  The evolution of non-potential perturbations to a current-free magnetic
X-point configuration is studied, taking into account electron inertial effects
as well as resistivity. Electron inertia is shown to have a negligible effect
on the evolution of the system whenever the collisionless skin depth is less
than the resistive scale length. Non-potential magnetic field energy in this
resistive MHD limit initially reaches equipartition with flow energy, in
accordance with ideal MHD, and is then dissipated extremely rapidly, on an
Alfvenic timescale that is essentially independent of Lundquist number. In
agreement with resistive MHD results obtained by previous authors, the magnetic
field energy and kinetic energy are then observed to decay on a longer
timescale and exhibit oscillatory behavior, reflecting the existence of
discrete normal modes with finite real frequency. When the collisionless skin
depth exceeds the resistive scale length, the system again evolves initially
according to ideal MHD. At the end of this ideal phase, the field energy decays
typically on an Alfvenic timescale, while the kinetic energy (which is equally
partitioned between ions and electrons in this case) is dissipated on the
electron collision timescale. The oscillatory decay in the energy observed in
the resistive case is absent, but short wavelength structures appear in the
field and velocity profiles, suggesting the possibility of particle
acceleration in oppositely-directed current channels. The model provides a
possible framework for interpreting observations of energy release and particle
acceleration on timescales down to less than a second in the impulsive phase of
solar flares.
