arXiv subjects

Jörg Büchner

Publications and source records attributed to Jörg Büchner.

At least 19 recordsLinked to original sources

arXiv2025

Preferential acceleration of heavy ions in magnetic reconnection: Hybrid-kinetic simulations with electron inertia

Solar energetic particles (SEPs) in the energy range 10s KeV/nucleon-100s MeV/nucleon originate from Sun. Their high flux near Earth may damage the space borne electronics and generate secondary radiations harmful for the life on Earth and thus understanding their energization on Sun is important for space weather prediction. Impulsive (or ${}^{3}$He-rich) SEP events are associated with the acceleration of charge particles in solar flares by magnetic reconnection (MR) and related processes. The preferential acceleration of heavy ions and the extra-ordinary abundance enhancement of ${}^3$He in the impulsive SEPs are not understood yet. We study heavy-ion acceleration and their abundance enhancements by MR, an established acceleration source for impulsive SEPs in which heavy-ion enhancement is observed. We simulate MR using a 2-D hybrid-kinetic plasma model (kinetic ions and inertial electron fluid) with all the ions species treated self-consistently. We find that heavy ions are preferentially accelerated to energies many times larger than their initial thermal energies by a variety of acceleration mechanisms operating in MR. Most efficient acceleration takes place in the flux pileup regions of MR. Heavy ions with sufficiently small values of charge to mass ratio ($Q/M$) can be accelerated by pickup mechanism in outflow regions even before any magnetic flux is piled up. The energy spectra of heavy ions develop a shoulder like region, a non-thermal feature, as a result of the acceleration. The spectral index of the power law fit to the shoulder region of the spectra varies approximately as $(Q/M)^{-0.64}$. Abundance enhancement factor, defined as number of particles above a threshold energy normalized to total number of particles, scales as $(Q/M)^{-α}$ where $α$ increases with the energy threshold. We discuss our simulation results in the light of the SEP observations.

physics.plasm-ph↗

arXiv2024

Poynting flux transport channels formed in polar cap regions of neutron star magnetospheres

Pair cascades in polar cap regions of neutron stars are considered to be an essential process in various models of coherent radio emissions of pulsars. The cascades produce pair plasma bunch discharges in quasi-periodic spark events. The cascade properties, and therefore also the coherent radiation, depend strongly on the magnetospheric plasma properties and vary significantly across and along the polar cap. Importantly, where the radio emission emanates from in the polar cap region is still uncertain. We investigate the generation of electromagnetic waves by pair cascades and their propagation in the polar cap for three representative inclination angles of a magnetic dipole, $0^\circ$, $45^\circ$, and $90^\circ$. We use two-dimensional particle-in-cell simulations that include quantum-electrodynamic pair cascades in a charge-limited flow from the star surface. We find that the discharge properties are strongly dependent on the magnetospheric current profile in the polar cap and that transport channels for high intensity Poynting flux are formed along magnetic field lines where the magnetospheric currents approach zero and where the plasma cannot carry the magnetospheric currents. There, the parallel Poynting flux component is efficiently transported away from the star and may eventually escape the magnetosphere as coherent radio waves. The Poynting flux decreases with increasing distance from the star in regions of high magnetospheric currents. Our model shows that no process of energy conversion from particles to waves is necessary for the coherent radio wave emission. Moreover, the pulsar radio beam does not have a cone structure; rather, the radiation generated by the oscillating electric gap fields directly escapes along open magnetic field lines in which no pair creation occurs.

astro-ph.HE↗

arXiv2024

Streaming instability in neutron star magnetospheres: No indication of soliton-like waves

