Vertical coherent instabilities in bunched particle beams
The approach used here to study coherent instabilities illuminates the effect of the synchrotron frequency in setting the time scale for an instability, without making restrictive assumptions on the relative size of the synchrotron frequency and the coherent frequency shift (or growth rate). To accomplish this we use the single particle equations of motion and the Vlasov equation to obtain an integral equation which governs the coherent motion of a single bunch of particles. The solutions to the integral equation are then examined in two different regions. For the case of a bunch long compared to the characteristic wavelength of the instability we find two regions of instability. The first is a region of slow blowup at low currents (growth rate less than the synchrotron frequency). This instability is basically the head-tail effect which in this case is sensitive to the local cancellation of the impedance at positive and negative frequencies. The second is a region of fast blowup (growth rate much greater than the synchrotron frequency). This is a coasting-beam-like instability sensitive to the peak current in a bunch. Connecting the two regions is a striking transition, a phase transition, in which the growth rate increases by two orders of magnitude. For the case of a bunch shorter than the characteristic wavelength of the instability the behavior is quite different. For low currents the head-tail effect is again important; however, in this case moments of the impedance times a bunch factor couple to drive the instability. For larger currents there is a new instability (the parallel to the fast blowup for a long bunch) which arises even for zero chromaticity.
- Research Organization:
- State Univ. of New York, Stony Brook (USA)
- OSTI ID:
- 6298145
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
430200 -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
640301* -- Atomic
Molecular & Chemical Physics-- Beams & their Reactions
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BEAM BUNCHING
BEAM DYNAMICS
BEAMS
BOLTZMANN-VLASOV EQUATION
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
INSTABILITY
INTEGRAL EQUATIONS
OSCILLATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE BEAMS
SYNCHROTRON OSCILLATIONS