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Critical kinetic plasma processes in relativistic astrophysics [Elektronische Ressource] / vorgelegt von Claus H. Jaroschek

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Ludwig-Maximilians-Universit¨at Munc¨ henCritical Kinetic Plasma ProcessesinRelativistic AstrophysicsDissertationder Fakult¨ at fur¨ Physikder Ludwig-Maximilians-Universit¨ atM¨ unchenvorgelegt vonClaus H. Jaroschekaus Wurzburg¨M¨ unchen, M¨ arz 20051. Gutachter: Prof.Dr. Harald Lesch2. Gutachter: Prof.Dr. Rudolf A. TreumannTag der mundl¨ ichen Pru¨fung: 20. Juli 2005In the universe, there are things that are known,and things that are unknown,and in between, there are doors ...If the doors of perception were cleansed,everything would appear to man as it is, infinite.William Blake, 1790Ich widme diese Arbeitall’ diesen Menschen, die mir nahestehenund immer noch zu mir haltenobschon ich Ihnen bis jetzt nie die Zeit schenken konnte, die Ihnen zusteht ...AbstractPlasma astrophysics deals with collective plasma processes in astrophysical scenarios. As observationalastronomy pushes towards unprecedented resolutions in space and time, the focus of theoretical researchnecessarily ventures towards a description of the plasma microphysics. On microphysical scales theplasma is pervasively collisionless and the magnetohydrodynamic approximation breaks down. Conse-quently theoretical concepts rely on a kinetic plasma description as the most sophisticated plasma model.

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Published 01 January 2005
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Ludwig-Maximilians-Universit¨at Munc¨ hen
Critical Kinetic Plasma Processes
in
Relativistic Astrophysics
Dissertation
der Fakult¨ at fur¨ Physik
der Ludwig-Maximilians-Universit¨ at
M¨ unchen
vorgelegt von
Claus H. Jaroschek
aus Wurzburg¨
M¨ unchen, M¨ arz 20051. Gutachter: Prof.Dr. Harald Lesch
2. Gutachter: Prof.Dr. Rudolf A. Treumann
Tag der mundl¨ ichen Pru¨fung: 20. Juli 2005In the universe, there are things that are known,
and things that are unknown,
and in between, there are doors ...
If the doors of perception were cleansed,
everything would appear to man as it is, infinite.
William Blake, 1790
Ich widme diese Arbeit
all’ diesen Menschen, die mir nahestehen
und immer noch zu mir halten
obschon ich Ihnen bis jetzt nie die Zeit schenken konnte, die Ihnen zusteht ...Abstract
Plasma astrophysics deals with collective plasma processes in astrophysical scenarios. As observational
astronomy pushes towards unprecedented resolutions in space and time, the focus of theoretical research
necessarily ventures towards a description of the plasma microphysics. On microphysical scales the
plasma is pervasively collisionless and the magnetohydrodynamic approximation breaks down. Conse-
quently theoretical concepts rely on a kinetic plasma description as the most sophisticated plasma model.
The present work discusses some fundamental kinetic plasma processes in relativistic astrophysics: Fast
Magnetic Reconnection (FMR) associated with discontinuities in the magnetic field topology, and the
Coupled Two-Stream-Weibel instability (CTW) in the wake of collisionless shocks. Both processes are
ubiquitous in astrophysical sites, prevail over competing plasma modes because of dominant growth
rates, experience significant relativistic modifications, and develop essential features solely in the highly
non-linear regime. The computational representation invokes the entire 6D phase space. These charac-
teristics distinguish FMR and the CTW as distinctively critical processes.
FMR and the CTW are studied here in the framework of self-consistent, relativistic and fully electro-
9magnetic Particle-In-Cell (PIC) simulations. Typical scenarios comprise ensembles of 10 particles and
4endure for several 10 time steps. The computational task is challenging and completely in the realm of
the massively parallelized architectures of state-of-the-art supercomputers.
We present the first self-consistent 3D simulations of FMR in relativistic pair plasma. Focusing on the
mechanism of particle acceleration we show that the highly dynamic evolution of the current sheet in
the non-linear regime is the essential stage. Therein non-stationary acceleration zones arise in the su-
perposition of the relativistic tearing and the relativistic drift kink mode as competing current sheet
instabilities. Though the topology of electromagnetic fields is highly turbulent, the FMR process shows
sthe remarkable quality to generate smooth and stable power-laws f(γ)dγ∝ γ dγ in the particle distri-
bution function (PDF) out of an initial Maxwellian. The upper PDF cut-off in relativistic energy γ is
determined by the ratio of light to Alfv´en velocity c/v . The power-law index assumes s? 1within
A
the reconnection X-zone irrespective of parameter variations. Intriguingly the power-law index appears
as the universal characteristic of the source process. The associated synchrotron spectra provide a valid
description of the extremely hard spectra and rapid variabilities of ‘Flat Spectrum Radio Quasars’.
