Computational study of impulsively generated standing slow acoustic waves in a solar coronal loop

We numerically investigated standing slow acoustic waves impulsively excited in a solar coronal loop by gas pressure and mass density perturbations in one-dimensional space. The corresponding computer model is described by the hydrodynamic equations that are solved numerically by means of the so-called flux limiters methods on uniformly structured mesh. We discuss the fundamental mode and the first harmonic mode which are generated in dependence on position of the initial perturbation in the numerical box. We show how the standing slow acoustic waves are generated in the corona, where they are trapped in space between two dense layers as in the resonator, and how their energy leaks from the corona to the dense layers. We found that this leakage increases with the decrease of the density jump at the transition region. We also studied the case when the perturbation is initiated at the transition region. We found that even in this case the standing wave is formed, but their energetics is influenced by the evaporation of the plasma from the transition region into the corona.     

Modulation instability of intense laser beam in an electron-positron plasma

Modulation instability of an intense right-hand elliptically polarized laser beam propagating through an electron-positron plasma is investigated by a new method. The nonlinear dispersion relation, in which the relativistic and ponderomotive nonlinearities are taken into account, is obtained for the laser radiation in electron-positron plasma by the Lorentz transformation. The Karpman equation is generalized to the case of three dimensions with three field components. When the nonlinear frequency shift of the electromagnetic field in plasma is involved, the nonlinear evolution equation for the slowly varying envelope of the laser field is obtained. Thus, modulation instability of the intense laser beam in electron-positron plasma is studied and the temporal growth rate of the instability is derived. The analysis shows that the growth rate of modulation instability is increased significantly near the critical surface in a laser-plasma.     

Modulation instability by intense laser beam in magnetized plasma

Modulation instability of an intense right-hand elliptically polarized laser beam propagating through magnetized plasma is investigated by a new method. The nonlinear dispersion relation, in which the relativistic and ponderomotive nonlinearities are taken into account, is obtained for the laser radiation in magnetized plasma by the Lorentz transformation. The Karpman equation is firstly generalized to the case of three dimensions with three field components. When the nonlinear frequency shift of the electromagnetic field in plasma is involved, the nonlinear evolution equation for the slowly varying envelope of the laser field is obtained. Thus, modulation instability of the intense laser beam in magnetized plasma is studied and the temporal growth rate of the instability is derived. The analysis shows that the peak growth rate of self-modulation instability is increased due to the axial magnetization of plasma. It is also shown that the growth rate of modulation instability is increased significantly near the critical surface in a laser-plasma.