Resistive instabilities of propagating electron beams

In recent years there has been substantial progress in understanding the resistive instabilities of a self-pinched relativistic beam. We will discuss the properties of the hose and axisymmetric instabilities under a wide variety of realistic conditions, including the effects of: (1) plasma return current or parallel-flowing current (as might be provided by an external discharge), (2) self-consistent evolution of the plasma conductivity, (3) variation of beam parameters during the pulse, (4) rapid erosion of the beam nose, and (5) Nordsieck expansion of the beam. Mathematical tools used include analytic techniques, particle simulations, and various macroscropic simulation models.