Flux Loss and Energy Balance in Magnetic Flux-Compression Experiments

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Abstract
A set of explosively driven flux-compression experiments with stainless steel liners and final fields in the range 2–6 MG is discussed. From experimentally determined field curves, the motion of the liner is derived by calculating the flux loss. Up to 80% of the initial flux is lost in these experiments. The variation of resistivity with temperature is taken into account, and the Joule heating energy is also determined. As can be verified by the energy balance, a consistent picture of the flux-compression process is obtained, including the phenomenon of field turnaround. The speed of sound in the liner material is comparable to the implosion speed; therefore, energy can be transferred to the magnetic field only from a thin inner layer of the liner. The energy accumulated in the magnetic field and in Joule heat increases very steeply at the end of the compression; thus, the inner layer of the liner is suddenly decelerated. There is still a large amount of kinetic energy in the outer layers of the liner at this instant. An empirical turnaround criterion is derived on the basis of these considerations. This shows that the peak field is practically independent of the initial field over a large range of initial fields. The final field depends essentially on the kinetic energy density of the liner. The influence of resistivity on flux compression is also found to be small. Nevertheless, an upper limit for the resistivity of stainless steel in a megagauss field environment can be derived from the experiments. A value of 120 μΩ·cm is found to be in best agreement with the experimental results. The methods developed in this paper can also be used to predict the performance of flux-compression devices. This is demonstrated with a few examples.

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