Harmonics of the Kruskal Limit and Field Diffusion in a Toroidal Pinch Discharge

Abstract

Measurement of the magnetic fields in a toroidal pinch discharge have shown that when the applied toroidal magnetic field ($B_{z0\mathrm{}}$) is comparable with or less than the self-field of the discharge ($B_{\theta }$), the $B_{\theta }$ field penetrates into the discharge more rapidly than expected by simple electromagnetic theory, and also the $B_z$ flux is enhanced within the discharge. This second effect was very marked in these experiments because of the high impedance of the supply circuit connected to the $B_z$ coils. In addition, the magnetic field oscillograms show steps which commence when the magnetic pitch (${\lambda }_B=\frac{2\pi r{B}_z}{B_{\theta }}$) satisfied ${\lambda }_B\simeq \frac{L}{n} or \frac{2L}{n}$, where $L$ is the torus circumference and $n$ is an integer. If it is assumed that instabilities prevent the formation of a large pressure gradient in the discharge, then $j_{\perp }\ll j_{\mathrm{II}}$, and the field configurations predicted for an applied electric field ($E_z$) are in good agreement with those observed experimentally after field penetration is complete. In particular, the enhancement of $B_z$ is explained. Further, the assumption of small $j_{\mathrm{II}}$ leads to the prediction of more rapid $B_{\theta }$ penetration at low $B_z$. The most likely instabilities which would cause the limitation in pressure gradient and produce the waveform steps are thought to be interchange modes.R. The most likely instabilities which would cause the limitation in pressure gradient and produce the waveform steps are thought to be interchange modeql