Nonlinear saturation of single-mode trapped ion instability

Abstract

The trapped ion instability appears as a single mode in the Columbia Linear Machine and is expected to appear as such in tandem mirrors. Using three-wave, nonresonant mode coupling of radially nonlocal eigenfunctions, two mode-coupling equations for the unstable fundamental and stable first-order radial harmonics are derived and solved. Mode coupling to the damped higher-order radial harmonics is the principal physical saturation mechanism of the unstable fundamental mode.