# Papers

 Title: Bunch Expansion as a Cause for Pulsar Radio Emissions Authors: Benáček, Jan, Muñoz, Patricio A., and Büchner, Jörg Publication: The Astrophysical Journal, 2021, 99 Publication Date: 12/2021 DOI: 10.3847/1538-4357/ac2c64 Bibliographic Code: 2021ApJ...923...99B Citation Count: 3

### Abstract

Electromagnetic waves due to electron-positron clouds (bunches), created by cascading processes in pulsar magnetospheres, have been proposed to explain the pulsar radio emission. In order to verify this hypothesis, we utilized for the first time Particle-in-Cell (PIC) code simulations to study the nonlinear evolution of electron-positron bunches dependant on the initial relative drift speeds of electrons and positrons, plasma temperature, and distance between the bunches. For this sake, we utilized the PIC code ACRONYM with a high-order field solver and particle weighting factor, appropriate to describe relativistic pair plasmas. We found that the bunch expansion is mainly determined by the relative electron-positron drift speed. Finite drift speeds were found to cause the generation of strong electrostatic superluminal waves at the bunch density gradients that reach up to E ~ 7.5 × 105 V cm-1 (E/(m e c ω p e -1) ~ 4.4) and strong plasma heating. As a result, up to 15% of the initial kinetic energy is transformed into the electric field energy. Assuming the same electron and positron distributions, we found that the fastest (in the bunch reference frame) particles of consecutively emitted bunches eventually overlap in momentum (velocity) space. This overlap causes two-stream instabilities that generate electrostatic subluminal waves with electric field amplitudes reaching up to E ~ 1.9 × 104 V cm-1 (E/(m e c ω p e -1) ~ 0.11). We found that in all simulations the evolution of electron-positron bunches may lead to the generation of electrostatic superluminal or subluminal waves, which, in principle, can be behind the observed electromagnetic emissions of pulsars in the radio wave range.

 Title: Pulsar Coherent Radiation by Linear Acceleration Emission Mechanism Authors: Benáček, Jan, Muñoz, Patricio A., and Büchner, Jörg Publication: arXiv e-prints, 2021, arXiv:2111.05262 Publication Date: 11/2021 DOI: Bibliographic Code: 2021arXiv211105262B Citation Count: 0

### Abstract

Linear acceleration emission is one of the mechanisms proposed to explain the intense pulsar radio emissions. This mechanism is however not well understood due to a lack of its proper mathematical analyses, e.g., of the collective plasma response and the resulting emission power. We utilize 1D relativistic particle-in-cell simulations to derive the emission properties of two instabilities in neutron star magnetospheres, relativistic beam instability and interactions of plasma bunches/clouds. We found that the emission power by plasma bunch interactions exceeds emission due to streaming instability by seven orders of magnitude. The wave power generated by a plasma bunch interaction can be obtained as large as $3.4\times10^{19}$ W. It alone can account for the total radio power emitted by typical pulsars ($10^{18}-10^{22}$ W). The emission of the plasma bunch has a number of features of the observed pulsar radiation. Its spectrum is characterized by an almost flat profile for lower frequencies and a power-law with an index $\approx-2.5$ for higher frequencies. The angular width of the radiation decreases with increasing frequency. The generated wave power depends on the pulsar rotation angle. It can cause fine structures in the observed intensity as it fluctuates between positive and negative wave interference as a function of the emission angle.

 Title: Wave Excitation by Power-law-Distributed Energetic Electrons with Pitch-angle Anisotropy in the Solar Corona Authors: Zhou, Xiaowei, Muñoz, Patricio A., Büchner, Jörg, Liu, Siming, and Yao, Xin Publication: The Astrophysical Journal, 2021, 147 Publication Date: 10/2021 DOI: 10.3847/1538-4357/ac18c1 Bibliographic Code: 2021ApJ...920..147Z Citation Count: 0

### Abstract

Radio waves from the Sun are emitted, as a rule, due to energized electrons. Observations infer that the related energized electrons follow (negative) power-law velocity distributions above a break velocity Ub. They might also distribute anisotropically in the pitch-angle space. To understand radio wave generation better, we study the consequences of anisotropic power-law-distributed energetic electrons in current-free collisionless coronal plasmas utilizing 2.5-dimensional particle-in-cell simulations. We assume that the velocity distribution fu of the energized electrons follows a plateau (∂fu/∂u = 0) and a power-law distribution with spectral index α for velocities below and above Ub, respectively. In the pitch-angle space, these energized electrons are spread around a center μc = 0.5. We found that the energetic plateau-power-law electrons can more efficiently generate coherent waves if the anisotropy of their pitch-angle distribution is sufficiently strong, i.e., a small pitch-angle spread μs. The break velocity Ub affects the excitation dominance between the electrostatic and electromagnetic waves: for larger Ub electrostatic waves are mainly excited, while intermediate values of Ub are required for an excitation dominated by electromagnetic waves. The spectral index α controls the growth rate, efficiency, saturation, and anisotropy of the excited electromagnetic waves as well as the energy partition in different wave modes. These excited electromagnetic waves are predominantly right-handed polarized, in X- and Z-modes, as observed, e.g., in solar radio spikes. Additionally about 90% of the kinetic energy loss of the energetic electrons is dissipated, heating the ambient thermal electrons. This may contribute to the coronal heating.

