Convective instabilities of bunched beams with space charge

Abstract

For a single hadron bunch in a circular accelerator at zero chromaticity, without multi-turn wakes and without electron clouds and other beams, only one transverse collective instability is possible, the mode-coupling instability, or TMCI. For sufficiently strong space charge (SC), the instability threshold of the wake-driven coherent tune shift normally increases linearly with the SC tune shift, as independently concluded by several authors using different methods. This stability condition has, however, a very strange feature: at strong SC, it is totally insensitive to the number of particles. Thus, were it correct, such a beam with sufficiently strong SC, being stable at some intensity, would remain stable at higher intensity, regardless of how much higher! This paper suggests a resolution of this conundrum: while SC suppresses TMCI, it introduces head-to-tail convective amplifications, which could make the beam even less stable than without SC, even if all the coherent tunes are real, i.e. all the modes are stable in the conventional absolute meaning of the word. This is done using an effective new method of analysis of the beam's transverse spectrum for arbitrary space charge and wake fields. Two new types of beam instabilities are introduced: the saturating convective instability, SCI, and the absolute-convective instability, ACI.

Transverse mode-coupling instability and space charge

“…A resolution of the contradictions between the observations and macroparticle simulations for the SPS, on the one hand, and the Vlasov analysis of this and preceding publications, on the other, was recently suggested by one of the authors [19]. As shown there, while SC moves up the TMCI wake threshold, it drives the saturating convective instability (SCI) and possibly the absoluteconvective instability (ACI), pretty much for the same wake parameters, if not even lower.…”

“…A resolution of the contradiction was recently suggested by one of the authors in Ref. [19], where he treats the SPS Q26 instability not as TMCI but as a convective one.…”

Electron Cooling with Space-Charge Dominated Proton Beams at Iota

“…[12] Besides enabling experiments on non-linear integrable optics by reducing energy spread and improving the lifetime of the beam by compensating for transverse emittance growth, the primary motivation of research with this cooler is to study the effect of space-charge forces in the regime of large transverse incoherent tune shift of Δ𝜈 𝑥,𝑦 ≈ −0.5 and compare with theoretical models. In addition, we are also planning experiments which uses electron cooling as a knob to study the interplay between space-charge and instabilities [13] and also control the phase space distribution in order to facilitate the realization of NIO in the presence of space-charge forces.…”

Reply to “Comment on “Instability Studies at the CERN Proton Synchrotron during transition crossing””

“…As suggested by the Author in the conclusion, if, apparently, we deal here with new physics, it could be very useful to check if the theory developed in [2] can reproduce the thresholds, as those reported in Fig. 14 of [1], under the different conditions of the machine, determining also the role of the space change in this instability at different longitudinal emittances.…”