Analysis of the operating regimes of microsecond-conduction-time plasma opening switches

Abstract

A theoretical model for the microsecond-conduction-time plasma opening switch (POS) based on magnetohydrodynamics is presented. The operating processes are associated with the magnetic field transport in the switch. The concept of the freezing-in of magnetic field in fluids is used to analyse the dynamics of this field in the plasma. One-dimensional and two-dimensional numerical simulations lead to the identification of two operating regimes, related to the Hall and the snowplow effects. The transition between these two regimes is determined by the plasma density. Scaling relations are developed from this model. In particular the electrical charge Q, conducted by the POS during the conduction time, provides a useful tool for comparisons between theory and experiments; it is shown to be the essential parameter for the switch design.

Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system

“…We use A, B = Ω A · B dx, for any pair A, B ∈ (L 2 (Ω)) 3 . We remark that ∇B (L 2 (Ω)) 9 = ∇ × B (L 2 (Ω)) 3 .…”

“…Thanks to the Sobolev imbedding in dimension 3, ∇ × A ∈ L ∞ (Ω) 3 and ∇ × A N k → ∇ × A strongly in L ∞ (Ω) 3 . Now, thanks to the convergences (4.12), we can take the limit N k → ∞ and get that B satisfies…”

“…We stress that the important contribution of this work is the account of the last term of the left-hand side of (1.3), known as the Hall effect term. The main theorem of this work is stated as follows: 3 with ∇·u 0 = 0, ∇ · B 0 = 0. Then, there exists a global weak solution (u, B) for the Hall MHD problem (1.1), (1.4).…”

“…For axisymmetric purely swirling magnetic fields, the Hall problem reduces to a viscous Burger's equation. By neglecting the resistivity, the resulting inviscid Burger's equation shows shock wave solutions which are known in physics textbooks as KMC waves for Kingsep, Mokhov and Chukbar [16] (see also [3,8]). They only exist if the Hall term is present.…”

Traveling waves in Hall-magnetohydrodynamics and the ion-acoustic shock structure

“…Hall-MHD has been used as an enhanced description of other phenomena that involve small length scales, for instance the dissipative range of turbulence 12 and ballooning modes 10 . The Hall effect enables the rapid penetration of a magnetic field into a plasma inside plasma opening switches, which are crucial components of pulsed plasma devices, radiation sources, and charged particle beams 4 .…”