Formal Derivation of Model for Electron Anisotropy in Expanding Flux Ropes and Collisionless Magnetic Reconnection

Based on mainly heuristic arguments and an understanding of single electron motion within reconnection regions an approximate solution to the Vlasov equation was previously obtained [1]. This solution accounts for the anisotropy in the electron distribution that develops non-linearly due to trapping in magnetic wells and parallel electric fields, and it has been used as closure yielding general equation of state for the parallel and perpendicular electron pressures [2]. The model has been confirmed in kinetic simulations and through measurements by spacecraft in the Earth magnetotail [3]. It has also formed the basis for new fluid simulations that for the first time reproduces the detailed geometry of the reconnection region seen in kinetic simulations including elongated current sheets [4]. Here we report on a new rigorous derivation of the model using the drift kinetic equation, emphasizing its broad range of validity and application. \\[1ex] [1] J Egedal et al., J. Geophys. Res., 113, A12207 (2008).\\[0ex] [2] A Le et al., Phys. Rev. Lett., 102, 085001 (2009). \\[0ex] [3] J Egedal et al., J. Geophys. Res., 115, A03214 (2010). \\[0ex] [4] O Ohia et al., Phys. Rev. Lett (in press 2012).