STABILITY OF A SELF- CONSISTENT LONGITUDINAL PHASE-SPACE DISTRIBUTION UNDER SPACE CHARGE PERTURBATIONS
David V. Neuffer · CERN Document Server (European Organization for Nuclear Research) · 1980
The equations of longitudinal motion for particles in a beam bunch with a linear external bunching field and with space charge forces are presented.A self-consistent phase-space distribution with an envelope equation, which is a solution to the Vlasov equation with these equations of motion, is described.The stability of the stationary distribution, the phase-space distribution with bunching and debunching balanced, is analyzed under normal mode perturbations.Eigenfrequencies and eigenmodes of these perturbations are descrrbed; they are found to be stable.Equations for numerical analysis of normal mode oscillations ofthe particle distribution in a system in which the external bunching force is periodic are derived.Results of the numerical analysis indicate that these oscillations can be unstable when the period of the bunching force and the period of the normal mode oscillation are in resonance.However, the numerical results also indicate that these instabilities are quite small in the case in which the bunching force period is much smaller then the individual particle motion period.NOTE: The lower case italic letter "v" should not be misconstrued with the lower case Greek letter nu "v".