Drift-Cyclotron Instability in a Toroidal Machine

Abstract

Low-frequency fluctuations have been observed in the plasma inside the toroidal machine at General Atomic. These excitations need high ion temperature and they occur where the plasma or the magnetic field is nonuniform. These oscillations propagate in the direction of the diamagnetic current with ${k}_{\ensuremath{\parallel}}\ensuremath{\ll}{k}_{\ensuremath{\perp}}$. They have a rather peaked growth rate as a function of ${k}_{\ensuremath{\perp}}$ and are characterized by a narrow-band spectrum. It has been conjectured that the oscillations are due to a drift instability near the ion cyclotron frequency ${\ensuremath{\Omega}}_{i}$ obtained by Mikhailovskii and Timofeev, occurring in a machine with high simulated gravity. The appropriate dispersion relation has been solved numerically in the Univac 1108 digital machine after converting it into a pair of nonlinear simultaneous first-order differential equations and starting from solutions obtained analytically for large ${k}_{\ensuremath{\perp}}$. The solution for the mode investigated with $\ensuremath{\omega}\ensuremath{\sim}{\ensuremath{\Omega}}_{i}+{k}_{\ensuremath{\perp}}{v}_{g}$, where ${v}_{g}$ is the gravitational drift, appears to have a prominent peak in the growth rate and a noticeably monochromatic frequency spectrum. If ${v}_{g}$ is set equal to zero, this mode turns into the usual Mikhailovskii-Timofeev drift-cyclotron mode. Various other properties of the mode have been found, including an interesting density variation of frequency.