff of the velocity distribution. The scatter is

quite large, but a trend is clearly visible, that higher PUI fluxes are observed

during times of higher proton density. This correlation was described in more

detail earlier in this chapter (see Figure 5.3).

The data points consisting of energy flux in the range range 1.8Vsw < V pui <

2VSw were binned, counting the total number of points in each range of proton

density. The mean in each bin was taken to emphasize the trend to produce

Figure 5.3. The points in this figure were fit to a linear model with the least

squares method.

Each energy flux measurement, taken in the reference range 1.8Vsw < Vpui <

2Vsw was then detrended according to the formula:

F \ t ) = F{t) + a(Np - NP(t )) (5.3)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Here a is the slope of the linear fit, F* is the modified or detrended flux, and N p

is the mean proton density in the dataset. This procedure ensures that the mean

flux will remain the same, while lowering the value during times of high proton

density and raising it during times of lower density.

The detrending of the helium integral energy flux according to a linear fit of

the SW density reduced the total variance by only 7%, bringing the standard

deviation of the 15 minute averages from 52,300 to 48,800 (the average value of

both real and smoothed integral energy flux was 76,721 (cm^sr'V1)). An

example of the original and detrended data is shown in Figure 5.13. Here it can

be seen that the detrened data is more constant, until a spike in the proton density

brings the corrected dataset into negative values. Figure 5.13 illustrates one

problem inherent in such compensation schemes, that correcting for variations in

the proton density will not always make the pickup ion data more constant but can

make it more variable during some time periods.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. distribution is effectively isotropized in the GSE x direction (sunward - anti-

sunward) by Larmor gyration, and the wave-power or pitch angle scattering rates

will not affect CTOF fluxes. For these reasons we consider a detrended PUI flux

defined as:

F* (/) = F{t) + a(NP - N P (0) + b * cos(6>(t)) * (log(PTR ) - log(Pra (/))) (5.4)

Here the coefficient b is determined analogous to the determination of a as just

described. Equation (5.4) corrects a given time series of PUI flux data assuming

linear relationships to proton density and the log of the wave-power.

Including the wave-power dependence reduced the variance of the dataset still

further. The standard deviation dropped to 37,000 crri'sr'V 1, -30% lower than

the deviation of the original dataset. A sample of the detrended data is shown in

Figure 5.14, which is taken from a particularly fluctuating time period previously

seen in Figure 5.7. It can be seen from this figure that the addition of IMF

orientation and wave-power to the correcting procedure (Equation 5.4)

significantly reduces the variance of the He+ flux data. However, there are still

substantial variations in pickup ion fluxes even after correcting the dataset using

proton density, wave-power, and IMF orientation.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Conclusions

The CTOF measurements of He+ pickup ions show strong correlations with

solar wind parameters, especially the proton density. This is perhaps not a

surprise; one would expect conditions that compress the bulk solar wind to

compress the PUIs contained in the wind. The observed correlation with IMF

magnitude was similar in character to that of the proton density, pointing to a

similar cause for these two correlations. This could also explain Ulysses

observations which show correlations between helium and hydrogen PUIs despite

the differing ionization processes involved in injecting the two species in the solar

wind [Gloeckler et al., 1994], although for the time periods considered in that

paper correlations were not found with bulk SW parameters. The observations

here are consistent with the hypothesis that compression regions are responsible

for many of the PUI flux variations, with IMF orientation and velocity

distribution anisotropies also playing a role.

The compressions not only enhance the overall flux, but change the shape of

the distribution, most notably in an enhancement near the injection velocity in

compressed regions. The observations are consistent with the compression

compensating for some of the adiabatic cooling of the PUIs, thus keeping their

speeds close to V sw in the solar wind frame (2 V Sw in the spacecraft frame). The

observed velocity shift due to magnetic discontinuities can be explained with

adiabatic effects. Further work is needed to model this effect more fully and

interpret its influence on different distributions or in different solar wind

conditions. However, strong shocks are known to affect PUI distributions in other

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ways, including heated electrons increasing the ionization. It could be that

something similar takes place in compression regions, contributing to the still

unexplained enhancement near the cutoff.

We also find PUI flux variations due to the location of the spacecraft in the

heliosphere, even outside the focusing cone. The upwind cutoff shift is due the

non-zero injection velocity of the interstellar neutrals, and this effect can be used

to estimate the LISM motion.

Finally, although we have found that many of the pickup ion flux variations

can be explained with compression regions and bulk effects, a number of PUI flux

variations, visible in both individual events and in statistical analyses, do not

conform to the simple models of solar wind compression. Even when the now

explained PUI flux variations are compensated for, substantial variations are

visible that still await an explanation.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 6

PUI WAVE-PARTICLE INTERACTIONS

In which our pickup ions are jostled and scattered by oscillations o f the IMF, leading to observations o f phase space scattering and diffusion in both pitch angle and energy.

In Chapter 5 the power in fluctuations of the IMF was used to correct PUI flux

data and reduce the variance. Here the relationship between the PUI distribution

and magnetic field wavepower is studied in more detail.

Pitch Angle Scattering by Waves

Magnetohydrodynamic waves play an important role in energetic particle and

pickup ion transport. AlfVenic (transverse) fluctuations can act as pitch angle

scatterers in the wave frame, which is important for particle transport processes

such as the modulation of cosmic rays. It has been assumed that diffusive

transport and diffusive shock acceleration are dominated by magnetic field

fluctuations [e.g. Skilling 1971, Lee & Volk 1975]. Quasi-linear theory uses the

assumptions of small fluctuations and resonance to calculate pitch angle diffusion

coefficients due to different types of waves in the solar wind (SW) [e.g. Jokipii,

1972 & 1974; Schlickeiser 1998]. While theoretical descriptions of such wave-

particle interactions abound, until now there had been no direct experimental

verification of a correlation between the power in the fluctuations and the strength

of observed transport effects. Because of their well defined initial distribution,

pickup ions provide a tracer for such transport.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Interstellar neutral helium enters the heliosphere and is ionized predominantly

by solar ultraviolet radiation. The resulting PUIs are then convected outwards

through the heliosphere with the SW, subject to such wave-particle interactions.

Long before the first in situ detection of interstellar PUIs [.Mobius et al., 1985], a

number of wave-particle effects had been suggested which could influence such

ions [e.g. Jokipii 1972]. The treatment of PUI evolution in the solar wind by

[Vasyliunas & Siscoe, 1976] is based on the assumptions of complete

isotropization of the distribution. Detailed models of the evolution of this

population have been devised [Isenberg, 1997, Schwadron 1998, Zank & Pauls

1997] which assume pitch angle diffusion by SW magnetic turbulence. The

helium is injected (picked up) at a speed slow compared to the solar wind speed,

and is created from the presumably constant interstellar neutral density, creating a

ring distribution in velocity space. This well known initially anisotropic

distribution of injected interstellar PUIs allows the study of their isotropization by

pitch angle scattering, where other less well known or more isotropic initial

populations (e.g. cosmic rays) would not permit such quantitative analysis. As

part of the research in this dissertation, we compared in situ PUI velocity

distributions with concurrent measurements of IMF wave power.

Wave Parameters

We used Fourier analysis in mean field coordinates to determine

components of the power spectrum distribution of IMF variations as observed by

WIND/MFI. The frequency range considered is from 0.002 Hz. to 0.16 Hz (the

Nyquist frequency for the 3s public MFI data). It is not possible to uniquely

identify frequency and wavevectors with only a single spacecraft, so this range of

frequencies is used as an indicator of resonant wave power. The typical He+

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. gyrofrequency in the SW is 0.015 Hz (2 nT) to 0.15 Hz (20 nT). For other details

in spectral decomposition of IMF vector measurements, see Chapter 3.

The power spectrum was computed for each contiguous 15 minute period in

the dataset, and each component was fit to a power law with the least squares

method. A sliding principal axis coordinate system was used to determine each

power spectrum distribution. The principal axes for each 3s field vector were

calculated using a 15 minute sliding mean field direction B . The z component is

chosen along the mean field, x along Ixf, and y along Bx(Bxr) [Belcher &

Davis, 1971]. We consider here two components of the spectral matrix, the power

in the z direction ,PZ , and the transverse power PTR - P(\Jx^ + y^). Pz is the

power in parallel (or compressive) fluctuations and PTR is the power in

perpendicular (or transverse) fluctuations [Matthaeus & Smith, 1981]. The

quantities Pz and PTR are taken from the power law fit, and are thus affected by

wave power over the entire frequency range considered. The numerical value

used for comparison is the value of the power law fit of the spectral component

evaluated at 0.1 Hz.

PUI Parameters

Helium PUIs are injected with a speed much less than the SW speed; they are

traditionally expected to scatter into a sphere in velocity space quickly, generating

a distribution with a sharp cutoff at V=2VS\v hi the spacecraft frame [e.g.

Vasyliunas & Siscoe, 1976]. However, slower pitch angle scattering rates

produce distributions that differ from this expectation, in particular during times

of near radial IMF. The PUIs are initially injected into the sunward hemisphere in

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. velocity space. If the IMF is near radial, injected PUIs must be pitch angle

scattered to enter the anti-sunward hemisphere (in the solar wind frame). This

leads to reduced PUI fluxes in this hemisphere during times of radial IMF, as has

been reported by [Gloeckler et al. 1995] and [Mobius et al. 1998].

PUIs ionized at smaller heliospheric radii have more time to be scattered, but

are also adiabatically cooled in the expanding solar wind and so will be observed

at a lower energy. The PUI velocity distribution is thus different for cases of near

radial and near perpendicular field, the perpendicular case exhibiting a much

sharper cutoff, with the two distributions approaching each other for lower

velocities in the solar wind frame. Therefore, a good proxy for the strength of

PUI pitch angle scattering during times of near radial IMF is the integral energy

flux in the range near the cutoff velocity 1.8 < V /V sw < 2.0 (in the spacecraft

frame), which we call here for simplicity He+c-

The CTOF aperture points sunward, with an opening angle of 50°, thus

sampling is done in the anti-sunward hemisphere of the PUI velocity distribution

in the spacecraft frame. This should allow sampling of all interstellar PUIs which

in the SW frame have speeds between -Vsw and Vsw- However, the collecting

power of electrostatic analyzers scales strongly with the ion energy, which

reduces the detection efficiency of PUIs at the low energy end. In addition, it is

difficult to separate PUIs from the solar wind at energies near that of the bulk SW.

In practice we consider here only PUIs with > Vsw in the spacecraft frame, or

Vn > 0 in the SW frame, which translates to preferential detection of PUIs in the

antisunward hemisphere in the SW frame. This selection results in the observed

reduction of flux during times of radial IMF [Gloeckler et al. 1995, Mobius et al.,

1998], as the PUIs start in the sunward hemisphere, and must be pitch angle 75

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. time periods of near perpendicular field corresponding with high PUI flux (He+c)

as expected [e.g. Moebius et al., 1998]. However, the transverse wave power (3rd

panel) is also changing by over an order of magnitude, and could also be

correlated with He+c. It is difficult to see in this figure the separate effects of a

dynamic IMF orientation and a dynamic wave power on the PUI distribution. To

distinguish between these effects, we pursue a statistical approach.

