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Four different schemes of final ionization cooling are discussed. The first scheme is the straight channel based on lithium rods, which can provide only 4D cooling, but which can be modified to obtain 6D cooling. The helical orbit scheme with decrement redistribution is one such modification. Two other modifications use emittance redistribution and emittance exchange procedures, respectively, to transfer phase-space volume from longitudinal to transverse degrees of freedom (where the transverse degrees of freedom alternate for each successive exchange or redistribution). By emittance redistribution is meant a arbitrary redistribution of phase-space volume from one degree of freedom to another and by emittance exchange is meant a symplectic operation of emittance swap. Estimates of the final emittance, calculations of the technical parameters and simulations of beam movement are presented for each scheme. The study focused on the scheme with emittance exchange because it looks the most promising and simple, both conceptually and in terms of implementation, and it can also extend the cooling process to handle a larger initial emittance relative to the basic straight channel scheme.
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