EXPLORATION OF COSMIC-RAY PROPAGATION AND THUNDERSTORM MODELS TO EXPLAIN UNUSUAL EVENTS MEASURED WITH THE SURFACE DETECTOR OF THE PIERRE AUGER OBSERVATORY

by Joseph Gibson c Copyright by Joseph Gibson, 2018

All Rights Reserved A thesis submitted to the Faculty and the Board of Trustees of the Colorado School of Mines in partial fulfillment of the requirements for the degree of Master of Science (Applied Physics).

Golden, Colorado Date

Signed: Joseph Gibson

Signed: Dr. Frederic Sarazin Thesis Advisor

Golden, Colorado Date

Signed: Dr. Uwe Greife Professor and Head Department of Physics

ii ABSTRACT

The Surface Detector at the Pierre Auger Observatory has recorded events that have an unusually large footprint on the array and lasts 100 times longer than a typical cosmic ray signal. This thesis explores possible models to explain the source of these unusual signals. The proposed models show that the unusual signals are not a result of a cosmic ray shower but are instead likely a result of a lightning-related phenomenon. The attachment process and the return stroke can create E-fields strong enough to create runaway relativistic electron avalanches. This process creates a cascade of high energy electrons that can span over 100 meters and induces high energy photons that can travel a few kilometers. The Surface Detector would be able to measure the high energy particles resulting from this runaway process. The simulated model of the return stroke produced a signal on the ground that was able to match the long-time of the unusual events. This very preliminary model provides some insights for some of the unusual events, but a complete explanation for the events remains elusive.

iii TABLE OF CONTENTS

ABSTRACT ...... iii

LISTOFFIGURESANDTABLES...... vi

LISTOFABBREVIATIONS ...... ix

ACKNOWLEDGMENTS ...... x

CHAPTER 1 UNUSUAL EVENTS OBSERVED WITH THE PIERRE AUGER COSMIC-RAYOBSERVATORY ...... 1

1.1 CosmicRayOverview ...... 1

1.2 PierreAugerObservatory ...... 4

1.3 ThePierreAugerSurfaceDetector ...... 5

1.3.1 EventReconstruction...... 8

1.4 Observation of unusual events with the SD Detector ...... 10

1.4.1 TimingandGeometryReconstruction ...... 11

CHAPTER 2 SIMPLE COSMIC RAY PROPAGATION MODELS ...... 17

2.1 PropagationModels...... 18

2.1.1 SubluminalPropagationModel ...... 19

2.1.2 ShockWavePropagationModel ...... 21

2.2 Conclusions ...... 26

CHAPTER 3 PRODUCTION OF RELATIVISTIC RUNAWAY ELECTRON AVALANCHES IN LIGHTNING STRIKES? ...... 28

3.1 TheLightningDischargeProcess ...... 28

3.1.1 Initiation of Lightning, and the Quasi-Static BackgroundField . . . . . 30

iv 3.1.2 LeaderSteppingProcess ...... 31

3.1.3 Attachmentprocess...... 34

3.1.4 ReturnStroke...... 34

3.1.5 OthertypesofCGLightning ...... 36

3.1.6 CharacteristicsofLightning ...... 36

3.2 Runaway Relativistic Electron Avalanche ...... 36

CHAPTER4 LIGHTNINGMODELS ...... 43

4.1 ChargedChannelModel ...... 45

4.2 AttachmentPointModel ...... 49

4.3 CurrentChannelModel ...... 53

4.4 ReturnStrokeModel ...... 55

4.5 Conclusions ...... 60

CHAPTER5 CONCLUSION...... 61

5.1 FutureWork...... 62

REFERENCESCITED ...... 63

APPENDIX ADDITIONAL UNUSUAL EVENT IMAGES ...... 68

v LIST OF FIGURES AND TABLES

Figure 1.1 Schematics for the development of a Extensive Air Shower...... 3

Figure1.2 HillasDiagram...... 4

Figure 1.3 Map of Pierre Auger Observatory and Main Components of an SD Station . 6

Figure1.4 ExampleofanEASsignalintheSD...... 9

Figure1.5 ExampleofthesignalintensityofanEAS...... 9

Figure 1.6 Timing and Geometrical Characteristics of an UnusualEvent ...... 12

Figure 1.7 Footprint and Lateral Distribution Function of an UnusualEvent. . . . . 13

Figure1.8 IncompleteLongSignalMeasurement ...... 15

Figure 2.1 Schematic of the Spherical Inflation Model ...... 18

Figure 2.2 Schematic and Simulated Results of a Propagation Model ...... 20

Figure 2.3 Lengthened Time Signature in the Propagation Model 4 km from the Source ...... 21

Figure 2.4 Schematic of the Subluminal Propagation Model ...... 22

Figure 2.5 Simulation Results of the Subluminal Model ...... 23

Figure2.6 SchematicoftheShockWaveModel ...... 24

Figure 2.7 Simulation Results of the Shock Wave Model ...... 25

Figure 3.1 Upper atmospheric lightning and electrical discharge phenomena associatedwiththunderstorms ...... 29

Figure 3.2 Processes in a typical negative downward lightning strike with a rough estimateofthetimingforeachprocess...... 30

Figure 3.3 A vertical tripole representing the charge structure inside a thundercloud ...... 32

vi Figure 3.4 Stepping process of the Lightning Leader ...... 33

Figure3.5 LightningCurrentDistribution ...... 37

Figure3.6 EffectiveFrictiononaFreeElectron ...... 39

Figure3.7 MonteCarloSimulationofRREA ...... 42

Figure 4.1 Cutoff Fields Imposed on Lightning Simulations ...... 45

Figure4.2 ChargeChannelSchematic ...... 46

Figure 4.3 2D projection of the electric field near the charged channel...... 46

Figure4.4 EffectsofacutoffonE-fieldMagnitude ...... 47

Figure 4.5 Paths of 1 MeV electrons in the Charged Channel Model ...... 48

Figure 4.6 Simulation Results of the Charged Channel Model ...... 49

Figure4.7 AttachmentPointModelSchematic ...... 50

Figure 4.8 2D projection of the electric field near the lightning attachment point. . . 50

Figure 4.9 Paths of particles in the Attachment Point Model ...... 52

Figure 4.10 Simulation Results of the Attachment Point Model ...... 53

Figure4.11 CurrentChannelModelSchematic ...... 54

Figure 4.12 2D projection of the electric field near the currentchannel...... 54

Figure 4.13 Paths of particles in the Current Channel Model ...... 56

Figure 4.14 Simulation Results of the Current Channel Model ...... 57

Figure4.15 ReturnStrokeModelSchematic ...... 58

Figure 4.16 Simulation Results of the Return Stroke Model ...... 59

Figure A.1 Unusual events without the annular geometry and smallfootprint. . . . . 68

Figure A.2 Lightning Correlation with Unusual Events ...... 69

Figure A.3 Additional ring shape footprints of unusual events ...... 69

vii Figure A.4 Lightning Correlation with Unusual Events ...... 70

FigureA.5 SignalTimingFits...... 71

Table 3.1 Parameters of downward negative lightning ...... 38

Table 3.2 Parameters of downward positive lightning ...... 38

viii LIST OF ABBREVIATIONS

ExtensiveAirShower...... EAS

SurfaceDetector ...... SD

FluorescenceDetectors...... FD

PhotomultiplierTube...... PMT

WorldWideLightningLocationNetwork...... WWLLN

RunawayRelativisticElectronAvalanche...... RREA

Intra-Cloud ...... IC

Cloud-to-Ground ...... CG

ElectromagneticPulse ...... EMP

ix ACKNOWLEDGMENTS

Firstly I would like to thank Dr. Fred Sarazin for his guidance and patience. I would also like to thank Dr. Kyle Leach and Dr. Lawrence Wiencke for serving on my committee. To everyone in the Mines Astroparticle group, Kevin Merenda, Johannes Eser, Jeff Johnsen, thank you for the helpful and continual advice. To my friends and family thank you for the support and occasional distractions. Thank you, Emily, for your support and grammatical knowledge.

x CHAPTER 1 UNUSUAL EVENTS OBSERVED WITH THE PIERRE AUGER COSMIC-RAY OBSERVATORY

1.1 Cosmic Ray Overview

Over 100 years ago, Victor Hess showed that the amount of ionizing radiation increases with altitude and concluded there is a source of radiation coming from outer space, this radiation would become known as cosmic rays. In 1939, Pierre Auger discovered time co- incidences of ionizing radiation over long distances, this observation yielded the discovery of Extensive Air Showers (EASs) [1]. An EAS forms when a high-energy primary cosmic ray enters Earth’s atmosphere and interacts with atmospheric molecules creating a large number of secondary particles, eventually creating an extensive cascade of particles [1]. At the highest energies, the properties of a cosmic ray can only be deduced from the measured properties of the EAS it induces in the atmosphere. The development of an EAS has three components, a muonic, a hadronic and an electro- magnetic component. The composition and decay paths of these components are shown in Figure 1.1(a). When a cosmic ray enters the atmosphere the first interaction that occurs high in the atmosphere is a hadronic interaction. The hadronic component contains kaons, pions, protons, and neutrons. These particles form the shower core, as they produce all the other components of a shower and stay close to the shower axis. 98% of the shower energy, however, is eventually contained in the electromagnetic component [2]. The electromagnetic compo- nent originates from neutral meson decays and contains electrons, positrons, and gamma rays. Electrons with energy greater than 85 MeV can produce secondary particle showers via scattering, pair production, and bremsstrahlung radiation [2]. The muonic component of showers comes from the decay of pions and kaons and consists of muon and neutrinos.

