Strong magnetically dominated Alfvénic turbulence is an efficient engine of nonthermal particle acceleration in a relativistic collisionless plasma. We argue that in the limit of strong magnetization, the type of energy distribution attained by accelerated particles depends on the relative strengths of turbulent fluctuations
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Abstract δ B _{0}and the guide fieldB _{0}. Ifδ B _{0}≪B _{0}, the particle magnetic moments are conserved, and the acceleration is provided by magnetic curvature drifts. Curvature acceleration energizes particles in the direction parallel to the magnetic field lines, resulting in lognormal tails of particle energy distribution functions. Conversely, ifδ B _{0}≳B _{0}, interactions of energetic particles with intense turbulent structures can scatter particles, creating a population with large pitch angles. In this case, magnetic mirror effects become important, and turbulent acceleration leads to powerlaw tails of the energy distribution functions. 
Whistler waves propagating nearly parallel to the ambient magnetic field experience a nonlinear instability due to transverse currents when the background plasma has a population of sufficiently low energy electrons. Intriguingly, this nonlinear process may generate oblique electrostatic waves, including whistlers near the resonance cone with properties resembling oblique chorus waves in the Earth’s magnetosphere. Focusing on the generation of oblique whistlers, earlier analysis of the instability is extended here to the case where lowenergy background plasma consists of both a “cold” population with energy of a few eV and a “warm” electron component with energy of the order of 100 eV. This is motivated by spacecraft observations in the Earth’s magnetosphere where oblique chorus waves were shown to interact resonantly with the warm electrons. The main new results are: 1) the instability producing oblique electrostatic waves is sensitive to the shape of the electron distribution at low energies. In the whistler range of frequencies, two distinct peaks in the growth rate are typically present for the model considered: a peak associated with the warm electron population at relatively low wavenumbers and a peak associated with the cold electron population at relatively high wavenumbers; 2) overall, the instability producing oblique whistler waves near the resonance cone persists (with a reduced growth rate) even in the cases where the temperature of the cold population is relatively high, including cases where cold population is absent and only the warm population is included; 3) particleincell simulations show that the instability leads to heating of the background plasma and formation of characteristic plateau and beam features in the parallel electron distribution function in the range of energies resonant with the instability. The plateau/beam features have been previously detected in spacecraft observations of oblique chorus waves. However, they have been attributed to external sources and have been proposed to be the mechanism generating oblique chorus. In the present scenario, the causality link is reversed and the instability generating oblique whistler waves is shown to be a possible mechanism for formation of the plateau and beam features.more » « lessFree, publiclyaccessible full text available July 9, 2025

Abstract In a strongly magnetized, magnetically dominated relativistic plasma, Alfvénic turbulence can extend to scales much smaller than the particle inertial scales. It leads to an energy cascade somewhat analogous to inertial or kineticAlfvén turbulent cascades existing in nonrelativistic space and astrophysical plasmas. Based on phenomenological modeling and particleincell numerical simulations, we propose that the energy spectrum of such relativistic kineticscale Alfvénic turbulence is close to
k ^{−3}or slightly steeper than that due to intermittency corrections or Landau damping. We note the analogy of this spectrum with the Kraichnan spectrum corresponding to the enstrophy cascade in 2D incompressible fluid turbulence. Such turbulence strongly energizes particles in the direction parallel to the background magnetic field, leading to nearly onedimensional particle momentum distributions. We find that these distributions have universal lognormal statistics. 
Diffusive shock acceleration requires the production of backstreaming superthermal ions (injection) as a first step. Such ions can be generated in the process of scattering of ions in the superthermal tail off the shock front. Knowledge of the scattering of highenergy ions is essential for matching conditions of upstream and downstream distributions at the shock transition. Here we analyze the generation of backstreaming ions as a function of their initial energy in a model stationary shock and in a similar rippled shock. Rippling substantially enhances ion reflection and the generation of backstreaming ions for slightly and moderately superthermal energies, and thus is capable of ensuring ion injection into a further diffusive shock acceleration process. For highenergy ions, there is almost no difference in the fraction of backstreaming ions produced and the ion distributions between the planar stationary shock and the rippled shock.more » « lessFree, publiclyaccessible full text available November 1, 2024