Coherent radiation of pulsars, magnetars, and fast radio bursts could, in theory, be interpreted as radiation from solitons and soliton-like waves. The solitons are meant to contain a large number of electric charges confined on long time-scales and may radiate strongly by coherent curvature emission. However, solitons are also known to undergo a wave collapse, which may cast doubts on the correctness of the soliton radio emission models of neutron stars. We investigate the evolution of the caviton type of solitons self-consistently formed by the relativistic streaming instability and compare their apparent stability in 1D calculations with more generic 2D cases, in which the solitons are seen to collapse. Three representative cases of beam Lorentz factors and plasma temperatures are studied to obtain soliton dispersion properties. We utilized 1D electrostatic and 2D electromagnetic relativistic particle-in-cell simulations at kinetic microscales. We found that no solitons are generated by the streaming instability in the 2D simulations. Only superluminal L-mode (relativistic Langmuir) waves are produced during the saturation of the instability, but these waves have smaller amplitudes than the waves in the 1D simulations. The amplitudes tend to decrease after the instability has saturated, and only waves close to the light line, $ω= c k$, remain. Solitons in the 1D approach are stable for $γ_\mathrm{b} \gtrsim 60$, but they disappear for low beam Lorentz factor $γ_\mathrm{b} < 6$. Our examples show that the superluminal soliton branch that is formed in 1D simulations will not be generated by the relativistic streaming instability when more dimensional degrees of freedom are present - unless one can show that there are alternative plasma mechanisms for the soliton generation.

astro-ph.HE↗

arXiv2023

Electron inertia effects in 3D hybrid-kinetic collisionless plasma turbulence

The effects of the electron inertia on the current sheets that are formed out of kinetic turbulence are relevant to understand the importance of coherent structures in turbulence and the nature of turbulence at the dissipation scales. We investigate this problem by carrying out 3D hybrid-kinetic Particle-in-Cell (PIC) simulations of decaying kinetic turbulence with our CHIEF code. The main distinguishing feature of this code is an implementation of the electron inertia without approximations. Our simulation results show that the electron inertia plays an important role in regulating and limiting the largest values of current density in both real and wavenumber Fourier space, in particular near and, unexpectedly, even above electron scales. In addition, the electric field associated to the electron inertia dominates most of the strongest current sheets. The electron inertia is thus important to accurately describe the properties of current sheets formed in turbulence at electron scales.

physics.plasm-ph↗

arXiv2023

Linear acceleration emission of pulsar relativistic streaming instability and interacting plasma bunches

Linear acceleration emission is one of the mechanisms that might explain intense coherent emissions of radio pulsars. This mechanism is not well understood, however, because the effects of collective plasma response and nonlinear plasma evolution on the resulting emission power must be taken into account. In addition, details of the radio emission properties of this mechanism are unknown, which limits the observational verification of the emission model. By including collective and nonlinear plasma effects, we calculate radio emission power properties by the linear acceleration emission mechanism that occurs via the antenna principle for two instabilities in neutron star magnetospheres: 1) the relativistic streaming instability, and 2) interactions of plasma bunches. We used 1D electrostatic relativistic particle-in-cell simulations to evolve the instabilities self-consistently. From the simulations, the power properties of coherent emission were obtained by novel postprocessing of electric currents. We found that the total radio power by plasma bunch interactions exceeds the power of the streaming instability by eight orders of magnitude. The wave power generated by a plasma bunch interaction can be as large as $2.6\times10^{16}$ W. The number of bunch interactions that are required to explain the typical pulsar power, $10^{18}$-$10^{22}$ W, depends on how the coherent emissions of bunches are added up together. Although $\sim$$4\times (10^1-10^5)$ simultaneously emitting bunches are necessary for an incoherent addition of their radiation power, $\gtrsim 6-600$ bunches can explain the total pulsar power if they add up coherently. The radio spectrum of the plasma bunch is characterized by a flatter profile for low frequencies and by a power-law index up to $\approx-1.6 \pm 0.2$ for high frequencies. The plasma bunches simultaneously radiate in a wide range of frequencies.

astro-ph.HE↗

arXiv2022

Reconstruction of Coronal Magnetic Fields Using a Poloidal-Toroidal Representation

