The role of loop footpoints rotation in single loop flares

Abstract

We consider that single loop flares can be caused by the rotation of loop footpoints. Choosing a typical geometry for this case we find from MHD equations self-consistent expressions and a set equations governing behaviour of all physical quantities. Numerical simulations have revealed that under the determined conditions for the initial azimuthal velocity and current the pinch instability takes place. The most important parameters of the problem are the plasma β and the ratio of the initial values of longitudinal and poloidal components of the magnetic field-B 1. Thus, calculations show that the critical pinch time increases with the increase ofB 1 and decreases with the increase of plasma β. So the most effective flares are probable for the most high loops with strong currents. ForB 1=10 and β=0.01 the critical pinch time is ≈2.5 s. The critical twist angle for magnetic field depends on the initial one. For low intial twist which corresponds to bigB 1 the critical one is more less. For exampleB 1=30 gives Φ≈1.8π (when ratio of loop length and radius is 10). Geometrical analysis shows that the present model can explain (for high photospheric rotation) single loop flares taking place on different parts of the loop as on the top of it as closer to one of the footpoints. It depends on the relative rotation momentum of loop footpoints. Subject headings: MHD-Sun:flares.