Electron Inertial Effects on Rapid Energy Redistribution at Magnetic X‐Points

The evolution of non-potential perturbations to a current-free magneticX-point configuration is studied, taking into account electron inertial effectsas well as resistivity. Electron inertia is shown to have a negligible effecton the evolution of the system whenever the collisionless skin depth is lessthan the resistive scale length. Non-potential magnetic field energy in thisresistive MHD limit initially reaches equipartition with flow energy, inaccordance with ideal MHD, and is then dissipated extremely rapidly, on anAlfvenic timescale that is essentially independent of Lundquist number. Inagreement with resistive MHD results obtained by previous authors, the magneticfield energy and kinetic energy are then observed to decay on a longertimescale and exhibit oscillatory behavior, reflecting the existence ofdiscrete normal modes with finite real frequency. When the collisionless skindepth exceeds the resistive scale length, the system again evolves initiallyaccording to ideal MHD. At the end of this ideal phase, the field energy decaystypically on an Alfvenic timescale, while the kinetic energy (which is equallypartitioned between ions and electrons in this case) is dissipated on theelectron collision timescale. The oscillatory decay in the energy observed inthe resistive case is absent, but short wavelength structures appear in thefield and velocity profiles, suggesting the possibility of particleacceleration in oppositely-directed current channels. The model provides apossible framework for interpreting observations of energy release and particleacceleration on timescales down to less than a second in the impulsive phase ofsolar flares.Comment: 30 pages, 8 figure