Collisional thermalization of a particle ensemble under the energy dissipation can be seen in variety of systems, such as heated granular gasses and particles in plasmas. Despite its universal existence, analytical descriptions of the steady-state distribution have been missing. Here, we show that the steady-state energy distribution of the wide class of collisional energy cascades can be well approximated by the generalized Mittag-Leffler distribution, which is one of stable distributions. This distribution has a power-law tail, as similar to Levy's stable distribution, the index of which is related to the energy dissipation rate. We demonstrate its universality by comparing Mont-Carlo simulations of dissipative gasses as well as the spectroscopic observation of the atom velocity distribution in a low-temperature plasma.
Turbulence at kinetic scales is an unresolved and ubiquitous phenomenon that characterizes both space and laboratory plasmas. Recently, new theories, {\it in-situ} spacecraft observations and numerical simulations suggest a novel scenario for turbulence, characterized by a so-called phase space cascade -- the formation of fine structures, both in physical and velocity space. This new concept is here extended by directly taking into account the role of inter-particle collisions, modeled through the nonlinear Landau operator or the simplified Dougherty operator. The characteristic times, associa…
Freely decaying turbulence in two-dimensional electrostatic gyrokinetics
在磁化等离子体中，在相空间中以小于热拉莫尔半径（“亚拉莫尔尺度”）的尺度发生湍流级联[Phys. Rev. Lett. 103，015003（2009）]。当湍流被限制在垂直于背景磁场的两个空间维度时，由于存在两个无碰撞不变量，两个独立的级联可能同时发生。本文采用唯象理论和直接数值模拟的方法研究了二维静电陀螺动力学的自由衰减湍流。一个双级联（正向和反向级联）观察到在速度空间，以及在位置空间，我们诊断的非线性传递函数的碰撞不变量。我们发现，湍流往往是一个时间渐近状态，占主导地位的一个单一的规模增长的时间。这种渐近状态的理论是以衰减定律的形式导出的。我们研究的每一种情况都属于三个区域之一（弱碰撞，边缘和强碰撞），由一个无量纲数D*，一个类似于雷诺数的量决定。边缘状态由在时间上保持的临界数D* = D 0来标记。初始化高于该值的湍流随时间变得越来越惯性，朝着越来越大的D* 发展;初始化低于D 0的湍流变得越来越碰撞，逐渐衰减到越来越小的D*。
The mechanism of heating for hot, dilute, and turbulent plasmas represents a long-standing problem in space physics, whose implications concern both near-Earth environments and astrophysical systems. In order to explore the possible role of interparticle collisions, simulations of plasma turbulence -- in both collisionless and weakly collisional regimes -- have been compared by adopting Eulerian Hybrid Boltzmann-Maxwell simulations, being proton-proton collisions explicitly introduced through the nonlinear Dougherty operator. Although collisions do not significantly influence the statistical c…
Astronomical Institute of the Czech Academy of Sciences（捷克科学院天文研究所）；Institute of Atmospheric Physics of the Czech Academy of Sciences（捷克科学院大气物理研究所）；Department of Electromagnetism and Electronics, University of Murcia（穆尔西亚大学电磁与电子系）
Plasma turbulence is studied via direct numerical simulations in a two-dimensional spatial geometry. Using a hybrid Vlasov-Maxwell model, we investigate the possibility of a velocity-space cascade. A novel theory of space plasma turbulence has been recently proposed by Servidio {\it et al.} [PRL, {\bf 119}, 205101 (2017)], supported by a three-dimensional Hermite decomposition applied to spacecraft measurements, showing that velocity space fluctuations of the ion velocity distribution follow a broad-band, power-law Hermite spectrum $P(m)$, where $m$ is the Hermite index. We numerically explore…
In weakly collisional astrophysical plasmas, such as the intracluster medium of galaxy clusters, the amplification of cosmic magnetic fields by chaotic fluid motions is hampered by the adiabatic production of magnetic-field-aligned pressure anisotropy. This anisotropy drives a viscous stress parallel to the field that inhibits the plasma's ability to stretch magnetic-field lines. I demonstrate through the use of kinetic simulations that in high-$β$ plasmas, kinetic ion-Larmor scale instabilities sever the adiabatic link between the thermal and magnetic pressures, reducing this viscous stress a…
I show a nontrivial functional giving a conservation quantity in the collisional energy cascade of dissipative Maxwell gases: a fractional-calculus extension of the mean energy. The conservation of this quantity directly leads the power-law energy tail that is stationary during the temporal evolution. In the thermal limit, this quantity naturally reduces to the standard mean energy. This conservation law and its extension to particles with other interactions are demonstrated with a Monte-Carlo simulation for inelastic gases.
We present results from three-dimensional hybrid-kinetic simulations of Alfvénic turbulence in a high-beta, collisionless plasma. The key feature of such turbulence is the interplay between local wave--wave interactions between the fluctuations in the cascade and the non-local wave-particle interactions associated with kinetic micro-instabilities driven by anisotropy in the thermal pressure (namely, firehose, mirror, and ion-cyclotron). We present theoretical estimates for, and calculate directly from the simulations, the effective collisionality and plasma viscosity in pressure-anisotropic hi…
The nature of the turbulent energy transfer rate is studied using direct numerical simulations of weakly collisional space plasmas. This is done comparing results obtained from hybrid Vlasov-Maxwell simulations of colissionless plasmas, Hall-magnetohydrodynamics, and Landau fluid models reproducing low-frequency kinetic effects, such as the Landau damping. In this partially developed turbulent scenario, estimates of the local and global scaling properties of different energy channels are obtained using a proxy of the local energy transfer (LET). This approach provides information on the struct…
Observational evidence in space and astrophysical plasmas with long collisional mean free path suggests that more massive charged particles may be preferentially heated. One possible mechanism for this is the turbulent cascade of energy from injection to dissipation scales, where the energy is converted to heat. Here we consider a simple system consisting of a magnetized plasma slab of electrons and a single ion species with a cross-field density gradient. We show that such a system is subject to an electron drift wave instability, known as the universal instability, which is stabilized only w…
In weakly collisional space plasmas, the turbulent cascade provides most of the energy that is dissipated at small scales by various kinetic processes. Understanding the characteristics of such dissipative mechanisms requires the accurate knowledge of the fluctuations that make energy available for conversion at small scales, as different dissipation processes are triggered by fluctuations of a different nature. The scaling properties of different energy channels are estimated here using a proxy of the local energy transfer, based on the third-order moment scaling law for magnetohydrodynamic t…
