Threshold Studies of the Microwave Instability in Electron Storage Rings
We use a Vlasov-Fokker-Planck program and a linearized Vlasov solver to study the microwave instability threshold of impedance models: (1) a Q = 1 resonator and (2) shielded coherent synchrotron radiation (CSR), and find the results of the two programs agree well. For shielded CSR we show that only two dimensionless parameters, the shielding parameter {Pi} and the strength parameter S{sub csr}, are needed to describe the system. We further show that there is a strong instability associated with CSR, and that the threshold, to good approximation, is given by (S{sub csr})th = 0.5 + 0.12{Pi}. In particular, this means that shielding has little effect in stabilizing the beam for {Pi} {approx}< 2; for larger {Pi} it is effective, with threshold current depending on shielding aperture as h{sup -3/2}. We, in addition, find another instability in the vicinity of {Pi} = 0.7 with a lower threshold, (S{sub csr}){sub th} {approx} 0.2. We find that the threshold to this instability depends strongly on damping time, (S{sub csr}){sub th} {approx} {tau}{sub p}{sup -1/2}, and that the tune spread at threshold is small - both hallmarks of a weak instability.
- Research Organization:
- SLAC National Accelerator Laboratory (SLAC)
- Sponsoring Organization:
- US DOE Office of Science (DOE SC)
- DOE Contract Number:
- AC02-76SF00515
- OSTI ID:
- 984333
- Report Number(s):
- SLAC-PUB-14191
- Journal Information:
- Phys.Rev.ST Accel.Beams 13:104402,2010, Journal Name: Phys.Rev.ST Accel.Beams 13:104402,2010 Journal Issue: 10 Vol. 13; ISSN 1098-4402
- Country of Publication:
- United States
- Language:
- English