Evaluation of conductor stresses in a pulsed high-current toroidal transformer

The Precision, High-Energy Density, Liner Implosion eXperiment (PHELIX) pulsed power driver is currently under development at Los Alamos National Laboratory. When operational PHELIX will provide 5-10 MAmps of peak current with pulse rise-time of ~5-10 ms. Crucial to the performance of PHELIX is a multi-turn primary, single-turn secondary, current step-up toroidal transformer, R
_major
~ 30 cm, R
_minor
~ 10 cm. The transformer lifetime should exceed 100 shots. Therefore it is essential that the design be robust enough to survive the magnetic stresses produced by high currents. In order to evaluate our design, two methods have been utilized. First, an analytical evaluation has been performed. By identifying the magnetic forces as J
₁

²
/2 ¿L
₁
+ J
₁
J
₂
¿M
₁₂
, where J
₁
and J
₂
are currents in two circuits, coupled by mutual inductance M
₁₂
and L
₁
is the self-inductance of the circuit carrying current J
₁
, analytical estimates of stress can be obtained. These results are then compared to a computational MHD model of the same system and to a full finite-element, electromagnetic simulation.