One-Dimensional Nonlinear Force-Free Current Sheets

  • Oliver AllansonEmail author
Part of the Springer Theses book series (Springer Theses)


In this chapter we present new exact collisionless equilibria for a 1D nonlinear force-free magnetic field, namely the force-free Harris sheet. In contrast to previous solutions (Harrison and Neukirch 2009a; Wilson and Neukirch 2011; Abraham-Shrauner 2013; Kolotkov et al. 2015), the solutions that we present allow the plasma beta (\(\beta _{pl}\)) to take any value, and crucially values below unity for the first time. In the derivations of the equilibrium DFs it is found that the most typical approach of Fourier Transforms can not be applied, and so we use expansions in Hermite polynomials, making use of the techniques developed in Chap.  2. Using the convergence criteria developed therein, we verify that the Hermite expansion representation of the DFs are convergent for all parameter values. As shown in Chap.  2, this also implies boundedness, and the existence of velocity moments of all orders. Despite the proven analytic convergence, initial difficulties in attaining numerical convergence mean that plots of the DF can be presented for the plasma beta only modestly below unity. In the effort to model equilibria with much lower values of the plasma, we use a new gauge for the vector potential, and calculate the DF consistent with this gauge, confirming the properties of convergence velocity moments. This new gauge makes attaining numerical convergence possible for lower values of the plasma beta, and we present results for \(\beta _{pl}=0.05.\)


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MeteorologyUniversity of ReadingReadingUK

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