 Title: Wave emission of non-thermal electron beams generated by magnetic reconnection Authors: Yao, Xin, Muñoz, Patricio, Büchner, Jörg, Benácek, Jan, Liu, Siming, and Zhou, Xiaowei Publication: arXiv e-prints, 2021, arXiv:2107.13746 Publication Date: 07/2021 DOI: Bibliographic Code: 2021arXiv210713746Y Citation Count: 0

### Abstract

Magnetic reconnection in solar flares can efficiently generate non-thermal electron beams. The accelerated electrons can, in turn, cause radio waves through kinetic instabilities as they propagate through the ambient plasma. We aim at investigating the wave emission caused by fast electron beams (FEBs) with characteristic non-thermal electron velocity distribution functions (EVDFs) generated by kinetic magnetic reconnection: bump-on-tail EVDFs along the separatrices and in the diffusion region, and perpendicular crescent-shaped EVDFs close to the diffusion region. For this sake we utilized 2.5D fully kinetic Particle-In-Cell (PIC) code simulations in this study. We found that: (1) the bump-on-tail EVDFs are unstable to cause electrostatic Langmuir waves via bump-on-tail instabilities and then multiple harmonic transverse waves from the diffusion region and the separatrices of reconnection. (2) The perpendicular crescent-shaped EVDFs, on the other hand, can cause multi-harmonic electromagnetic electron cyclotron waves through electron cyclotron maser instabilities in diffusion region of reconnection. Our results are applicable to diagnose the plasma parameters which control reconnection in solar flares by means of radio waves observations.

 Title: Nonthermal electron velocity distribution functions due to 3D kinetic magnetic reconnection for solar coronal plasma conditions Authors: Yao, Xin, Alejandro Muñoz, Patricio, and Büchner, Jörg Publication: arXiv e-prints, 2021, arXiv:2106.12558 Publication Date: 06/2021 DOI: Bibliographic Code: 2021arXiv210612558Y Citation Count: 2

### Abstract

Magnetic reconnection can convert magnetic energy into kinetic energy of non-thermal electron beams. Those accelerated electrons can, in turn, cause radio emission in astrophysical plasma environments such as solar flares via micro-instabilities. The properties of the electron velocity distribution functions (EVDFs) of those non-thermal beams generated by reconnection are, however, still not well understood. In particular properties that are necessary conditions for some relevant micro-instabilities. We aim at characterizing the EVDFs generated in 3D magnetic reconnection by means of fully kinetic particle-in-cell (PIC) code simulations. In particular, our goal is to identify the possible sources of free energy offered by the generated EVDFs and their dependence on the strength of the guide field. By applying a machine learning algorithm on the EVDFs, we find that: (1) electron beams with positive gradients in their 1D parallel (to the local magnetic field direction) velocity distribution functions are generated in both diffusion region and separatrices. (2) Electron beams with positive gradients in their perpendicular (to the local magnetic field direction) velocity distribution functions are observed in the diffusion region and outflow region near the reconnection midplane. In particular, perpendicular crescent-shaped EVDFs (in the perpendicular velocity space) are mainly observed in the diffusion region. (3) As the guide field strength increases, the number of locations with EVDFs featuring a perpendicular source of free energy significantly decreases. The formation of non-thermal electron beams in the field-aligned direction is mainly due to magnetized and adiabatic electrons, while in the direction perpendicular to the local magnetic field it is attributed to unmagnetized electrons.

 Title: Refining pulsar radio emission due to streaming instabilities: Linear theory and PIC simulations in a wide parameter range Authors: Manthei, Alina C., Benáček, Jan, Muñoz, Patricio A., and Büchner, Jörg Publication: Astronomy and Astrophysics, 2021, A145 Publication Date: 05/2021 DOI: 10.1051/0004-6361/202039907 Bibliographic Code: 2021A&A...649A.145M Citation Count: 4

### Abstract

Context. Several important mechanisms that explain coherent pulsar radio emission rely on streaming (or beam) instabilities of the relativistic pair plasma in a pulsar magnetosphere. However, it is still not clear whether the streaming instability by itself is sufficient to explain the observed coherent radio emission. Due to the relativistic conditions that are present in the pulsar magnetosphere, kinetic instabilities could be quenched. Moreover, uncertainties regarding specific model-dependent parameters impede conclusions concerning this question.
Aims: We aim to constrain the possible parameter range for which a streaming instability could lead to pulsar radio emission, focusing on the transition between strong and weak beam models, beam drift speed, and temperature dependence of the beam and background plasma components.
Methods: We solve a linear relativistic kinetic dispersion relation appropriate for pulsar conditions in a more general way than in previous studies, considering a wider parameter range. In doing so, we provide a theoretical prediction of maximum and integrated growth rates as well as of the fractional bandwidth of the most unstable waves for the investigated parameter ranges. The analytical results are validated by comparison with relativistic kinetic particle-in-cell (PIC) numerical simulations.
Results: We obtain growth rates as a function of background and beam densities, temperatures, and streaming velocities while finding a remarkable agreement of the linear dispersion predictions and numerical simulation results in a wide parameter range. Monotonous growth is found when increasing the beam-to-background density ratio. With growing beam velocity, the growth rates firstly increase, reach a maximum and decrease again for higher beam velocities. A monotonous dependence on the plasma temperatures is found, manifesting in an asymptotic behaviour when reaching colder temperatures. A simultaneous change of both temperatures proves not to be a mere linear superposition of both individual temperature dependences. We show that the generated waves are phase-coherent by calculating the fractional bandwidth.
Conclusions: Plasma streaming instabilities of the pulsar pair plasma can efficiently generate coherent radio signals if the streaming velocity is ultra-relativistic with Lorentz factors in the range 13 &lt; γ &lt; 300, if the background and beam temperatures are small enough (inverse temperatures ρ0; ρ1 ≥ 1, i.e., T0; T1 ≤ 6 × 109), and if the beam-to-background plasma density ratio n1/(γbn0) exceeds 10−3, which means that n1/n0 has to be between 1.3 and 20% (depending on the streaming velocity).