1 Muons travel all the way to Earth’s surface with little interaction, thus the muons provide insight into the initial hadronic interaction of cosmic rays and are therefore important for composition studies of cosmic rays [3]. Cosmic rays that produce EAS that extend to the ground have energies above 1014 eV, the flux of cosmic rays as a function of energy follows an inverse power law. This means higher energy events are rarer, the flux of cosmic-rays impinging our atmosphere with energy on the order of 108 eV is about one per cm2 per second, the flux of cosmic rays with energy 1020 eV is less than one per km2 per century [4, 5]. The source of low energy cosmic rays is the sun but the precise sources of the highest energy cosmic rays remain unknown. In each energy range, there are a number of candidate sources which could accelerate subatomic particles to the observed energies. At the highest energies (1018 eV) multiple types of sources could produce cosmic rays. Both size and magnetic field strength contribute to the maximum energy that a possible source could accelerate a cosmic ray [4]. For example, a small source with a strong field, such as a neutron star, could produce the same energy particles as a large source with a weak field, such as a galactic cluster. This relationship can be seen in Figure 1.2. Three main experimental measurements exist that allow for the reconstruction of a cosmic ray, these are the longitudinal profile, lateral distribution, and timing of a signal [2]. The longitudinal profile is the energy deposited as a function of atmospheric depth. This profile is modeled by a Gaisser-Hillas function [9]:

(XMax−X0)/λ dE X X − f (x)= − 0 e(XMax X0)/λ (1.1) gh dX  X X  max Max − 0 dE Where ( dX )max is the maximum deposited energy per distance traveled, X is atmospheric g dE depth in cm2 , XMax is the atmospheric depth where ( dX )max occurs, X0 is a minimum atmospheric depth where the first hadronic interaction occurs. The longitudinal profile can be measured from fluorescence and Cherenkov light produced as the shower travels through the atmosphere [7]. The lateral distribution is the particle or signal density as a function

2 (a) The components and decay paths of an EAS [6]

(b) Schematic representation of the development of a shower front modeled as an inflating sphere[7]

Figure 1.1: Schematics for the development of a Extensive Air Shower

3 Figure 1.2: Hillas Diagram showing the magnetic field versus size of potential UHECR sources. Acceleration of protons to 1 ZeV=1021 eV, or protons or Fe nuclei to 100 EeV =1020 eV require conditions above the respective line. [8].

of distance from the shower axis measured at ground level. This is measured by detectors located on the ground arranged in a sparse array that samples the particle density reaching the ground. Finally, the timing of an EAS is the time at which the signals reach the ground at different distances from the shower core. This is modeled as the intersect time of the ground and an inflating spherical front originating from a shower core, a schematic of the model front is in Figure 1.1(b). Using information from the timing and lateral distribution from a cosmic ray, for example, the arrival direction of the EAS and therefore the cosmic ray primary can be reconstructed.

1.2 Pierre Auger Observatory

The Pierre Auger Observatory is the world’s largest cosmic ray observatory. The obser- vatory covers 3000 km2 of a semiarid desert in Mendoza Province, Argentina at an average altitude of 1400 meters. The study of cosmic rays brought together a collaboration of 18

4 countries to construct the observatory. Construction began in 2002 and was completed in 2008 [7]. The objective of the observatory is the study of the highest energy cosmic rays (above 1018 eV) in an attempt to discover and understand the origin of those cosmic rays. Cosmic rays are measured indirectly via the EAS they produce. The measurements of an EAS allows the reconstruction of the cosmic ray’s arrival direction and energy as well as a statistical determination of the primary’s mass composition as a function of energy. The observatory is composed of two elements: the Surface Detector (SD) and the Fluorescence Detector (FD). The FD observes the longitudinal profile of a shower, and is comprised of 24 telescopes that detect the isotropic emission of ultraviolet light from the electromagnetic components of an EAS as it travels through the lower part of the atmosphere [7]. The FD’s observation periods are limited to dark nights with good weather, thus it has a 15% duty factor. The SD measures the lateral distribution and timing of a shower at ground level. The SD is an array of water-Cherenkov detectors that observe the electromagnetic and muonic components of a shower at ground level. The hybrid design allows for independent measurements of the same properties of a cosmic ray. In addition to the cosmic ray detec- tors, Pierre Auger Observatory is equipped with multiple weather stations placed across the observatory, these can be seen in Figure 1.3(a). The weather stations report temperature, pressure, humidity and wind speed every five minutes [7]. Additionally, an electric field meters record the value of the electric field every second. This measurement is important for Lightning and thunderstorm detection [7]. All of these measurements provide a detailed record of the atmospheric conditions over the observatory. For this study, we will focus on the SD detector.

1.3 The Pierre Auger Surface Detector

The SD detector contains 1660 water-Cherenkov stations spaced 1.5 km apart in a tri- angular grid pattern covering the total area of Pierre Auger Observatory, see Figure 1.3(a). The goal of the SD detector is to measure the lateral distribution and timing of an EAS on the surface of the Earth, the detector measures these as discrete spatial and temporal

5 (a) Map of the Pierre Auger Observatory showing locations of atmo- spheric monitoring, FD stations, and the SD stations shown as tan dots [7].

(b) The main components of an individual SD tank [10]

Figure 1.3: Map of Pierre Auger Observatory and main components of the SD station

6 observations of particle flux. The combination of the observations allows for a reconstruction of arrival direction and initial energy of a cosmic ray [7]. The individual water tanks are made of polyethylene, 3.6 meters in diameter, and 1.55 meters tall. Each tank has a global positioning system and radio communications to relay data to a central Data acquisition center. The tanks contain a highly reflective Tyvek liner and 12,000 liters of ultra-pure water, a schematic of an SD tank is given in Figure 1.3(b). When a relativistic charged particle travels through the water, the particle emits Cherenkov light, this light is detected by three PhotoMultiplier Tubes (PMTs) inside the tank and converted into an electric signal [7]. The tanks are also sensitive to gamma rays as they produce electron-positron pairs in the water volume. The tanks are optically isolated from the outside, they can continuously operate giving the SD detector nearly a 100% duty cycle. Each photomultiplier tube records two signals, one from the anode of the tube and one

particle from the last dynode. The two signals give each tube a detection range between 1 µs to particles 1000 µs traveling through the tank [11]. The tanks record the measured intensity signal in units of the signal produced by a centered vertical muon traveling through the water volume. This unit is called a vertical equivalent muon. This conversion is done to provide a common reference energy for all tanks [7]. The energy of initial cosmic rays optimally detectable by the SD is 3 1018 and above. Below this range, the shower parameters cannot × be fully reconstructed. Note that, the PMTs may become saturated close to the core, but a reconstruction of the lateral distribution function is still possible [12]. The PMTs report the measured signal to the individual station electronics at a sampling rate of 40 MHz. The operation of the SD is largely independent of weather conditions, although SD tanks can pick up electromagnetic noise interfering with the electronics and the detection process. This frequently occurs during thunderstorms. Lightning can produce an ElectroMagnetic Pulse (EMP). When this occurs near SD stations the EMP can induce a voltage in the antenna and the cables of the SD station. This induced voltage has unique characteristics and is recorded as a lightning trigger [13].

7 To reconstruct an EAS lateral distribution the signal must pass a series of triggers in order to be reported to the central station. These samples are then analyzed and must match certain criteria before they are reported. These triggers include a threshold trigger, and a time over threshold trigger, the triggers remove noise from atmospheric muons and other background noise. If a signal passes these triggers it is reported to a central data acquisition system. At the central data acquisition system, additional triggers must be passed. These additional triggers are made to ensure a geometric reconstruction of the shower can be made. The geometric triggers select events where a certain number of tanks within a certain distance of each other are triggered [11]. These central triggers ensure that the signals are from an EAS [11]. The detection pattern is important to recognize an event as an EAS. The Pierre Auger SD is constantly bombarded by cosmic rays. In one year the detector sees about 14,500 events with energy greater than 3 1018 eV and about 1500 × events with energy greater than 1018 eV that pass all levels of triggering [7]. For high energy showers, (> 1018eV ) the footprint of the shower can extend over 25 km2 allowing for greater resolution on the reconstruction of arrival direction [7].

