Comments on Landau damping due to synchrotron frequency spread
An inductive/space-charge impedance shifts the synchrotron frequency downwards above/below transition, but it is often said that the coherent synchrotron frequency of the bunch is not shifted in the rigid-dipole mode. On the other hand, the incoherent synchrotron frequency due to the sinusoidal rf always spreads in the downward direction. This spread will therefore not be able to cover the coherent synchrotron frequency, implying that there will not be any Landau damping no matter how large the frequency spread is. By studying the dispersion relation, it is shown that the above argument is incorrect, and there will be Landau damping if there is sufficient frequency spread. The main reason is that the coherent frequency of the rigid-dipole mode will no longer remain unshifted in the presence of a synchrotron frequency spread.
- Research Organization:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC02-76CH03000
- OSTI ID:
- 15020208
- Report Number(s):
- FERMILAB-FN-0762-AD; TRN: US200606%%421
- Country of Publication:
- United States
- Language:
- English
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