Collisionless distribution functions for force-free current sheets : using a pressure transformation to lower the plasma beta
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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.
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
Journal of Plasma Physics
© 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
DescriptionWe 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.
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