Kinetic entropy-based measures of distribution function non-Maxwellianity: theory and simulations

Abstract

We investigate kinetic entropy-based measures of the non-Maxwellianity of distribution functions in plasmas, i.e. entropy-based measures of the departure of a local distribution function from an associated Maxwellian distribution function with the same density, bulk flow and temperature as the local distribution. First, we consider a form previously employed by Kaufmann & Paterson (J. Geophys. Res., vol. 114, 2009, A00D04), assessing its properties and deriving equivalent forms. To provide a quantitative understanding of it, we derive analytical expressions for three common non-Maxwellian plasma distribution functions. We show that there are undesirable features of this non-Maxwellianity measure including that it can diverge in various physical limits and elucidate the reason for the divergence. We then introduce a new kinetic entropy-based non-Maxwellianity measure based on the velocity-space kinetic entropy density, which has a meaningful physical interpretation and does not diverge. We use collisionless particle-in-cell simulations of two-dimensional anti-parallel magnetic reconnection to assess the kinetic entropy-based non-Maxwellianity measures. We show that regions of non-zero non-Maxwellianity are linked to kinetic processes occurring during magnetic reconnection. We also show the simulated non-Maxwellianity agrees reasonably well with predictions for distributions resembling those calculated analytically. These results can be important for applications, as non-Maxwellianity can be used to identify regions of kinetic-scale physics or increased dissipation in plasmas.

Dissipation measures in weakly-collisional plasmas

“…The first class employs both collisionless and weaklycollisional and Gkeyll simulations of a single current sheet that undergoes symmetric anti-parallel magnetic reconnection. In the collisionless case, we find that and a separate PIC code P3D (Zeiler et al 2002), adopted in Liang et al (2020), provide consistent and qualitatively similar results. Although the and Gkeyll simulations are very similar in their choice of parameters, there are small differences we make note of in the subsequent discussion.…”

“…proposed by Liang et al (2020). Here, 𝑠 M, 𝛼 (𝒓, 𝑡) is the entropy density evaluated using the equivalent Maxwellian distribution function 𝑔 𝛼 (𝒓, 𝒗, 𝑡) associated with the VDF 𝑓 𝛼 (𝒓, 𝒗, 𝑡), given by…”

Generalized entropy production in collisionless plasma flows and turbulence

“…In addition, characterizing entropy yield insights on magnetic self-organization (a means of counteracting entropy production) and plasma phase transitions [23]. Despite these motivations, there are relatively few studies that attempt to directly measure kinetic entropy or related proxies in first-principles simulations of plasmas [e.g., 18,[23][24][25][26][27]. This is due not only to numerical issues (such as high resolution demands), but also conceptual issues such as how to meaningfully normalize entropy [18].…”

Non-Maxwellianity of electron distributions near Earth's magnetopause

“…At present various papers have considered the non-Maxwellianity of particle distributions in both simulations and observations [Greco et al, 2012;Valentini et al, 2016;Chasapis et al, 2018;Perri et al, 2020;Liang et al, 2020]. These studies have focused on plasma turbulence in Earth's magnetosheath and magnetic reconnection.…”

“…The simulation results showed that ion non-Maxwellianity was spatially non-uniform and was associated with strong currents and temperature anisotropy [Greco et al, 2012;Valentini et al, 2016]. Similarly, electron non-Maxwellianity was found to increase the electron diffusion region (EDR) and separatrices of magnetic reconnection [Liang et al, 2020]. In kinetic simulations the background distributions, such as in modeling of magnetosheath turbulence and magnetic reconnection, are assumed to be Maxwellian.…”