1.3.1 Event Reconstruction

The reconstruction of a cosmic rays energy and arrival direction using the SD is done by fitting templates to the size, timing, and location of signals recorded by SD stations. These three reconstructions provide a model to understand the full geometry of a typical cosmic ray shower. First, the signal start times of individual stations are fitted to a concentric spherical model. This models the evolution of a shower front as it expands in the atmosphere from a virtual origin as an inflating sphere, Figure 1.1(b) shows a schematic of this model. The evolution of this front is modeled with the equation:

c(t t )= x x (1.2) i − 0 |−→sh − −→i |

8 Figure 1.4: Example of an EAS signal in the SD. Colors represent arrival time of the shower front from early (yellow) to late (red). The line represents the projected reconstructed arrival direction [7].

Figure 1.5: Example of the signal intensity of an EAS as a function of distance from shower axis [7].

9 where −→xi are positions of stations and −→xsh and t0 provide an origin of shower development [7], see Figure 1.1(b). The curvature of the sphere is determined from an estimate of when the shower core hits the ground. This fit recreates the evolution of a shower front. Next, the impact point or center of a footprint is obtained from a fit of the lateral distri- bution of a shower. The lateral distribution is modeled by an empirically chosen Nishimura- Kamata-Greisen function [7]:

β β+γ r r + r1 S(r)= S(ropt) (1.3) ropt  ropt + r1  where S(ropt) is an estimator of the shower size, β and γ are slope parameters that depend on zenith angle and shower size. ropt is where the signal is most constrained for a variety of β values. For the Pierre Auger detector, this occurs at about 1000 m. An example of this lateral distribution function for a cosmic ray with 104 1018 eV and a zenith angle of 25 × degrees is given in Figure 1.5 and the footprint on the SD is shown in Figure 1.4. The arrival direction is modeled by the shower axis, which can be obtained by looking at the virtual shower origin (−→xsh), used in the shower geometry reconstruction (−→xgr), to the and the shower impact point, modeled as the center of lateral distribution function reconstruction [7]. This fit uses the equation:

x x a = −→sh − −→gr (1.4) −→ x x |−→sh − −→gr| 1.4 Observation of unusual events with the SD Detector

A new type of event has been discovered in the Pierre Auger Event database. The unusual events differ in time-scale and signal geometry from a typical cosmic ray signal. Originally discovered in 2006, these events are characterized by a large number of triggered detectors arranged in a roughly symmetric ring shape and whose station signals typically last for approximately 10µs [13], much longer than what is expected from typical cosmic ray signals. The first of these events discovered contains 65 triggered surface detectors in ring pattern with an outer diameter of 20 kilometers as well as signal timing 100 times longer than a

10 typical cosmic ray signal [14], these characteristics can be seen in Figure 1.6. This type of events have become known as SD Rings due to their strange geometry, but I will continue to refer to these events as unusual events due to the variety in the lateral distribution of the events (more pictures of the spatial distribution of these events are available in Appendix A) and the possibility that the “hole” at the center of the footprint is due to a detector artifact [13, 15, 16]. Between 2004 and 2017, a total of 34 events have been found with the long characteristic signals, lasting for 10-20 µs .

1.4.1 Timing and Geometry Reconstruction

The unusual events have two characteristic timing structures, the timing for an individual station and the timing of the propagation signal. The signal timing for an individual station can be fitted to an asymmetric Gaussian with the equation [16]:

− z 2 (ti µi ) 2 exp 2 , if ti >µ . z 2 2 1 2σi i A(ti; µ ,σ ,ri)=  − − z 2 (1.5) i i 2 (ti µi )
√2π σi (ri + 1) exp 2 2 , otherwise. − 2ri σi p
where /muz is the time of the peak, σ2 is the variance in the fall time, r σ is the variance i i i × of the rise time [15]. There are some general characteristics of the timing signals for the unusual events [15]. First, the rise time is always smaller than the fall time. Second, σi is always greater than 2.5µs. Finally, the rise time appears to be a constant function with respect to fall time. Due to the long station timing, the stations will not always record both the rise and the fall of the signal, an example showing a station only capturing the full rise time is presented in Figure 1.8. The propagation of signal can be reconstructed by a process similar to the timing reconstruction of a cosmic ray signal. A point is defined vertically above the “hole” and the intersection of an inflating sphere and the ground is calculated. The fits from this reconstruction can be seen in Figure A.5. The timing reconstruction shows the propagation of signal across tanks for the unusual event corresponds to a point source less than 3-4 km above the ground [13, 15].

11 (a) Comparison of timing for a station in event 4067441 and a typical cosmic ray timing for a single tank, unusual signal in black and a cosmic ray signal in red [13].

(b) Event 4067441 as seen by the Surface Detector, showing the extended geometry of an unusual. A ring is formed due to triggered tanks surrounding a region of non triggered tanks. Some tanks registered a signal that is associated with lightning [13].

Figure 1.6: Timing and geometrical characteristics of an unusual event [13]

12 (a) Footprint of a ring event, colors represent ground time from early (yellow) to late (red), the size of markers is proportional to the log of signal intensity [14].

(b) Lateral distribution function fit with a modified Nishimura-Kamata-Greisen function [14].

(c) Lateral distribution function fit with a modified Nishimura-Kamata-Greisen function with weak sig- nal stations removed [14].

Figure 1.7: Footprint and lateral distribution function of an unusual event.

13 An attempt to fit the lateral distribution function of an unusual event is shown in Fig- ure 1.7(a). The fit of a lateral distribution function of a typical cosmic ray using equation 1.3 clearly does not appropriately describe the unusual events [14], as seen in Figure 1.7(b).The lateral distribution function approximates the timing better if the stations that reported less than 10 VEM are removed from the fit, as seen Figure 1.7(c). While the events have a variety of different geometries, all have a similar timing distribution. The typical events have extended geometry, a roughly symmetric disk extending up to 20 km in diameter with an annular geometry and an inner radius of 4 km diameter [13], this footprint shown in Figure 1.6(b) and Figure A.3. Some unusual events do not have a “hole” at the center. The number of triggered stations triggered by a single unusual event can range from 10 to more than 100, Figure A.1 and Figure A.2. There are a number of clues that suggest the unusual events may be caused by lightning. The weather stations during observations reported high wind speeds and high humidity, suggesting that a rainstorm was present. In most unusual events multiple stations near the “hole” in unusual events report a lightning trigger, this can be seen in Figure 1.6(b). As mentioned, Pierre Auger is equipped with electric field sensors that can detect lightning. Correlation between lightning and the unusual events were found for two of the events, this correlation can be seen in Figure A.4. Detectors external to Pierre Auger can provide additional insight. The World Wide Lightning Location Network (WWLLN) is a network of lightning detection stations all over the world that record a triangulated position and time of lightning strikes [17]. The lightning detection is only accurate within 50µs and the reported location is within 15-20 km of the actual lightning strike [17]. This accuracy is not good enough to correlate a WWLLN event to the center of the footprint of an unusual event but it can confirm that a lightning strike occurred near the unusual event within a millisecond of one. For 22 unusual events between 2009 and 2017 9 of them were spatially and temporally correlated with a lightning strike in the WWLLN data [16]. The detection efficiency of WWLLN is highly dependent on peak current, for typical lightning strikes,

14 Figure 1.8: Incomplete measurement of the long signal timing, and comparison of high and low gain signal as a check for particles entering tanks. The low gain channel multiplied by the Dynode over Anode gain factor match perfectly [13]. the detection efficiency is only 4% but this increases for greater peak currents [17]. The correlation of 40% of the unusual events to WWLLN suggests that the unusual events may all be caused by powerful lightning strikes. An early study showed that the signals induced in the individual stations are NOT due to an EMP but are actually due to particle interaction inside the water tank [13]. This confirmation can be shown in two ways. First, a comparison of the two signals of a PMT, the signals in the anode and dynode of a PMT were compared and the signal shape matches identically. Additionally, the ratio of amplitudes of the signal matches the ratio of gains between the anode and dynode, showing that the signal was a real signal, this comparison is shown in Figure 1.8. If the two signal shape and gains did not match it would indicate noise was picked up in the wiring of the SD tank electronics. Second, photomultiplier tubes that were turned off did not report signal. Reports of a signal in inactive PMTs also occurs when an EMP induces a voltage in the wiring of the PMTs [13]. There were no cases of inactive PMTs reporting signal showing the signal in these tanks was in fact particles producing light

15 in the tanks. At the initial discovery of these events the “hole” seemed physical by showing the tanks were operating as expected at this time [13]. However, more recently, an analysis was done that called into question the physicality of the annular geometry. The wide variety of geometry corresponding to signals with long timing may suggest the hole may be a detector artifact [16]. The Observatory is designed to detect cosmic ray events, the triggering scheme is designed to record events with the characteristics of a cosmic ray. The unusual events do not have these characteristics, therefore the triggering scheme needs to be altered to properly detect these events [16].