 Title: The effects of density inhomogeneities on the radio wave emission in electron beam plasmas Authors: Yao, Xin, Muñoz, Patricio A., Büchner, Jörg, Zhou, Xiaowei, and Liu, Siming Publication: Journal of Plasma Physics, 2021, 905870203 Publication Date: 03/2021 DOI: 10.1017/S0022377821000076 Bibliographic Code: 2021JPlPh..87b9003Y Citation Count: 2

### Abstract

Type III radio bursts are radio emissions associated with solar flares. They are considered to be caused by electron beams travelling from the solar corona to the solar wind. Magnetic reconnection is a possible accelerator of electron beams in the course of solar flares since it causes unstable distribution functions and density inhomogeneities (cavities). The properties of radio emission by electron beams in an inhomogeneous environment are still poorly understood. We capture the nonlinear kinetic plasma processes of the generation of beam-related radio emissions in inhomogeneous plasmas by utilizing fully kinetic particle-in-cell code numerical simulations. Our model takes into account initial electron velocity distribution functions (EVDFs) as they are supposed to be created by magnetic reconnection. We focus our analysis on low-density regions with strong magnetic fields. The assumed EVDFs allow two distinct mechanisms of radio wave emissions: plasma emission due to wave-wave interactions and so-called electron cyclotron maser emission (ECME) due to direct wave-particle interactions. We investigate the effects of density inhomogeneities on the conversion of free energy from the electron beams into the energy of electrostatic and electromagnetic waves via plasma emission and ECME, as well as the frequency shift of electron resonances caused by perpendicular gradients in the beam EVDFs. Our most important finding is that the number of harmonics of Langmuir waves increases due to the presence of density inhomogeneities. The additional harmonics of Langmuir waves are generated by a coalescence of beam-generated Langmuir waves and their harmonics.

 Title: Radio Emission by Soliton Formation in Relativistically Hot Streaming Pulsar Pair Plasmas Authors: Benáček, Jan, Muñoz, Patricio A., Manthei, Alina C., and Büchner, Jörg Publication: arXiv e-prints, 2021, arXiv:2101.03083 Publication Date: 01/2021 DOI: Bibliographic Code: 2021arXiv210103083B Citation Count: 0

### Abstract

A number of possible pulsar radio emission mechanisms are based on streaming instabilities in relativistically hot electron-positron pair plasmas. At saturation the unstable waves can form, in principle, stable solitary waves which could emit the observed intense radio signals. We searched for the proper plasma parameters which would lead to the formation of solitons, investigated their properties and dynamics as well as the resulting oscillations of electrons and positrons possibly leading to radio wave emission. We utilized a one-dimensional version of the relativistic Particle-in-Cell code ACRONYM initialized with an appropriately parameterized one-dimensional Maxwell-Jüttner velocity space particle distribution to study the evolution of the resulting streaming instability in a pulsar pair plasma. We found that strong electrostatic superluminal L-mode solitons are formed for plasmas with normalized inverse temperatures $\rho \geq 1.66$ or relative beam drift speeds with Lorentz factors $\gamma &gt; 40$. The parameters of the solitons fulfill the wave emission conditions. For appropriate pulsar parameters the resulting energy densities of superluminal solitons can reach up to $1.1 \times 10^5$ erg$\cdot$cm$^{-3}$, while those of subluminal solitons reach only up to $1.2 \times 10^4$ erg$\cdot$cm$^{-3}$. Estimated energy densities of up to $7 \times 10^{12}$ erg$\cdot$cm$^{-3}$ suffice to explain pulsar nanoshots.

 Title: Wave Excitation by Energetic Ring-distributed Electron Beams in the Solar Corona Authors: Zhou, Xiaowei, Muñoz, Patricio A., Büchner, Jörg, and Liu, Siming Publication: The Astrophysical Journal, 2020, 92 Publication Date: 03/2020 DOI: 10.3847/1538-4357/ab6a0d Bibliographic Code: 2020ApJ...891...92Z Citation Count: 8

### Abstract

We analyzed properties of waves excited by mildly relativistic electron beams propagating along the magnetic field with a ring-shape perpendicular momentum distribution in neutral and current-free solar coronal plasmas. These plasmas are subject to both the beam and the electron cyclotron maser instabilities driven by the positive momentum gradients of the ring-beam electron distribution in the directions parallel and perpendicular to the ambient magnetic field, respectively. To explore the related kinetic processes self-consistently, 2.5D fully kinetic particle-in-cell simulations were carried out. To quantify excited wave properties in different coronal conditions, we investigated the dependences of their energy and polarization on the ring-beam electron density and magnetic field. In general, electrostatic waves dominate the energetics of waves, and nonlinear waves are ubiquitous. In weakly magnetized plasmas, where the electron cyclotron frequency ωce is lower than the electron plasma frequency ωpe, it is difficult to produce escaping electromagnetic waves with frequency ω &gt; ωpe and small refractive index | {ck}/ω | &lt; (k and c are the wavenumber and the light speed, respectively). Highly polarized and anisotropic escaping electromagnetic waves can, however, be effectively excited in strongly magnetized plasmas with ωcepe ≥ 1. The anisotropies of the energy, circular polarization degree (CPD), and spectrogram of these escaping electromagnetic waves strongly depend on the number density ratio of the ring-beam electrons to the background electrons. In particular, their CPDs can vary from left-handed to right-handed with the decrease of the ring-beam density, which may explain some observed properties of solar radio bursts (e.g., radio spikes) from the solar corona.