-1------1------11 "1 ■■ "T— - " " i r— 1— ■t -*— f------r '" " " " 'i ------'-"p-^ _

a . 4

CO 3T 0 • dooO •0 Vp* 00 50 O o n O* _0° oo o6 J* ^ O 0 O ,o° ^ o ° * % <% XJ O - o ‘O , v> > • * 0 m 10 § D O n. t o r , 151 a> o° to* B°a p D 0*6 ‘b 0 n af5-6 d ? 130 „ n a-u™ % J . D o “Q_n - ua dd □ plJonA m -2 a o° □ n D # a a S 0 n ttjJj uo ua u iPm ao D0 “ -2.4 , H % a. “ “ YhoDtFm 710 H (- H 1 H I nl l-H +■---1----

x 31q‘

♦

82.20 82,60 83.00 83,40 83.80 DOY (days)

10000 20000 30000 40000 50000 Diff. EFlux (1/cm*2/s/sr)

Figure 6.2. Dynamic PUI energy flux spectra from SOHO/CTOF (bottom panel) and related SW data for day of year 82.2 - 84.2 in 1996. 1st panel: proton density from'SOHO/MTOF/PM. 2nd panel: IMF angle to radial. 3rd panel: log|0 of transverse wave power (B2). 4th panel: He+ integral energy flux density near cutoff velocity (see text). The normalized velocity is on the vertical axis, with the expected cutoff at V/Vsw=2 shown with a dashed line.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Statistical Correlations

To see whether there is a quantitative correlation between the wave power and

the PUI distribution, we use Pearson’s correlation coefficient [e.g. Richardson &

Paularena, 2001] to correlate the PUI and wave parameters. For two variables

X i and Yi, with n values that change over time with the i index, and have

averages X and Y , the correlation coefficient is defined:

I (X -X)(Y -Y) - 1 = 0 _ (61) n _ 0 n _ 0 z (X -X )1- z (Y -Y)2 ]ji = 0 j 0 =1

This coefficient can vary from -1 to 1, for perfectly anti-correlated variables to

perfectly correlated variables. We also want to determine the uncertainty for a

calculation of this coefficient. The correlation is not normally distributed,

however its normally distributed transform (“Fisher’s z”) is within 1% of the

correlation r for r < 0.3. For such correlations we take a statistical uncertainty

equal to the standard deviation of that function [e.g. Freund, 1962]:

Ar s yll/(n-3) ^ ^

Statistical correlations of PUI fluxes and wave power are shown in Table 6.1.

As in Figs. 6.3 & 6.4, only events during which the SW proton density was <15

cm' 3 were included. . The strongest correlation is observed between the energy

flux of He+ near the cutoff (He+c ) and the transverse power in IMF fluctuations

(P tr). The range of He+c is from 1.8 < V/Vsw <2.1. The correlation is calculated

using data from all IMF orientations in Column 1. This correlation coefficient

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. increases when only periods of near radial field are considered (Column 3), and

decreases in near perpendicular IMF (Column 2). The important result is the

significant difference between the correlation coefficients in the radial and

perpendicular cases. The correlation even disappears in perpendicular fields, for

the case of parallel wave-power. This is again consistent with pitch angle

scattering by IMF waves isotropizing the distribution in radial IMF. However, the

Table 6.1. Wave/PUI parameter correlation coefficients

(r) He+C He+C - (Perp.) He c - (Par.)

PTR 0.19 ±.01 0.12 ± .03 0.21 ± .06

Pz 0.14 + .01 0.00 ± .03 0.19 ± .06

Second column includes only IMF within 80°- 90° from radial; the last column within 0° - 10° from radial.

This statistical correlation can also be made visible in a plot of helium fluxes

versus wave power. Observed fluxes near the cutoff velocity (from 1.8 to 2.1

times the solar wind speed in the spacecraft frame) are shown for radial and

perpendicular IMF respectively in Figs. 6.6 & 6.7. Fifteen-minute flux averages

were taken of this quantity He+c (y axis), and binned in the mean value of the

transverse wave power or PTr ( x axis) during those times. The error bars

represent the statistical variation of the mean energy flux for each transverse wave

power bin, i.e. the statistical error in determination of the mean from the samples

in the histogram. The visible trend of increasing flux near the cutoff with

increasing resonant wave power is consistent with a decreased anisotropy due to

pitch angle scattering by resonant waves.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SOHO/CTOF He+ EFIux in Parallel IMF (0°-10°) 10

‘ Li CN(A E _o_ 104 3X U. 104 a> X

0 -3.5 3 -2.5 2 1.5 1 -0.5 lg(P ) (WIND/MFI) TR Figure 6.6 Average helium PUI energy fluxes during times of IMF in near radial or parallel to Vsw are shown binned in different powers transverse resonant wave power. Only flux near the cutoff velocity (1.9 < V/Vsw < 2.1) is included. The trend of more PUIs present near the cutoff velocity for greater transverse wave-power is visible.

SOHO/CTOF He+ EFIux in Perpendicular IMF (80°-90°) 1.4

1.2

j n

E X 3 U. Ill + 0)

o -o o

-3.53 -2.5 2 1.51 -0.5 0 lg(PTR) (WIND/MFI)

Figure 6.7 Average helium PUI energy fluxes during times of IMF near perpendicular to Vsw are shown binned in different powers transverse resonant wave power. Only flux near the cutoff velocity (1.9 < V/Vsw <2.1) is included. The flux near cutoff is mostly flat over two orders of magnitude in wave-power, consistent with isotropic injection and no dependence on pitch angle scattering for perpendicular fields.

The last two data points in Figure 6.7 show an increase in PUI flux for the

highest transverse wave-powers, even in perpendicular IMF. The reason for this

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. increase is not known at this time, although it could be that in compression

regions both PUI fluxes and wave-powers are higher.

Preliminary Conclusions

The observed correlations of PUI fluxes at the cutoff and IMF wave power as

presented so far provide compelling evidence for pitch angle scattering due to

wave - particle interactions. While this scattering has a strong theoretical

framework, the observational evidence had so far had been limited. These studies

give both qualitative and quantitative evidence of PUI isotropization by transverse

IMF waves.

However, these studies do not provide direct evidence of the scattering

mechanism. In particular, the wave vectors have not been identified, and so

counter-propagation, resonant and/or non-resonant scattering, or other effects

could be involved. The data is also limited in time, being taken during solar

minimum in slow SW. It is possible that the observed correlation will change in

SW with different flow and turbulent properties. The observed correlations with

wave power at speeds closer to the bulk of the PUI velocity distribution (i.e. 1.6<

V/Vsw <1-8 could be due to the correlations between PUI fluxes and proton

density or field strength, as wave power is statistically correlated with these

parameters as well.

To study further the pitch angle scattering due to wave-particle interactions,

we must model more completely the diffusive process - including not only a

finite diffusion coefficient but a diffusion coefficient that is not constant but a

function of pitch angle.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Hemispheric Model of Pitch Angle Diffusion

We consider here an anisotropic model of pitch angle scattering, in which

pickup ions are expected to scatter quickly in either hemisphere of velocity space

but scatter diffusively across the perpendicular (90 degree pitch angle), following

[Isenberg, 1997]. The idea behind this model is that a particle at 90 degree pitch

angle cannot be in resonance with transverse parallel propagating waves. This is

referred to as the “resonance gap”, and particles are only scattered through this

barrier by changes in mean field or non-resonant interactions.

The condition that a wave is in resonance with a proton is (Eq. 2.7):

(o - = -D c/) (for parallel propagation we need only consider the first

harmonic). A particle at 90 degree pitch angle (v|( = 0) is therefore in resonance

only with waves whose frequency co = -ClCP, where no wave power is present due

to ion-cyclotron damping.

In fact, a resonance gap can exist for more complex cases including other

modes of wave propagation and some kinds of turbulence [e.g. Ng & Reames,

1995; Schlickeiser, 1998; Isenberg et al., 2003]. The details of this interaction for

the case of helium depend on the dispersion relation of the waves in question,

where the power is present in co and k space, and where the dispersion relation

intersects the helium resonance condition: co - ^ = -ClCHe [see e.g. Dusenbury

& Hollweg, 1981]. If we consider parallel propagating AlfVen waves at

frequencies including the proton gyrofrequency (ion-cyclotron waves) [e.g. Stix,

1992] the dispersion relation can be written as:

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. From Figure 6.8 it can be seen that any helium ion (any parallel velocity) can

be in resonance with a finite wave-number k, provided that power is present in all

four quadrants. This is not the case for proton resonance, for which the lines

would intercept the vertical axis at -Q CP creating a resonance gap at v([ = 0 .

However, it can also be seen that a parallel velocity exists for which helium can

no longer be in resonance with outgoing waves. Because more power exists in

outward modes at 1AU, a particle reaching such a parallel velocity will have a

lower chance of begin scattered. This parallel velocity will be on the order of the

AlfVen speed.

Because Vsw » VA , and the pickup ion is injected in the plasma rest frame with

velocity Vsw, it’s speed |v| is also much greater than the AlfVen speed. From this

it can be seen that the pitch angle as the particle leaves resonance with outward

propagating waves is near 90 degrees, as /u = Vy «Vy v «1. For this reason ' v / ' sw

we assume the first order anisotropies of pickup helium can still be described with

a hemispheric model.

The Fokker-Planck pitch angle diffusion coefficient is in general a function of

pitch angle, and for the case of resonant wave-particle interactions with parallel

propagating waves, this coefficient tends toward zero for pitch angle a = 0 , or

fj. = cos(a) = 1 [see also Jokipii, 1972 & 1974], The precise dependence of pitch

angle scattering rates (and all Fokker-Planck diffusion coefficients) on the

magnetic field fluctuation spectrum has been the subject of much theoretical work,

mostly in terms of the application of quasi-linear theory [see e.g. Hasselmann &

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Wibberenz, 1968; Jokipii, 1972; Schlickeiser, 1994; Ragot, 1999; Isenberg et al.,

2003]. The form of the dependence depends on the type of fluctuations which

cause the scattering, and many authors choose different combination of wave-

modes or correlation scales when calculating diffusion coefficients. However, a

simple model predicts a linear dependence of pitch angle diffusion on the wave-

power [Fisk et al., 1974], These authors arrive at an expression for the pitch angle

diffusion coefficient:

(6.4)

where PL is the transverse wave-power, v is the particle speed, s = Xc/rg is the

ratio of the correlation length of the field fluctuations to the particle gyroradius,

and t) is the ratio of the mean square field strength to the mean field strength

squared. Although many problems with the derivation of Equation 6.4 are

addressed in [ Fisk et al., 1974], the linear dependence on wave-power can be used

as a starting point for the predictions of quasi-linear theory [e.g. Jokipii, 1972],

The motivations and the transport equations for a hemispheric distribution

were presented by [Isenberg, 1997]. The pitch angle diffusion coefficient is

treated as an inverse delta function in pitch angle space, being infinite everywhere

except at p = 0 where it is a constant. This effectively reduces the problem to a

first order anisotropic treatment, dividing the PUI distribution function into two

hemispheres in velocity space, where fast scattering leads to isotropy in each

hemisphere. We follow the procedure outlined therein which arrives at

expressions for the normalized pickup ion distribution functions in the anti-

sunward and sunward hemispheres. The model is modified when appropriate for

our consideration of singly charged interstellar helium PUIs, assuming that a

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. resonance gap or a decrease in scattering rate occurs near // = 0. Remarkably, an

analytic solution exists which can be expressed as an integral of Bessel functions,

for the case of radial magnetic field. The distribution in the anti-sunward

hemisphere takes the form:

^ /j 2 r\ i 2q f ( w,r) = JT4 3/2 exp(-oD) f N[rwV2 exp(z- a)]J{){<4>)dz (6.5) SttU rw i

Here J30 is the ionization rate at rQ, D is a dimensionless scattering parameter

representing the cross-hemispheric diffusion rate, w is the normalized velocity

v/vsw, r is the heliocentric distance, a = 3(\-w)/4, and the argument

O = [z(2a - z)(l - D 2 )]1/2. The inflowing neutral particle density N[r] considered

in [Isenberg, 1997] was that of hydrogen, for which the radiation pressure nearly

balances the gravitational force. We use here the appropriate numbers for

consideration of upstream insterstellar helium, the ionization rate at

1AU /?0 =3.0* 10 '8 s'1, and the cold model for the neutral density:

(6.6)

Here we have assumed that radiation pressure does not influence the trajectory of

the incoming neutral helium atoms. It is important to note that this model

includes not only the effects of pitch angle scattering between the two

hemispheres, but also convection terms including adiabatic focusing due to the

diverging magnetic field. This focusing can act to bring particles from one

hemisphere to the other even in the absence of waves [Isenberg, 1997].

