PROPAGATION OF SHORT ELECTRON PULSES IN UNDERDENSE PLASMAS

Dense relativistic electron beams traversing a plasma, in what is know n as the underdense, or ion focusing, regime experience a strong, line ar transverse restoring force. This force arises from the nearly immob ile ions which form a channel of uncompensated positive charge when th e plasma electrons are ejected in response to the introduction of the beam charge. This phenomenon can be used for focusing the electron bea m to very high densities over long propagation distances. Several sche mes have been proposed, including the nonlinear plasma wake-field acce lerator, the adiabatic plasma lens, and the ion-channel laser, whose v iability is based on this focusing effect for very short pulse, high c urrent electron beams propagating in plasma. In this paper we examine, analytically and numerically, the self-consistent requirements on pla sma density, beam current, length, and transverse emittance which must be satisfied in order for ion-channel formation and near equilibrium beam propagation to exist over the majority of the length of the elect ron beam. The dynamics of the beam-plasma system are modeled by a simu ltaneous solution of the plasma electron cold-fluid equations, and the Maxwell-Vlasov equation governing the beam's thermal equilibrium. The effects of introducing a strong axial magnetic field on the plasma re sponse and beam equilibria are examined. In addition to developing cri teria for self-consistent equilibrium focusing, a time-dependent analy sis where the beam particles are treated as mobile particles in cells is developed in order to study the dynamical approach of this equilibr ium. Inherently time-dependent phenomena, such as matching of the beam into the plasma and adiabatic lenses, are then examined with this met hod.