Abstract
The stability of longitudinal dipole oscillations in Gaussian bunches is studied for different rf wave forms and with nonlinear space charge. In a previous study [O. Boine-Frankenheim and T. Shukla, Phys. Rev. ST Accel. Beams 8, 034201 (2005)], the space charge induced loss of Landau damping and the bunch response to rf phase modulations was analyzed for elliptic distributions. The present study investigates Landau damping of dipole modes with nonlinear space charge in Gaussian bunches. The stability boundary resulting from a dispersion relation is compared with stability scans performed within a self-consistent simulation scheme. The results are compared with numerically obtained beam transfer functions.
Highlights
The longitudinal space charge force plays an important role in the design and in the operation of storage rings or synchrotrons for high current ion beams
The magnitude of the rf voltage reduction for an elliptic bunch distribution can be expressed by means of the longitudinal space charge parameter
Ref. [2] it has been pointed out that the loss of Landau damping in the case of an elliptic bunch distribution in a double rf bucket occurs at very small space charge parameters (
Summary
The longitudinal space charge force plays an important role in the design and in the operation of storage rings or synchrotrons for high current ion beams. The stability boundary for short bunches in single rf buckets with elliptic distributions and space charge was studied analytically in Ref. The effect of the space charge induced synchrotron frequency spread on Landau damping in Gaussian bunches has been addressed in Ref. Besides the actual role of mode coupling, an important remaining question is whether nonlinear space charge stabilizes or destabilizes dipolar-type oscillations in Gaussian bunches. In the present study we analyze the stability boundaries for dipolar oscillations with nonlinear space charge in single and in double rf buckets, using different approaches.
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