A new method for reconstruction of coronal magnetic fields as force-free fields (FFFs) is presented. Our method employs poloidal and toroidal functions to describe divergence-free magnetic fields. This magnetic field representation naturally enables us to implement the boundary conditions at the photospheric boundary, i.e., the normal magnetic field and the normal current density there, in a straightforward manner. At the upper boundary of the corona, a source-surface condition can be employed, which accommodates magnetic flux imbalance at the bottom boundary. Although our iteration algorithm is inspired by extant variational methods, it is non-variational and requires far fewer iteration steps than most of them. The computational code based on our new method is tested against the analytical FFF solutions by Titov & Démoulin (1999). It is found to excel in reproducing a tightly wound flux rope, a bald patch and quasi-separatrix layers with a hyperbolic flux tube.

astro-ph.SR↗

arXiv2022

Hybrid-Kinetic Approach: Inertial Electrons

Hybrid-kinetic simulations describe ion-scale kinetic phenomena in space plasmas by considering ions kinetically, i.e. as particles, while electrons are modelled as a fluid. Most of the existing hybrid-kinetic codes neglect the electron mass (see chapter 3) for a simplified calculation of the electromagnetic fields. There are, however, situations in which delay in the electrons response due to the electron inertia matters. This chapter concentrates on hybrid-kinetic simulation models which take the finite mass of the electron fluid into account. First a review is given of the history of including the finite electron mass in hybrid-kinetic models. Then the equations are discussed which additionally have to be solved compared to the mass-less hybrid-kinetic models. For definiteness their numerical implementation without additional approximations is illustrated by describing a hybrid-kinetic code, CHIEF. The importance of the consideration of the finite electron mass are discussed for typical applications (magnetic reconnection, plasma turbulence, collisionless shocks and global magnetospheric simulations). In particular the problem of guide field magnetic reconnection is addressed in some detail. Possible next steps towards further improvements of hybrid-kinetic simulations with finite electron mass are suggested.

physics.plasm-ph↗

arXiv2022

Electron-to-ion bulk speed ratio as a parameter reflecting the occurrence of strong electron-dominated current sheets in the solar wind

Current sheets (CSs) are preferred sites of magnetic reconnection and energy dissipation in collisionless astrophysical plasmas. Electric currents in them may be carried by both electrons and ions. In our prior theoretical studies of processes associated with the CS formation in turbulent plasmas, for which we utilized fully kinetic and hybrid code simulations with ions considered as particles and electrons - as a massless fluid, we found that electron-dominated CSs may form inside or nearby ion-dominated CSs. Electrons become the main carrier of the electric current and contributors to energy dissipation in electron-dominated CSs. These magneto-plasma structures represent a distinguished type of CSs and should not be mixed up with so-called electron-scale CSs. Our simulations show that such CSs are characterized by the electron-to-ion bulk speed ratio Ue/Ui increases. Theoretical predictions and high-resolution observations from the MMS mission suggest that strong electron-dominated CSs can be seen at ion scales. Therefore, we suggest that applying the Ue/Ui parameter to the solar wind data may allow locating the strongest electron-dominated CSs with an ordinary spacecraft resolution of one-three seconds at least approximately. The results show that, indeed, an impact of electron-dominated CSs on the plasma observed during a period of quiet solar wind conditions at 1 AU may be associated with sharp changes in Ue/Ui. Electron-dominated CSs are found to be localized in the vicinity of ion-dominated CSs identified via changes in the magnetic field and plasma parameters Ue/Ui, displaying the same clustering. We conclude that Ue/Ui may be used as one of key parameters for probing CSs in the solar wind and the role of electrons in them.