16 CHAPTER 2 SIMPLE COSMIC RAY PROPAGATION MODELS

In an attempt to characterize these unusual events, computer simulations of EAS fronts were constructed. The goal of these simulations was to reproduce the apparent ring geometry and extended signal timing of the unusual events. The models were implemented with C++ and the ROOT Data Analysis Framework, using an iterative development approach. A model was developed, the results of this model were compared to the characteristics of the unusual events, and then the model was subsequently changed in an attempt to better match the characteristics. This procedure was iterated several times, resulting in multiple attempts to simulate a cosmic ray front. The simple cosmic ray models all share the same basic components. First, the geometry of an EAS front is modeled in the same way the Pierre Auger Collaboration simulates the cosmic ray front as described in Section 1.4. It is described as an inflating sphere originating at a single point as illustrated in Figure 1.1(b). A point source is defined, and from that point source, a sphere inflates at a constant rate. The rate at which the radius of the sphere

increases will be referred to as VFront. Second, the energy of each inflating front is defined as a fixed value, and the initial energy is evenly distributed across the entire surface area. When sphere expands the energy density decreases as the area increases, this is proportional

1 to a factor of the sphere’s radius R: R2 . Finally, all of the simulations measure the signal on the ground in the same way; discrete points are chosen to detect the relative signal intensity over time, this is a similar measurement to the one performed by the SD stations. These simulated detectors are spaced 1 km apart from each other in a straight line. These three characteristics form the simple cosmic ray model, as illustrated in Figure 2.1.

17 Figure 2.1: Schematic of the simple spherical inflation model. This schematic shows, the point source as a red dot, the surface stations as blue squares, and the inflating sphere.

2.1 Propagation Models

A stationary source could not reproduce the signal characteristics [15], but the simple model can be artificially altered in an attempt to reproduce the unusual characteristics. An initial model explores the effects of a propagating source. The source used in this model is initially at an altitude of 10 km, at the top of the troposphere, and propagates vertically downward at a velocity VSource. For this model both VSource and VFront are equal to the speed of light The propagation must be vertical because the unusual events have rough circular symmetry. If the source propagated at an angle to the zenith, the simulated signal would not have the same symmetry. A propagating source behaves similarly to the simple model, but instead of emitting one inflating spherical front, the propagating source emits a new front for every meter it travels. A Gaisser-Hillas function models the energy deposited in the atmosphere by an EAS as a function of atmospheric depth. Assuming that the energy loss process of the source comes from a cosmic ray shower, in the propagation models, the initial energy of each front as a function of altitude is weighted by a Gaussian approximation of the Gaiser-Hillas function. For each emitted front, the source’s initial energy is multiplied by

18 the value of the Gaussian approximation at the height the front is emitted at. This weights the initial energy of the fronts according to the energy lost in the atmosphere by an EAS. An approximation was used because it reduces the number of free parameters in the model, and can be calculated using built-in functions. A schematic of this propagation model is presented in Figure 2.2(a) and the results of the simulation are presented in Figure 2.2(b). In this approach, the “physicality” of the parameters is not considered. The objective here was to see if any parameterization of a shower propagating downward would produce ring- like events on the ground. The selected parameters were the altitude where the maximum energy is deposited and the width of the Gaussian approximation. The width was chosen to be σ = 1500 because this would result in a range of 3000 meters within 1 standard deviation of the peak, this range corresponds to the distance a particle moving at the speed of light would travel in 10 µs. Therefore the time that the emitted spheres have the highest energy would be equal to the approximate length of an unusual signal. Xmax was chosen to be at an altitude of 5 km. This would be a very high altitude for Xmax of a typical EAS [3]. If the

Xmax is at a lower altitude the magnitude of signal intensity near the axis of propagation is too high and the signal is dominated by the central stations. The results of this simulation are shown in Figure 2.2(b). This plot shows that the signal is most intense near the shower

1 core and much weaker beyond a kilometer. The geometric factor of R2 is dominating, and the signal is attenuated at large distances. This model is unable to reproduce a ring geometry. One notable result of this model is that the signal at 4 km was shown to broaden to a length of about 10µs, the relative signal length at distances greater than 4 km is presented in Figure 2.3. This is expected because of the choice of parameters for the model.

2.1.1 Subluminal Propagation Model

The next step in developing propagation models was to vary the velocity of the source. Initially, the source was propagating at the speed of light, thus it is only possible to propagate the source at a slower velocity. For this model the simulation is exactly the same as before

except the velocity of propagation has slowed, the velocities are now Vfront = c and VSource <

19 (a) Propagation Model showing the direction of propagation (pur- ple), emitted inflating spheres (red), and points where a signal is measured (colored squares)

(b) Measured intensity and timing at distances along the ground from the source, colors correspond to 1 km distances and match the squares in Figure 2.2(a). Time is measured from the beginning of the propagation, T=0 corresponds to the source at an altitude of 10 km.

Figure 2.2: Schematic and simulated results of a propagation model with both VSource and VFront equal to the speed of light. 20 Figure 2.3: Lengthened time signature in the propagation model 4 km from the source c. A schematic of this model is shown in Figure 2.4. Multiple velocities of the source were sampled and there were no signs of a ring geometry present in the resulting simulations. Two of the velocities sampled were 0.95 c presented × in Figure 2.5(a) and 0.75 c presented Figure 2.5(b). These velocities show that there is × a relationship between source velocity and signal width. When the source velocity is 75% the speed of light the timing signal is lengthened to the requisite 10µs needed to explain the unusual signals.

2.1.2 Shock Wave Propagation Model

Next in attempt to force a ring geometry, both the velocity of the source and the velocity of the front were altered. In the initial model, the velocity of the source and the velocity of

the signal were equal. The case where VFront >VSource is seen in the subluminal model. The

remaining situation where VSource >VFront results in a similar phenomenon as a sonic boom. For a sonic boom to occur an airplane must travel faster than the speed of sound. The air behind the plane begins to form a shock wave as the signal bunches up. This shock wave can be used to build up a signal away from the center of the shower. When the source and

21 Figure 2.4: Subluminal Propagation Model schematic showing the direction of propagation (purple), emitted inflating spheres (red), and points where a signal is measured (colored squares), with Vfront = c and VSource

VFront VFront ratios, vSource =0.85 in Figure 2.7(a) and VSource =0.65 in Figure 2.7(b) The results of the shock wave model simulations show that the peak signal intensity no

VFront longer occurs at the shower core, but can now be set at a tunable distance. For VSource =0.85

VFront this peak begins to form at 2 km while the slower source for VSource =0.65 this peak begins to form at 4 km. This model may be able to reproduce the ring geometry. The SD stations have a minimum threshold of signal needed to trigger, if the signals under 2 km do not peak above that threshold they will not trigger SD stations. If the peak signal intensity is above

22 (a)

(b)

Figure 2.5: Simulation results of a source with a subluminal propagation velocity. Results are for a V of (a) 0.95 c and (b) 0.75 c. source × ×

23 Figure 2.6: Propagation Model showing the direction of travel (purple), emitted signal (blue), points where the signal was measured (colored squares) and the shock wave (red)

24 (a)

(b)

Figure 2.7: Simulated results of shock wave models showing measured signal intensity and VFront timing at distances along the ground from the source, for two ratios of velocities (a) VSource = VFront 0.85 and (b) VSource =0.65.

25 the threshold then a “hole” in the center of the signal footprint could form. The shock wave model, however, does not reproduce the elongated signal timing seen in the unusual signals. In order for the signal to peak at a distance away from the center the signal is compressed in time and therefore the peak signal only lasts for approximately 5µs.

2.2 Conclusions

The simple propagation models presented here were unable to reproduce both the ring geometry and the elongated timing signature in the same model. Additionally, these models do not hold up when a more physical situation is considered. First cosmic rays do not typically arrive perpendicular to Earth’s surface, the median angle of arrival is 38 degrees from the zenith [7]. If the source of unusual events were cosmic rays it would be unlikely that the majority of events were cylindrically symmetric. Most importantly the mean free path of particles is extremely limiting for these models. When the signal propagates slower than the source, a ring could be constructed but it would require the signal to propagate at 85% of the speed of light. For electrons with less than 1 MeV of energy (electrons traveling with a velocity under 0.94c), the mean free path in the atmosphere is less than a meter [18]. Therefore the emitted particles cannot travel the kilometers needed to reach the SD stations. The cosmic ray propagation models are therefore unable to reproduce the ring geometry and long signal characteristics and thus the source of the unusual events is most likely not related to cosmic rays. After the cosmic ray modeling was performed, the ring geometry was found to not exist in all of the unusual events. The long time characteristic was found in events with a footprint similar to a typical cosmic ray. Therefore the ring geometry may not be characteristic of the unusual events. Nevertheless, the propagation models are also unable to explain the unusual events where the ring is not present. The shock wave and subluminal source models were capable of recreating an elongated time signal in tanks near the shower core as shown in Figure 2.5(b) and Figure 2.7(b). However, Both of these models would require particles moving at a fraction of the speed of light. These particles would be quickly attenuated by

26 the atmosphere. Those models, therefore, remain unable to physically reproduce the long time signal of the unusual events without making unphysical assumptions on propagation velocities.