 Title: Ion acceleration in non-relativistic quasi-parallel shocks using fully kinetic simulations Authors: Schreiner, Cedric, Kilian, Patrick, Spanier, Felix, Muñoz, Patricio A., and Büchner, Jörg Publication: arXiv e-prints, 2020, arXiv:2003.07293 Publication Date: 03/2020 DOI: Bibliographic Code: 2020arXiv200307293S Citation Count: 0

### Abstract

The formation of collisionless shock fronts is an ubiquitous phenomenon in space plasma environments. In the solar wind shocks might accompany coronal mass ejections, while even more violent events, such as supernovae, produce shock fronts traveling at relativistic speeds. While the basic concepts of shock formation and particle acceleration in their vicinity are known, many details on a micro-physical scope are still under discussion. In recent years the hybrid kinetic simulation approach has allowed to study the dynamics and acceleration of protons and heavier ions in great detail. However, Particle-in-Cell codes allow to study the process including also electron dynamics and the radiation pressure. Additionally a further numerical method allows for crosschecking results. We therefore investigate shock formation and particle acceleration with a fully kinetic particle-in-cell code. Besides electrons and protons we also include helium and carbon ions in our simulations of a quasi-parallel shock. We are able to reproduce characteristic features of the energy spectra of the particles, such as the temperature ratios of the different ion species in the downstream which scale with the ratio of particle mass to charge. We also find that approximately 12-15% of the energy of the unperturbed upstream is transferred to the accelerated particles escaping the shock.

 Title: Kinetic turbulence in fast three-dimensional collisionless guide-field magnetic reconnection Authors: Muñoz, P. A. and Büchner, J. Publication: Physical Review E, 2018, 043205 Publication Date: 10/2018 DOI: 10.1103/PhysRevE.98.043205 Bibliographic Code: 2018PhRvE..98d3205M Citation Count: 14

### Abstract

Although turbulence has been conjectured to be important for magnetic reconnection, still very little is known about its role in collisionless plasmas. Previous attempts to quantify the effect of turbulence on reconnection usually prescribed Alfvénic or other low-frequency fluctuations or investigated collisionless kinetic effects in just two-dimensional configurations and antiparallel magnetic fields. In view of this, we analyzed the kinetic turbulence self-generated by three-dimensional guide-field reconnection through force-free current sheets in frequency and wave-number spaces, utilizing 3D particle-in cell code numerical simulations. Our investigations reveal reconnection rates and kinetic turbulence with features similar to those obtained by current in situ spacecraft observations of MMS as well as in the laboratory reconnection experiments MRX, VTF, and VINETA-II. In particular, we found that the kinetic turbulence developing in the course of 3D guide-field reconnection exhibits a broadband power-law spectrum extending beyond the lower-hybrid frequency and up to the electron frequencies. In the frequency space the spectral index of the turbulence appeared to be close to -2.8 at the reconnection X line. In the wave-number space it also becomes -2.8 as soon as the normalized reconnection rate reaches 0.1. The broadband kinetic turbulence is mainly due to current-streaming and electron-flow-shear instabilities excited in the sufficiently thin current sheets of kinetic reconnection. The growth of the kinetic turbulence corresponds to high reconnection rates which exceed those of fast laminar, nonturbulent reconnection.

 Title: Two-stage Electron Acceleration by 3D Collisionless Guide-field Magnetic Reconnection Authors: Muñoz, P. A. and Büchner, J. Publication: The Astrophysical Journal, 2018, 92 Publication Date: 09/2018 DOI: 10.3847/1538-4357/aad5e9 Bibliographic Code: 2018ApJ...864...92M Citation Count: 12

### Abstract

We report a newly found two-stage mechanism of electron acceleration near X-lines of 3D collisionless guide-field magnetic reconnection in the nonrelativistic regime typical, e.g., for stellar coronae. We found that after electrons are first pre-accelerated during the linear growth of reconnection, they become additionally accelerated in the course of the nonlinear stage of 3D guide-field magnetic reconnection. This additional acceleration is due to the filamentation of electric and magnetic fields caused by streaming instabilities. In addition to enhanced parallel electric fields, the filamentation leads to additional curvature-driven electron acceleration in the guide-field direction. As a result, part of the accelerated electron spectra becomes a power law with a spectral index of ∼-1.6 near the X-line. This second stage of acceleration due to nonlinear reconnection is relevant for the production of energetic electrons in, e.g., thin current sheets of stellar coronae.

 Title: A new hybrid code (CHIEF) implementing the inertial electron fluid equation without approximation Authors: Muñoz, P. A., Jain, N., Kilian, P., and Büchner, J. Publication: Computer Physics Communications, 2018, 245 Publication Date: 03/2018 DOI: 10.1016/j.cpc.2017.10.012 Bibliographic Code: 2018CoPhC.224..245M Citation Count: 5

### Abstract

We present a new hybrid algorithm implemented in the code CHIEF (Code Hybrid with Inertial Electron Fluid) for simulations of electron-ion plasmas. The algorithm treats the ions kinetically, modeled by the Particle-in-Cell (PiC) method, and electrons as an inertial fluid, modeled by electron fluid equations without any of the approximations used in most of the other hybrid codes with an inertial electron fluid. This kind of code is appropriate to model a large variety of quasineutral plasma phenomena where the electron inertia and/or ion kinetic effects are relevant. We present here the governing equations of the model, how these are discretized and implemented numerically, as well as six test problems to validate our numerical approach. Our chosen test problems, where the electron inertia and ion kinetic effects play the essential role, are: 0) Excitation of parallel eigenmodes to check numerical convergence and stability, 1) parallel (to a background magnetic field) propagating electromagnetic waves, 2) perpendicular propagating electrostatic waves (ion Bernstein modes), 3) ion beam right-hand instability (resonant and non-resonant), 4) ion Landau damping, 5) ion firehose instability, and 6) 2D oblique ion firehose instability. Our results reproduce successfully the predictions of linear and non-linear theory for all these problems, validating our code. All properties of this hybrid code make it ideal to study multi-scale phenomena between electron and ion scales such as collisionless shocks, magnetic reconnection and kinetic plasma turbulence in the dissipation range above the electron scales.

