Time- and frequency-domain hybridizable discontinuous Galerkin solvers for the calculation of the Cherenkov radiation

We present the first a priori error analysis of a class of space-discretizations by Hybridizable Discontinuous Galerkin (HDG) methods for the time-dependent Maxwell's equations introduced in Comput. Methods Appl. Mech. Engrg., vol. 396, paper. No. 114969, 27 pages, 2022. The distinctive feature of these discretizations is that they display a discrete version of the Hamiltonian structure of the original Maxwell's equations. This is why they are called "Hamiltonian" HDG methods. Because of this, when combined with symplectic time-marching methods, the resulting methods display an energy that does not drift in time. We provide a single analysis for several of these methods by exploiting the fact that they only differ by the choice of the approximation spaces and the stabilization functions. We also introduce a new way of discretizing the static Maxwell's equations in order to define the initial condition in a manner consistent with our technique of analysis. Finally, we present numerical tests to validate our theoretical orders of convergence and to explore the convergence properties of the method in situations not covered by our analysis.

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Semi-analytic model for plasma production and Cherenkov radiation emission from hypervelocity impacts on soda–lime glass

Spina

Fletcher

Fish

2023

Physics of Plasmas

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A semi-analytic method is proposed to compute the produced plasma and the emitted Cherenkov radiation from hypervelocity impacts on soda–lime glass for various projectiles and impact velocities. First, the Taylor–von Neumann–Sedov blast wave model, coupled with the system of nonlinear Saha equations for multispecies, strongly coupled plasma, is adopted to estimate the hydrodynamic profiles and the ionization state of the target material in the early stage of the impact. Second, the Frank–Tamm formula is considered to investigate the onset of the Cherenkov radiation and to compute the emitted energy. The present approach predicts a linear dependence of the produced total electric charge on the projectile density and a quadratic dependence on the projectile velocity, whereas the emitted Cherenkov radiation scales quadratically with the produced charge if the onset conditions are met.

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Time- and frequency-domain hybridizable discontinuous Galerkin solvers for the calculation of the Cherenkov radiation

Cited by 3 publications

References 58 publications

A hybridizable discontinuous Galerkin formulation for the Euler–Maxwell plasma model

A hybridizable discontinuous Galerkin formulation for the Euler–Maxwell plasma model

A priori error analysis of new semidiscrete, Hamiltonian HDG methods for the time-dependent Maxwell’s equations

Semi-analytic model for plasma production and Cherenkov radiation emission from hypervelocity impacts on soda–lime glass

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