Abstract
Instead of analyzing a portion of an hydromagnetic pinch apparatus in detail, and replacing the remainder by a boundary condition, the entire pinch apparatus is treated here as a single dynamical system. A circuit equation and a mechanical equation, coupled together, result. These equations describe the dynamical development of the pinch and exhibit explicity its dependence on the physical parameters (electrical and mechanical) of the system. As examples, the equations have been used to analyze the snow-plow model and the adiabatic pinch, yielding curves that show the geometrical development of the pinch in time, as well as the distribution of mechanical and magnetic energies at any stage. Analogous analyses may be made for other physical quantities of interest, and can be used to adjust the parameters of the system so as to optimize specific pinch characteristics.
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