A relativistic fluid model for magnetically insulated transmission line flow*

Numerical modeling of magnetically insulated transmission line (MITL) electron flow is traditionally accomplished with a particle-in-cell (PIC) method. A PIC method can efficiently solve the collisionless Vlasov model for MITL flow. Additionally, space charge limited (SCL) emission boundary conditions have been well developed for PIC methods [1]. However, a cold electron fluid model may have utility for studying MITL flow. To this end, we have formulated an approximate SCL emission boundary condition for a relativistic charged fluid model. We show the results of a benchmarking activity which compares computed solutions to the relativistic electron fluid equations against corresponding solutions for canonical, cold electron fluid benchmark problems. We consider a one-dimensional Child-Langmuir diode, a canonical two-dimensional diode problem [2] and magnetically insulated planar flow which is representative of MITL flow.

[1] Stoltz, P. H., Luginsland, J. W., Chap, A., Smithe, D. N., & Cary, J. R. (2020). A new simple algorithm for space charge limited emission. Physics of Plasmas, 27(9), 093103.

[2] Luginsland, J. W., Lau, Y. Y., Umstattd, R. J., & Watrous, J. J. (2002). Beyond the Child–Langmuir law: A review of recent results on multidimensional space-charge-limited flow. Physics of Plasmas, 9(5), 2371-2376.