Heat flux in magnetospheric convection: A calculation based on adiabatic drift theory

Liu, W. William

doi:10.1029/2006gl027218

Cited by 6 publications

(29 citation statements)

References 14 publications

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“…In section 4, we prove via analytical transformation that all three models reduce to the equations of the same form if the distribution function is assumed Maxwellian in the RCM case and average model. It follows that the model of Liu [2006] is identical to that of the fluid model of Heinemann [1999]. In section 5.1, we reanalyze the one‐dimensional case of Heinemann and Wolf [2001a, 2001b], deriving their analytic solution in the linearized case in a different way, thus verifying their results.…”

Section: Introductionmentioning

confidence: 80%

“…Therefore, the equation set and is not closed without a model for the evolution of the distribution function, knowledge of which is needed to evaluate S . Expression can be evaluated in a closed form for a kappa distribution function, yielding [ Liu , 2006] However, it is easy to see that assuming a kappa distribution function in general would be inconsistent with the adiabatic drift laws (section 2.1) assumed in the model of [ Liu , 2006]. Thus it appears that Liu [2006] suffered from the well‐known problem of the closure of moment equations [e.g., Schunk , 1977].…”

Section: Comments On Liu's [2006] Modelmentioning

confidence: 99%

“…Most recently, Liu [2006] published a model that is based on the RCM‐like adiabatic drift theory but is a single‐fluid model (with ions carrying all of the particle pressure and electrons assumed to be cold) with a heat‐flux term. With a clever choice of a Cartesian coordinate system and by employing the concept of time reversal mapping, Liu [2006] presents two partial differential equations describing the evolution of density and energy that supposedly include the RCM drift physics formalism in an average way. Thus the model of Liu [2006] would appear to have the best of the RCM and fluid descriptions published before.…”

Section: Introductionmentioning

confidence: 99%

“…With a clever choice of a Cartesian coordinate system and by employing the concept of time reversal mapping, Liu [2006] presents two partial differential equations describing the evolution of density and energy that supposedly include the RCM drift physics formalism in an average way. Thus the model of Liu [2006] would appear to have the best of the RCM and fluid descriptions published before. We will refer to this model as the “ensemble‐averaged”, or simply “average”, model in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…Our first reason for this work is an attempt to further understand what minimum amount of physics is necessary in order to treat the electrodynamics of the inner magnetosphere in a realistic manner. While the fluid model of Heinemann [1999] displays properties in stark contrast to those of the RCM formalism, at least in the simple case published by Heinemann and Wolf [2001a, 2001b], the model of Liu [2006] is supposed to include the full RCM drift physics but in only two partial differential equations. Thus it would be imperative to understand how this model is related to the previously published two formalisms.…”

Section: Introductionmentioning

confidence: 99%

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

2008

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[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,

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Section: Introductionmentioning

confidence: 80%

Section: Comments On Liu's [2006] Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2008

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Effect of heat flux on Alfvén ballooning modes in isotropic Hall‐MHD plasmas

2014

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The magnetosphere undergoes a transition from a dipole-like to taillike structure in the antisunward direction. In this region, Alfvén ballooning instability has been considered as a leading candidate to be responsible for the onset and expansion phase of observed impulsive substorms. We apply the generalized Ohm's law in isotropic Hall-MHD equations and study the effect of heat flux on the ballooning modes under substorm circumstances. The set of partial differential equations is obtained for a general ballooning dispersion relation from which all classical Alfvén waves and fundamental ballooning modes are recovered, e.g., the decoupled shear Alfvén and magnetosonic modes, the classical ballooning instability in incompressible plasmas. In the absence of the heat flux, the ballooning mode is featured by the coupling of the two modes by the superposition of the independent Hall effect and the independent plasma inhomogeneity effect. By contrast, heat flux exerts its influence on the ballooning mode by updating the coefficients of the terms in the dispersion relation. The results expose that the growth rate ( BM ) has two branches. If k p is free, one branch shifts versus , while the other branch is damped substantially by the heat flux, leading to a more stable ballooning mode; if k c is free, one branch shifts little versus , but the other one has higher BM driven by the heat flux, leading to a more unstable ballooning mode.

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The Harang reversal and the interchange stability of the magnetotail

et al. 2016

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The present study addresses steady convection in the plasma sheet in terms of the interchange stability with special attention to the Harang reversal. The closure of the tail current with a field‐aligned current (FAC) results from the divergence/convergence of the pressure gradient current. If the magnetotail is in a steady state, the associated change of local plasma pressure p has to balance with its advective change. Accordingly, for adiabatic transport, the flux tube entropy parameter pVγ increases and decreases along the convection path in regions corresponding to downward and upward FACs, respectively. This requirement, along with the condition for the interchange stability imposes an important constraint on the direction of convection especially in the regions of downward FACs. It is deduced that for the dusk cell, the convection in the downward R2 current has to be directed azimuthally duskward, which follows the sunward, possibly dawnward deflected, convection in the region of the premidnight upward R1 current. This duskward turn of convection takes place in the vicinity of the R1‐R2 demarcation, and it presumably corresponds to the Harang reversal. For the dawn cell the convection in the postmidnight downward R1 current has to deflect dawnward, and then it proceeds sunward in the upward R2 current. The continuity of the associated ionospheric currents consistently reproduces the assumed FAC distribution. The proposed interrelationships between the convection and FACs are also verified with a quasi‐steady plasma sheet configuration and convection reproduced by a modified Rice Convection Model with force balance.

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Heat flux in magnetospheric convection: A calculation based on adiabatic drift theory

Cited by 6 publications

References 14 publications

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

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

Effect of heat flux on Alfvén ballooning modes in isotropic Hall‐MHD plasmas

The Harang reversal and the interchange stability of the magnetotail

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