27 CHAPTER 3 PRODUCTION OF RELATIVISTIC RUNAWAY ELECTRON AVALANCHES IN LIGHTNING STRIKES?

Due to the number of clues that link the unusual events to thunderstorms, it is very possible that these events are caused by a process related to other known energetic emissions from lightning. Thunderstorms are a source of large-scale energetic phenomena. Thunder- storms have been observed to cause multiple optical phenomena in the upper and middle atmosphere. These phenomena include Blue Jets, Red Sprites, and Emission of Light and Very Low Frequency perturbations due to Electromagnetic Pulse Sources (ELVES). An il- lustration of these phenomena is presented in Figure 3.1. While jets are not associated with individual lightning discharges, sprites and ELVES are known to accompany lightning flashes. Red sprites have been observed to occur at altitudes between 50 and 90 kilometers. Elves, caused by the interaction of the lightning EMP with the ionosphere, have been observed to span hundreds of kilometers from the initial return stroke [19]. Lightning may produce other phenomena such as x-ray and gamma ray flashes, runaway electrons, and EMP bursts. These events have been observed to occur at various heights in the atmosphere and may be the cause of some of the mentioned transient luminous events [19, 20]. The large-scale emission of radiation associated with a lightning strike is explored as a possible source of the unusual events observed by the surface detector of the Pierre Auger Observatory.

3.1 The Lightning Discharge Process

A lightning strike is a form of electrostatic discharge. Most lightning strikes do not interact with the ground, but rather discharge between two charged regions in a cloud. These are called Intra-Cloud (IC) lightning. Only about 25% of all lightning discharges occur between the cloud and the ground, this type of discharge is called Cloud to Ground (CG) lightning [22]. CG lightning is classified by the direction of charge flow. Most CG lightning

28 Figure 3.1: Upper atmospheric lightning and electrical discharge phenomena associated with thunderstorms [21]

29 Figure 3.2: Processes in a typical negative downward lightning strike with a rough estimate of the timing for each process. [22] strikes are negative downward lightning, meaning that the negative charge is transported from the cloud to the ground. The steps involved in a negative CG discharge are described in this section and are illustrated in Figure 3.2.

3.1.1 Initiation of Lightning, and the Quasi-Static Background Field

Inside a cumulonimbus cloud, small pockets of charges are formed by interactions of small ice crystals and water droplets, similar to the generation of static electricity. These small pockets of charge undergo large-scale charge separation as a result of gravity and convection within the cloud. Even though this large-scale distribution of charges in a cloud is complex

30 and is constantly evolving, a simplified model of this charge structure exists in the form of a vertical tripole structure, this is illustrated in Figure 3.3. This tripole structure consists of three charged regions, the first with a lower positive charge, second a middle negative charge, and finally an upper positive charge. The typical charge of these regions are respectively 3C, 40C, 40C and are placed at 2km, 7km, and 12km from the ground. This tripole structure − is capable of replicating the measured background field strength on the ground during a thunderstorm [19]. The fields within the thundercloud range from 100 to 400 kV/m. This is about an order of magnitude lower than the field required to initiate a conventional electrical breakdown of air, at about 3200 kV/m. therefore lightning does not initiate spontaneously. The process that initiates lightning has yet to be discovered. There are two leading theories [22]. In the first, electric fields may become enhanced near highly deformed water droplets to such an extreme that conventional breakdown may occur near the water droplets, this is called the hydro-meteor theory. The other is through cosmic ray seeded runaway breakdown which will be described in section 3.2. In either case, a local ionized region is created in the cloud that greatly enhances the electric field in a small region. In this enhanced field region, a self-propagating lightning channel can form: this is the first step of a lightning strike. This then becomes a slow propagating stepped leader.

3.1.2 Leader Stepping Process

The stepped leader is the process that establishes a connection between the cloud and the ground. For negative CG discharges the stepped leader is composed of electrons and forms in the negatively charged region of the cloud. When initiated, the stepped leader moves downward to the lower positive charge region. The magnitude of the lower positive region relative to the negative region determines the type of lightning that is formed by the stepped leader [22]. If the magnitude of the lower positive region is small, the stepped leader can break through without altering its path and will form a simple CG lightning strike. But if the magnitude of the lower positive charge is large enough that the stepped leader cannot break through the lower cloud layers an IC discharge will form.

31 Figure 3.3: A vertical tripole representing the charge structure inside a thundercloud [19]

After the stepped leader breaks through the cloud base, it will begin taking steps towards the ground. The exact mechanism of this process is unknown, but the process has been observed using high speed cameras and electric field measurements, therefore the properties of this process is known [19]. The stepped leader forms discrete steps. The steps are 10-200 m in length and the leader tip moves with a velocity on the orderof 107m.s−1. Between individual steps there is a pause of 10 50µs [19]. Each individual step forms over the − course of about 1 µs. Again the exact mechanism of the formation of the long leader steps is unknown, but lightning leader formation is likely similar to long laboratory sparks. A theoretical model of leader formation based on laboratory spark experiments exists [23]. This theory involves a series of steps to form a new step. First, due to the large potential formed at the leader tip a region of plasma, known as a corona develops from the leader tip. The corona consists of a negative charge avalanche outward from the tip. More simply, the leader tip accumulates electrons, some of which are emitted and form a corona. After the initial negative corona develops charges begin to redistribute themselves within the corona region, this redistribution allows for a positive corona to develop back towards the leader tip. This bipolar corona is called the pilot system. The region where pilot systems develop

32 ally Figure 3.4: Detailed scheme of the inter-step processes. Abbreviations are as follows: CN, negative coronas; CP, positive coronas; PL, pilot system; LS, space leader; LN, negative leader. The time ti indicates the development of a negative corona; t1, t1’, and t1” show the development of pilot systems; t2 is the beginning of the extension of the negative leader tip; t3-t5 is the multi-directional expansion of the negative leader tip; t6 is the final junction extension of the negative leader tip and the start of a new stepping cycle [23]. is called the streamer zone. Several of these pilot systems can develop over the course of one step, which can lead to the branching observed in stepping process of lightning. This step consists of the ionizing of the air in front of the leader tip. Finally, the leader channel takes a rapid step. During the course of propagation of the pilot systems, the corona region heats up to about 1500 K, which allows for the creation of a conducting region that forms an extension of the stepped leader channel. The formation of the leader channel occurs in multiple regions, it can extend from the previous leader tip or it can form between positive and negative corona in a pilot system, in which case, it is referred to as a space leader. The previous leader channel merges with the space leaders forming a complete step. These steps are illustrated in Figure 3.4. The leader tip has been observed to be the source of X-rays observed at a distance of couple hundred meters [22, 24]. Simulations of the leader tip channel have shown that the

33 fields around the leader tip are capable of accelerating “cold” electrons to MeV energies [25], this occurs in the development of the negative corona and via bremsstrahlung radiation X-rays can be produced from the stepped leader [24, 25].

3.1.3 Attachment process

The attachment process is the least understood process that occurs during CG discharges. The attachment process begins when the stepped leader approaches the ground. A potential difference exists between the stepped leader and the ground, which may cause an upward leader to be initiated. Upward leaders are oppositely charged compared to the downward leader though they are believed to behave roughly the same. These can be initiated from the ground but are more likely to be initiated from a pointed metal object such as a lightning rod. The streamer zones of the upward and downward leaders meet and form a common streamer zone. In this common streamer zone, the two leader tips meet. The attachment point typically occurs under 50 meters above the ground but this height can be much higher if the upward leader is initiated from a tall pointed object [19]. During the attachment process, the fields between the tips can be greatly amplified over a distance of less than a meter for a few nanoseconds [26]. The connection of the plasma tips is similar to the closing of a switch; a conducting path between the cloud and ground is formed when this occurs.

3.1.4 Return Stroke

The channel that forms between the cloud and the ground after attachment has been observed to have a low resistance (1-3 Ωm−1). This allows the charges located in the leader channel to be rapidly lowered to the ground, this charge transport is known as the return stroke. Beginning at the point of attachment a region of accelerating electrons is formed, this region moves up the channel at a velocity between 1 108m.s−1 and 2 108m.s−1. This × × creates a front where a current is established. If the current is measured at one point along the channel, the current begins at a low value but, as the front moves past, the current at that point rises to its peak values within a few microseconds. The peak current measured

34 during the return stroke is typically about 30 kA but has been observed to peak at values greater than 200 kA [27]. As the front moves beyond the point in the channel, the current at that point falls to a half peak value in a few tens of microseconds. This current produces electric and magnetic fields along the channel. These electric fields are difficult to calculate due to the tortuosity of the lightning channel, but an “engineering” model is commonly used in which a vertical channel and perfectly conducting ground are assumed [19, 28]. This model is capable of matching the measured electric field of about 6 V/m at 100 km. During the return stroke, the channel is heated to over 50,000 K producing the brightest optical emission during a CG discharge. The channel quickly cools as the current dissipates, the rapid temperature variations expand and contract the atmosphere around the channel creating thunder. Once the initial return stroke ceases, additional charge transport occurs and then sub- sequent return strokes may occur. Following the return stroke, a relatively low current of roughly a few hundred amps exists in the channel. The continuing current may last for 10 to 100 milliseconds. During the continuing current phase, the current can suddenly rise to a few kiloamps, these perturbations are known as M components. Once the continuing cur- rent stops, the channel degrades and additional charge transfer occurs in the cloud. These intra-cloud transfers are known as the J and K processes, these serve to transport additional charges from the cloud into upper parts of the lightning channel. These processes occur over about 100 ms but they allow for additional lightning discharges to occur in the same channel. For each additional discharge, a new leader forms and steps down along the same channel. When subsequent leaders reach the ground, additional return strokes occur. The subsequent strokes are similar to the first return stroke but they typically have a lower current. There are typically between 3-5 return strokes in a negative CG lightning strike, but up to 28 return strokes have been observed for one lightning strike.

