Contents I. Introduction
There is a growing interest on intense charged particle beams [1]–[5] due to a wide range of applications, including basic scientific research, spallation neutron source, nuclear waste transmutation, and heavy ion fusion [6]–[7] [8]. Background electrons and plasmas are often present at the high ion current densities of practical interest. It has been recognized [9] [10]–[19] for many years that the relative streaming motion of a charged particle beam through a background charge species provides a free energy to drive the classical two-stream instability. In addition, the presenting background plasma may act like a resistive medium, which may drive the resistive hose instability [20]–[27] in the propagating ion beam. When a current-carrying beam moves through conducting plasma, its self-magnetic field may follow the beam with a delay time called the magnetic decay time . The magnetic field lines are frozen into the plasma, pulling back the distorted beam segment if the plasma is highly conducting. However, this restoring mechanism, which leads to the resistive hose instability, overshoots and grows due to the motionless resistive plasma medium [21]–[26] [27], where the electron collision time is much shorter than the magnetic decay time . The electron collision frequency for an electron temperature eV is about s in ambient air at one atmospheric pressure leading to , where the electron collisions are dominated by electron-neutral collisions.
