Formulation of electron motion in a storage ring with a betatron tune varying with time and a dipole shaker working at a constant frequency

In order to reduce the beam density efficiently for a safe beam abort, we analytically studied the motion of an aborted electron beam undergoing a sinusoidal kick by a beam shaker working at a constant frequency. Since the rf power is switched off, the betatron tune changes gradually with time due to chromatic effects. Chromatic aberration, together with a finite energy spread, enhances the dilution effect of the beam density, while the change in betatron tune with time causes a phase slippage that suppresses the growth of oscillation amplitude by the beam shaker. In order to treat such a situation properly, we formulated the motion of an aborted electron beam, taking into account nonlinear chromatic effects, under the adiabatic condition that the change in betatron tune is much slower than the betatron oscillation. In addition, by considering the case of a linearly varying betatron tune, it is shown that the response of an aborted electron beam can be interpreted as a superposition of waves, i.e., diffraction of waves. Our investigation not only provides a criteria for the determination of shaker’s frequency for a safe beam abort but also has applications to resonance crossing phenomena.

Abstract licence: CC BY

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