astro-ph.SR↗

arXiv2022

Wave emission of non-thermal electron beams generated by magnetic reconnection

Magnetic reconnection in solar flares can efficiently generate non-thermal electron beams. The energetic electrons can, in turn, cause radio waves through microscopic plasma instabilities as they propagate through the ambient plasma along the magnetic field lines. We aim at investigating the wave emission caused by fast moving electron beams (FEBs) with characteristic non-thermal electron velocity distribution functions (EVDFs) generated by kinetic magnetic reconnection: two-streaming EVDFs along the separatrices and in the diffusion region, and perpendicular crescent-shaped EVDFs closer to the diffusion region. For this purpose, we utilized 2.5D fully kinetic Particle-In-Cell (PIC) code simulations in this study. We found that:(1) the two-streaming EVDFs plus the background ions are unstable to electron/ion (streaming) instabilities which cause ion acoustic waves and Langmuir waves due to the net current. This can lead to multiple harmonic plasma emission in the diffusion region and the separatrices of reconnection. (2) The perpendicular crescent-shaped EVDFs can cause multiple harmonic electromagnetic electron cyclotron waves through the electron cyclotron maser instabilities in the diffusion region of reconnection. Our results are applicable to diagnose the plasma parameters which control magnetic reconnection in solar flares by means of radio waves observations.

astro-ph.SR↗

arXiv2022

Nonthermal electron velocity distribution functions due to 3D kinetic magnetic reconnection for solar coronal plasma conditions

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.

physics.plasm-ph↗

arXiv2022

Importance of accurate consideration of the electron inertia in hybrid-kinetic simulations of collisionless plasma turbulence: 1. The 2D limit

The dissipation mechanism of the magnetic energy in turbulent collisionless space and astrophysical plasmas is still not well understood. Its investigation requires efficient kinetic simulations of the energy transfer in collisionless plasma turbulence. In this respect, hybrid-kinetic simulations, in which ions are treated as particles and electrons as an inertial fluid, have begun to attract a significant interest recently. Hybrid-kinetic models describe both ion- and electron scale processes by ignoring electron kinetic effects so that they are computationally much less demanding compared to fully kinetic plasma models. Hybrid-kinetic codes solve either the Vlasov equation for the ions (Eulerian Vlasov-hybrid codes) or the equations of motion of the ions as macro-particles (Lagrangian Particle-in-Cell (PIC)-hybrid codes). They consider the inertia of the electron fluid using different approximations. We check the validity of these approximations by employing our recently massively parallelized three-dimensional PIC-hybrid code CHIEF which considers the electron inertia without any of the common approximations. In particular we report the results of simulations of two-dimensional collisionless plasma turbulence. We conclude that the simulation results obtained using hybrid-kinetic codes which use approximations to describe the electron inertia need to be interpreted with caution. We also discuss the parallel scalability of CHIEF, to the best of our knowledge, the first PIC-hybrid code which without approximations describes the inertial electron fluid.

physics.plasm-ph↗

arXiv2021

Free energy sources in current sheets formed in collisionless plasma turbulence

Collisionless dissipation of macroscopic energy into heat is an unsolved problem of space and astrophysical plasmas, e.g., solar wind and Earth's magnetosheath. The most viable process under consideration is the turbulent-cascade of macroscopic energy to kinetic-scales where collisionless-plasma-processes dissipate the energy. Space observations and numerical simulations show the formation of kinetic scale current sheets in turbulent plasmas. Instabilities in these CS can provide collisionless dissipation and influence the turbulence. Spatial gradients of physical quantities and non-Maxwellian velocity distribution functions provide the free-energy-sources for CS plasma instabilities. To determine the free-energy-sources provided by the spatial gradients of plasma density and electron/ion bulk velocities in CS formed in collisionless turbulent plasmas with an external magnetic field $\mathbf{B}_0$, we carried out two-dimensional PIC-hybrid simulations and interpret the results within the limitations of the simulation model. We found that ion-scale CS in a collisionless turbulent plasma are formed primarily by electron shear flows, i.e., electron bulk velocity inside CS is much larger than ion bulk velocity while the density variations through the CS are relatively small ($<$ 10\%). The electron-bulk-velocity and, thus, the current density inside the sheets are directed mainly parallel to $\mathbf{B}_0$. The shear in the perpendicular electron- and ion-bulk-velocities generates parallel electron- and ion-flow-vorticities. Inside CS, parallel electron-flow-vorticity exceeds the parallel ion-flow-vorticity, changes sign around the CS centers and peaks near the CS edges. An ion temperature anisotropy develops near CS during the CS formation. It has positive correlation with the parallel ion- and electron-flow-vorticities. Theoretical estimates support the simulation results.

