Energy loss to conductors operated at lineal current densities ≤ 10     MA / cm : Semianalytic model, magnetohydrodynamic simulations, and experiment

We have developed a semianalytic expression for the total energy loss to a vacuum transmission-line electrode operated at high lineal current densities. (We define the lineal current density jℓ≡B/μ0 to be the current per unit electrode width, where B is the magnetic field at the electrode surface and μ0 is the permeability of free space.) The expression accounts for energy loss due to Ohmic heating, magnetic diffusion, j×B work, and the increase in the transmission line’s vacuum inductance due to motion of the vacuum-electrode boundary. The sum of these four terms constitutes the Poynting fluence at the original location of the boundary. The expression assumes that (i) the current distribution in the electrode can be approximated as one-dimensional and planar; (ii) the current I(t)=0 for t