On the relationship between kinetic and fluid formalisms for convection in the inner magnetosphere

Abstract

[1] In the inner magnetosphere, the plasma flows are mostly slow compared to thermal or Alfvén speeds, but the convection is far away from the ideal magnetohydrodynamic regime since the gradient/curvature drifts become significant. Both kinetic (Wolf, 1983) and two-fluid (Peymirat and Fontaine, 1994;Heinemann, 1999) formalisms have been used to describe plasma dynamics, but it is not fully understood how they relate to each other. We explore the relations among kinetic, fluid, and recently developed ''average'' (Liu, 2006) models in an attempt to find the simplest yet realistic way to describe the convection. First, we prove analytically that the model of (Liu, 2006), when closed with the assumption of a Maxwellian distribution, is equivalent to the fluid model of (Heinemann, 1999). Second, we analyze the transport of both one-dimensional and two-dimensional Gaussian-shaped blob of hot plasma. For the kinetic case, it is known that the time evolution of such a blob is gradual spreading in time. For the fluid case, Heinemann and Wolf (2001a, 2001b) showed that in a one-dimensional idealized case, the blob separates into two drifting at different speeds. We present a fully nonlinear solution of this case, confirming this behavior but demonstrating what appears to be a shocklike steepening of the faster drifting secondary blob. A new, more realistic two-dimensional example using the dipole geometry with a uniform electric field confirms the one-dimensional solutions. Implications for the numerical simulations of magnetospheric dynamics are discussed.Citation: Song, Y., S. Sazykin, and R. A. Wolf (2008), On the relationship between kinetic and fluid formalisms for convection in the inner magnetosphere,

Initial results from a dynamic coupled magnetosphere‐ionosphere‐ring current model

“…However, they also demonstrated that enforcing a Maxwellian in the RCM solution can drastically affect the evolution of pressures and densities. That conclusion was also confirmed using more realistic conditions by Song et al [2008]. By coupling the RCM to the LFM, the effects of energy dependent drifts on MHD quantities, such as pressure and density, are incorporated into the LFM without the problems that accompany artificially enforcing a Maxwellian.…”

Dynamics of ring current and electric fields in the inner magnetosphere during disturbed periods: CRCM–BATS‐R‐US coupled model

“…However, Song et al [2008] have concluded that all these fluid models produce different results from an original RCM model with a non‐Maxwellian distribution function, at least in some test cases. Therefore the description of the inner magnetosphere by fluid models should be done very cautiously.…”

“…Much effort was put into understanding the relations between RCM formalism (such as a drift physics formalism) and fluid formalism [ Heinemann , 1999; Heinemann and Wolf , 2001]. Recently, Song et al [2008] established the equivalence of three models: (1) the fluid model of Fontaine et al [1985] and Peymirat and Fontaine [1994] with an additional heat flux describing the energy transfer due to gradient drift; (2) the fluid model of Liu [2006] with an assumption that distribution is Maxwellian; (3) the RCM equations with an assumption that distribution function is not only isotropic as in the original RCM, but also Maxwellian.…”

Self‐consistent inner magnetosphere simulation driven by a global MHD model

“…To our knowledge there has been no study of adding the terms prescribed by Heinemann and Wolf [2001] to a global three‐dimensional magnetospheric MHD code in order to try to reproduce the full kinetic physics. There have been studies analyzing this issue in a more local setting, however; recently, such a study [ Song et al , 2008] has shown that as a practical matter such improvements in magnetospheric fluid models could be problematic, as shock waves tend to form in the simulation.…”