 Title: Kinetic Simulations of Electron Acceleration at Mercury Authors: Büchner, Jörg, Kilian, Patrick, Muñoz, Patricio A., Spanier, Felix, Widmer, Fabien, Zhou, Xiaowei, and Jain, Neeraj Publication: Magnetic Fields in the Solar System, 2018, 201 Publication Date: 01/2018 DOI: 10.1007/978-3-319-64292-5_8 Bibliographic Code: 2018ASSL..448..201B Citation Count: 2

### Abstract

 Title: Recovering the Damping Rates of Cyclotron Damped Plasma Waves from Simulation Data Authors: Schreiner, Cedric, Kilian, Patrick, and Spanier, Felix Publication: Communications in Computational Physics, 2017, 947 Publication Date: 04/2017 DOI: 10.4208/cicp.OA-2016-0091 Bibliographic Code: 2017CCoPh..21..947S Citation Count: 5

### Abstract

Plasma waves with frequencies close to the particular gyrofrequencies of the charged particles in the plasma lose energy due to cyclotron damping. We briefly discuss the gyro-resonance of low frequency plasma waves and ions particularly with regard to particle-in-cell (PiC) simulations. A setup is outlined which uses artificially excited waves in the damped regime of the wave mode's dispersion relation to track the damping of the wave's electromagnetic fields. Extracting the damping rate directly from the field data in real or Fourier space is an intricate and non-trivial task. We therefore present a simple method of obtaining the damping rate {\Gamma} from the simulation data. This method is described in detail, focusing on a step-by-step explanation of the course of actions. In a first application to a test simulation we find that the damping rates obtained from this simulation generally are in good agreement with theoretical predictions. We then compare the results of one-, two- and three-dimensional simulation setups and simulations with different physical parameter sets.

 Title: Turbulent transport in 2D collisionless guide field reconnection Authors: Muñoz, P. A., Büchner, J., and Kilian, P. Publication: Physics of Plasmas, 2017, 022104 Publication Date: 02/2017 DOI: 10.1063/1.4975086 Bibliographic Code: 2017PhPl...24b2104M Citation Count: 7

### Abstract

Transport in hot and dilute, i.e., collisionless, astrophysical and space, plasmas is called "anomalous." This transport is due to the interaction between the particles and the self-generated turbulence by their collective interactions. The anomalous transport has very different and not well known properties compared to the transport due to binary collisions, dominant in colder and denser plasmas. Because of its relevance for astrophysical and space plasmas, we explore the excitation of turbulence in current sheets prone to component- or guide-field reconnection, a process not well understood yet. This configuration is typical for stellar coronae, and it is created in the laboratory for which a 2.5D geometry applies. In our analysis, in addition to the immediate vicinity of the X-line, we also include regions outside and near the separatrices. We analyze the anomalous transport properties by using 2.5D Particle-in-Cell code simulations. We split off the mean slow variation (in contrast to the fast turbulent fluctuations) of the macroscopic observables and determine the main transport terms of the generalized Ohm's law. We verify our findings by comparing with the independently determined slowing-down rate of the macroscopic currents (due to a net momentum transfer from particles to waves) and with the transport terms obtained by the first order correlations of the turbulent fluctuations. We find that the turbulence is most intense in the "low density" separatrix region of guide-field reconnection. It is excited by streaming instabilities, is mainly electrostatic and "patchy" in space, and so is the associated anomalous transport. Parts of the energy exchange between turbulence and particles are reversible and quasi-periodic. The remaining irreversible anomalous resistivity can be parametrized by an effective collision rate ranging from the local ion-cyclotron to the lower-hybrid frequency. The contributions to the parallel and the perpendicular (to the magnetic field) components of the slowly varying DC-electric fields, balanced by the turbulence, are similar. This anomalous electric field is, however, smaller than the contributions of the off-diagonal pressure and electron inertia terms of Ohm's law. This result can now be verified by in-situ measurements of the turbulence, in and around the magnetic reconnection regions of the Earth's magnetosphere by the multi-spacecraft mission MMS and in laboratory experiments like MRX and VINETA-II.

 Title: Particle Scattering off of Right-Handed Dispersive Waves Authors: Schreiner, C., Kilian, P., and Spanier, F. Publication: The Astrophysical Journal, 2017, 161 Publication Date: 01/2017 DOI: 10.3847/1538-4357/834/2/161 Bibliographic Code: 2017ApJ...834..161S Citation Count: 8

### Abstract

Resonant scattering of fast particles off low frequency plasma waves is a major process determining transport characteristics of energetic particles in the heliosphere and contributing to their acceleration. Usually, only Alfvén waves are considered for this process, although dispersive waves are also present throughout the heliosphere. We investigate resonant interaction of energetic electrons with dispersive, right-handed waves. For the interaction of particles and a single wave a variable transformation into the rest frame of the wave can be performed. Here, well-established analytic models derived in the framework of magnetostatic quasi-linear theory can be used as a reference to validate simulation results. However, this approach fails as soon as several dispersive waves are involved. Based on analytic solutions modeling the scattering amplitude in the magnetostatic limit, we present an approach to modify these equations for use in the plasma frame. Thereby we aim at a description of particle scattering in the presence of several waves. A particle-in-cell code is employed to study wave-particle scattering on a micro-physically correct level and to test the modified model equations. We investigate the interactions of electrons at different energies (from 1 keV to 1 MeV) and right-handed waves with various amplitudes. Differences between model and simulation arise in the case of high amplitudes or several waves. Analyzing the trajectories of single particles we find no microscopic diffusion in the case of a single plasma wave, although a broadening of the particle distribution can be observed.

