Theoretical Aspects of Astron Buildup by Multiple Pulses

The time asymptotic response to an incoming current source in the presence of a partially built up $E$ layer in the astron geometry is examined. A one‐dimensional Vlasov model which considers only motion in the exial direction (perpendicular to the current direction and tank radius) is studied. It is shown that (1) A back current is induced in the $E$ layer. (2) A new dissipation mechanism (Landau damping) occurs in the $E$ layer as well as in the resistors. (3) The dissipation in the layer causes particle scattering that leads to axial expansion which competes with contraction due to the addition of current. The net effect for a neutralized layer can lead to a saturation in $E$ layer strength, a behavior encountered in numerical experiment. For the unneutralized layer, however, this situation is not nearly as severe and there appears to be a parameter range where stacking should occur.