Abstract
The Cartesian magnetically insulated transmission line (MITL) theory of Mendel et al. [Appl. Phys. 50, 3830 (1979); Phys. Fluids 26, 3628 (1983)] is extended to cylindrical coordinates. A set of equations that describe arbitrary electron flows in cylindrical coordinates is presented. These equations are used to derive a general theory for laminar magnetically insulated electron flows. The laminar theory allows one to specify the potentials, fields, and densities across a coaxial line undergoing explosive electron emission at the cathode. The theory is different from others available in cylindrical coordinates in that the canonical momentum and total energy for each electron may be nonzero across the electron sheath. A nonzero canonical momentum and total energy for the electrons in the sheath allows the model to produce one-dimensional flows that resemble flows from lines with impedance mismatches and perturbing structures. The laminar theory is used to derive two new self-consistent cylindrical flow solutions: (1) for a constant density profile and (2) for a quadratic density profile of the form ρ=ρc[(r2m−r2)/(r2m−r2c)]. This profile is of interest in that it is similar to profiles observed in a long MITL simulation [Appl. Phys. 50, 4996 (1979)]. The theoretical flows are compared to numerical results obtained with two-dimensional (2-D) electromagnetic particle-in-cell (PIC) codes.
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