 Title: Plasma Waves as a Benchmark Problem Authors: Kilian, Patrick, Muñoz, Patricio A., Schreiner, Cedric, and Spanier, Felix Publication: arXiv e-prints, 2016, arXiv:1611.01127 Publication Date: 11/2016 DOI: Bibliographic Code: 2016arXiv161101127K Citation Count: 0

### Abstract

A large number of wave modes exist in a magnetized plasma. Their properties are determined by the interaction of particles and waves. In a simulation code, the correct treatment of field quantities and particle behavior is essential to correctly reproduce the wave properties. Consequently, plasma waves provide test problems that cover a large fraction of the simulation code. The large number of possible wave modes and the freedom to choose parameters make the selection of test problems time consuming and comparison between different codes difficult. This paper therefore aims to provide a selection of test problems, based on different wave modes and with well defined parameter values, that is accessible to a large number of simulation codes to allow for easy benchmarking and cross validation. Example results are provided for a number of plasma models. For all plasma models and wave modes that are used in the test problems, a mathematical description is provided to clarify notation and avoid possible misunderstanding in naming.

 Title: Non-Maxwellian electron distribution functions due to self-generated turbulence in collisionless guide-field reconnection Authors: Muñoz, P. A. and Büchner, J. Publication: Physics of Plasmas, 2016, 102103 Publication Date: 10/2016 DOI: 10.1063/1.4963773 Bibliographic Code: 2016PhPl...23j2103M Citation Count: 15

### Abstract

Non-Maxwellian electron velocity space distribution functions (EVDFs) are useful signatures of plasma conditions and non-local consequences of collisionless magnetic reconnection. In the past, EVDFs were obtained mainly for antiparallel reconnection and under the influence of weak guide-fields in the direction perpendicular to the reconnection plane. EVDFs are, however, not well known, yet, for oblique (or component-) reconnection in case and in dependence on stronger guide-magnetic fields and for the exhaust (outflow) region of reconnection away from the diffusion region. In view of the multi-spacecraft Magnetospheric Multiscale Mission (MMS), we derived the non-Maxwellian EVDFs of collisionless magnetic reconnection in dependence on the guide-field strength bg from small ( b g ≈ 0 ) to very strong (bg = 8) guide-fields, taking into account the feedback of the self-generated turbulence. For this sake, we carried out 2.5D fully kinetic Particle-in-Cell simulations using the ACRONYM code. We obtained anisotropic EVDFs and electron beams propagating along the separatrices as well as in the exhaust region of reconnection. The beams are anisotropic with a higher temperature in the direction perpendicular rather than parallel to the local magnetic field. The beams propagate in the direction opposite to the background electrons and cause instabilities. We also obtained the guide-field dependence of the relative electron-beam drift speed, threshold, and properties of the resulting streaming instabilities including the strongly non-linear saturation of the self-generated plasma turbulence. This turbulence and its non-linear feedback cause non-adiabatic parallel electron acceleration. We further obtained the resulting EVDFs due to the non-linear feedback of the saturated self-generated turbulence near the separatrices and in the exhaust region of reconnection in dependence on the guide field strength. We found that the influence of the self-generated plasma turbulence leads well beyond the limits of the quasi-linear approximation to the creation of phase space holes and an isotropizing pitch-angle scattering. EVDFs obtained by this way can be used for diagnosing collisionless reconnection by using the multi-spacecraft observations carried out by the MMS mission.

 Title: Energy loss in intergalactic pair beams: Particle-in-cell simulation Authors: Kempf, A., Kilian, P., and Spanier, F. Publication: Astronomy and Astrophysics, 2016, A132 Publication Date: 01/2016 DOI: 10.1051/0004-6361/201527521 Bibliographic Code: 2016A&A...585A.132K Citation Count: 18

### Abstract

Aims: The change in the distribution function of electron-positron pair beams determines whether GeV photons can be produced as secondary radiation from TeV photons. We will discuss the instabilities driven by pair beams.
Methods: The system of a thermal proton-electron plasma and the electron-positron beam is collision free. We have, therefore, used the particle-in-cell simulation approach. It was necessary to alter the physical parameters, but the ordering of growth rates has been retained.
Results: We were able to show that plasma instabilities can be recovered in particle-in-cell simulations, but their effect on the pair distribution function is negligible for the beam-background energy density ratios typically found in blazars.

 Title: Gyrokinetic and kinetic particle-in-cell simulations of guide-field reconnection. I. Macroscopic effects of the electron flows Authors: Muñoz, P. A., Told, D., Kilian, P., Büchner, J., and Jenko, F. Publication: Physics of Plasmas, 2015, 082110 Publication Date: 08/2015 DOI: 10.1063/1.4928381 Bibliographic Code: 2015PhPl...22h2110M Citation Count: 10

### Abstract

In this work, we compare gyrokinetic (GK) with fully kinetic Particle-in-Cell (PIC) simulations of magnetic reconnection in the limit of strong guide field. In particular, we analyze the limits of applicability of the GK plasma model compared to a fully kinetic description of force free current sheets for finite guide fields (bg). Here, we report the first part of an extended comparison, focusing on the macroscopic effects of the electron flows. For a low beta plasma (βi = 0.01), it is shown that both plasma models develop magnetic reconnection with similar features in the secondary magnetic islands if a sufficiently high guide field (bg ≳ 30) is imposed in the kinetic PIC simulations. Outside of these regions, in the separatrices close to the X points, the convergence between both plasma descriptions is less restrictive (bg ≳ 5). Kinetic PIC simulations using guide fields bg ≲ 30 reveal secondary magnetic islands with a core magnetic field and less energetic flows inside of them in comparison to the GK or kinetic PIC runs with stronger guide fields. We find that these processes are mostly due to an initial shear flow absent in the GK initialization and negligible in the kinetic PIC high guide field regime, in addition to fast outflows on the order of the ion thermal speed that violate the GK ordering. Since secondary magnetic islands appear after the reconnection peak time, a kinetic PIC/GK comparison is more accurate in the linear phase of magnetic reconnection. For a high beta plasma (βi = 1.0) where reconnection rates and fluctuations levels are reduced, similar processes happen in the secondary magnetic islands in the fully kinetic description, but requiring much lower guide fields (bg ≲ 3).

