A bunched beam from an accelerator can excite and power an rf cavity which then drives either a deflecting or focusing (including nonlinear focusing) rf cavity with an amplitude related to beam current. Rf power, generated when a bunched beam loses energy to an rf field when traversing an electric field that opposes the particle's motion, is used to drive a separate (or the same) cavity to either focus or deflect the beam. The deflected beam can be stopped by an aperture or directed to a different area of a target depending on beam current. The beam-generated rf power can drive a radio-frequency quadrupole that can change the focusing properties of a beam channel as a function of beam current (space-charge-force compensation or modifying the beam distribution on a target). An rf deflector can offset a beam to a downstream sextupole, effectively producing a position-dependent quadrupole field. The combination of rf deflector plus sextupole will produce a beam current dependent quadrupole-focusing force. A static quadrupole magnet plus another rf deflector can place the beam back on the optic axis. This paper describes the concept, derives the appropriate equations for system analysis, and gives examples. A variation on this theme is to use the wake field generated in an rf cavity to cause growth in the beam emittance. The beam current would then be apertured by emittance defining slits.
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