Abstract
The validity of the traditional plasma continuum is predicated on a hierarchy of scale-lengths, with the Debye length being considered to be effectively unresolvable in the continuum limit. In this article, we revisit the strong magnetic field case in which the Larmor radius is comparable or smaller than the Debye length in the classical plasma, and also for a relativistic plasma. Fresh insight into the validity of the continuum assumption in each case is offered, including a fluid limit on the Alfvén speed that may impose restrictions on the validity of magnetohydrodynamics (MHD) in some solar and fusion contexts. Additional implications concerning the role of the firehose instability are also explored.
Highlights
Introduction and motivationConventionally, plasmas are described by continuum descriptions such as MHD or kinetic theory, each of which assumes that the density of discrete charges in the medium is sufficiently large that very small-scale effects associated with random fluctuations are negligible in the continuum limit, and can be safely neglected
In order to ensure that the Larmor radius for electrons is not smaller than the Debye length, in the classical case, the Alfvén speed must be less than the speed of light times the square root of the electron to ion mass ratio: ca
Plasmas that do not satisfy this criterion are vulnerable to firehose instability
Summary
Plasmas are described by continuum descriptions such as MHD or kinetic theory, each of which assumes that the density of discrete charges in the medium is sufficiently large that very small-scale effects associated with random fluctuations are negligible in the continuum limit, and can be safely neglected. This concept is discussed in most of the classical textbooks (for example, [1,2,3,4,5]) where the Debye length is defined as the smallest considered scalelength for plasmas, at which any discontinuity is averaged or smoothed when constructing the macroscopic equations. The transition from the classical plasma continuum model into one in which the scale-lengths over which charge imbalance persists are significant has long been a matter of routine concern in plasma physics generally, and in particular for low-temperature plasma modelling, and the conclusions in this article may have wider impact
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