Abstract In a collisionless shock the energy of the directed flow is converted to heating and acceleration of charged particles, and to magnetic compression. In lowMach number shocks the downstream ion distribution is made of directly transmitted ions. In higherMach number shocks ion reflection is important. With the increase of the Mach number, rippling develops, which is expected to affect ion dynamics. Using ion tracing in a model shock front, downstream distributions of ions are analyzed and compared for a planar stationary shock with an overshoot and a similar shock with ripples propagating along the shock front. It is shown that rippling results in the distributions, which are substantially broader and more diffuse in the phase space. Gyrotropization is sped up. Rippling is able to generate backstreaming ions, which are absent in the planar stationary case.more » « less

ABSTRACT Threedimensional kineticscale turbulence is studied numerically in the regime where electrons are strongly magnetized (the ratio of plasma species pressure to magnetic pressure is βe = 0.1 for electrons and βi = 1 for ions). Such a regime is relevant in the vicinity of the solar corona, the Earth’s magnetosheath, and other astrophysical systems. The simulations, performed using the fluidkinetic spectral plasma solver (sps) code, demonstrate that the turbulent cascade in such regimes can reach scales smaller than the electron inertial scale, and results in the formation of electronscale current sheets (ESCS). Statistical analysis of the geometrical properties of the detected ESCS is performed using an algorithm based on the medial axis transform. A typical halfthickness of the current sheets is found to be on the order of electron inertial length or below, while their halflength falls between the electron and ion inertial length. The pressure–strain interaction, used as a measure of energy dissipation, exhibits high intermittency, with the majority of the total energy exchange occurring in current structures occupying approximately 20 per cent of the total volume. Some of the current sheets corresponding to the largest pressure–strain interaction are found to be associated with Alfvénic electron jets and magnetic configurations typical of reconnection. These reconnection candidates represent about 1 per cent of all the current sheets identified.

Abstract Relativistic magnetically dominated turbulence is an efficient engine for particle acceleration in a collisionless plasma. Ultrarelativistic particles accelerated by interactions with turbulent fluctuations form nonthermal powerlaw distribution functions in the momentum (or energy) space,
f (γ )d γ ∝γ ^{−α}d γ , whereγ is the Lorenz factor. We argue that in addition to exhibiting nonGaussian distributions over energies, particles energized by relativistic turbulence also become highly intermittent in space. Based on particleincell numerical simulations and phenomenological modeling, we propose that the bulk plasma density has lognormal statistics, while the density of the accelerated particles,n , has a powerlaw distribution function, . We argue that the scaling exponents are related as $P(n)\mathit{dn}\phantom{\rule{0.25em}{0ex}}\propto \phantom{\rule{0.25em}{0ex}}{n}^{\beta}\mathit{dn}$β ≈α + 1, which is broadly consistent with numerical simulations. Nonspacefilling, intermittent distributions of plasma density and energy fluctuations may have implications for plasma heating and for radiation produced by relativistic turbulence. 
Abstract Using ion tracing in a model shock front we study heating of thermal (Maxwellian) and superthermal (Vasyliunas–Siscoe) populations of protons, singly charged helium, and alpha particles. It is found that heating of thermal and superthermal populations is different, mainly because of substantially higher ion reflection in the superthermal populations. Accordingly, the temperature increase of initially superthermal populations is substantially higher than that of the thermal ions. Heating per mass decreases with the increase of the masstocharge ratio because of the reduced effect of the crossshock potential and, accordingly, weaker ion reflection. The findings are supported by twodimensional hybrid simulations.more » « less

A collisionless shock is a selforganized structure where fields and particle distributions are mutually adjusted to ensure a stable mass, momentum and energy transfer from the upstream to the downstream region. This adjustment may involve rippling, reformation or whatever else is needed to maintain the shock. The fields inside the shock front are produced due to the motion of charged particles, which is in turn governed by the fields. The overshoot arises due to the deceleration of the ion flow by the increasing magnetic field, so that the drop of the dynamic pressure should be compensated by the increase of the magnetic pressure. The role of the overshoot is to regulate ion reflection, thus properly adjusting the downstream ion temperature and kinetic pressure and also speeding up the collisionless relaxation and reducing the anisotropy of the eventually gyrotropized distributions.more » « less

Abstract Collisionless shocks channel the energy of the directed plasma flow into the heating of the plasma species and magnetic field enhancement. The kinetic processes at the shock transition cause the ion distributions just behind the shock to be nongyrotropic. Gyrotropization and subsequent isotropization occur at different spatial scales. Accordingly, for a given upstream plasma and magnetic field state, there would be different downstream states corresponding to the anisotropic and isotropic regions. Thus, at least two sets of Rankine–Hugoniot relations are needed, in general, to describe the connection of the downstream measurable parameters to the upstream ones. We establish the relation between the two sets.more » « less