Nonlinear saturation of collisionless trapped particle instability in tandem mirrors

A collisionless trapped particle instability with magnetohydrodynamiclike growth rate is expected in tandem mirrors. To study its nonlinear state, a two-dimensional polarization drift nonlinearity in a cylindrical geometry is considered. 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. The solution of mode-coupled equations yields the nonlinear saturation level. Mode coupling to the damped higher-order radial harmonics is the principal saturation mechanism of the unstable fundamental radial harmonic.