High frequency betatrons

The scaling of the betatron technique with the use of high-frequency, low-loss magnetic materials (ferrites, Metglas, etc.) is discussed. Because of synchrotron radiation, the maximum betatron energy E/sub max/(GeV) scales as approximately 0.013 f(Hz)/B/sub s//sup 2/(T), where B/sub s/ is the maximum magnetic field on the orbit and f is the full-wave acceleration frequency. Eddy current losses in laminated iron limit f to approximately 120 Hz, thereby limiting E/sub max/ to 300-400 MeV for a classical betatron, with a low acceleration gradient, and low current. With low-loss, high-frequency materials, one may consider f approximately 1-100 kHz and energies in the gigaelectronvolt regime, or betatrons with substantially higher current. Practical considerations, potential advantages, and possible applications are considered.<>