The hemispheric model was compared to PUI data from SOHO/CTOF taken

during times of near radial IMF, and for several different ranges of resonant

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. observed in the best fit to data hemispheric diffusion coefficient in Figure 6.11.

The quasi-linear pitch angle diffusion coefficient is clearly of a different character

than that of the hemispheric model. However, their comparison could shed light

on the differences of the theories and help interpret observations of pickup ion

pitch angle transport. Because it is not clear which wave modes are responsible

for the bulk of cross-hemispheric diffusion, or which wave vectors have been

observed with a single spacecraft, it is difficult to compare these results with

quasi-linear theory.

The large mean free path for cross-hemisphere scattering derived from the

observations is not unreasonable. PUI anisotropies observed at 1AU [Mobius et

al., 1998] and further out in the heliosphere [Gloeckler et al., 1995] suggest pitch

angle scattering mean free paths on the order of an astronomical unit. This

analysis shows (hemispheric) pitch angle scattering mean free paths that do not

average below two tenths of an AU even at the highest wave-powers. We also

find mean free paths as large as six AU for the case of the lowest wave-power.

Conclusions

The comparison of SOHO/CTOF pickup ion data and convected WIND IMF

fluctuation data with the hemispheric model gives compelling qualitative and

quantitative evidence that the hemispheric model and wave-particle scattering

provide a good picture of PUI transport in the inner heliosphere. Application of

the model allows a measurement of the functional dependence of pitch angle

diffusion coefficients on wavepower. However, many questions are left to be

answered. In particular, the exact form of the relation of the scattering parameter

or mean free path to the wave-power as observed in Figure 6.11 remains

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. unexplained. The nature of interactions that scatter pickup ions across the

resonant gap is not specified, though the reliance of such an interaction on IMF

fluctuations is clear. The applicability of the hemispheric model to other IMF

orientations has also not been demonstrated here. There is much room for further

work in the arena of PUI pitch angle scattering models which extend this result to

more general transport regimes.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 7

ENERGY SPACE DIFFUSION

In which our pickup ions are accelerated, by the geometry and oscillations o f the IMF

In Chapter 6 measured PUI distributions were compared to a transport model

based on Equation (2.3), and considering only the pitch angle diffusion term. We

now consider diffusion in energy space as well.

2nd Order Fermi Acceleration

It has been suggested [e.g. Fisk, 1976] that energy diffusion of ion velocity

distributions is enhanced by the presence of magnetic field fluctuations. Although

the details vary, and such phenomenon are described by a number of names (e.g.

transit time damping, 2nd order Fermi acceleration, statistical acceleration), the

basic concept is similar. Particles can gain or lose energy in a scattering process

in which there is an electric field parallel to the particles motion. While the bulk

of these particles will gain and lose energy equally, some individual particles will

continue to gain energy and become part of the high energy particle population.

A variety of theoretical work has been done on the problem of pickup ion

transport and related acceleration by waves and the details of scattering

mechanisms [e.g. Isenberg, 1987, Bogdan et al. 1991], but the experimental

record in the solar wind remains thin, especially in comparison to the evidence of

shock acceleration. Nonetheless, the observation of suprathermal tails in PUI

populations even in quiet solar wind suggests that a 2nd order Fermi or stochastic

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. acceleration mechanism is at work [Gloeckler, 2002], while numeric simulation

has shown that such mechanisms could explain these observed tails [e.g. Chalov

& Fahr, 1998 & 2002], Further studies of PUIs near CIRs with Ulysses observed

enhanced supra-thermal tail during times of strong IMF fluctuations, again

suggesting a statistical acceleration mechanism [Gloeckler et al., 1994;

Schwadron et al., 1996].

Observations of Accelerated PUIs

The CTOF dataset shows clear evidence of acceleration or energy space

diffusion of the PUIs after their injection into the solar wind. For example,

logarithmic energy flux density spectra are shown in Figure 7.1. In this figure the

CTOF average is compared to a time period from the dataset with the most

prominent acceleration beyond the PUI cutoff velocity. During that time period

the spectrum is nearly flat across the instrument energy range, and the expected

cutoff at twice the solar wind speed is not visible. This period showed the largest

flux of PUIs at speeds above the cutoff velocity observed, and was related to the

passage of an interplanetary shock discussed later in this chapter.

In addition, even in the time averaged spectra there is clear acceleration visible

in the form of a supra-thermal tail. This tail is clearly observed up to three times

the solar wind speed, suggesting that acceleration mechanisms are at work, as this

is far above the cutoff including the bulk flow and the thermal velocity of

interstellar neutrals.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SOHQ/CTOF He

X 1000

o CTOF Average 100 □ DOY 99.02-99.09

1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 v/v SW Figure 7.1. Pickup ion velocity spectum and suprathermal tail. The energy flux density during the strongest acceleration region (squares) and for the the whole dataset (circles) are shown logarithmically versus normalized velocity.

To work towards identifying the origin of this tail, we used further statistical

analysis of the dataset. The first step was to remove the times during which shock

acceleration was clearly playing a role in generating the higher energy PUIs. By

using a list of interplanetary shocks published by the WIND spacecraft team [see

Lin et al., 1995], and maintained by the Berkeley Space Physics Research Group,

we removed all time periods around these shocks, and compared this to the

spectra obtained by only including shocked solar wind (or time periods near an

interplanetary shock). The results are striking as the differences in the supra-

thermal tail span almost two orders of magnitude, as seen in Figure 7.2. From this

figure the efficiency of acceleration by shocks is clear, as predicted by generally

accepted models of shock acceleration, or 1st order Fermi acceleration. Shocks

are responsible for most of the energetic particle populations, and in this process

particles with initial speeds greater than the bulk solar wind speed are

preferentially injected [Blanford & Ostriker, 1978; Lee, 1984; Zank et al., 2001].

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. t | i i i | i i i | i i i | i i i | i i i | i i r

104 O O, O -gi $5 G 'ui

C\lw 1000 \Vl*% E u X E 100 LU + Q> X 10

1 J I I I I I I 1 I I 1 I I I I I I I I I ill 1.8 2 2.2 2.4 2.6 2.8 3 V/Vsw Figure 7.2. Pickup ion velocity spectum and suprathermal tails are shown for three different sets o f solar wind conditions. Times within one hour of a shock (from the WIND shock list) are shown as diamonds, times within six hours of a shock are shown as squares, and times that are not within twelve hours o f a shock are shown as circles.

In addition to shocks, strong 1st order Fermi acceleration is predicted to occur

in compression regions [Giacalone et al., 2002]. There were some strong

acceleration regions visible in the PUI data that did not correspond to WIND

shock list events. This can be seen in Figure 7.3, where after removing time

periods of known shocks the spectrum becomes softer. Removing other time

periods of pronounced PUI acceleration makes the spectrum still softer. The

difference in the overall averaged spectra produced by these non-shock events is

not large, but is significant, and is consistent with the theory that 1st order Fermi

acceleration does occur in compression regions that have not steepened to form

shocks.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SOHO/CTOF) are not always associated with the strongest compression ratios (r)

of shocks or compressions.

Two criteria, the maximum intensity I m a x , defined as the largest flux at speeds

above the nominal cut-off over a 15 minute time period, and the total supra-

thermal energy flux E t o t , defined here as total energy from PUIs at speeds above

the cutoff over the entire event, are listed for each event in Table 7.1. In the table

it can also be seen that most PUI acceleration events were observed offset in time

from the arrival of a change in proton density. Many other parameters are not

listed in the table, for example the steadiness of the acceleration and the IMF

properties.

100

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 7.1. The Largest Helium PUI acceleration events observed by SOHO/CTOF.

DOY WIND Duratio Offset E tot I m a x r(NP) Comments (1996) shocklis n (hrs) (hrs) t 93.42 Yes 1.8 -1.2 6007 3280 1.7 SIR 94.38 Yes 4.1 -0.5 246473 59874 1.4 See Figure 6.9 99.08 Yes 3.1 -0.4 974735 318462 2.0 See Figure 6.10 99.53 No 5.8 0.4 250422 94602 2.3 See Figure 6.10 150.47 No 7.9 n.a. 428077 76953 n.a. No shock 170.95 Yes 6.0 4.8 574493 76484 4.2 Magnetic Cloud 174.50 No 4.3 n.a. 133883 37043 2.0 No shock 183.55 Yes 10.1 -3.4 846962 55421 1.7 Magnetic Rotation

185.76 No 0.3 0.0 74872 74872 0 Normalization relic- see text 198.15 No 9.6 -4.8 331685 59822 2.5 Compressions before & after 210.49 Yes 7.4 -1.2 1099514 213598 2.2 See Figure 6.11

212.72 No 7.4 -3.7 1684996 113210 0 . 8 Radial field. Possible SIR 225.88 No 9.4 -2.4 813849 78559 3.0 Radial field. SIR. 1st column: day of year 1996 of the shock or compression as observed in SW proton data. 2nd column: event listed on the WIND interplanetary shock list? 3nd column: duration of observed accelerated PUIs. 4th column: the offset in time from the center of PUI acceleration to the SW disturbance (n.a. if exact disturbance time unclear). 5th column: total energy flux for VHe >2.2Vsw (keV cm"2 sr'1) during event. 6lh column: peak 15 min. average VHE>2.2VSw energy flux density during event (keV cm'2 s"1sr I). 7th column: compression ratio for proton density.

To see the details of the solar wind conditions that underlie a PUI acceleration

event, it is necessary to show more parameters than are visible in Table 7.1, and to

see the time evolution of the event as observed with SOHO and WIND in bulk

SW data as well as PUI spectra. For example, the parameters E t o t and I m a x

indicate not only the acceleration rate but also the number of PUIs available to be

accelerated. Although some effort was made to normalize these parameters to the

bulk PUI flux, the large variations of bulk flux observed around acceleration

regions made the normalization less useful.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Three strong acceleration regions are included here as Figures 7.4, 7.5, and 7.6,

in which the relation of the bulk PUI fluxes to high energy fluxes can be

compared. The PUIs observed by SOHO/CTOF are in the bottom panel of these

figures and are shown as grayscale energy spectra with normalized velocity on the

y axis. Other acceleration times are not included in this thesis but interested

readers can find them in the PUI catalog produced as part of this dissertation work,

currently available at:

ftp://www-ssg.sr.unh.edu/pub/lsaul/catalog.

In Figure 7.4, a shock can be seen in the SW speed (top panel) and the proton

density (second panel). The helium pickup ion spectrum shows acceleration

around the shock, but is not centered around the shock but rather exists

predominantly before the passage of the shock. Additional PUI acceleration is

seen four hours before the shock arrived at the spacecraft.

The most intense acceleration in the dataset I m a x , defined here as the largest

flux at speeds above the nominal cut-off over a 15 minute time period, was

observed around an interplanetary shock at DOY 99.08. The duration of that

acceleration was only 3.1 hours, and the color-coded spectrum is shown as a

function of time in Figure 7.5. The strongest total supra-thermal flux E t o t ,

defined here as total energy from PUIs at speeds above the cutoff over the entire

event, was observed around a compression at DOY 212.72 (Figure 7.6), although

the maximum intensity of that event was a factor of three smaller than the DOY

99.08 event.

