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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 kinetic-Alfvén turbulent cascades existing in nonrelativistic space and astrophysical plasmas. Based on phenomenological modeling and particle-in-cell numerical simulations, we propose that the energy spectrum of such relativistic kinetic-scale Alfvénic turbulence is close tok⁻³or 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 one-dimensional particle momentum distributions. We find that these distributions have universal log-normal statistics.

 

Three-dimensional kinetic-scale 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 fluid-kinetic 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 electron-scale 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 half-thickness of the current sheets is found to be on the order of electron inertial length or below, while their half-length 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.

 

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 power-law distribution functions in the momentum (or energy) space,f(γ)dγ∝γ^−αdγ, whereγis the Lorenz factor. We argue that in addition to exhibiting non-Gaussian distributions over energies, particles energized by relativistic turbulence also become highly intermittent in space. Based on particle-in-cell 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 power-law distribution function,$P(n)\mathit{dn}\propto n^{-\beta }\mathit{dn}$. We argue that the scaling exponents are related asβ≈α+ 1, which is broadly consistent with numerical simulations. Non-space-filling, intermittent distributions of plasma density and energy fluctuations may have implications for plasma heating and for radiation produced by relativistic turbulence.

 

We provide evidence that the sunward-propagating 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 SPAN-E 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 0.18-0.79 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 sunward-propagating population that originates somewhere in the outer heliosphere by a yet-unknown mechanism.

 

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 quasi-neutrality. Our 2D particle-in-cell numerical simulations of turbulence in a relativistic pair plasma find that the spectrum of the total energy has the scalingk^−3/2, while the difference between the magnetic and electric energies, the so-called residual energy, has the scalingk^−2.4. The electric and magnetic fluctuations at scaleℓexhibit dynamic alignment with the alignment angle scaling close to$\cos {\varphi }_{\mathit{\ell }}\propto {\mathit{\ell }}^{1/4}$. At scales smaller than the (relativistic) plasma inertial scale, the energy spectrum of relativistic inertial Alfvén turbulence steepens tok^−3.5.

 

In a collisionless plasma, the energy distribution function of plasma particles can be strongly affected by turbulence. In particular, it can develop a nonthermal power-law tail at high energies. We argue that turbulence with initially relativistically strong magnetic perturbations (magnetization parameterσ≫ 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 exponentαin the power-law particle-energy distribution function,f(γ)dγ∝γ^−αdγ, depends on magnetic compressibility of turbulence. Our analytic prediction for the scaling exponentαis in good agreement with the numerical results.

 

Recent in situ measurements by the MMS and Parker Solar Probe missions bring interest to small-scale 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 low-electron-beta regimes, discuss their conservation laws and their limits of applicability.