Magnetohydrodynamic transport equations for high current propagation in overdense plasmas

In this paper, it is presented that the full set of magnetohydrodynamic (MHD) equations which may be used to study the transport mechanism for the high current relativistic electron beams (current intensity 100∼1000 MA, electron energy ∼ MeV) by the laser in background overdense plasma (1022-1026cm−3). The transport of intense relativistic electron beams (REB) has two basic characteristics: the first is that the forward current is a giga-ampere and the forward current density is about 1014 A/cm2 which exceeds the Alfven current limit [M. Tabak et al., Phys. Plasmas 12, 057305 (2005)]; the second is the propagation of the intense forward current in the presence of a background overdense plasma which may have very strong MHD instability. The transport problem can be solved by MHD equations that describe the dynamic, self consistent collisional and electromagnetic interaction of REB with overdense hydrogenic plasmas or arbitrary atomic-number plasmas. The full set of equations consists of the REB transport equations which are coupled to Maxwell's equations through the electromagnetic-field terms and two-fluid plasma dynamical equations for the background overdense plasma through the collision term.