Time dependent Z-pinch equilibria

Abstract
Two classes of self‐similar time dependent Z‐pinch equilibria (in which pressure balance is maintained while the internal energy is rising) are described. In the first class the total current is rising and the pinch is stationary, in the second the total current is falling and the pinch is expanding. It is found that, in contrast to the steady state case, both gas embedded and thermally isolated equilibria can be obtained at low (I≪1 MA) currents by varying the pinch parameters. Furthermore, a skin current can be maintained during the current rise or fall. The pinch parameter regimes corresponding to the various categories of equilibrium are derived and the spatial structures of the equilibrium profiles are described in detail.

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