35 3.1.5 Other types of CG Lightning

There are multiple types of lightning, these include downward negative, upward negative, downward positive and upward positive. The most common type is the previously described downward negative, 10% or less of all CG discharges are downward positive strikes. Upward lightning discharges are rare and typically only occur during artificially triggered lightning events. Positive downward lightning is particularly interesting for a few reasons [19]. Down- ward positive lightning has the highest directly measured currents (nearly 300 kA [27]) and largest charge transfers (hundreds of coulombs). Secondly, positive lightning has been found to be related to luminous phenomena in the middle atmosphere. Finally positive lightning typically has only one return stroke [19]. The development of a positive discharge follows the same steps as negative discharge but one key difference is the leader for a negative discharge propagates in steps while the leader for a positive discharge propagates in a more continuous manner. Despite these properties, the work done in this thesis will focus on negative CG lightning because more is known about negative CG lightning and more work has been done in modeling the fields from negative CG lightning [19].

3.1.6 Characteristics of Lightning

Karl Berger and co-workers gave the most complete characterization of a downward neg- ative flash in 1975 [27]. The data was collected on top of 70-meter tall towers in Switzerland and is still used today in engineering and scientific applications. A few key parameters for negative lightning are detailed in Table 3.1 and for positive lightning are detailed in Table 3.2. The distribution of currents for different types of lightning is illustrated in Figure 3.5

3.2 Runaway Relativistic Electron Avalanche

The idea of a single runaway electron originated from observations of β particles in a cloud chamber by C.T.R. Wilson in 1925 [29]. Wilson’s quantification of energy loss of the β particle was in units of eV per unit track length, these are the units of an electric field. Wilson theorized that if an electric field of the same magnitude as the energy loss was

36 Figure 3.5: Cumulative statistical distribution of return stroke peak current from measure- ment at a tower top for (1) negative first strokes, (2) negative subsequent strokes, and (3) positive first strokes [19]

37 Table 3.1: Parameters of downward negative lightning, 90% of measured values fall in mea- surement range [27]

Parameter Measurement Unit Typical first stroke peak current 14-80 kA Typical subsequent stroke peak current 4.6-30 kA Transported charge for a complete strike 1.3-40 Coulomb Front duration (time for the current to rise from 2 kA to peak) 1.8-18 µs Stroke duration (2 kA to half peak value on the tail) 90-200 µs Time interval between strokes 7-150 ms Flash duration 0.15-1100 ms

Table 3.2: Parameters of downward positive lightning, 90% of measured values fall in mea- surement range [27]

Parameter Measurement Unit Typical first stroke peak current 4.6-250 kA Transported charge for a complete strike 20-350 Coulomb Front duration (time for the current to rise from 2 kA to peak) 3.5-200 µs Stroke duration (2 kA to half peak value on the tail) 25-2000 µs

present in the cloud chamber then the β particle would lose no energy. this also implies that if the electric field was significantly stronger than the energy lost per unit length an electron would continuously gain energy and “run away”. Wilson proposed electrons of sufficient initial energy could be accelerated by electric fields present in thunderclouds and become runaway electrons. Two conditions must exist in order for an electron to run away. First, an electron must have sufficient initial energy. Second, the electric field must be strong enough in order to overcome the frictional forces present in the atmosphere. The effective friction force on electrons at standard temperature and pressure is shown in Figure 3.6. At low energies, this friction force is dominated by long-range, low angle scattering from Coulomb interactions, however, this force is inversely dependent on the velocity of the particle, σαv−4 [30]. Thus an energy threshold can be found where the friction force cannot prevent the acceleration of a relativistic electron by an electric field. At higher energies, other frictional forces become

38 Figure 3.6: Effective friction force on a free electron in the atmosphere as a function of energy, compared to an applied electric field. The calculated field for required for runaway electrons is shown as the red dashed line. [18]

dominant. Bremsstrahlung radiation increases logarithmically with energy [30] and becomes dominant at higher energies. Radiative forces prevent the electrons from accelerating without bound. The minimum frictional force for electrons occurs at 1.2 MeV [30]. The electric field threshold for runaway electrons to propagate large distances is slightly higher than the minimal friction force. This minimum field strength needed is 284 kV/m [31]. This electric field threshold is much lower than the conventional electrical breakdown in air. A single runaway electron produces an avalanche of electrons. The runaway electron ionizes gas molecules, producing more free electrons. Some of these secondary electrons will have enough energy to become runaway electrons themselves. In this process an exponential number of particles are produced and a Runaway Relativistic Electron Avalanche (RREA) forms. The initiation of RREAs requires a seed electron with energy inside the runaway regime. The energies that fall within this regime are dependent on the strength of electric field present. Using Figure 3.6, the runaway regime can be estimated, the intersections between the field strength and the effective friction force define the endpoints of the runaway

39 regime. For example, at the threshold field of 284 kV/m the intersection of the field line and the fiction force curve occurs at approximately 0.1 MeV and 10 MeV. Electrons with this energy are present in the atmosphere as secondaries in EASs or near lightning leader tips. RREAs have four important properties [30].

The field required to cause RREAs is lower than the conventional breakdown of air. •

RREAs require an initial seed electron. •

The RREA develops in the direction opposite of the electric field lines. •

The electrons can eventually produce X-ray and γ-ray photons through bremsstrahlung • emission.

If RREAs occur in a cloud it can create a highly ionized region that could theoretically produce a self-sustaining lightning leader. The background electric fields in a thundercloud can reach strengths greater than the threshold field for RREAs. Therefore RREA is a candidate to explain the initiation of lightning [32]. Gurevich et al [32] showed that the number of electrons produced over a distance traveled is described by the following equation:

L N (L)= N exp (3.1) electrons seed ∗  λ 

where Nelectrons(L) is the number of final electrons as a function of the distance from the start

to the end of an avalanche L, Nseed is the number of seed electrons, and λ is a characteristic length of the avalanche. An empirical formula for lambda was chosen to be dependent on the electric field E [31]: 7300kV λ = (3.2) E 276 kV − m This equation works for conditions where the pressure is 1 atm. For different pressures, the calculated length scales are increased by a factor of P −1 and electric fields are reduced by a factor of P, where P is the pressure in atm.

40 RREAs have been shown to be a possible source of Terrestrial Gamma-ray Flashes (TGF) [33]. TGFs can occur in different regions of the atmosphere but are more common in the upper atmosphere. The atmosphere is thinner and therefore the magnitude of the field required to create RREAs is lower. TGFs were discovered in 1994 by a satellite designed to observe cosmic gamma-ray sources [20]. Roughly 1014 to 1017 runaway electrons are needed to produce a TGF observable from a satellite. Calculating the number of electrons from a runaway process under similar conditions as the observed TGF using equation 3.1 gives only 1012 runaway electrons [18]. In order to reproduce the magnitude of electrons, a feedback mechanism is needed [31]. During an RREA, two forms of feedback can occur, positron feedback and gamma-ray feedback. Positron feedback occurs when a gamma ray produces a positron via pair production, which travels in the opposite direction to the electron. The positron can excite more electrons via Bhabha scattering [31]. Gamma-ray feedback occurs when a gamma ray is produced and travels in the opposite direction of the runaway electrons and can produce addition seed electrons via the photoelectric effect or Compton scattering. These feedback mechanisms allow for the required magnitude of electrons to recreate a TGF [31]. A Monte Carlo simulation of RREA and its feedback mechanisms are shown in Figure 3.7.

