Current Sheet Formation, Equilibria and Heating in the Closed Corona

Abstract:

Parker model for coronal heating is investigated within the
framework of reduced magnetohydrodynamics (RMHD) in cartesian geometry.
A popular hypothesis is that in response to slow photospheric motions
the magnetic field evolves quasi-statically through a series
of unstable equilibria. Instabilities, e.g., kink modes or else,
allow the release of energy while the field relaxes to a new equilibrium.
On the other hand it has long been suggested that the
dynamics relevant to the basic heating of coronal loops may not entail
a quasi-static evolution (Parker 1972, 1994), and recently it has been
shown that the relaxation of an initial configuration out of equilibrium
develops current sheets without accessing intermediate equilibria (Rappazzo & Parker 2013).
The properties of the equilibria are therefore key in understanding the
dynamics of coronal heating both in the case of low-frequency photospheric
motions (DC) and for propagating waves (AC).
Equilibria and nonlinear dynamics are studied numerically and theoretically,
explaining why dynamics are inhibited below a critical twist, while for higher
values of the fluctuations nonlinear dynamics lead to the formation of current
sheets (and magnetic reconnection in the non ideal case), whose thickness is
tracked with the analiticity strip method and shown to decrease at least exponentially
down to dissipative lenght-scales on fast ideal Alfvenic timescales. The impact on
the heating of solar and stellar coronae will be discussed.