102

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 440 -£• 420 400 MTOF-PM = 380 = •360 . *340 ^ 320

WIND-MFI

I I I I I I ii iii 11' 11

SOHO-CTOF

> to./-rfbAUVAflC * *3 ’•

x m z i

94.10 94.30 94. SO 94. 70 94.90 DO Y (days)

I------T 20000 30000 40000 30000 Diff. EFIux (1 /nm A2/s/sr)

Figure 7.4. An interplanetary shock as observed by MTOF/PM (solar wind proton data), WIND- MFI (magnetic field), and CTOF (helium PUIs). From the top, the panels show: SW speed, proton density, proton thermal velocity, IMF magnitude and radial component, IMF wave power transverse and parallel to the mean field. The velocity spectrum of He+ is shown in grayscale on the bottom panel, with a horizontal dashed line at the nominal cut-off velocity. Accelerated PUIs are observed before the arrival o f the first shock (dashed line).

103

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. MTOF-PM

* 20

WIND-MF - ' 1111

SOHO-CTOF

W> ¥

99.10 99.30 99.50 99.70 99.90 D O Y (days)

i r I I I I I I I I 10000 20000 30000 40000 50000 60000 Diff. EFIux (1/em *2/s/sf)

Figure 7.5. Two interplanetary shocks observed on April 8, 1996. For panel descriptions see Figure 7.4. The first shock corresponds to the most intense (see text) tail EFIux in the dataset, which appears before the compression of the bulk PUIs visible in the bottom panel.

104

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. MTOF-PM

m o L1111111 lFi 11,11 ii^'iTm TTj i ^ i

SOHO-CTOF

210.00 210.20 210.40 210.60 210.80 D O Y (days)

0 20000 40000 60000 Diff. EFIux (1/emA2/s/sr)

Figure 7.6. A SIR, shock, and associated strong PUI acceleration as observed on July 28, 1996. For panel descriptions see Figure 7.4.

Figures 7.4-7.6 and Table 7.1 show that PUI acceleration does not behave in

an easily predictable manner, and depends on effects not usually included in

105

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. simple shock acceleration models. More work is necessary to determine shock

geometries and histories that determine such acceleration in order to more

accurately predict energetic particle populations around interplanetary

disturbances. However we have attempted a statistical evaluation to determine

whether the tails, after a subtraction of the known acceleration events, correlate

with wave activity.

Acceleration by IMF Fluctuations and Waves

To determine the extent that 2nd order Fermi processes are effective on the

accelerated PUI population observed by CTOF, we first duplicated the analysis

for 1AU that had been performed in CIRs with Ulysses [Schwadron et al., 1996].

We used 15 minute magnetic field averages to determine the relative level of

fluctuations of the magnitude of the IMF, comparing them to the sliding 12 hour

mean field. We follow [Schwadron et al., 1996] and call the level of fluctuations

determined in this way eta:

\b - b \ ’ = V <7i)

We then binned helium energy flux spectra in different ranges of this parameter to

see what the effects of relative fluctuations are on the supra-thermal tails. The

results are shown in Figure 7.7.

106

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. require. To examine the specific effects of resonant wave power we pursued a

separate analysis designed to specifically capture resonant wave power.

We examined logarithmic PUI flux spectra obtained by combining times of

similar background wave-powers as determined with three second data from

WIND in a superposed epoch analysis. The determination of the wave spectra by

minimum variance analysis was identical to the analysis described in Chapter 6 as

related to determination of pitch angle scattering. Times within 12 hours of a

shock (as determined by the published WIND shock list) were excluded from the

spectra, in order to isolate the effects of resonant wave-particle interactions from

those of shock acceleration. The results are shown in Figure 7.8, where three

spectra are shown for different ranges of resonant transverse wave-power.

108

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. index of the diffusion coefficient in attempts to observe a correlation with PUI

supra-thermal tails. The index used was calculated as:

D'yyjl^-^aDyy {12) np

where the star indicates that this is not an actual calculation of the momentum

diffusion coefficient but merely a proxy, differing from the actual value by an

undetermined factor a which could be a function of pitch angle as well as other

quantities involved.

While the wave-power is the active mechanism for scattering the particles (in

energy space), other parameters affect the diffusion coefficient as it is calculated

in the literature [Wibberenz et al., 1969, see also Mobius et al., 1982; Chalov &

Fahr, 1998], such as the magnetic field strength and the proton density. We

repeated the superposed epoch analysis, removing shocks from the WIND shock

list as before, using this proxy instead of just the transverse resonant wave-power

Ptr. The results, which are shown in Figure 7.10., still did not show different PUI

spectral characteristics for different ranges of the momentum diffusion index.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The solar wind speed itself is also a potential indicator of 2nd order Fermi

acceleration by IMF waves, as in slower solar wind the PUIs have more time to

diffuse in energy space. Thus, one might expect stronger supra-thermal tails to be

observed during times of slower solar wind speed. To look for this effect, a

superposed epoch analysis was performed on the PUI normalized velocity

spectrum. The resulting spectra again showed a null result, in that the PUI spectra

for different ranges of Vsw showed almost identical shape.

Conclusions

Strong acceleration of interstellar pickup ions was observed on numerous

occasions by SOHO/CTOF, the strongest of which were tabulated in Table 7.1.

Almost all of these time periods corresponded with the passage of an

interplanetary shock. However, the characteristics of the shocks (such as

compression ratio) were poor predictors of the PUI acceleration characteristics.

This suggests that the simple planar and time independent models of interstellar

shocks are not accurate enough for predicting detailed time profdes and energy

characteristics of high energy particle populations. Acceleration was also

observed during compression regions which had not steepened to form a shock,

confirming the idea of 1st order Fermi acceleration by compressions presented in

[Giacalone et al., 2002].

The presence of supra-thermal tails during quiet interplanetary conditions was

also observed, though at greatly reduced levels. Initial analysis suggested that

IMF fluctuations were correlated with these tails. However, PUI spectra obtained

through two and a half orders of magnitude in resonant wave-power showed

similar high energy tails. Other analyses of the AlfVen speed to solar wind speed

113

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ratio and the solar wind speed itself showed only small changes in the He+

velocity distribution. We conclude that mechanisms other than 2nd order Fermi

scattering by resonant waves are required to explain quiet-time supra-thermal tails

on the PUI distributions.

114

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 8

RESULTS AND CONCLUSIONS

Review of Results

The main motivation behind this work has been a better understanding of the

physical processes that cause observed PUI flux variations. To this end we have

worked with the hypothesis that the variations are caused by transport effects

induced by the solar wind. The hypothesis has been quite successful, with co

measured solar wind parameters showing strong correlations to PUI fluxes

observed with SOHO/CTOF. For example, the existence of compression regions

in the solar wind was found to greatly influence PUI distributions. Strong

correlations were found between PUI energy flux density and both solar wind

proton density and magnetic field strength. In addition, the onset of a

compression region with a magnetic field discontinuity was found to affect the

PUI distribution adiabatically via a shift in the cutoff velocity.

An observation of similar character to the aforementioned cutoff shift is the

change to the PUI distribution produced by a non-zero injection velocity of

interstellar neutrals. This effect enables another estimate of the LISM velocity

[Mobius et al., 1999]. Further study of PUI distributions merited compensating

for this effect when constructing superposed epoch spectra.

1)5

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. An important process in shaping PUI velocity distributions is pitch angle

scattering, as the ions are injected into the solar wind with an anisotropic

distribution. Although the CTOF instrument did not record the angular

distribution of PUI fluxes, information about pitch angle isotropy was obtained in

this work from the energy spectra. In particular, data taken during radial

magnetic field showed that pitch angle anisotropy was reduced at times of higher

IMF wave-power. This observation confirms the hypothesis that pitch angle

scattering of PUIs can be caused by Alfvenic fluctuations [Saul et al., 2004].

Diffusion coefficients and mean free paths for pitch angle scattering were

calculated using a hemispheric model of pitch angle diffusion. The observations

showed a deviation from simple quasi-linear wave-power dependencies for low

wave-power.

PUIs are also efficiently accelerated as they move out through the heliosphere.

Strong acceleration was found to occur near shocks and compression regions,

confirming theories of shock acceleration and also 1st order Fermi acceleration by

compression regions [Giacalone et ah, 2002], Flowever, the amount of

acceleration during such events was not easily predictable from solar wind

parameters. This observation points to complex dynamics of shocks and solar

wind structures.

In addition to acceleration by shocks and solar wind disturbances, we observed

a supra-thermal tail present even in quite times, consistent with other

measurements [e.g. Gloeckler, 2002]. However, we did not find the strength of

this tail to correlate with resonant IMF wave-power in the solar wind, contrary to

116

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. expectations of a simple statistical acceleration theory involving 2nd order Fermi

acceleration by waves.

Open Questions for Further Research

Despite the success of the hypothesis that solar wind transport causes PUI flux

variations, many unexplained variations exist. It remains difficult to predict PUI

fluxes, using only co-located solar wind and magnetic field measurements. A

simple attempt to smooth the PUI energy flux data based on a linear dependence

to solar wind proton density and to IMF orientation and wave-power reduced the

deviation by only 30%. However, some of the remaining variations are still

without any explanation at this time.

While this research was successful in observing the role played by IMF waves

in pitch-angle scattering, the details of the interaction leave much room for further

work. With improved measurements of PUI velocity distributions, for example

with multiple sectors giving angular information about incoming ions, much more

detailed analysis will be possible. In addition, a more detailed knowledge of the

IMF waves would be valuable, for example in determination of the contribution

of various wave-modes or wave-vectors to pitch angle diffusion coefficients.

There is also much room for improvement in the modeling of PUI distributions.

For simplicity we considered here static models of the global IMF, for example

assuming that a measured radial field implies that the field was radial throughout

the path of a PUI. More realistic models would include the twists and turns of the

IMF as it makes its way from the inner heliosphere [see e.g. lsenberg & Lee,

1998],

117

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. REFERENCES

Aellig, M. R. and P. Bochsler (1998)."Freeze-in Temperatures and Relative Abundances of Iron Ions in the Solar Wind Measured With SOHO/CEL!AS/CTOF.” Inauquraldissertation der Universitat Bern: 116.

Altwegg, K., H. Balsiger, J. Geiss, R. Goldstein, W.-H. Ip and e. al (1993). "The ion population between 1300 km and 230000 km in the coma of comet P/Halley.” Astronomy and Astrophysics. 279: 260-266.

Askew, S. D. and J. A. Kune (1984)."Role of "core" and "halo" solar electrons in ionization of the interstellar medium." Planet. Space Sci. 32(6): 779-784.

Baranov, V. B., M. K. Ermakov and M. G. Lebedev (1981)."A Three-Component Model of the Solar Wind - Interstellar Ineraction - Some Numerical Results." Soviet Astron. Lett. 7(3): 206.

Barbosa, D. D. (1989)."Stochastic Acceleration of Cometary Pickup Ions: The Classic Leaky Box Model." Astroohvsical Journal 341: 493-496.

Baring, M. G., D. C. Ellison and F. C. Jones (1994)."Monte Carlo simulations of particle acceleration at oblique shocks." Astrophvsical Journal Supplement Series 90(2): 547-552.

Belcher, J. W. (1971)."Alfvenic Wave Pressures and the Solar Wind." Astrophvsical Journal 168: 509-524.

Belcher, J. W. and L. J. Davis (1971)."Large Amplitude Alfven Waves in the Interplanetary Medium II." Journal of Geophysical Research 76: 3534.

Bieber, J. W., W. Wanner and W. H. Matthaeus (1996)."Dominant two- dimensional solar wind turbulence with implications for cosmic ray transport." Journal of Geophysical Research 10KA21: 2511-2522.

Blandford, R. D. and J. P. Ostriker (1978)."Particle Acceleration by Astorphysical Shocks." Astrophvsical Journal 221: L29-L32.

Bogdan, T. J., M. A. Lee and P. Schneider (1991)."Coupled Quasi-Linear Wave Damping and Stochastic Acceleration of Pickup Ions in the Solar Wind." Journal of Geophysical Research 96(A1): 161-178.

