Pure Transvers Optical Stochastic Cooling
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   Imagine a single pickup and two correction locations all "isochronous". The 
two correction locations have a difference of dispersion between them: e.g. 
the first has D_1=+D_o and D'_1=0; the second has D_2=-D_o and D'_2=0. The 
energy kicks of the first and second correction stations are of opposite sign 
so that the net energy change is zero, but the presence of the intervening 
energy shift interacting with the dispersion change introduces a transverse 
displacement of the particles by \Delta E \Delta D. 

The above describes an optical deflector that does not change the momentum. It 
must be used with an optical position sensitive device, of which there are 
probably many. An alternating quadrupole wiggler is one, but it is probably 
not practical. Better might be a normal wiggler in a non dispersive region 
with optical elements that shift the phase of the signal from one side 
relative to that from the other. By "side", I could mean y or y', both may be 
possible, but y would seem easier. Beam on one side generates a phase that 
accelerates in corrector 1 and decelerates in the other, generating a 
deflection one way. Beam on the other side generates the other phase causing 
deceleration in 1 and acceleration in the other, and generates a deflection 
the other way. 

The cooling functions only in one phase of one direction - as does 
conventional trasverse stochastic cooling. Of course one cannot have multiple 
samples in that phase and direction, but one could still, in principle, 
subdivide the other three. 

  Thus the energy-displacement coupling, and the requirement that dp/p D 
\approx \sqrt{\beta \epsilon} are removed. We note that the power reuqirement 
is no longer related to dp/p, but is related to D and the beam emittance. 

I am not arguing that all this is necessarily useful, but it is a possibility.