Conceptual γ-ray burst (GRB) synchrotron emission models depend on a plasma process which ensures
efficient magnetic field generation. The CTW converts bulk-kinetic energy of counter-streaming plasma
shells into Weibel magnetic fields. Pivoted by the linear analysis of the CTW, the PIC simulations
confirm the correspondence between saturation magnetic fields and bulk-kinetic energy. Plasma shell
collisions in GRBs are either associated with internal or external shocks. As direct consequence of the
energy dependence the CTW evolves from a complex 3D topology in internal collisions towards quasi-
2D, Weibel-dominated conformalizations at the higher external shock energies. The PIC results prove
that the Weibel fields are sufficiently strong to sustain synchrotron emission scenarios, particularly in
external shocks. By determining the first lifetime limits we show that Weibel fields are also sufficiently
long-lived with respect to typical synchrotron cooling times. We further identify the stability-limiting
diffusion process as of ‘Bohm’-type, i.e. the diffusion coefficient exhibits the ∝ T/B-dependence and
herewith represents a conservative stability criterion. The CTW generates stable power-law spectra in
the magnetic fields implying power-law shaped PDFs as self-similar solutions for diffusive particle scat-
tering. This suggests a universal power-law index as the characteristic of the CTW process.
Imposing a magnetic guide field of well-defined strength suppresses the Weibel contributions of the CTWin favour of the electrostatic Two-Stream instability (TSI). The pulsar magnetosphere is the paradig-
matic scenario in which we discuss the mechanism of Coherent Collisionless Bremsstrahlung (CCB)
triggered by the TSI. The PIC simulations show that the CCB mechanism provides a valid description
of the phenomenon of ‘Giant Radio Pulses’ as recently observed from the Crab pulsar.Contents
1 Introduction 1
1.1 Motivation - Self-Consistent Modelling of
CriticalPlasmaProcesesinAstrophysicalScenarios............ 1
1.2 Magnetic Reconnection -
TopicalProblemsofaLong-DiscusedProces................ 4
1.3 The Weibel Mechanism -
MicrophysicalOriginofAstrophysicalMagneticFields........... 15
1.4 The Weibel-Two-Stream-Connection -
ThePlasmaMicrophysicsofJetsandPulsars................ 20
2 The Computational Method of Choice: Particle-In-Cell 23
3 Collisionless Magnetic Reconnection 33
3.1 The Relativistic Harris Equilibrium . . . ................... 3
3.2RelativisticParticlesinElectromagneticFields ........... 38
3.3 The Mechanism of Relativistic Particle Acceleration . ............ 40
3.3.1Abstract.............................. 40
3.3.2Introduction........................ 40
3.3.3SimulationDescription...................... 42
3.3.4SimulationResults..................... 4
General Time Evolution of Reconnection in a Pair Plasma . . . . . . 44
Initial Plasma Parameter / Acceleration Efficiency Correspondence . 50
Characteristicsofthe3DConfiguration................. 53
Detailed Analysis of the Acceleration Mechanism . . . . . . . . . . . 54
3.3.5Discussion................................. 59
Particle Acceleration in Electron-Proton Plasma Reconnection . . . . 59
Comparison with Previous Results on 2D Scenarios . . . . . . . . . . 60
Concluding Remarks on Particle Acceleration in FMR . . . . . . . . . 60
3.4SynchrotronSignaturesoftheSelf-ConsistentModel............ 62
3.4.1Abstract.............................. 62
3.4.2Introduction........................ 62
3.4.3SimulationModel......................... 63
3.4.4NumericalResultsandPhysicalPicture................. 64
Non-thermal Particle Generation in the Late-time Evolution . . . . . 64SynchrotronEmision........................... 65
3.4.5SummaryandConclusions............ 69
4 Magnetic Fields in 3D Weibel Scenarios 71
4.1 Magnetic Fields in γ-Ray Burst Models - Generation,
TopologyandLifetime............................. 71
4.2 Ultra-Relativistic Plasma Shell Collisions -
TheMagneticEquipartitionRatio....................... 84
4.2.1Abstract...................... 84
4.2.2Introduction............................ 84
4.2.3SimulationDescription.......................... 86
4.2.4 Dimensional Effects in Relativistic Plasma Shell Collisions .. 87
Linear Progenitors of the Preeminent Plasma Instability Modes . . . 87
EffectsofaFiniteThermalSpread:KineticModifications....... 91
4.2.5TheSaturatedandSteady-StateFinalMagneticFields.... 96
4.2.6SummaryandPerspectives........................ 104
4.3 Topology and Lifetime - A Critical Test for Synchrotron Emission Models 106
4.3.1Abstract.................................. 106
4.3.2Introduction................ 106
4.3.3SimulationDescription.......................... 108
4.3.4DiffusionLimitedLifetimeofMagneticFields..... 10
DiffusionCoefficientsObtainedbythePICSimulation ........ 110
DiffusionisIdentifiedas‘Bohm’-type.................. 115
4.3.5ConsequencesforSynchrotronEmision......... 16
4.4Self-ConsistentSynchrotronCascades..................... 19
5 The Weibel-Two-Stream Connection 125
5.1 The Electromagnetic Counterstreaming Instability
withMagneticGuideField........................... 125
5.2 The Connection to Pulsar Physics -
Stimulation of Collisionless Bremsstrahlung . . . . . ............ 135
6 Final Remarks 151
6.1Achievements.................................. 151
6.2Perspectives................... 157
A Dimensionless Representation of Physical Quantities 159
B Linear Theory of the 2D EM Counterstreaming Instability 163
List of Publications 177
Acknowledgements 179
Curriculum Vitae 181Chapter 1
Introduction
1.1 Motivation - Self-consistent Modelling of
Critical Plasma Processes in Astrophysical Scenarios
During the recent decades the observational techniques of modern astronomy have
reached an unprecedented degree of sophistication. The radiative signatures of astro-
physical phenomena are resolved on progressively refined scales in space and time. The
wealth of new discoveries challenges the theorist to provide a viable explanation. Plasma
physics plays a key role in the solution to the puzzles which have been posed by the
recent observational data. Paradigms are the σ-problem of the Crab pulsar wind (section
1.2), the discovery of γ-ray bursts (GRBs) (section 1.3) and the observation of extremely
intense pulsar radio outbursts on nanosecond time scales (section 1.4). At a superficial
glance diversity proliferates in the observational characteristics of these phenomena:
Wavelengths encompass the entire range from γ-rays in GRBs to the radio regime in
pulsars. Time scales span from nanoseconds in pulsar radio outbursts to seconds for the
‘synchrotron wisps’ associated with pulsar winds.
