Transverse Microwave Convective Instability at Transition Crossing

Abstract

An analytical model of transverse convective instability of a bunch at transition crossing is presented for the microwave case, when the wake is sufficiently short compared with the bunch length. The space charge is assumed to be strong, as it typically is for the low and medium energy synchrotrons. A simple formula for the intensity threshold is obtained and its prediction is compared with available CERN PS data; without a single fitting parameter, a good agreement is demonstrated.

Space charge effects for collective instabilities in circular machines

“…It is clear now, that convective instabilities constitute a common obstacle for high-intensity circular machines of low and medium energy, where SC is significant; they take place at CERN SPS [47,48] and PS [49] rings, as well as at the Fermilab Booster [50]. That is why it is important to understand how they behave together with other factors of beam dynamics.…”

Space Charge Effects for Collective Instabilities in Circular Machines

“…[47], measurements of a microwave instability at transition crossing in PS were reported; the instability was characterized as convective. Recently an analytical model for it was proposed [48] by means of Eq. (8).…”

“…[47] that "The bunch parameter measurements demonstrate... that the space-charge effect does not affect the instability thresholds" does not actually contradict to the rather weak dependence of the threshold bunch intensity N th on the transverse emittance, N th ∝ ǫ 1/4 ⊥ of Ref. [48], since the limited range of the emittances examined in Ref. [47] and the measurement errors do not allow to resolve the rather weak dependence on the emittance on the ground of this set of measurements alone [50].…”

Space Charge Effects for Transverse Collective Instabilities in Circular Machines

“…[39], measurements of a microwave instability at transition crossing in PS were reported; the instability was characterized as convective. Recently an analytical model for it was proposed [40] by means of Eq. (8).…”

“…[39] that "The bunch parameter measurements demonstrate... that the space-charge effect does not affect the instability thresholds" does not actually contradict to rather weak dependence of the threshold bunch intensity N th on the transverse emittance, N th ∝ ǫ 1/4 ⊥ of Ref. [40], since the limited of the emittances examined in Ref. [39] and the measurement errors do not allow to resolve rather weak dependence on the emittance on the ground of this set of measurements alone [42].…”