Burlaga, L. F., N. F. Ness, E. C. Stone, F. B. McDonald, M. H. Acuna, R. P. Lepping and E. P. Connerney (2003)."Search for the heliosheath with Voyager 1 magnetic field measurements." Geophysical Research Letters 30(20): 2072.

Buttighoffer, A., L. J. Lanzerotti, D. J. Thomson, C. G. Maclennan and R. J. Forsyth (1999)."Spectral analysis of the magnetic field inside particle propagation channels detected by Ulysses." Astronomy and Astrophysics. 1999(351): 385-392.

118

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Bzowski, M., H. Fahr, D. Rucinski and H. Scherer (1997)."Variation of bulk velocity and temperature anisotropy of neutral heliospheric hydrogen during the solar cycle.”

Cairns, I. H. and G. P. Zank (2002). "Turn-on of 2-3 kHz radiation beyond the heliopause.” Geophysical Research Letters 29(7): 47.

Chalov, S. V. and H. Fahr (2000)."Keplerian injection velocities reflected in helium pick-up ion spectra." Astron. & Astrophvs. 363: L21-L24.

Chalov, S. V., H. Fahr and V. Izmodenov (1995)."Spectra of energized pick-up ions upstream of the heliospheric termination shock." Astronomy and Astrophysics. 204: 609-616.

Chalov, S. V. and H. J. Fahr (1998)."Phase space diffusion and anisotropic pick up distributions in the solar wind: an injection study." Astronomy and Astrophysics. 335: 746-756.

Chalov, S. V. and H. J. Fahr (2000)."Pick-up ion acceleration at the termination shock and the post-shock pick-up ion energy distribution." Aston. Astrophvs 360: 381-390.

Chalov, S. V. and H. J. Fahr (2002). "Different solar wind types reflected in pick up ion spectral signatures." Astronomy and Astrophysics. 384: 299-302.

Chalov, S. V. and H. J. Fahr (2003)."Energetic particles from the outer heliosphere appearing as a secondary pick-up ion component." Aston. Astrophvs 401: L1-L4.

Chalov, S. V., H. J. Fahr and V. Izmodenov (1997)."Spectra of energized pick-up ions upstream of the two-dimensional heliospheric termination shock.” Astronomy and Astrophysics. 320: 659-671.

Chashei, I. V. and H. J. Fahr (2000)."A thermokinetic study of wave-modulated solar wind electrons using truncated maxwellians." Astronomy and Astrophysics. 363: 295-305.

Chassefiere, E., J. L. Bertaux and V. Sidis (1986)."Elastic collisions of solar wind protons with interstellar neutrals (H and He) inside the heliosphere: a new approach." Astronomy and Astrophysics. 169: 298-304.

Chen, F. F. (1984). Introduction to Plasma Physics and Controlled Fusion. New York, Plenum Press.

Claften, H.-T., G. Mann, R. J. Forsyth and E. Keppler (1999)."Low frequency plasma turbulence and high energy particles at CIR-related shock waves.” Astronomy and Astrophysics. 347: 313.

Collier, M. R., T. E. Moore, K. W. Ogilive and e. al (2001). "Observations of neutral atoms from the solar wind." Journal of Geophysical Research 106(A11): 24893-24906.

119

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Crooker, N. U., J. T. Gosling, V. Bothmer, R. J. Forsyth, P. R. Gazis, A. Hewish, T. S. Horbury, D. S. Intrilligator, J. R. Jokipii, J. Kota, A. J. Lazarus, M. A. Lee, E. Lucek, E. Marsch, A. Posner, I. G. Richardson, E. C. Roelof, J. M. Schmidt, G. L. Siscoe, B. T. Tsurutani and R. F. Wimmer-Schweingruber (1999)."CIR morphology, turbulence, discontinuities, and energetic particles." Space Science Reviews 89: 179-220.

Cummings, A. C., R. A. Mewaldt, J. B. Blake, J. R. Cummings, M. Franz, D. Hovestadt, B. Klecker, G. M. Mason, J. E. Mazur, E. C. Stone, T. T. von Rosenvinge and W. R. Webber (1995)."Anomalous cosmic ray oxygen gradients throughout the heliosphere." Geophysical Research Letters 22(4): 341-344.

Czechowski, A., H. J. Fahr, G. Lay and M. Hilchenbach (2001)."Pick-up ions upstream and downstream of the termination shock." Astronomy and Astrophysics. 379: 601-610.

Danby, J. M. A. and G. L. Camm (1957)."Statistical dynamics and accretion." Monthly Notices of the Royal Astronomical Society 117: 50-71.

Dastgeer, S. and G. P. Zank (2004). "Density spectrum in the diffuse interstellar medium and solar wind." Astrophvsical Journal 602(L): 0.

Desai, M. I., G. M. Mason, J. R. Dwyer, J. E. Mazur, R. E. Gold, S. M. Krimigis, C. W. Smith and R. M. Skoug (2003). "Evidence for a suptrathermal seed population of heavy ions accelerated by interplanetary shocks near 1AU." Astrophvsical Journal 588: 1149-1162.

Dusenbury, P. B. and J. V. Hollweg (1981)."lon-cyclotron heating and acceleration of solar wind minor ions." Journal of Geophysical Research 86: 153- 164.

Earl, J. A. (1976)."The effect of adiabatic focusing upon charged-particle propagation in random magnetic fields." Astrophvsical Journal 205: 900-919.

Earl, J. A., D. Ruffolo, H. L. Pauls and J. W. Bieber (1995)."Comparison of three numerical treatments of charged particle transport." Astrophvsical Journal 454: 749-761.

Fahr, H. J. (1978)."Change of Interstellar Gas Parameters in Stellar-wind- dominated Astrspheres: Solar Case." Astronomy and Astrophysics. 66:103-117.

Fahr, H. J. (1979)."Interstellar Hydrogen Subject to a Net Repulsive Solar Force Field." Astronomy and Astrophysics. 77: 101-109.

Fahr, H. J. (1991)."Aspects of the Present Heliospheric Research." Reviews in Modern Astronomy 4: 126-144.

Fahr, H. J. and G. Lay (2000). "Remote diagnostic of the heliospheric termination shock using neutralized post shock pick-up ions as messengers." Astronomy and Astrophysics. 356: 327-334.

Fahr, H. J., H. U. Nass and D. Rucinski (1985)."Drag-like effects on heliospheric neutrals due to elastic collisions with solar wind ions." Astronomy and Astrophysics. 142: 476-486.

Faison, M. D. and W. M. Goss (2001)."The structure of the cold neutral interstellar medium on 10-100 AU scales." Astrophvsical Journal 121: 2706-2722.

120

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fedorov, Y. I. (2001). Angular distribution of cosmic rays in the interplanetary magnetic field. ICRCCopernicus Gesellschaft.

Fisk, L. A. (1976)."The Acceleration of Energetic Particles in the Interplanetary Medium by Transit Time Damping." Journal of Geophysical Research 81(25): 4633-4640.

Fisk, L. A. (1976)."On the Acceleration of Energetic Particles in the Interplanetary Medium." Journal of Geophysical Research 81(25): 4641-4645.

Fisk, L. A., M. L. Goldstein, A. J. Klimas and G. Sandri (1974)."The Fokker-Plank Coefficient for Pitch-Angle Scattering of Cosmic Rays." Astrophvsical Journal 190: 417-428.

Fisk, L. A., B. Kozlovsky and R. Ramaty (1974)."An interpretation of the observed oxygen and nitrogen enhancements in low-energy cosmic rays." Astrophvsical Journal 190: L35-L37.

Fisk, L. A., N. A. Schwadron and G. Gloeckler (1997)."Implications of fluctuations in the distribution functions of interstellar pick-up ions for the scattering of low rigidity particles." Geophysical Research Letters 24(1): 93-96.

Florinski, V. and G. P. Zank (2003)."Comment on "On nonideal MHD properties of the partially ionized interstellar gas" by V. B. Baranov and H. J. Fahr." Journal of Geophysical Research 108(A2): 1438.

Florinski, V., G. P. Zank and W. I. Axford (2003)."The Solar System in a dense interstellar cloud: Implications for cosmic-ray fluxes at Earth and 10Be records.” Geophysical Research Letters 30(23): 2206.

Flynn, B., J. Vallerga, F. Dalaudierand G. R. Gladstone (1998)."EUVE measurement of the local interstellar wind and geocorona via resonance scattering of solar He 1584-A line emission." Journal of Geophysical Research 103(A4): 6483-6494.

Freund, J. E. (1962). Mathematical Statistics. Englewood Cliffs, NJ, Prentice-Hall.

Frisch, P. C. (2004). "Why study interstellar matter very close to the Sun?” Adv. Space Res. 34(1): 20-26.

Frisch, P. C., J. M. Dorschnerand J. Geiss (1999)."Dustin the local interstellar wind.” Astrophvsical Journal 525: 492-516.

Giacalone, J., J. R. Jokipii and J. Kota (2002)."Particle Acceleration in Solar Wind Compression Regions." Astrophvsical Journal 537: 845-850.

Gloeckler, G. (2002). "Ubiquitous Suprathermal Tails on the Solar Wind and Pickup Ion Distributions." AIP Conference Proceedings 679(1): 583.

Gloeckler, G., L. A. Fisk, F. M. Ipavich, K. W. Ogilive, L. J. Lanzerotti, R. v. Steiger and B. Wiken (1994)."Acceleration of interstellar pickup ions in the disturbed solar wind observed on Ulysses." Journal of Geophysical Research 99(A9): 17637-17644.

121

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Gloeckler, G., J. Geiss, H. Balsiger, L. A. Fisk, A. B. Galvin, F. M. Ipavich, K. W. Ogilvie, R. v. Steiger and B. Wilken (1993). "Detection of Interstellar Pick-Up Hydrogen in the Solar System." Science 261: 70-73.

Gloeckler, G., J. Geiss and R. v. Steiger (1995)."Observations of the solar wind and interstellar pick-up ion populations in the heliosphere with Ulysses." Adv. Space Res. 16(9): 343.

Gloeckler, G., J. R. Jokipii, J. Giacalone and J. Geiss (1994)."Concentration of Interstellar Pickup H+ and He+ in the solar wind." Geophysical Research Letters 21(14): 1565-1568.

Gloeckler, G., N. A. Schwadron, L. A. Fisk and J. Geiss (1995)."Weak Pitch Angle Scattering of few MV Rigidity Ions from Measurements of Anisotropies in the Distribution Function of Interstellar Pickup H+." Geophysical Research Letters 22(19): 2665-2668.

Goldstein, B. E., M. Neugebauer and E. J. Smith (1995)."Alfven Waves, Alpha Particles, and Pickup Ions in the Solar Wind.” International Solar Wind Conference 8: 77.

Goldstein, B. E., E. J. Smith, A. Balogh, T. S. Horbury, M. L. Goldstein and D. A. Roberts (1995)."Properties of magnetohydrodynamic turbulence in the solar wind as observed by Ulysses at high heliographic latitudes." Geophysical Research Letters 22(23): 3393-3396.

Gosling, J. T. and E. C. Roelof (1974)."A comment on the detection of closed magnetic structures in the solar wind.” Solar Physics 39: 405-408.

Gruntman, M. A. (1982)."The effect of the neutral solar-wind component upon the interaction of the solar system with the interstellar gas stream." Sov. Astron. Lett 8(1): 24-28.

Hasselmann, K. and G. Wibberenz (1970)."A Note on the Parallel Diffusion Coefficient." Astrophvsical Journal 162: 1049-1051.

Hefti, S. (1997). Solar Wind Freeze-in Temperatures and Fluxes Measured with SOHO/CELIAS/CTOF and Calibration of the CELIAS Sensors. Philosophisch- naturwissenschaftlichen. Universitat Bern: 103.