41 Figure 3.7: Monte Carlo simulation of RREA. A 1 MeV electron is injected at the top of the center avalanche. The left and right showers were selected to show gamma ray feedback and positron feedback respectively. The dashed lines connecting the showers indicate gamma rays and the thick dark line emerging from the right avalanche indicates a positron. For clarity, only a small fraction of electrons are illustrated [31]

42 CHAPTER 4 LIGHTNING MODELS

Modeling RREAs requires handling calculations of high energy interactions for an enor- mous amount of particles. The simulations of the cosmic ray models do not consider par- ticle interactions. In order to include these interactions the RREA simulations presented in this chapter utilize a physics simulation framework. The GEometry ANd Tracking GEANT4 toolkit consists of detailed libraries of interactions between particles and matter [34]. GEANT4 is a well-established toolkit for the simulation of particles traveling through matter and is widely used in the fields of particle physics, nuclear physics, and medical research [18]. The GEANT4 toolkit has been shown to accurately reproduce RREAs [18]. Simulations using GEANT4 require the specification of three components of the simulation. First, the specification of physical interactions used to simulate trajectories and interactions for different energy ranges. Second, the specification of the physical geometry; a detector, a body, the atmosphere, etc. Third, simulations require defining a source of particles; an electron gun, a radioactive source, a particle accelerator, etc. GEANT4 then calculates the trajectories and interactions of source particles and any secondary particles as they pass through the geometry. The thunderstorm simulations all include the same basic components. First, the physics lists used to simulate interactions are standard physics lists recommended by GEANT4, with the Livermore Physics list to specify electromagnetic interactions. The Livermore list was used in additional validation of other RREA simulations [18]. Second, the simulated atmosphere consists of a cylinder that has a 10 km radius and is 4 km tall filled with air at standard temperature and pressure. Third, the source of initial particles is unknown so an assumed source will be created, this is an isotropic source of 1 MeV electrons unless otherwise stated. Fourth, the simulations measure particles in the same way. If any particle

43 hits the ground the position, energy, time of the hit, and particle type are recorded. Fifth, a limit is imposed on the magnitude of the electric field present. The conventional electrical

kV breakdown for air is 3200 m , and air does not breakdown outside the lightning strike, kV kV therefore, a limit is imposed. Two values were used for this limit, 500 m and 2000 m , these values represent the range for the magnitude of fields measured within two meters of a channel of a triggered lightning strike [35]. The chosen limits are shown in Figure 4.1 on top of the plot of effective friction on a free electron in air. This plot shows the expected range of energy for runaway electrons for the two field values. The lower energy limit for the low field limit and the high field limit are approximately 500 keV and 50 keV respectively [36]. This means that electrons with energy greater than the lower energy limit will run away and create an RREA, given their momentum is roughly aligned to the E-field. Finally, a production threshold in the simulation was imposed at 150 keV due to computational limitations, the number of particles that is produced is too great and the computer does not have enough memory to track all the particles. This means particles that fall under this threshold will no longer produce additional particles but will be simulated until they lose the remainder of their energy. This production threshold will not affect simulations with the low field cutoff but will cut out part of the RREA for the high field limits. An RREA produces a characteristic number of electrons for a distance traveled under a known constant field. This is calculated using equation 3.1. To ensure our simulation was behaving as expected a preliminary simulation was made to compare the theoretical number of electrons produced and the simulated number of electrons produced. 10,000

kV initial electrons of 500 keV were placed in a uniform field of 400 m for 200 m. The simulated results for 10 trials averaged 309,000 12000 electrons produced, this is within one root ± mean square error of the theoretical number of 299,000. Therefore we can conclude that the GEANT4 simulation is replicating the number of electrons produced in an RREA accurately. In order to get charged particles or gamma rays to propagate up to 10 km from a central location, a strong radial field must be present. This force could potentially come from

44 Figure 4.1: Effective friction force on a free electron in the atmosphere as a function of energy, compared to an applied electric field. Imposed high and low cutoff fields are shown in magenta. The vertical lines show the minimal energy an electron needs to run away under the cutoff fields. [18] the large electromagnetic fields associated with thunderstorms. Three thunderstorm fields were investigated as possible sources of the unusual events; the background field, the field created by leaders, and the field created by the return stroke. The background is commonly modeled as a tripole inside the thundercloud. The electric field from the background field is not strong enough for RREA to develop below the cloud, thus the focus of modeling will be to the stepped leader and return strokes.

4.1 Charged Channel Model

The initial model models the field from the leader channel. The leader channel is com- posed of charges deposited by the leader tip along its path. This forms a channel of charge connecting the cloud and the ground. To simply model this, a channel with uniform charge density was created and the fields were computed from a line charge. This line charge is placed below the background field formed from tripole charge in the cloud. A schematic of this model is presented in Figure 4.2. This model resulted in a radial field that may acceler-

45 Figure 4.2: Conceptual model of a channel of charge deposited by the lightning leaders. A single line charge with uniform density below the tripole background field. A source of MeV electrons is assumed

Figure 4.3: 2D projection of the electric field near the charged channel.

46 Figure 4.4: The effect of imposing a limit on the magnitude of the field. The plot shows the magnitude of a field as a function of the distance away from the source, no cutoff: orange, high field cutoff: Blue, and low field cutoff: red.

ate electrons away from the channel, a cross-section of this field is presented in Figure 4.3. The effect on the magnitude of the E-field as a function of distance from the charge channel with and without the field limits is shown in Figure 4.4. The free parameter of this model is the charge density along the channel. If the charge density is a realistic charge density for the leader channel (less than µCm−1 [37]) the field is not strong enough to create an RREA. But if the charge density is increased to the charge density in the leader tip (greater than 100 µCm−1 [37]) electrons can accelerate and create RREAs. For the channel model, the charge density is constant along the entire channel and is chosen to be the charge density associated with the leader tip. This is not a physical model but it does provide a starting point for future models. There isn’t an explanation for the source of the electrons, but the unknown source is placed at an elevation of 50 m. Figure 4.5 shows the path of electrons under the fields from the charged channel. These results show two distributions. First, a Time-Distance distribution. The ground distance from the source to where a particle hit is shown along the x-axis of the histogram.

47 Figure 4.5: Paths of 1 MeV electrons in the Charged Channel Model

Normalized time is shown along the y-axis of the histogram. This is the time difference between a particle hitting the ground at some distance and a beam of light traveling directly from the source to the same distance on the ground. The color indicates the number of particles hitting the ground at the same time and distance. Second, an Energy-Distance distribution. The ground distance away from the source where a particle hit is shown along the x-axis. The energy of the particle is shown along the y-axis. The results of the channel model are shown in Figure 4.6. The results indicate that a ring geometry does not form and there is a large number of particles hitting the ground under 2 kilometers, although under the high field cutoff a few particles do reach 4 kilometers. The timing of the signals is under 4 microseconds, which is too short to explain the unusual signals. Additionally, the energy distribution plots show that the full distribution of energy we would expect for the respective field cutoffs is not achieved. The highest energy observed for a particle in the low field cutoff was about 25 MeV, but the upper limit for the range of runaway electron energy for the low field cutoff is approximately 100 MeV. This can be explained due to the fact we are not observing the particles along the direction of the runaway. Rather, our model observed particles that hit the ground and we are observing particles that scatter and are

48 directed toward the ground. Therefore, a truncated energy range is expected. This model is insufficient in explaining the unusual signals. If the signal were to match the unusual events, the results would show little signal in the 0 to 2 km bins and show a large number of counts spread over 10 µs for bins with distances greater than 2 km. The results in Figure 4.6 show that particles do not travel far from the origin and are restricted to approximately 2 µs in time. This model isn’t sufficient to explain the unusual event characteristics.

Figure 4.6: Simulated results of Charge Channel Model showing the distribution of the num- ber of particles hitting the ground. The top row shows the temporal and spatial distribution of particles on the ground. The bottom row shows the energy of particles at a distance away from the source. The left column shows simulation results with the low field limit. The right column shows simulation results with the high field limit

4.2 Attachment Point Model

A model of the attachment point was constructed in an attempt to remove any assumption of a particular source of high energy particles. The leader tips are a known source of X-rays and MeV electrons [25, 38]. There have been multiple attempts to model the leader tips,

49 Figure 4.7: Conceptual model of the lightning attachment point, showing the dipole between the downward and upward leader tips and trailing charges deposited in the lightning channel.

Figure 4.8: 2D projection of the electric field near the lightning attachment point.

50 but little is known about the attachment process itself due to difficulty with measurements. Therefore, there are few models of the attachment point [19, 25]. The modern leader models construct a stepped leader with a large concentration of charge at the leader tip and trailing charges that form a channel between the cloud and the leader tip. For the attachment point model, a static model of the attachment point is considered. The ground is assumed to be a perfect conductor and at 50 meters a vertical dipole is constructed from two point charges 10 meters apart. This dipole represents the convergence of the downward negative tip and the upward positive leader. Channels of constant charge density connect the cloud and the negative point charge to each other and additionally connect the positive point charge and the ground. A schematic of this model is shown in Figure 4.7. The field near the attachment point does not have a strong radial component as seen in Figure 4.8. The field will cause the majority of electrons to travel upward as seen in Figure 4.9. The charges in the model were chosen such both the leader tips and the channels contained a realistic amount of charge, 4 mC and 1 µCm−1 respectively [37]. A source of 1 MeV electrons is placed in the middle of the dipole. The propagation of the leader tip requires the emission of MeV electrons, therefore, it is reasonable to place a source in between the two leader tips. The two field

kV cutoffs used previously are not used in this model. Instead, a single field cutoff of 3200 m is used. In between the leader tips, we expect an electrical break down to occur therefore the

kV field cutoff is set at the conventional breakdown field of 3200 m . The results show that detected particles are restricted to under 1 kilometer and under 2 microseconds with very little energy per particle, these results are shown in Figure 4.10. The distributions can be explained by the loss of the strong outward radial component in the field. The principal direction of runaway electrons is upward as shown in Figure 4.9. Therefore, the particles detected on the ground will be those particles that are scattered out of the avalanche. Although the results do not show characteristics of the unusual events, the results are consistent with observations of X-rays on the ground prior to the attachment process [24]. It is also worth noting that the time that the field near the leader tip is strong

51 Figure 4.9: Simulated trajectories of 1 MeV electrons (red) and resulting photons (green) in the Attachment Point Model.

