Three-dimensional magnetohydrodynamic numerical simulations of coronal loop oscillations associated with flares

We performed three-dimensional MHD numerical simulations for solar coronal magnetic loop oscillations and found: (1) The loop oscillation period is determined by its Alfven time. (2) The amplitude of oscillation decreases exponentially in time. This is explained as energy transport by fast-mode MHD waves. The damping rate, omega(damp), is described as omega(damp) proportional to V-a/R, where V-a is the Alfven speed around loops and R is the radius of the loop. Because of computer resources limitations, the plasma beta value is much larger than that of the real corona. We thus applied a scaling law derived from numerical simulation results to the real corona parameter ranges and analyzed the results.