However, a closer look unveils that these observed features are all deeply connected to
two fundamental plasma processes: Collisionless magnetic reconnection and collisionless
shocks. The quantitative differences in the observations arise solely due to the variety
in the plasma parameters of the specific source. Both processes are central problems
of plasma-physical research for more than 40 years. So what makes them so special to
continuously keep up the minds of theoreticians? The unifying element common to both
processes is that they are connected to discontinuities. Magnetic reconnection takes
place at a discontinuity in the magnetic field topology. The free energy of shocks is
stored in a discontinuity in phase space. Within the realm of classical physics, disconti-
nuities are a mathematical idealization and generally point out critical assumptions in
non-selfconsistent physical models.
The crucial point is the combination with collisionless conditions. The plasma in astro-
physical sites is usually highly rarefied in density. As the direct consequence, the mean
free path of an individual particle becomes large compared to the typical dynamic length
scales introduced by kinetic plasma processes. The particles are not anymore scattered inCoulomb collisions between nearest neighbours, but merely in the collective electromag-
netic fields of plasma modes. Coulomb collisions isotropize and thermalize the particle
distribution function (PDF) in phase space towards the Maxwellian equilibrium. In the
absence of Coulomb collisions the PDF is potentially highly non-thermal.
Theoretical models of the plasma state observe a hierarchical structure of sophistication
(cf. chapter 2): The crudest approach is realized in the magnetohydrodynamic (MHD)
plasma model. The MHD description is based on the first order moment of the PDF
assuming Maxwellian conditions. Consequently the MHD approach is valid only on the
macroscopic scales on which the Maxwellian approximation of the PDF is justified.
The basic MHD model is successively refined by taking into account higher order mo-
ments of the PDF. The trend to reduce the restrictive idealizations culminates in the
kinetic plasma description. The kinetic approach considers the complete PDF. In the
kinetic model time scales are unambiguously linked to the particle gyro motion and
length scales to the plasma inertial length, respectively. Consequently the kinetic model
is completely self-consistent. The crucial point is that the kinetic approach is also the
most complicated. The numerical treatment is utmostly costly with respect to compu-
tational expenses. The dawn of massively parallel supercomputer architectures in the
recent years has given a new quality to kinetic plasma modelling. As one freak of nature,
the discontinuities associated with collisionless reconnection and collisionless shocks test
the microphysical scales. As observational techniques advance to successively higher res-
olutions, the global MHD description breaks down and microphysics makes a kinetic
treatment of plasma processes indispensable.
Plasma astrophysics currently performs a metamorphosis equivalent to the one space
plasma physics has been confronted with 30 years ago as satellites paved the way towards
in-situ measurements in the earth’s magnetosphere. The presented work is dedicated to
the self-consistent, kinetic modelling of plasma processes critical in the context of astro-
physical research. Explicitly, these processes are collisionless kinetic reconnection and
the Coupled Two-Stream-Weibel (CTW) instability. The CTW is the electromagnetic
instability mode which proceeds in the wake of collisionless shocks.
Which characteristics distinguish these plasma processes as distinctively critical?
• Both processes are of fundamental nature, i.e. are ubiquitous in astrophysical plas-
mas. The reason is obvious: Magnetic discontinuities and plasma entities with
significant relative bulk drift appear necessarily at the boundaries of different
source environments. Reconnection and the CTW mode are kinetic instabilities
and therefore fast by definition. The inherent growth rates supersede the growth
of competing modes. Consequently both prevail as the dominant processes.
• Essential features appear in the highly dynamic phase during the late-time evolu-
tion. Since plasma dynamic scales are short compared to astrophysical time scales,
the non-linear saturation at late times is the prevalent state in astrophysical sites.
This instability regime is entirely in the domain of numerical simulations.
• The physics of both processes crucially depends on microscopic plasma scales.