Higham, D. J. (2001). "An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations." SIAM Review 43(3): 525-546.

Ho, C. M., B. T. Tsurutani, R. Sakurai, B. E. Goldstein, A. Balogh and J. L. Phillips (1996)."Interplanetary discontinuities in corotating streams and their interaction regions." Astronomy and Astrophysics. 316: 346-349.

Hoffmeister, C. (1943)."Physikaiische Untersuchungen an Kometen. I. Die Beziehungen des primaren Schweifsrahls zum Radiusvektor." Zeitschrift fuer Astrophvsik 22: 265.

122

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Hovestadt, D., M. Hilchenbach, A. Burgi, B. Klecker, P. Laeverenz, M. Scholer, H. Grnwaldt, W. I. Axford, S. Livi, E. Marsch, B. Wilken, P. Winterhoff, F. M. Ipavich, P. Bedini, M. Coplan, A „ A. B. Galvin, G. Gloeckler, P. Bochsler, H. Balsiger, J. Fischer, J. Geiss, R. Kallenbach, P. Wurz, K.-U. Reiche, F. Gliem, D. L. Judge, K. H. Hsieh, E. Mobius, M. A. Lee, G. G. Managadze, M. I. Verigin and M. Neugebauer (1995)."CELIAS: The Charge Element and Isotope Analysis System for SOHO." Solar Physics 162: 441-481.

Hu, Q., C. W. Smith and N. F. Ness (2003)."Double flux-rope magnetic cloud in the solar wind at 1 AU." Geophysical Research Letters 30(7): 1385.

Hundhausen, A. J. (1968)."Direct Observations of Solar Wind Particles." Space Science Reviews 8: 690.

Ichimaru, S. (1992). Plasma Physics: An Introduction to the Statistical Physics of Charged Particles. Torrence, CA, Cummings.

Ipavich, F. M., A. B. Galvin, S. E. Lasley, J. A. Paquette, S. Hefti, K.-U. Reiche, M. Coplan, A,, G. Gloeckler, P. Bochsler, D. Hovestadt, H. Grunwaldt, M. Hilchenbach, F. Gliem, W. I. Axford, H. Balsiger, A. Burgi, J. Geiss, K. C. Hsieh, R. Kallenbach, B. Klecker, M. A. Lee, G. G. Managadze, E. Marsch, E. Mobius, M. Neugebauer, M. Scholer, M. I. Verigin, B. Wiken and P. Wurz (1998)."Solar wind measurements with SOHO: The CELIAS/MTOF proton monitor." Journal of Geophysical Research 103(A8): 17205-17214.

Isenberg, P. A. (1987). "Evolution of interstellar pickup ions in the solar wind.” Journal of Geophysical Research 92:1067-1073.

Isenberg, P. A. (1995)."Interstellar pickup ions: Not just theory anymore.” Reviews of Geophysics. Supplement: 623-627.

Isenberg, P. A. (1997). "A hemispherical model of anisotropic interstellar pickup ions." Journal of Geophysical Research 102(A3): 4719-4724.

Isenberg, P. A. (1999). Interstellar pickup ions in the solar wind. Solar Wind Nine.S. R. Habbal, R. Esser, J. V. Hollweg and P. A. Isenberg. American Institute of Physics.

Isenberg, P. A. and W. C. Feldman (1995)."Electron-impact ionization of interstellar hydrogen and helium at interplanetary shocks.” Geophysical Research Letters 22(8): 873-875.

Isenberg, P. A. and M. A. Lee (1998). "Transport of anisotropic interstellar pickup ions on bent flux tubes." Journal of Geophysical Research 103(A6): 12037-12047.

Isenberg, P. A., C. W. Smith and W. H. Matthaeus (2003). "Turbulent Heating of the Distant Solar Wind by Interstellar Pickup Protons." Astrophvsical Journal 592: 564-573.

Izmodenov, V., Y. G. Malama, G. Gloeckler and J. Geiss (2003)."Effects of Interstellar and Solar Wind Ionized Helium on the Interaction of the Solar Wind with the Local Interstellar Medium." Astrophvsical Journal 594: L59-L62.

Jaekel, U. (1998)."Magnetic mirroring and and cosimic ray pitch-angle diffusion." Physical Review E 58(3): 4033-4036.

123

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Johnstone, A. D., A. J. Coates, D. E.-. Huddleston, K. Jockers, B. Wiken, H. Borg, C. Gurgiolo, J. D. Winningham and E. Amata (1993)."Observations of the solar wind and cometary ions during the encounter between Giotto and comet P/Grigg- Skjellerup." Astronomy and Astrophysics. 273: L1-L4.

Jokipii, J. R. (1972)."Fokker-planck equations for charged-particle transport in random fields." Astrophvsical Journal 172: 319-326.

Jokipii, J. R. (1974)."Pitch-angle scattering of charged particles in a random magnetic field." Astrophvsical Journal 194: 465-469.

Kaghashvili, E. K., G. P. Zank, J. Y. Lu and W. Droge (2004)."Transport of Energetic Charged Particles Part 2: Small-angle Scattering." Journal of Plasma Physics 70(4).

Kallenrode, M.-B. (1998). Space Physics. New York, Springer.

Khazanov, G. V., M. W. Liemohn, E. N. Krivorutsky, J. U. Kozyra and B. E. Gilchrist (1999)."Interhemispheric transport of relativistic electron beams." Geophysical Research Letters 26(5): 581-584.

Klecker, B., A. T. Bogdanov, F. M. Ipavich, M. Hilchenbach, E. Mobius and P. Bochsler (2001). "On the Variability of Suprathermal He+ at 1 AU." ICRC Proceedings: 3100-3103.

Krimigis, S. M., R. B. Decker, M. E. Hill, T. P. Armstrong, G. Gloeckler, D. C. Hamilton, L. J. Lanzerotti and E. C. Roelof (2003)."Voyager 1 exited the solar wind at a distance of -8 5 au from the Sun." Nature 426: 45-48.

Krisher, T. P., L. Maleki, George F. Lutes, Lori E. Primas, R. T. Logan and J. D. Anderson (1990)."Test of the isotropy of the one-way speed of light using hydrogen-maser frequency standards." Physical Review D 42(2): 731-734.

Kucharek, H., E. Mobius, W. Li, C. J. Farrugia, M. A. Popecki, A. B. Galvin, B. Klecker, M. Hilchenbach and P. A. Bochsler (2003)."On the source and acceleration of energetic He+: A long-term observation with ACE/SEPiCA." Journal of Geophysical Research 108(A10): LIS 15-1.

Lallement, R. (1998). Observations of the Local Interstellar Cloud. IAU Colloquia Number 166.Breitschwerdt. New York.

Lallement, R., J. R. Raymond and J. Vallerga (2004). "Diagnostics of the Local Interstellar Medium using particles and U V radiation." Adv. Space Res. 34(1): 46- 52.

Lallement, R., B. Y. Welsh, J. L. Vergely, F. Crifo and D. Sfeir (2003). "3D mapping of the dense interstellar gas around the Local Bubble." Aston. Astrophvs 441:447-464.

Leamon, R. J., W..H. Matthaeus, C. W. Smith and H. K. Wong (1998). "Contribution of cyclotron-resonant damping to kinetic dissipation of interplanetary turbulence." Astrophvsical Journal 507: L181-L184.

Leamon, R. J., N. F. Ness, C. W. Smith and H. K. Wong (1999). Dynamics of the Dissipation Range for Solar Wind Magnetic Fluctuations. Solar Wind 9, Nantucket, MA.S. R. Habbal, R. Esser, J. V. Hollweg and P. A. Isenberg. AIP.

124

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Leblanc, F. and D. Hubert (1997)."A generalized model for the proton expansion in astrophysical winds. I. The velocity distribution function representation." Astrophvsical Journal 483: 464-474.

Leblanc, F. and D. Hubert (1998)."A generalized model for the proton expansion in astrophysical winds II. The associated set of transport equations." Astrophvsical Journal 501: 375-385.

Lee, M. A. (1984). "Particle acceleration and MHD wave excitation upstream of interplanetary shocks." Adv. Space Res. 4(2-3): 295-304.

Lee, M. A. and W.-H. Ip (1987)."Hydromagnetic Wave Excitation by Ionized Interstellar Hydrogen and Helium in the Solar Wind." Journal of Geophysical Research 92(A10): 11041-11052.

Lee, M. A. and H. J. Volk (1975)."Hydromagnetic Waves and Cosmic-Ray Diffusion Theory." Astrophvsical Journal 198: 485-492.

Lepping, R. P., M. H. Acuna, L. F. Burlaga, W. M. Farrel, J. A. Slavin, K. H. Schatten, F. Mariani, N. F. Ness, F. M. Neubauer, Y. C. Whang, J. B. Byrnes, R. S. Kennon, P. V. Panetta, J. Scheifele and E. M. Worley (1995)."The WIND Magnetic Field Investigation." Space Science Reviews 71: 207.

Lerche, I. (1973)."On Kraichnan's direct interaction approximation applied to charged-particle transport in turbulent magnetic fields." Astrophvsical Journal 184: 995-1005.

Lerche, I. (1974)."A variational approach to charged-particle transport." Astrophvsical Journal 193: 711-719.

Liboff, R. L. (1969). Introduction to the Theory of Kinetic Equations. New York, John Wiley and Sons, Inc.

Lin, R. P., K. A. Anderson, S. Ashford, C. W. Carlson, D. Curtis, R. Ergun, D. Larson, J. McFadden, M. McCarthy, G. K. Parks, H. Reme, J. M. Bosqued, J. Coutelier, F. Cotin, C. D'Uston, K.-P. Wenzel, T. R. Sanderson, J. Henrion, J. C. Ronnet and G. Paschmann (1995)."A Three-Dimensional Plasma and Energetic Particle Investigation for the Wind Spacecraft." Space Science Reviews 71: 125- 153.

Longair, M. S. (1981). High Energy Astrophysics. New York, Cambridge University Press.

Lu, J. Y. and G. P. Zank (2001). "Numerical solution of the time-dependent kinetic equation for anisotropic pitch-angle scattering." Astrophvsical Journal 550: 34-51.

MacDonald, F. B., E. C. Stone, A. C. Cummings, B. Heikkila, N. Lai and W. R. Webber (2003). "Enhancements of energetic particles near the heliospheric termination shock." Nature 426: 48-51.

MacKinnon, A. L. and I. J. D. Craig (1991)."Stochastic simulation of fast particle diffusive transport." Astronomy and Astrophysics. 251: 693-699.

Mall, U., H. Fichtnerand D. Rucinski (1996)."Interstellar atom and pick-up ion fluxes along the Ulysses flight-path." Astronomy and Astrophysics. 316: 511-518.

125

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Matsui, H., C. J. Farrugia and R. B. Torbert (2002). "Wind-ACE solar wind correlations, 1999: An approach through spectral analysis." Journal of Geophysical Research 107(A11): 1355.

Matthaeus, W. H. and C. Smith (1981)."Structure of correlation tensors in homogeneous anisotropic turbulence." Physical Review A 24(4): 2135-2144.

Matthaeus, W. H., C. W. Smith and S. Oughton (1997)."Dynamical age of solar wind turbulence in the outer heliosphere." Journal of Geophysical Research 103: 6495.

McComas, D., F. Allegrini, P. Bochsler, M. Bzowski, M. R. Collier, H. Fahr, H. Fichtner, P. C. Frisch, H. Funsten, S. Fuselier, G. Gloeckler, M. A. Gruntman, V. Izmodenov, P. Knappenberger, M. A. Lee, S. Livi, D. Mitchell, E. Mobius, T. E. Moore, D. Reisenfeld, E. C. Roelof, N. A. Schwadron, M. Wieser, M. Witte, P. Wurz and G. P. Zank (2004). The Interstellar Boundary Explorer (IBEX). Physics of the Outer Heliosphere, Riverside, CA.V. Florinski. AIP.

