Time dependent electron deposition with thermal transport as applied to survivable anodes in flash X-ray machines

The in-depth instantaneous temperature distribution in the anode was calculated for a flash X-ray (FXR) machine. This analysis was compared with measurements made on the Arnold Engineering Development Corporation, AEDC, MBS (Modular Bremsstrahlung Source) FXR and applied to predicting the maximum electron beam loading acceptable for the Defense Threat Reduction Agency (DTRA) Compact X-ray Simulator (CXS). The time dependent calculation of the anode temperature was done in three steps. First, the dose deposition profile from a small time increment of the electrical pulse was obtained by interpolation using range scaling from a table of ITS generated deposition profiles. Next, this additional change in energy (enthalpy) was converted to an increase in temperature. Finally, the thermal transport during the time increment was calculated by using a finite difference procedure for solving the partial differential equation for thermal transport. The thermal transport solution was applicable to the solid-to-liquid phase transition so that the depth of vaporization could be estimated. The vaporized material was thermally decoupled from the rest of the anode. Experimental measurements were made on the AEDC MBS FXR using a smaller area anode and cathode than normally used on the MBS to purposely increase the electron energy density on the anode. The analytical modeling of the heating of the anode showed that the anode material remained on the anode surface until the anode reached its boiling point. The material ejected from the anode not only eroded the anode surface but caused unacceptable damage to the cathode.