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,
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Abstract 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 We provide evidence that the sunwardpropagating half of the solar wind electron halo distribution evolves without scattering in the inner heliosphere. We assume the particles conserve their total energy and magnetic moment, and perform a ‘Liouville mapping’ on electron pitch angle distributions measured by the Parker Solar Probe SPANE instrument. Namely, we show that the distributions are consistent with Liouville’s theorem if an appropriate interplanetary potential is chosen. This potential, an outcome of our fitting method, is compared against the radial profiles of proton bulk flow energy. We find that the inferred potential is responsible for nearly 100 per cent of the proton acceleration in the solar wind at heliocentric distances 0.180.79 AU. These observations combine to form a coherent physical picture: the same interplanetary potential accounts for the acceleration of the solar wind protons as well as the evolution of the electron halo. In this picture the halo is formed from a sunwardpropagating population that originates somewhere in the outer heliosphere by a yetunknown mechanism.

Abstract We present a phenomenological and numerical study of strong Alfvénic turbulence in a magnetically dominated collisionless relativistic plasma with a strong background magnetic field. In contrast with the nonrelativistic case, the energy in such turbulence is contained in magnetic and electric fluctuations. We argue that such turbulence is analogous to turbulence in a strongly magnetized nonrelativistic plasma in the regime of broken quasineutrality. Our 2D particleincell numerical simulations of turbulence in a relativistic pair plasma find that the spectrum of the total energy has the scaling
k ^{−3/2}, while the difference between the magnetic and electric energies, the socalled residual energy, has the scalingk ^{−2.4}. The electric and magnetic fluctuations at scaleℓ exhibit dynamic alignment with the alignment angle scaling close to . At scales smaller than the (relativistic) plasma inertial scale, the energy spectrum of relativistic inertial Alfvén turbulence steepens to $\mathrm{cos}{\varphi}_{\mathit{\ell}}\propto {\mathit{\ell}}^{1/4}$k ^{−3.5}. 
Abstract In a collisionless plasma, the energy distribution function of plasma particles can be strongly affected by turbulence. In particular, it can develop a nonthermal powerlaw tail at high energies. We argue that turbulence with initially relativistically strong magnetic perturbations (magnetization parameter
σ ≫ 1) quickly evolves into a state with ultrarelativistic plasma temperature but mildly relativistic turbulent fluctuations. We present a phenomenological and numerical study suggesting that in this case, the exponentα in the powerlaw particleenergy distribution function,f (γ )d γ ∝γ ^{−α}d γ , depends on magnetic compressibility of turbulence. Our analytic prediction for the scaling exponentα is in good agreement with the numerical results. 
null (Ed.)ABSTRACT We present a kinetic stability analysis of the solar wind electron distribution function consisting of the Maxwellian core and the magneticfield aligned strahl, a superthermal electron beam propagating away from the sun. We use an electron strahl distribution function obtained as a solution of a weakly collisional driftkinetic equation, representative of a strahl affected by Coulomb collisions but unadulterated by possible broadening from turbulence. This distribution function is essentially nonMaxwellian and varies with the heliospheric distance. The stability analysis is performed with the Vlasov–Maxwell linear solver leopard. We find that depending on the heliospheric distance, the corestrahl electron distribution becomes unstable with respect to sunwardpropagating kineticAlfvén, magnetosonic, and whistler modes, in a broad range of propagation angles. The wavenumbers of the unstable modes are close to the ion inertial scales, and the radial distances at which the instabilities first appear are on the order of 1 au. However, we have not detected any instabilities driven by resonant wave interactions with the superthermal strahl electrons. Instead, the observed instabilities are triggered by a relative drift between the electron and ion cores necessary to maintain zero electric current in the solar wind frame (ion frame). Contrary to strahl distributions modelled by shiftedmore »

Recent in situ measurements by the MMS and Parker Solar Probe missions bring interest to smallscale plasma dynamics (waves, turbulence, magnetic reconnection) in regions where the electron thermal energy is smaller than the magnetic one. Examples of such regions are the Earth’s magnetosheath and the vicinity of the solar corona, and they are also encountered in other astrophysical systems. In this brief review, we consider simple physical models describing plasma dynamics in such lowelectronbeta regimes, discuss their conservation laws and their limits of applicability.

We present a drift kinetic model for the free expansion of a thermal plasma out of a magnetic nozzle. This problem relates to plasma space propulsion systems, natural environments such as the solar wind, and end losses from the expander region of mirror magnetically confined fusion concepts such as the gas dynamic trap. The model incorporates trapped and passing orbit types encountered in the mirror expander geometry and maps to an upstream thermal distribution. This boundary condition and quasineutrality require the generation of an ambipolar potential drop of 5Te=e, forming a thermal barrier for the electrons. The model for the electron and ion velocity distributions and fluid moments is confirmed with data from a fully kinetic simulation. Finally, the model is extended to account for a population of fast sloshing ions arising from neutral beam heating within a magnetic mirror, again resulting in good agreement with a corresponding kinetic simulation.