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Register a new userTransverse Instabilities of a Bunch with Space Charge, Wake and Feedback
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Authors
Alexey Burov
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When a resistive feedback and single-bunch wake act together, it is known that some head-tail modes may become unstable even without space charge. This feedback-wake instability, FWI, modified by space charge to a certain degree, is shown to have a special single-maximum increasing- dropping pattern with respect to the gain. Also, at sufficiently large Coulomb and wake fields, as well as the feedback gain, a new type of transverse mode-coupling instability is shown to take place, 3FMCI, when head-to-tail amplified positive modes couple and the growth rate saturates with the gain.
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Transverse beam stability is strongly affected by the beam space charge. Usually it is analyzed with the rigid-beam model. However this model is only valid when a bare (not affected by the space charge) tune spread is small compared to the space charge tune shift. This condition specifies a relatively small area of parameters which, however, is the most interesting for practical applications. The Landau damping rate and the beam Schottky spectra are computed assuming that validity condition is satisfied. The results are applied to a round Gaussian beam. The stability thresholds are described by simple fits for the cases of chromatic and octupole tune spreads.
A brief historical review is presented of progressing understanding of transverse coherent instabilities of charged particles beams in circular machines when both Coulomb and wake fields are important. The paper relates to a talk given at ICFA Workshop on Mitigation of Coherent Beam Instabilities in Particle Accelerators, 23-27 September 2019 in Zermatt, Switzerland.
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 {it absolute} meaning of the word. This is done using an effective new method of analysis of the beams transverse spectrum for arbitrary space charge and wake fields. Two new types of beam instabilities are introduced: the {it saturating convective instability}, SCI, and the {it absolute-convective instability}, ACI.
To understand and control the dynamics in the longitudinal phase space, time-resolved measurements of different bunch parameters are required. For a reconstruction of this phase space, the detector systems have to be synchronized. This reconstruction can be used e.g. for studies of the micro-bunching instability. It occurs if the interaction of the bunch with its own radiation leads to the formation of sub-structures on the longitudinal bunch profile. These sub-structures can grow rapidly -- leading to a sawtooth-like behaviour of the bunch. At KARA, we use a fast-gated intensified camera for energy spread studies, Schottky diodes for coherent synchrotron radiation studies as well as electro-optical spectral decoding for longitudinal bunch profile measurements. For a synchronization, a hardware synchronization scheme is used which compensates for eventual hardware delays. In this paper, the different experimental setups and their synchronization are discussed and first results of synchronous measurements are presented.
Coulomb fields of charged particle beams in circular machines determine, together with wake fields, modes of the collective beam oscillations, both for transverse and longitudinal degrees of freedom. Recent progress in these two areas of beam dynamics is discussed.
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