McMullin, D., D. L. Judge, M. Hilchenbach, F. M. Ipavich, P. Bochsler, P. Wurz, A. Burgi, W. T. Thompson and J. S. Newmark (2002). In-flight Comparisons of Solar EUV Irradiance Measurements Provided by the CELIAS/SEM on SOHO. The Radiometric Calibration of SOHO. ISSI Scientific Report. A. Pauluhn, M. C. E. Huber and R. v. Steiger. Noordwijk, The Netherlands, ESA.

Michalek, G. (2001). "On the cosmic ray cross-field diffusion for solar wind turbulence." Aston. Astrophvs 376: 667-671.

Michalek, G., M. Ostrowski and R. Schlickeiser (1999)."Cosmic-Ray Momentum Diffusion in Magnetosonic versus Alfvenic Turbulent Field." Solar Physics 184(2): 339-352.

Michels, J. G., J. C. Raymond, J. L. Bertaux, E. Quemerais and e. al (2002). "The helium focusing cone of the local interstellar medium close to the sun." Astrophvsical Journal 568: 385-395.

Mobius, E. (1983)."Critical velocity experiments in space." Active Experiments in Space ESA SP-195: 215.

Mobius, E. (1986)."Pick-up of interstellar neutrals by the solar wind." Adv. Space Res, 6(1): 199-208.

Mobius, E. (1996)."The local interstellar medium viewed through pickup ions, recent results and future perspectives." Space Science Reviews 78(1-2): 375- 386.

Mobius, E., D. Hovestadt, B. Klecker and M. Scholer (1986)."Observation of lithium pick-up ions in the 5- to 2 -k e V energy range following the AM PTE solar wind releases." Journal of Geophysical Research 91 (A2): 1325-1332.

Mobius, E., D. Hovestadt, B. Klecker, M. Scholer, G. Gloeckler and F. M. Ipavich (1985)."Direct observation of He+ pick-up ions of interstellar origin in the solar w ind” Nature 318: 426-429.

Mobius, E., B. Klecker, D. Hovestadt and M. Scholer (1988)."Interaction of interstellar pick-up ions with the solar wind." Astrophysics and Space Science 144(1-2): 487-505.

126

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Mobius, E., Y. Litvinenko, H. Grunwaldt, M. R. Aellig, A. T. Bogdanov, F. M. Ipavich, P. Bochsler, M. Hilchenbach, D. L. Judge, B. Klecker, M. A. Lee and H. Ogawa (1999)."Direct evidence of the interstellar gas flow velocity in the pickup ion cut-off as observed with SOHO CELIAS CTOF." Geophysical Research Letters 26(20): 3181.

Mobius, E., D. Rucinski, D. Hovestadt and B. Klecker (1995)."The helium parameters of the very local interstellar medium as derived from the distribution of He+ pickup ions in the solar wind." Astronomy and Astrophysics. 304: 505-519.

Mobius, E., D. Rucinski, P. A. Isenberg and M. A. Lee (1996)."Determination of interstellar pickup ion distributions in the solar wind with SOHO and Cluster." Annales Geophvsicae 14: 492-496.

Mobius, E., D. Rucinski, M. A. Lee and P. A. Isenberg (1998)."Decreases in the antisunward flux of interstellar pickup He+ associated with radial interplanetary magnetic field." Journal of Geophysical Research 103: 257.

Mobius, E., M. Scholer, D. Hovestadt and B. Klecker (1982)."Comparison of helium and heavy ion spectra in 3He-rich solar flares with model calculations based on stochastic Fermi acceleration in Alfven turbulence." Astrophvsical Journal 259: 397-410.

Neubauer, F. M., H. J. Beinroth, H. Barnstorf and G. Dehmel (1977)."Initial results from the Helios-1 search-coil magnetometer experiment." Zeitschrift fuer Geophvsik 42(61: 599-614.

Ng, C. K. and D. V. Reames (1995)."Pitch angle diffusion coefficient in an extended quasi-linear theory." Astrophvsical Journal 453: 890-905.

Oka, M., T. Terasawa, H. Noda, Y. Saito and T. Mukai (2002). "'Torus' distribution of interstellar pickup ions: Direct observation." Geophysical Research Letters 29(12): 1612.

Opher, M., P. C. Liewer, T. I. Gombosi, W. Manchester, D. L. DeZeeuw, I. Sokolov and G. Toth (2003)."Probing the edge of the solar system: formation of an unstable jet-sheet." Astrophvsical Journal 591: L61-L65.

Owens, M. J. and P. J. Cargill (2002). "Correlation of magnetic field intensities and solar wind speeds of events observed by ACE." Journal of Geophysical Research 107(A5): SSH 1-1.

Paresce, F. and S. Bowyer (1973)."Resonance Scattering from Interstellar and Interplanetary Helium." Astron. & Astrophvs. 27: 399-406.

Paresce, F. and S. Bowyer (1986)."The Sun and the Interstellar Medium." Scientific American 255: 92-99.

Parker, E. N. (1960). "The Hydrodynamic Treatment of the Expanding Solar Corona." Astrophvsical Journal 132: 175.

Pauls, H. L., G. P. Zank and L. L. Williams (1995)."Interaction of the solar wind with the local insterellar medium." Journal of Geophysical Research 100(A11): 21595-21604.

127

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Perez-Tijerina, E., H. Perez-de-Tejada and M. Reyes-Ruiz (2000). "Spatial distribution of pick-up ions in velocity shears." Astronomy and Astrophysics. 354: 321-327.

Petelski, E. F., H. J. Fahr, H. W. Ripken, N. Brenning and I. Axnas (1980). "Enhanced Interaction of the Solar Wind and the Interstellar Neutral Gas by Virtue of a Critical Velocity Effect." Astronomy and Astrophysics. 87: 20-30.

Pizzo, V., R. Schwenn, E. Marsch, H. Rosenbauer, K.-H. Muhlhauser and F. M. Neubauer (1983)."Determination of the solar wind angular momentum flux from the helios data - an observational test of the Weber and Davis theory." Astrophvsical Journal 271: 335-354.

Pogorelov, N. V. and T. Matsuda (2004)."Comment on "On the interaction of the solar wind with the interstellar medium: Field aligned flow" by R. Ratkiewicz and G. M. Webb." Journal of Geophysical Research 109(A2).

Porcelli, F., D. Borbobno, F. Califano, D. Grasso, M. Ottaviani and F. Pegoraro (2002). "Recent advances in collisionless magnetic reconnection." Plasma Phvs. Control. Fusion 44: B389-B405.

Ragot, B. R. (1999)."Nongyroresonant Pitch Angle Scattering." Astrophvsical Journal 518: 974-984.

Ragot, B. R. and R. Schlickeiser (1998)."Cosmic ray acceleration by fast magnetosonic waves." Aston. Astrophvs 331: 1066-1069.

Richardson, J. D. and K. I. Paularena (2001)."Plasma and Magnetic Field Correlations in the Solar Wind.” Journal of Geophysical Research 106(A1): 239- 251.

Robinson, P. A. (1989)."New contributions to transit-time damping in multidimensional systems." Phvs. Fluids B 1(3): 490-498.

Robinson, P. A. (1990)."Transit-time damping and the arrest of wave collapse." Phvs. Fluids B 3(3): 545-554.

Roelof, E. C. (1969). Propagation of Solar Cosmic Rays in the Interplanetary Magnetic Field. Lectures in High Energy Astrophysics. H. Ogelmann and J. R. Wayland, NASA. SP-199: 111.

Roux, J. A. I., H. Fichtner and G. P. Zank (2000)."Self-consistent acceleration of multiply reflected pickup ions at a quasi-perpendicular solar wind termination shock: a fluid approach." Journal of Geophysical Research 105(A6): 12557- 12578.

Rucinski, D., A. C. Cummings, G. Gloeckler, A. J. Lazarus, E. Mobius and M. Witte (1996)."Ionization processes in the heliosphere - rates and methods of their determination." Space Science Reviews 78: 73-84.

Rucinski, D. and H. J. Fahr (1989)."The influence of electron impact ionization on the distribution of interstellar helium in the inner heliiosphere; possible consequences for determination of interstellar helium parameters." Astronomy and Astrophysics. 224: 290-298.

128

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Rucinski, D., H. J. Fahr and S. Grzedzielski (1993)."The production of different pick-up ion species in the heliosphere and their convection towards the three- dimensional termination shock.” Planet. Space Sci. 41(10): 773-783.

Saul, L. (2003). Interstellar Pickup Ion Flux Variations: New Results from SOHO/CTOF. 11th CELIAS Postlauch Workshop, Schwarzee, Switzerland.

Saul, L., E. Mobius, Y. Litvinenko, P. A. Isenberg, H. Kucharek, M. A. Lee, H. Grunwaldt, F. M. Ipavich, B. Klecker and P. Bochsler (2003)."SOHO CTOF Observations of Interstellar He+ Pickup Ion Enhancements in Solar Wind Compression Regions." AIP Conference Proceedings 679(1): 778.

Saul, L., E. Mobius and C. W. Smith (2004)."Variations of Pickup Ion Distributions and their Relation to Interplanetary Conditions and Waves." Physics of the Outer Heliosphere 719: 207.

Saul, L., E. Mobius, C. W. Smith, P. Bochsler, H. Grunwaldt, B. Klecker and F. M. Ipavich (2004). "Observational evidence of pickup ion isotropization by waves.” Geophysical Research Letters 31 (L05811).

Schlickeiser, R. (1994)."Cosmic-Ray Transport and Acceleration." Astrophvsical Journal 90: 929-936.

Schlickeiser, R. (1998)."Quasi-linear theory of cosmic ray transport and acceleration: the role of oblique magnetohydrodynamic waves and transit-time damping." Astrophvsical Journal 492: 352-378.

Schlickeiser, R. (1999)."Mean free path of solar electrons and nucleons.” Astronomy and Astrophysics. 351: 382-384.

Scholer, M., G. Mann, S. V. Chalov, M. I. Desai, L. A. Fisk, J. R. Jokipii, R. Kallenbach, E. Keppler, J. Kota, H. Kunow, M. A. Lee, T. R. Sanderson and G. M. Simnett (1999)."Origin, injection, and acceleration o fC IR particles: theory." Space Science Reviews 89: 369-399.

Schwadron, N. A. (1998)."A model for pickup ion transport in the heliosphere in the limit of uniform hemispheric distributions." Journal of Geophysical Research 103(A9): 20643-20649.

Schwadron, N. A., L. A. Fisk and G. Gloeckler (1996)."Statistical acceleration of interstellar pick-up ions in co-rotating regions." Geophysical Research Letters 23(21): 2871-2874.

Schwadron, N. A. and J. Geiss (2000). "On the processing and transport of inner source hydrogen." Journal of Geophysical Research 105(A4): 7473-7481.

Schwadron, N. A., J. Geiss, L. A. Fisk, G. Gloeckler, T. H. Zurbuchen and R. v. Steiger (2000). "Inner source distributions: Theoretical interpretation, implications, and evidence for inner source protons." Journal of Geophysical Research 105(A4): 7465-7472.

Schwadron, N. A., T. H. Zurbuchen, L. A. Fisk and G. Gloeckler (1999). "Pronounced enhancements of pickup hydrogen and helium in high-latitude compressional regions." Journal of Geophysical Research 104(A1): 535-547.

129

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Schwartz, S. J., M. F. Thomsen and J. T. Gosling (1983)."Ions upstream of the Earth's bow shock: a theoretical comparison of alternative source populations.” Journal of Geophysical Research 88(A3): 2039-2047.

Sckopke, N., G. Paschmann, A. L. Brinca, C. W. Carlson and H. Luhr (1990). "Ion Thermalization in Quasi-Perpendicular Shocks involving Reflected Ions." Journal of Geophysical Research 95(A5): 6337-6352.

