Ionization cooling in a straight beamline reduces the transverse emittance of a
beam, and has little effect on the longitudinal emittance (generally, in fact,
it increases the longitudinal emittance).  Once the beamline bends, the
introduction of dispersion creates a coupling between the transverse and
longitudinal planes.  If this coupling is handled properly, one can achieve
cooling in all three phase space planes.  This is usually done by placing a
wedge-shaped absorber in a region where there is dispersion.  I will
demonstrate using an eigenvalue analysis that there are other configurations of
dispersion and absorber shape that will achieve ionization cooling in all phase
space planes.  In particular, I will show that a one can even achieve cooling
in all phase planes with a parallel-faced absorber in a dispersion-free region.
I will use perturbation theory to approximate the change in the cooling rates
due to longitudinal-transverse coupling.  I will then describe how the cooling
of longitudinal oscillations can be understood via the projection of the
"longitudinal" eigenmodes into the transverse plane.

This is a PDF document
URL http://www-mucool.fnal.gov/mcnotes/public/pdf/muc0339/muc0339.pdf
Posted by J. Scott Berg