Electromagnetic Diffusion into a Cylindrical Plasma Column during the Early Stages of Pinch Formation

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Abstract
The diffusion of electromagnetic energy into a cylindrical plasma column due to the discharge of the energy stored in a capacitor is formulated taking into account the effects of the capacitance and inductance of the discharge circuit. The discharge circuit reflects the linear pinch geometry in that the energy source is a charged condenser and the return lead is a perfectly conducting cylindrical shell concentric with and surrounding the plasma column. The plasma properties enter the formulation through an extended Ohm's law which includes the time rate of change of current density. Under the assumption that changes in the ionization density and collision frequency may be neglected, Maxwell's equations lead to a third-order linear partial differential equation for the diffusion current. An exact solution is obtained by Laplace transform techniques using appropriate initial and boundary conditions which take into account the finite external circuitry. The spatial and temporal behavior of the current density distribution as functions of the parameters which characterize both the circuit and the plasma are discussed and compared with that of an ordinary conductor obeying the simple Ohm's law.