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تسجيل مستخدم جديدTransverse Instabilities of Coasting Beams with Space Charge
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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.
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The mode coupling instability for coasting beams has been discussed in a previous paper using macroparticle tracking simulations from the pyHeadTail code and a simple analytical formula which was proposed as an extension of the ansatz used for the si
ngle-particle formalism. In this paper, we propose a self-consistent derivation of this formula based on the linearized Vlasov equation. The proposed mode coupling instability for coasting beams was never predicted or discussed in the past and we believe that the reason is twofold. First, to derive it analytically from the linearized Vlasov equation, one should not make the usual approximation $sin(phi)simeq (e^{jphi})/(2j)$, where $phi$ is the transverse betatron phase, but really consider the two terms of $sin(phi)=(e^{jphi}-e^{-jphi})/(2j)$ as the second term is the one responsible for the mode coupling in coasting beams. It should be stressed here that mode coupling is found already with driving impedance only. Note that the previous approximation is also usually made for bunched beams and this case should therefore also be carefully reviewed in the future. Second, by including the detuning impedance, the coupling is much stronger and this is what we found also in pyHeadTail simulations.
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