 Title: Effects of dispersive wave modes on charged particles transport Authors: Schreiner, C. and Spanier, F. Publication: 34th International Cosmic Ray Conference (ICRC2015), 2015, 177 Publication Date: 07/2015 DOI: Bibliographic Code: 2015ICRC...34..177S Citation Count: 0

### Abstract

The transport of charged particles in the heliosphere and the interstellar medium is governed by the interaction of particles and magnetic irregularities. For the transport of protons a rather simple model using a linear Alfvén wave spectrum which follows the Kolmogorov distribution usually yields good results. Even magnetostatic spectra may be used. For the case of electron transport, particles will resonate with the high-k end of the spectrum. Here the magnetic fluctuations do not follow the linear dispersion relation, but the kinetic regime kicks in. We will discuss the interaction of fluctuations of dispersive waves in the kinetic regime using a particle-in-cell code. Especially the scattering of particles following the idea of Lange et al. (2013) and its application to PiC codes will be discussed. The effect of the dispersive regime on the electron transport will be discussed in detail.

 Title: Instabilities of collisionless current sheets revisited: The role of anisotropic heating Authors: Muñoz, P. A., Kilian, P., and Büchner, J. Publication: Physics of Plasmas, 2014, 112106 Publication Date: 11/2014 DOI: 10.1063/1.4901033 Bibliographic Code: 2014PhPl...21k2106M Citation Count: 6

### Abstract

In this work, we investigate the influence of the anisotropic heating on the spontaneous instability and evolution of thin Harris-type collisionless current sheets, embedded in antiparallel magnetic fields. In particular, we explore the influence of the macroparticle shape-function using a 2D version of the PIC code ACRONYM. We also investigate the role of the numerical collisionality due to the finite number of macroparticles in PIC codes. It is shown that it is appropriate to choose higher order shape functions of the macroparticles compared to a larger number of macroparticles per cell. This allows to estimate better the anisotropic electron heating due to the collisions of macroparticles in a PIC code. Temperature anisotropies can stabilize the tearing mode instability and trigger additional current sheet instabilities. We found a good agreement between the analytically derived threshold for the stabilization of the anisotropic tearing mode and other instabilities, either spontaneously developing or initially triggered ones. Numerical effects causing anisotropic heating at electron time scales become especially important for higher mass ratios (above m i / m e = 180 ). If numerical effects are carefully taken into account, one can recover the theoretical estimated linear growth rates of the tearing instability of thin isotropic collisionless current sheets, also for higher mass ratios.

 Title: Fundamental and harmonic plasma emission in different plasma environments Authors: Ganse, U., Kilian, P., Spanier, F., and Vainio, R. Publication: Astronomy and Astrophysics, 2014, A15 Publication Date: 04/2014 DOI: 10.1051/0004-6361/201322834 Bibliographic Code: 2014A&A...564A..15G Citation Count: 11

### Abstract

Aims: Emission of radio waves from plasmas through plasma emission with fundamental and harmonic frequencies is a familiar process known from solar type II radio bursts. Current models assume the existence of counterstreaming electron beam populations excited at shocks as sources for these emission features, which limits the plasma parameters to reasonable heliospheric shock conditions. However, situations in which counterstreaming electron beams are present can also occur with different plasma parameters, such as higher magnetisation, including but not limited to our Sun. Similar radio emissions might also occur from these situations.
Methods: We used particle-in-cell simulations to compare plasma microphysics of radio emission processes from counterstreaming beams in different plasma environments that differed in density and magnetization.
Results: Although large differences in wave populations are evident, the emission process of type II bursts appears to be qualitatively unaffected and shows the same behaviour in all environments.

 Title: Different Choices of the Form Factor in Particle-in-Cell Simulations Authors: Kilian, P., Ganse, U., and Spanier, F. Publication: Numerical Modeling of Space Plasma Flows (ASTRONUM2012), 2013, 208 Publication Date: 04/2013 DOI: Bibliographic Code: 2013ASPC..474..208K Citation Count: 2

### Abstract

Numerical simulations have proven a valuable tool to study plasma behavior, especially for conditions in astrophysical scenarios and which are not readily accessible under laboratory conditions. Whenever single particle behavior becomes important or the development of non-thermal components is of interest fluid descriptions have to be replaced by more accurate but also more expensive kinetic descriptions. A very popular such method is the Particle-in-Cell method. Conceptually this method combines the integration of motion if individual elementary particles with field quantities that are restricted to a spatial grid. Both the analytic derivation of the method as well as the computational feasibility require the use of phase space samples instead of the more readily envisioned individual elementary particles. Each macroparticle represents an ensemble of particles of one species that are close to each other in phase space and carries the total charge and mass of the ensemble. Unlike the elementary particles the macroparticle does not necessarily have a vanishing spatial extent. Different choices of the form factor, that is spatial distribution of the particle quantities within the macroparticle, are investigated. Included are the standard choices NGP, CIC and TSC as well as new schemes of higher order.

