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Title |
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| MOPF09 |
Signals from a Beam Performing Betatron Oscillations Using an Electrostatic Electrode Model with Rectangular Boundaries |
51 |
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- F. Nolden
GSI, Darmstadt, Germany
- J.X. Wu
IMP/CAS, Lanzhou, People's Republic of China
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We present a novel electrostatic electrode model with rectangular boundaries. The fields are calculated using a conformal mapping. These fields are used to calculate the signal due to a relativistic beam. The response at harmonics of the revolution frequency and at the corresponding horizontal and vertical sidebands is given. The underlying nonlinear formalism is due to Bisognano and Leeman. The electrode geometry of the new stochastic cooling system at the CSRe ring at the IMP in Lanzhou is taken to derive the responses in the sum mode, the horizontal difference mode, and the vertical difference mode.
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| FRWAUD02 |
Fokker-Planck Approach to the Description of Transverse Stochastic Cooling |
170 |
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- F. Nolden
GSI, Darmstadt, Germany
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A Fokker-Planck model of transverse stochastic cooling (without feedback through the beam) is presented, which relies on moderately simplified assumptions about the underlying cooling system. The equilibrium emittance distribution turns out to be always exponential. Furthermore, if the initial distribution is already exponential, then the solution of the fully time-dependent Fokker-Planck equation remains exponential. The average emittance decays with a rate towards equilibrium, which is completely consistent with the classical van der Meer rate, including undesired mixing, desired mixing and thermal noise.
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Slides FRWAUD02 [1.088 MB]
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