Three-Dimensional Force-Free Equilibria in Open Traps Driven by Electron Beams

Some open traps, like GOL-3, may be heated by axial electron beams. Since the heating is turbulent, it is associated with anomalous resistivity, so that the reverse induction current is pushed out to flow in the shell plasma along the beam edge. It is shown that such complicated distribution of axial current in equilibrium causes exponential amplification along the trap of any initial (at entrance) azimuthal modulation of the beam current density. As a result, the shape of the beam cross-section develops features like spiral arms, etc. at the end-plate, even if its shape was nearly circular at the entrance. Amplification occurs whenever there is an off-axis extremum on the radial distribution of the axial current density.