It is necessary to establish confidence in high-consequence codes containing an extensive suite of physics algorithms in the regimes of interest. Verification problems allow code developers to assess numerical accuracy and increase confidence that specific sets of model physics were implemented correctly in the code. The two main verification techniques are code verification and solution verification. In this work, we present verification problems that can be used in other codes to increase confidence in simulations of relativistic beam transport. Specifically, we use the general plasma code EMPIRE to model and compare with the analytical solution to the evolution of the outer radial envelope of a relativistic charged particle beam. We also outline a benchmark test of a relativistic beam propagating through a vacuum and pressurized gas cell, and present the results between EMPIRE and the hybrid code GAZEL. Further, we discuss the subtle errors that were caught with these problems and detail lessons learned.
In this work, we use the Brillouin flow analytic framework to examine the physics of Magnetically Insulated Transmission Lines (MITL). We derive a model applicable to any particle species, including both positive and negative ions, in planar and cylindrical configurations. We then show how to self-consistently solve for two-species simultaneously, using magnetically insulated electrons and positive ions as an example. We require both layers to be spatially separated and magnetically insulated (mutually magnetically insulated); for a 7.5 cm gap with a 2 MV bias voltage, this condition requires magnetic fields in excess of 2.73 T. We see a close match between mutually insulated MITL performance and “superinsulated” (high degree of magnetic insulation) electron-only theory, as may be expected for these high magnetic fields. However, the presence of ions leads to several novel effects: (1) Opposite to electron-only theory, total electron currents increase rather than decrease as the degree of magnetic insulation becomes stronger. The common assumption of neglecting electrons for superinsulated MITL operation must be revisited when ions are present—we calculate up to 20× current enhancement. (2) The electron flow layer thickness increases up to double, due to ion space-charge enhancement. (3) The contributions from both ions and electrons to the MITL flow impedance are calculated. The flow impedance drops by over 50% when ions fill the gap, which can cause significant reflections at the load if not anticipated and degrade performance. Additional effects and results from the inclusion of the ion layer are discussed.
This report documents the progress made in simulating the HERMES-III Magnetically Insulated Transmission Line (MITL) and courtyard with EMPIRE and ITS. This study focuses on the shots that were taken during the months of June and July of 2019 performed with the new MITL extension. There were a few shots where there was dose mapping of the courtyard, 11132, 11133, 11134, 11135, 11136, and 11146. This report focuses on these shots because there was full data return from the MITL electrical diagnostics and the radiation dose sensors in the courtyard. The comparison starts with improving the processing of the incoming voltage into the EMPIRE simulation from the experiment. The currents are then compared at several location along the MITL. The simulation results of the electrons impacting the anode are shown. The electron impact energy and angle is then handed off to ITS which calculates the dose on the faceplate and locations in the courtyard and they are compared to experimental measurements. ITS also calculates the photons and electrons that are injected into the courtyard, these quantities are then used by EMPIRE to calculated the photon and electron transport in the courtyard. The details for the algorithms used to perform the courtyard simulations are presented as well as qualitative comparisons of the electric field, magnetic field, and the conductivity in the courtyard. Because of the computational burden of these calculations the pressure was reduce in the courtyard to reduce the computational load. The computation performance is presented along with suggestion on how to improve both the computational performance as well as the algorithmic performance. Some of the algorithmic changed would reduce the accuracy of the models and detail comparison of these changes are left for a future study. As well as, list of code improvements there is also a list of suggested experimental improvements to improve the quality of the data return.
Cartwright, Keith C.; Komrska, Allison M.; Breen, Lorin I.; Loveless, Amanda M.; Garner, Allen L.
Crossed-field diodes (CFDs) are used in multiple high-power applications and are characterized by an applied magnetic field orthogonal to the electric field, induced by the applied voltage across the anode-cathode gap. In vacuum, the Hull cutoff magnetic field (HCMF) represents the maximum applied magnetic field for which an electron from the cathode can reach the anode. This study investigates the effects of non-vacuum conditions on electron trajectories by introducing electron mobility, which represents particle collisions. We used numerical solutions of the electron force law and particle-in-cell simulations (XPDP1) to assess electron motion for various electron mobilities. For magnetic fields above the HCMF in vacuum, reducing the electron mobility increases the time for an electron emitted from the cathode to reach the anode. Reducing mobility below 22 C s/kg eliminates the HCMF for any magnetic field, meaning that an emitted electron will always cross the gap. We derived the magnetic field, mobility, and electron transit time corresponding to this condition by solving for the condition when the electron velocity in the direction across the anode-cathode gap going to zero at the anode. A parametric study of these conditions using theory and XPDP1 is performed under different gap distances, voltages, and magnetic fields.
An approach to numerically modeling relativistic magnetrons, in which the electrons are represented with a relativistic fluid, is described. A principal effect in the operation of a magnetron is space-charge-limited (SCL) emission of electrons from the cathode. We have developed an approximate SCL emission boundary condition for the fluid electron model. This boundary condition prescribes the flux of electrons as a function of the normal component of the electric field on the boundary. We show the results of a benchmarking activity that applies the fluid SCL boundary condition to the one-dimensional Child-Langmuir diode problem and a canonical two-dimensional diode problem. Simulation results for a two-dimensional A6 magnetron are then presented. Computed bunching of the electron cloud occurs and coincides with significant microwave power generation. Numerical convergence of the solution is considered. Sharp gradients in the solution quantities at the diocotron resonance, spanning an interval of three to four grid cells in the most well-resolved case, are present and likely affect convergence.
We introduce a robust verification tool for computational codes, which we call Stochastic Robust Extrapolation based Error Quantification (StREEQ). Unlike the prevalent Grid Convergence Index (GCI) [1] method, our approach is suitable for both stochastic and deterministic computational codes and is generalizable to any number of discretization variables. Building on ideas introduced in the Robust Verification [2] approach, we estimate the converged solution and orders of convergence with uncertainty using multiple fits of a discretization error model. In contrast to Robust Verification, we perform these fits to many bootstrap samples yielding a larger set of predictions with smoother statistics. Here, bootstrap resampling is performed on the lack-of-fit errors for deterministic code responses, and directly on the noisy data set for stochastic responses. This approach lends a degree of robustness to the overall results, capable of yielding precise verification results for sufficiently resolved data sets, and appropriately expanding the uncertainty when the data set does not support a precise result. For stochastic responses, a credibility assessment is also performed to give the analyst an indication of the trustworthiness of the results. This approach is suitable for both code and solution verification, and is particularly useful for solution verification of high-consequence simulations.