On electrostatic acceleration of plasmas with the Hall effect using electrode shaping

Abstract

Resistive magnetohydrodynamics (MHD) is used to model the electromagnetic acceleration of plasmas in coaxial channels. When the Hall effect is considered, the inclusion of resistivity is necessary to obtain physically meaningful solutions. In resistive MHD with the Hall effect, if and only if the electric current and the plasma flow are orthogonal (J·U=0), then there is a conserved quantity, in the form of U2/2 + w + eΦ/M, along the flow, where U is the flow velocity, Φ is the electric potential, w is the enthalpy, and M is the ion mass. New solutions suggest that in coaxial geometry the Hall effect along the axial plasma flow can be balanced by proper shaping of conducting electrodes, with acceleration then caused by an electrostatic potential drop along the streamlines of the flow. The Hall effect separation of ion and electron flow then just cancels the electrostatic charge separation. Assuming particle ionization increases with energy density in the system, the resulting particle flow rates (Jp) scales with accelerator bias (Vbias) as Jp∝V2bias, exceeding the Child-Langmuir limit. The magnitude of the Hall effect (as determined by the Morozov Hall parameter, Ξ, which is defined as the ratio of electric current to particle current) is related to the energy needed for the creation of each ion-electron pair. © 2001 American Institute of Physics.