Wave amplitude variation and energy flow in autoresonant collective ion acceleration

An expression for the energy of small-amplitude waves in a radially inhomogeneous cold-fluid unneutralized relativistic electron beam is obtained in terms of the wave amplitudes. The result is employed together with conservation of wave energy to determine how the axial electric field strength and beam-edge modulation associated with slow cyclotron waves change with position in an electron beam propagating along the adiabatically spatially decreasing magnetic guide field of an autoresonant collective ion accelerator. The resulting axial profiles are found to depart markedly from those of earlier radially homogeneous beam calculations. Possible impacts of these findings on a planned autoresonant acceleration feasibility experiment are discussed.