Inverse estimate of heat flux on a plasma discharge tube to steady-state conditions using thermocouple data and a radiation boundary condition

Abstract

The heat flux incident upon the inner surface of a plasma discharge tube during a helicon plasma discharge was estimated using an inverse method. Temperature readings were taken from the outer surface of the tube using thermocouples, and the temperature data were interpolated over the tube surface. A numerical inverse procedure based on the Alifanov iterative regularisation method was used to reconstruct the heat flux on the tube inner surface as a function of space and time. In contrast to previously-used inverse models for this application, the current model implements a thermal radiation boundary condition to realistically model the energy exchange in the device. Additionally in these experiments, steady-state operation was reached, and the accurate modelling of the steady-state condition was facilitated by the thermal radiation boundary condition. The variation of heat flux with helicon discharge power, propellant flowrate, and electromagnet current was studied, and it was found that the waste heat flux increased with applied RF power and propellant flowrate, and decreased with current supplied to the electromagnets, over the range of parameter variation tested.

Thermo-structural modelling of a plasma discharge tube for electric propulsion

“…Rather than being composed of a discrete endplate, GCT and choke, the VX-50 prototype used a long fused quartz GCT, which extended past the electromagnets in both the upstream and downstream directions [22]. The conceptual design studied has similar geometrical configuration to that of the VX-CR prototype [23], but has a GCT outer diameter approximately twice that of the VX-CR.…”

“…Dielectric heating of the GCT has not been considered in the current analyses. The heat flux values calculated by Berisford et al [16], Mulcahy et al [36] and de Faoite et al [23] were for a fused quartz GCT, which has a low dielectric loss tangent, so dielectric heating would be low. The dielectric loss tangent tends to increase at higher temperatures, so a ceramic operating at high temperature would experience increased dielectric heating.…”

“…For this class of device the standard materials to use for the plasma discharge tube are fused quartz or borosilicate glass [18,19,20,6,21,22]. At these power levels a dedicated cooling system is typically not required for the plasma discharge tube, as the tube may radiate away sufficient heat without exceeding its maximum allowable operation temperature [23]. Primarily for this reason little exists in the open literature about the design of cooling strategies for helicon plasma generation devices.…”

“…The waste heat from the plasma has been previously investigated [35,22,16,23]. Berisford et al [35,16]…”

“…Analysis of the VX-CR helicon section found that the temporal variation of plasma waste heat flux was slight [23]. The heat load is therefore considered steady in the current analysis.…”