Energy variations at the onset of the tearing instability
Abstract
The resistive instability of a simple onedimensional current sheet model has been investigated both in the long and in the short wavelength approximation. For the linear phase of the instability it is possible to derive, by means of an expansion technique, an analytical expression for the growth rate and for the perturbation itself. The variations of each kind of energy (magnetic, kinetic and dissipated energies, Poynting vector, work against pressure gradients and magnetic forces) are then exactly computed. Different behaviour of the System is obtained for different wavelengths. In particular, the driving energy for the instability is found to come from different regions: for high wavenumber α there is a decrease of the magnetic energy in the inner resistive region where the reconnection occurs, whereas for lowα modes the magnetic energy decreases in the outer ideal region. Moreover, the amount of Joule dissipation is found to increase with decreasing α so that the lowα regime is the most efficient.
 Publication:

Journal of Plasma Physics
 Pub Date:
 October 1986
 DOI:
 10.1017/S0022377800011739
 Bibcode:
 1986JPlPh..36..251T
 Keywords:

 Current Sheets;
 Energy Distribution;
 Magnetohydrodynamic Stability;
 Tearing Modes (Plasmas);
 Controlled Fusion;
 Kinetic Energy;
 Magnetic Field Reconnection;
 Ohmic Dissipation;
 Poynting Theorem;
 Plasma Physics