Collisionless distribution functions for force-free current sheets : using a pressure transformation to lower the plasma beta
Abstract
So far, only one distribution function giving rise to a collisionless nonlinear force-free current sheet equilibrium allowing for a plasma beta less than one is known (Allanson et al., Phys. Plasmas, vol. 22 (10), 2015, 102116; Allanson et al., J. Plasma Phys., vol. 82 (3), 2016a, 905820306). This distribution function can only be expressed as an infinite series of Hermite functions with very slow convergence and this makes its practical use cumbersome. It is the purpose of this paper to present a general method that allows us to find distribution functions consisting of a finite number of terms (therefore easier to use in practice), but which still allow for current sheet equilibria that can, in principle, have an arbitrarily low plasma beta. The method involves using known solutions and transforming them into new solutions using transformations based on taking integer powers (N) of one component of the pressure tensor. The plasma beta of the current sheet corresponding to the transformed distribution functions can then, in principle, have values as low as 1/N. We present the general form of the distribution functions for arbitrary and then, as a specific example, discuss the case for N = 2 in detail.
Citation
Wilson , F , Neukirch , T & Allanson , O 2018 , ' Collisionless distribution functions for force-free current sheets : using a pressure transformation to lower the plasma beta ' , Journal of Plasma Physics , vol. 84 , no. 3 , 905840309 . https://doi.org/10.1017/S0022377818000570
Publication
Journal of Plasma Physics
Status
Peer reviewed
ISSN
0022-3778Type
Journal article
Rights
© Cambridge University Press 2018. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1017/S0022377818000570
Description
We acknowledge the support of the Science and Technology Facilities Council via the consolidated grants ST/K000950/1 and ST/N000609/1 and the doctoral training grant ST/K502327/1 (O. A.), and the Natural Environment Research Council via grant no. NE/P017274/1 (Rad-Sat) (O. A.). F. W. and T. N. would also like to thank the University of St Andrews for general financial support.Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.