 Title: Emission of Type II Radio Bursts - Single-Beam Versus Two-Beam Scenario Authors: Ganse, U., Kilian, P., Vainio, R., and Spanier, F. Publication: Solar Physics, 2012, 551 Publication Date: 10/2012 DOI: 10.1007/s11207-012-0077-7 Bibliographic Code: 2012SoPh..280..551G Citation Count: 30

### Abstract

The foreshock region of a CME shock front, where shock accelerated electrons form a beam population in the otherwise quiescent plasma is generally assumed to be the source region of type II radio bursts. Nonlinear wave interaction of electrostatic waves excited by the beamed electrons are the prime candidates for the radio waves' emission. To address the question whether a single, or two counterpropagating beam populations are a requirement for this process, we have conducted 2.5D particle-in-cell simulations using the fully relativistic ACRONYM code. Results show indications of three-wave interaction leading to electromagnetic emission at the fundamental and harmonic frequency for the two-beam case. For the single-beam case, no such signatures were detectable.

 Title: Numerical Challenges in Kinetic Simulations of Three-wave Interactions Authors: Ganse, U., Kilian, P., Siegel, S., and Spanier, F. Publication: Numerical Modeling of Space Plasma Slows (ASTRONUM 2011), 2012, 265 Publication Date: 07/2012 DOI: Bibliographic Code: 2012ASPC..459..265G Citation Count: 0

### Abstract

Generation of radio bursts in CME foreshock regions and turbulent cascades in the solar wind are assumed to be results of three-wave interaction processes of dispersive plasma modes. Using our Particle in Cell code ACRONYM, we have studied the behaviour of kinetic wavemodes in the presence of beamed electron populations, with a focus on type II radio burst emission processes. We discuss the numerical challenges in generating and analyzing self-consistently evolving wave coupling processes with a PiC-Code and present preliminary results of said project.

 Title: Nonlinear Wave Interactions as Emission Process of Type II Radio Bursts Authors: Ganse, Urs, Kilian, Patrick, Spanier, Felix, and Vainio, Rami Publication: The Astrophysical Journal, 2012, 145 Publication Date: 06/2012 DOI: 10.1088/0004-637X/751/2/145 Bibliographic Code: 2012ApJ...751..145G Citation Count: 21

### Abstract

The emission of fundamental and harmonic frequency radio waves of type II radio bursts are assumed to be products of three-wave interaction processes of beam-excited Langmuir waves. Using a particle-in-cell code, we have performed simulations of the assumed emission region, a coronal mass ejection foreshock with two counterstreaming electron beams. Analysis of wavemodes within the simulation shows self-consistent excitation of beam-driven modes, which yield interaction products at both fundamental and harmonic emission frequencies. Through variation of the beam strength, we have investigated the dependence of energy transfer into electrostatic and electromagnetic modes, confirming the quadratic dependence of electromagnetic emission on electron beam strength.

 Title: Kinetic Simulations of Solar Type II Radio Burst Emission Authors: Ganse, U., Kilian, P., Spanier, F., and Vainio, R. Publication: EGU General Assembly Conference Abstracts, 2012, 2081 Publication Date: 04/2012 DOI: Bibliographic Code: 2012EGUGA..14.2081G Citation Count: 0

### Abstract

Propagation of coronal mass ejection (CME) shock fronts in the heliosphere is often accompanied by the emission of so-called type II radio bursts, which are multi banded emission features. Their complex emission spectra indicate that interaction processes of multiple plasma waves are responsible for their creation, but the requirement for kinetic treatmet of the problem, together with the large separation of involved lengthscales have made simulations of this phenomenon challenging. Using the ACRONYM particle-in-cell code, we have investigated the plasma microphysics in the CME foreshock region. We were able to consistently reproduce the electron beam-driven excitation of electrostatic waves and their subsequent nonlinear coupling to form fundamental and harmonic radio emissions.

 Title: The Influence of the Mass Ratio on the Acceleration of Particles by Filamentation Instabilities Authors: Burkart, Thomas, Elbracht, Oliver, Ganse, Urs, and Spanier, Felix Publication: The Astrophysical Journal, 2010, 1318 Publication Date: 09/2010 DOI: 10.1088/0004-637X/720/2/1318 Bibliographic Code: 2010ApJ...720.1318B Citation Count: 2

### Abstract

Almost all sources of high-energy particles and photons are associated with jet phenomena. Prominent sources of such highly relativistic outflows are pulsar winds, active galactic nuclei (AGNs), and gamma-ray bursts. The current understanding of these jets assumes diluted plasmas which are best described as kinetic phenomena. In this kinetic description, particle acceleration to ultrarelativistic speeds can occur in completely unmagnetized and neutral plasmas through insetting effects of instabilities. Even though the morphology and nature of particle spectra are understood to a certain extent, the composition of the jets is not known yet. While Poynting-flux-dominated jets (e.g., occurring in pulsar winds) are certainly composed of electron-positron plasmas, the understanding of the governing physics in AGN jets is mostly unclear. In this paper, we investigate how the constituting elements of an electron-positron-proton plasma behave differently under the variation of the fundamental mass ratio mp /me . We initially studied unmagnetized counterstreaming plasmas using fully relativistic three-dimensional particle-in-cell simulations to investigate the influence of the mass ratio on particle acceleration and magnetic field generation in electron-positron-proton plasmas. We covered a range of mass ratios mp /me between 1 and 100 with a particle number composition of n_{p^+} / n_{e^+} of 1 in one stream, therefore called the pair-proton stream. Protons are injected in the other one, therefore from now on called the proton stream, whereas electrons are present in both to guarantee charge neutrality in the simulation box. We find that with increasing proton mass the instability takes longer to develop and for mass ratios &gt;20 the particles seem to be accelerated in two phases which can be accounted for by the individual instabilities of the different species. This means that for high mass ratios the coupling between electrons/positrons and the heavier protons, which occurs in low mass ratios, disappears.