52 enough to produce outward runaway electrons is less than 10 µs, the time needed to match the unusual signals. The field near the leader tip is strong enough for only a few meters before the attachment happens, and the leaders are propagating at roughly 107ms−1, thus a strong field around the attachment point would only exist for approximately a microsecond [19]. The static model of the attachment point is not sufficient to describe the unusual events and it is unlikely that the attachment process is the cause.

Figure 4.10: Simulated results of Attachment Point Model showing the distribution of the number of particles hitting the ground. The top row shows the temporal and spatial dis- tribution of particles on the ground. The bottom row shows the energy of particles at a distance away from the source. The left column shows simulation results with the low field limit. The right column shows simulation results with the high field limit

4.3 Current Channel Model

In a lightning strike, after the attachment process charge is carried between the cloud and the ground, this will create large electromagnetic fields around the channel. An exact model of the fields around a lightning strike has yet to be created. This would be difficult to model

53 Figure 4.11: Schematic of the engineering model of the Current Channel Model, showing the direction of current, and assumed source of electrons.

Figure 4.12: 2D projection of the electric field near the current channel.

54 due to the high level of tortuosity of the lightning channel, but several mathematical models exist [19, 28]. For this simulation, one of the mathematical models (an “engineering model”) is used. In an engineering model of the return stroke, the ground is considered to be a perfect conductor and is at a potential of 0 V. A channel that is perfectly straight, narrow, and has a constant width and resistivity is formed. Additionally, a constant current is assumed throughout the channel. A schematic of this model is shown in Figure 4.11. The resulting E and B fields are calculated with the standard equations of the electric and magnetic fields around a resistive wire carrying constant relativistic current [39]. This situation results in a strongly radial E-field as shown in Figure 4.12. When the current is approximately 80 kA, the radial fields become strong enough for electrons to run away. In the simulation, the current is assumed to be 100 kA or 150 kA. These currents are the peak current for only a small portion of negative CG lightning [19]. The high and low field cut is again used in this model, a current of 100 kA is used with the low field cutoff and a current of 150 kA is used with the high field cutoff. The fields in this model are similar to the charged channel model but the parameters used here are realistic. For this model, there is not a known source of electrons and the source of 1 MeV electrons is assumed at a height of 50 meters. The paths of electrons under the calculated fields are shown in Figure 4.13. The results of the current channel model are similar to the charge channel model. This was an expected outcome because the electric field produced by the charge channel and the current channel models were similar. As shown in Figure 4.14, the amount of time that the signal lasted on the ground is at most about 4 microseconds and did not extend past 3 km. The model of a current channel is not sufficient to explain the unusual events.

4.4 Return Stroke Model

The source of electrons in the process that produces the unusual events is likely to be more complex than a point source. The next step is to improve the model of the source of electrons. For this, we consider the return stroke process. After the attachment process, the return stroke serves to transfer charges from the charged channel to the ground. The

55 Figure 4.13: Simulated trajectories of 1 MeV electrons (red) and resulting photons (green) in the Current Channel Model.

56 Figure 4.14: Simulated results of Current Channel Model showing the distribution of the number of particles hitting the ground. The top row shows the temporal and spatial distribu- tion of particles on the ground. The bottom row shows the energy of particles at a distance away from the source. Left column shows simulation results with the low field limit. Right column shows simulation results with the high field limit

57 Figure 4.15: Schematic of return stroke model. The current channel is used for the fields. 1 The source is a cylinder travelling upwards at a velocity of 3 c traveling in discrete steps emitting 10,000 1 MeV electrons every step.

return stroke travels up the channel at roughly one-third of the speed of light [19]. As it travels up the channel, the negative charges left by the leader are rapidly accelerated down the channel towards the ground. The peak current under the return stroke can be above 100 kA. This current is strong enough to create a field powerful enough to induce runaway electrons. The source of electrons will be modeled after the upward movement of the return stroke. The source will be modeled as a 10-meter tall cylinder with the same radius as the channel traveling vertically upwards in discrete steps at a velocity of one third the speed of light, during each step the source will emit 10000 1 MeV electrons. The height of the cylinder serves to surround the tip of the return stroke where electrons experience the greatest acceleration. This is repeated until the source reaches 1 km in altitude. The fields around the return stroke will be calculated in the same way as the current channel model. A schematic of this model is shown in Figure 4.15. The results of the return stroke model are shown in Figure 4.16. These results show that the simulation of the propagating source produced a signal on the ground for at least 10 µs, the length of the unusual events. In the simulation with a high field cutoff, and for distances

58 Figure 4.16: Simulated results of Return Stroke Model showing the distribution of the num- ber of particles hitting the ground. The top row shows the temporal and spatial distribution of particles on the ground. The bottom row shows the energy of particles at a distance away from the source. The left column shows simulation results with the low field limit. The right column shows simulation results with the high field limit

59 under 3 km, particles were hitting the ground for at least 10 microseconds. But, the shape of the signal isn’t the same as the unusual signals. The simulated signal does not have a rise time. Instead, it peaks almost instantly and then falls off slowly. The spatial distribution and time length of the simulated signal is consistent with unusual events without the “hole” and a small footprint such as those seen in Figure A.1. Additionally, it is worth noting that the maximum number of counts in a single bin occurred at about 300 meters and not directly under the lightning channel. This was caused by a combination of the field strength and the starting altitude of the source.

4.5 Conclusions

The models presented in this chapter show multiple important clues about the origin of the unusual events. First, that the fields generated around high energy lightning strikes appear to be strong enough to create a radial runaway relativistic electron avalanche. Sec- ond, the characteristic timing of the unusual signals is likely a result of the structure of the source of high energy electrons and independent of the fields the electrons are propagated in. Attempts to create a model that explained the “hole” in the unusual events were unsuc- cessful, but the models were able to show that the RREA process around a lightning strike could produce MeV photons that are capable of reaching the ground at distances beyond 3 kilometers. Finally, the energy per observed particle quickly falls off beyond the radius where the E-field falls below the RREA threshold for all models. This is important because it means the particles measured by the SD tanks are not the original electrons but are the byproducts of the RREA. These exploratory models do not fully explain the unusual events but they provide insight to which processes in lightning could produce the unusual signals observed by the Pierre Auger Observatory.

60 CHAPTER 5 CONCLUSION

This thesis explored models to explain the unusual events observed at the Pierre Auger Observatory. This was done by comparing the characteristics of the unusual signals to the results of computer simulations of EAS propagation and lightning. The unusual events are likely not a result of cosmic ray propagation. This is because the mean free path of particles freely traveling in air on the order of a meter, this prevents any particle from traveling the kilometers needed to match the footprint of the unusual events. A radial force needs to be present to give particles the energy allowing them to propagate outward. The need for a central force and clues present in the data pointed towards lightning as a possible source for the unusual events. Models of different processes in lightning were constructed using the GEANT4 framework. The attachment point is likely not the cause of the unusual events because most of the radiation is directed upward and the time period when the leader tips are close enough for the fields to be intense enough to induce an RREA occurs over less than a microsecond. The simulated attachment point confirmed the expectations. The return stroke process provided the most likely way of recreating the unusual events. This model was capable of producing fields strong enough to create an RREA and the return stroke process occurs over approximately 10 microseconds. Therefore the return stroke provides a possible source that has the same time length characteristic of the unusual event and a method of propagating the signal to SD stations far away. The results of the return stroke simulation were capable of matching the characteristics of the unusual events without the “hole” in the center of the extended geometry such as those in Figure A.1. Therefore this exploratory model was successful in providing a starting point for understanding the unusual events.

61 5.1 Future Work

There are still many steps needed to further describe the nature of the unusual events. Further refinements to the lightning return stroke model, improvements could include time- dependent fields, a more accurate model of the return stroke current, a better estimate of the maximum field around the lightning channel, and a further exploration of the phase space of the parameters. Additions such as the consideration of an EMP pulse that would move outwards with the electrons in an RREA, this may increase the range in which particles are observed on the ground. Additionally, it is important to model the response of the SD tanks to the signal generated by the purposed lightning models. Finally, improving the simulation code, additional visualizations would provide additional insight into the RREAs around the simulated lightning strikes, this could include a measure of all particles that reach a certain distance.

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67 APPENDIX ADDITIONAL UNUSUAL EVENT IMAGES

Figure A.1: Unusual events without the annular geometry and small footprint[16].

68 Figure A.2: Unusual event with extended geometry, millisecond correlation with a lightning strike, and no ring geometry [15].

Figure A.3: Additional ring shape footprints of unusual events [16]

69 ((a))

((b))

Figure A.4: Unusual signals with correlation of lightning from Pierre Auger weather sta- tions. Colored stations represent triggered tanks, blue circle is an approximate location of a lightning strike [15].

70 Figure A.5: Signal timing fits assuming a spherical propagation from a point source at (x0,y0,z0) produced in time at t0 and with velocity fixed at the speed of light. These fits show that the unusual events are correlated to a spherical emission at a low altitude [13].

71