Computer modeling of linear theta pinch machines

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Abstract
A zero-dimensional time dependent computer model is developed to describe post implosion behavior of a radially diffuse plasma column in linear theta pinch machines. The model consists of five first-order differential equations for electron temperature Te, ion temperature Ti, plasma column area Ap, magnetic field embedded in the plasma column Bi, and number of electrons in the plasma column N, and incorporates the effects of particle end loss, electron and ion thermal conduction, magnetic compression of the plasma, electron-ion energy transfer, Ohmic heating of the electrons, and magnetic field diffusion. End-on interferometric experimental data, which indicate that particle confinement time scales as L[mi/(Te+Ti)]1/2, where mi is the ion mass and L is the compression coil length, are used as a guide to the choice of an end loss parameter. Numerical predictions of on-axis density and plasma temperature are found to be in reasonably good agreement with experimental results from both the collisional Scylla I-C experiment and the hot collisionless Scylla IV-P experiment. These comparisons are used to identify important physical mechanisms characterizing the behavior of a particular machine including: the significance of thermal conduction on both plasma temperature and particle end loss; the importance of magnetic field diffusion; and the impact of using a time independent end loss scaling parameter.