Shizgal, B. (1977)."On the departure from translational equilibrium for interstellar malecular hydrogen." Astrophvsical Journal 217: 78-82.

Shklovskii, I. S. (1975). Stars, their Birth. Life, and Death. San Francisco, W.H. Freeman.

Short, R. and A. Simon (1998)."Landau Damping and Transit-Time Damping of Localized Plasma Waves in General Geometries." LLE Review 75: 200-211.

Skilling, J. (1971). "Cosmic Rays in the Galaxy: Convection or Diffusion?" Astrophvsical Journal 170: 265-273.

Slavin, J. D. and P. C. Frisch (2002). "The ionization of nearby interstellar gas.” Astrophvsical Journal 565: 364-379.

Smith, C. W. (2003)."Magnetic helicity in the solar wind." Adv. Space Res. 32(19): 1971-1980.

Smith, C. W., M. L. Goldstein and W. H. Matthaeus (1983)."Turbulence analysis of the Jovian upstream 'wave' phenomenon." Journal of Geophysical Research 88: 5581-5593.

Smith, C. W., P. A. Isenberg, W. H. Matthaeus, J. D. Richardson, S. Oughton and G. P. Zank (2004). Heating the Outer Heliosphere by Pickup Ions. IGPP, Riverside, CA.V. Florinski. AIP.

Smith, C. W., J. L'Heureux, N. F. Ness, M. H. Acuna, L. F. Burlaga and J. Scheifele (1988). "The ACE Magnetic Fields Experiment." Space Science Reviews 86: 613-632.

Stix, T. H. (1992). Waves in Plasmas. NYC, American Institute of Physics.

Tam, S. W. Y. and T. Chang (1999)."Kinetic evolution and acceleration of the solar wind.” Geophysical Research Letters 26(20): 3189-3192.

Trumpler, R. J. (1930)."Spectrophotometric Measures of Interstellar Light Absorption." Publications of the Astronomical Society of the Pacific 42(249): 267.

Valley, G. C. (1971). "Propagation of hydromagnetic waves in a stochastic magnetic field." Astrophvsical Journal 168: 251-264.

van de Hulst, H. C. (1951)."Observations of the interstellar hydrogen line of wave length 21 cm made at Kootwijk, Netherlands." Astronomical Journal 56: 144.

Vasyliunas, V. M. and G. L. Siscoe (1976)."On the flux and energy spectrum of interstellar ions in the solar system." Journal of Geophysical Research 81:1247- 1252.

130

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Vocks, C. (2002). "A kinetic model for ions in the solar corona including wave- particle interactions and coulomb collisions." Astrophvsical Journal 568:1017- 1029.

Volk, H. J., G. Morfill, W. Alpers and M. A. Lee (1974)."Spatial Dependence of the Pitch-Angle and Associated SPatial Diffusion Coefficients for Cosmic Rays in Interplanetary Space." Astrophysics and Space Science 26: 403.

Walker, D. N. and W. E. Amatucci (2001). "Characterization of Joule heating in structured electric field environments." Journal of Geophysical Research 106(A2): 1807-1815.

Wang, C., J. D. Richardson and J. T. Gosling (2000)."Slowdown of the Solar Wind in the Outer Heliosphere and the Interstellar Neutral Hydrogen Density." Geophysical Research Letters 27(16): 2429-2432.

Wegmann, R., H. U. Schmidt, W. F. Huebnerand D. C. Boice (1987)."Cometary MHD and chemistry." Astronomy and Astrophysics. 187: 339-350.

Wibberenz, G., K. Hasselmann and D. Hasselmann (1969). Comparison of particle-field interaction theory with solar proton diffusion coefficients. ICRC, BudapestActa Physica.

Wilken, B., A. Johnstone, A. Coates, H. Borg and e. al (1987)."Pick-up ions at comet P/Halley's bow shock: observations with the IIS spectrometer on Giotto.” Astronomy and Astrophysics. 187: 153-159.

Williams, L. L. (1997)."Nonclassical theory of turbulent collisionless plasmas." Astrophvsical Journal 481: 515-523.

Williams, L. L., N. A. Schwadron, J. R. Jokipii and T. I. Gombosi (1993)."A unified transport equation for both cosmic rays and thermal particles." Astrophvsical Journal 405: L79-L81.

Wilson, S. J. and K. K. Sen (1963)."A modified spherical harmonic method for solving equation of transfer and neutron transport equation." Astonomical Society of Japan 15(4): 351-367.

Wimmer-Schweingruber, R. F. and P. Bochsler (2003)."On the origin ofinner- source pickup ions." Geophysical Research Letters 30(2): 49-51.

Witte, M., M. Banaszkiewicz, H. Rosenbauer and D. McMullin (2004)."Kinetic parameters of interstellar neutral helium: updated results from the ULYSSES/GAS-instrument." Adv. Space Res. 34: 61-65.

Witte, M., H. Rosenbauer, M. Banaszkiewicz and H. Fahr (1993)."The ULYSSES neutral gas experiment - Determination of the velocity and temperature of the interstellar neutral helium." Adv. Space Res. 13(6): 121-130.

Wu, F. M. and D. L. Judge (1979)."Temperature and flow velocity of the interplanetary gases along solar radii." Astrophvsical Journal 231: 594-605.

Wu, F. M. and D. L. Judge (1980)."A reanalysis of the observed interplanetary hydrogen lyman alpha emission profiles and the derived local interstellar gas temperature and velocity.” Astrophvsical Journal 239: 389-394.

131

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Wu, T.-Y. (1966). Kinetic Equations of Gases and Plasmas. Reading, Massachusetts, Addison-Wesley.

Wurz, P., M. R. Aellig and S. Hefti (1997). The Dataphase Manual for CELIAS on the SOHO Mission.

Yan, H. and A. Lazarian (2002). "Scattering of cosmic rays by magnetohydrodynamic interstellar turbulence." Physical Review Letters 89(28).

Zank, G. P. and I. H. Cairns (2000). "Pickup ion driven turbulence in the polar heliosphere: a stochastic growth model." Astrophvsical Journal 541:489-494.

Zank, G. P. and H.-R. Muller (2003). "The dynamical heliosphere." Journal of Geophysical Research 108(A6): 1240.

Zank, G. P. and H. L. Pauls (1997)."Shock propagation in the outer heliosphere 1. Pickup ions and gasdynamics." Journal of Geophysical Research 102(A4): 7037-7050.

Zank, G. P., W. K. M. Rice, J. A. I. Roux and W. H. Matthaeus (2001)."The injection problem for anomalous cosmic rays.” Astrophvsical Journal 556: 494- 500.

132

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX A

Documented here are software packages and data products used during this

thesis work. Further details on the implementation of these packages are included

with the software itself, including documentation on both the source code and the

data used, currently available at:

ftp ://www-ssq.sr.unh.edu/pub/lsaul/ .

The material is divided into two main packages described below.

CTOFGui

This package contains most of the utilities used to analyze the helium events

observed by SOHO/CTOF. The routines that calculate the flux based on

instrument geometry are here, as well as the routines that create superposed epoch

histograms in bins of normalized velocity. The raw data from the telemetry is

converted to binary format for enhanced speed of analysis and to save storage

space. A graphical user interface (GUI) is built in the main class, CTOFGui,

while the calculations are carried out in the separate class CTOFHistogrammer.

Various data readers are used to read binary files with the SW parameters. This

GUI was of great use in speeding up data analysis, for the many different filtering

criteria needed. Other classes here are used to read data from various ancillary

datasets, to modify the superposed epoch analyses. The data products read and

analyzed by this program are listed in Table Al. Output from this class is mostly

text based, although some routines for generating spectra, both line and color

plots, are included. These utilities are built using the Scientific Graphics Toolkit

133

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. for Java library distributed by the National Oceanic and Atmospheric

Administration.

JLISM

This package contains routines written to model interstellar PUI distributions.

Neutral distributions are calculated based on the hot model (see Chapter 2), and

the class Hemispheric which models hemispheric pitch angle transport resides

here (see Chapter 6 ). No GUI class exists for this package. The package

PICKSIM, including routines created by E. Mobius, A. Bogdanov, D. Rucinski,

M. Bzowski, and others, was also used to model PUI distributions for this

dissertation.

Solar Wind Parameters

In analyzing the PUI flux data, many separate ancillary data products were

used for comparison with He+ measurements and to build superposed epoch

spectra. These parameters are listed here with some explanation on their origin

and purpose, in Table Al. The reference numbers used in coding were chosen to

reflect the primary data source. All listed parameters are available as a time series.

134

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table A.l Ancillary Data Parameters Name Ref. Sources Description # POLAR 1 WIND/MFI Polar angle of IMF in GSE cords. AZIMUTH 2 WIND/MFI Azimuthal angle o f IMF in GSE coords. MAGNITUDE 3 WIND/MFI IMF magnitude in (nT). ALFVEN 4 WIND/MFI + AlfVen speed MTOF/PM ALFVENRATIO 5 WIND/MFI + Alfven to solar wind speed ratio MTOF/PM ANGLE TO RADIAL 6 WIND/MFI IMF angle to radial (0-90 degrees) B RADIAL COMPONENT 7 WIND/MFI Component of IMF in ecliptic DELTAB 8 WIND/MFI Fluctuation of |B| from 15 minute avg. (nT) AV MAG 9 WIND/MFI 12 hour sliding average |B| (nT). AV ETA 10 WIND/MFI Fluctuation parameter VELOCITY 101 MTOF/PM Solar wind velocity (km/s) DENSITY 102 MTOF/PM Proton Density (cm'3) THERMAL VELOCITY 103 MTOF/PM SW proton thermal speed (km/s) VELOCITYWIND 104 WIND/SWE SW velocity measured by WIND (km/s) DENSITYWIND 105 WIND/SWE Proton density measured by WIND (cm'3) THERMALVELOCITY 103 WIND/SWE SW proton thermal speed at WIND (km/s) FLUX 201 SOHO/CTOF Flux of He+ (cm"1s"1sr'1keV'1) TAIL 202 SOHO/CTOF Integral EFlux above a specified cutoff velocity EFLUX 203 SOHO/CTOF EFlux of He+ (cm'V’sr1) INTEGRAL FLUX 204 SOHO/CTOF EFlux over specified velocity range CUTOFF 205 SOHO/CTOF EFlux over specified velocity range near cutoff ADIABATICINDEX 206 SOHO/CTOF Fit of spectra to model of adiabatic cooling TAIL PARAM 207 SOHO/CTOF Tail flux divided by bulk PUI flux TAIL POWER 208 SOHO/CTOF Power law fit to high energy tail CUTOFF FIT 209 SOHO/CTOF Least square fit to step function FLUX_SMOOTHED_ 1 210 SOHO/CTOF + PUI EFlux detrended with linear MTOF/PM dependence on proton density FLUXSM OOTHED2 211 SOHO/CTOF + PUI EFlux detrended with linear MTOF/PM + dependence of proton density, IMF WIND/MFI orientation, and wave-power DOY 301 Day of year PARINTERCEPT 403 WIND/MFI Wave-power in parallel fluctuations from spectral fit PARINDEX 404 WIND/MFI Power index of wave-power in parallel fluctuations. TRINTERCEPT 405 WIND/MFI Wave-power in transverse fluctuations from spectral fit TR INDEX 406 WIND/MFI Power index of wave-power in transverse fluctuations. TR/PARINTERCEPT 407 WIND/MFI Ratio of wave-power in parallel fluctuations to transverse fluctuations. DVVINDEX 408 WIND/MFI + Parameter to approximate energy MTOF/PM diffusion coefficient from simple theory (see text) ELECTRONPARAM 501 WIND/3DP Electron impact ionization rate

135

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.