physics.plasm-ph↗

arXiv2021

Radio Emission by Soliton Formation in Relativistically Hot Streaming Pulsar Pair Plasmas

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 $ρ\geq 1.66$ or relative beam drift speeds with Lorentz factors $γ> 40$. 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.

astro-ph.HE↗

arXiv2021

Bunch Expansion as a cause for Pulsar Radio Emissions

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 in dependence on the relative drift speeds of electrons and positrons, on the initial plasma temperature, and on the initial 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 electric fields that reach up to $E \sim 7.5 \times 10^{5}$ V/cm ($E / (m_\mathrm{e} c ω_\mathrm{p} e^{-1}) \sim 4.4$) 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 the momentum (velocity) space. This overlap causes two-stream instabilities that generate (electrostatic) subluminal L-mode waves with electric field amplitudes reaching up to $E \sim 1.9\times 10^{4}$ V/cm ($E / (m_\mathrm{e} c ω_\mathrm{p} e^{-1}) \sim 0.11$). We found that the interaction of electron-position bunches leads to plasma heating, to the generation of strong electric fields and of intense superluminal L-mode waves which, in principle, can be behind the observed electromagnetic emissions of pulsars in the radio wave range.

astro-ph.HE↗

arXiv2021

Refining pulsar radio emission due to streaming instabilities: Linear theory and PIC simulations in a wide parameter range

Several important mechanisms that explain the 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 a 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. 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. 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. The analytical results are validated by comparison with relativistic kinetic particle-in-cell (PIC) numerical simulations. 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. We show that the generated waves are phase-coherent by calculating the fractional bandwidth. We provide an explicit parameter range of plasma conditions for efficient pulsar radio emission.

astro-ph.HE↗

arXiv2021

The effects of density inhomogeneities on the radio wave emission in electron beam plasmas

Type III radio bursts are radio emissions associated with solar flares. They are considered to be caused by electron beams traveling 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 non-linear kinetic plasma processes of generation of beam-related radio emissions in inhomogeneous plasmas by utilizing fully-kinetic Particle-In-Cell (PIC) 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 emissions due to wave-wave interactions and so-called electron cyclotron maser emissions (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.

physics.plasm-ph↗

arXiv2020

Identification and characterization of current sheets in collisionless plasma turbulence

The properties of current sheets forming in a ion-kinetically turbulent collisionless plasma are investigated by utilizing the results of two-dimensional hybrid-kinetic numerical simulations. For this sake the algorithm proposed by Zhdankin et al. (2013) for the analysis of current sheets forming in MHD-turbulent plasmas, was extended to analyse the role and propertes of current sheets formating in a much noisier kinetically turbulent plasma. The applicability of this approach to the analysis of kinetically-turbulent plasmas is verified. Invesigated are, e.g., the effects of the choice of parameters on the current sheet recognition, viz. the threshold current density, the minimum current density and of the local regions around current density peaks. The main current sheet properties are derived, their peak current density, the peak current carrier velocity (mainly electrons), the thickness and length of the current sheets, i.e. also their aspect ratio (length/thickness). By varying the grid resolution of the simulations it is shown that, as long as the electron inertia is not taken into account, the current sheets thin down well below ion inertial length scale until numerical (grid-resolution based) dissipation stops any the further thinning.

physics.plasm-ph↗

arXiv2020

Ion acceleration in non-relativistic quasi-parallel shocks using fully kinetic simulations

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.

astro-ph.HE↗