STABILITY OF ANISOTROPIC BEAMS WITH SPACE-CHARGE

Based on self-consistent Vlasov-Poisson equations, we derive coherent frequencies and stability properties of anisotropic or ''nonequipartit ioned'' beams with different focusing constants and emittances in the two transverse directions. The thus obtained dispersion relations of t ransverse multipole oscillations with quadrupolar, sextupolar, and oct upolar symmetries are solved numerically. We find that for sufficientl y large energy anisotropy some of the eigenmodes become unstable in th e space-charge-dominated regime. Applying our results to high-current linear accelerators, we find that ''nonequipartitioned'' beams may exi st in relatively large regions of parameter space under stable conditi ons. It is only in beams with strongly space-charge-depressed betatron tunes that harmful instabilities leading to emittance exchange should be expected.