Relativistic Spherical Plasma Waves in a Collisional and Warm Plasma

Under Lagrange coordinates, the relativistic spherical plasma wave in a collisional and warm plasma is discussed theoretically. Within the Lagrange coordinates and using the Maxwell and hydrodynamics equations, a wave equation describing the relativistic spherical wave is derived. The damped oscillating spherical wave solution is obtained analytically using the perturbation theory. Because of the coupled effects of spherical geometry, thermal pressure, and collision effect, the electron damps the periodic oscillation. The oscillation frequency and the damping rate of the wave are related to not only the collision and thermal pressure effect but also the space coordinate. Near the center of the sphere, the thermal pressure significantly reduces the oscillation period and the damping rate of the wave, while the collision effect can strongly influence the damping rate. Far away from the spherical center, only the collision effect can reduce the oscillation period of the wave, while the collision effect and thermal pressure have weak influence on the damping rate.