Mechanisms for suppressing the transverse mode coupling instability in a circular accelerator
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AL, NONLINEAR, AND SOFT MATTER PHYSICS
Mechanisms for Suppressing the Transverse Mode Coupling Instability in a Circular Accelerator V. V. Smaluk Budker Institute of Nuclear Physics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrent’eva 11, Novosibirsk, 630090 Russia e-mail: [email protected] Received July 23, 2008
Abstract—The chromatic and nonlinear suppression of the transverse mode coupling instability in a circular accelerator is analyzed. Analytical estimates are compared with the results of experiments and numerical simulations. The transverse mode coupling (or fast head–tail) instability is a significant factor that limits the beam intensity in circular accelerators. This instability arises when the bunch current exceeds a threshold value determined by the broadband impedance of the vacuum chamber. Feedback systems are traditionally used to suppress the instability. The experience of working with such systems shows that their efficiency depends strongly on the operating parameters of the amplifier, particularly on the chromaticity and nonlinearity of the magnetic lattice. Thus, both chromatic and nonlinear effects should be taken into account to better understand the physical processes and to increase the feedback efficiency. PACS numbers: 29.20.-c, 29.27.-a, 29.27.Bd DOI: 10.1134/S1063776109030121
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∆νβ 20 I, mA
An intense beam of particles moving in the vacuum chamber of an accelerator induces strong electromagnetic (wake) fields that, in turn, affect the beam itself. The concept of a wake potential, which is defined as the integral of the electromagnetic interaction forces taken along the beam path, is used to analyze the interaction of the beam with the surrounding structure. In frequency domain, each part of the vacuum chamber can be represented as a frequency-dependent coupling impedance that is the Fourier transform of the wake potential of a point charge [1]. The resonant interaction between the beam and short-lived wake fields is responsible for the transverse mode coupling (TMC) (or fast head–tail) instability. The short-lived wake fields induced by the head of the bunched beam affect the particles of its tail (head–tail effect). Because of the longitudinal synchrotron oscillations, the beam head and tail periodically change places; the amplitude of the betatron oscillations, which lead to the losses of beam particles, grows indefinitely when the resonance conditions are met. Figures 1a shows an example of the turn-by-turn current (upper panel) and vertical coordinate (lower panel) measurements for a beam injected into the VEPP-4M electron– positron collider of the Budker Institute of Nuclear Physics, the Siberian Branch of the Russian Academy of Sciences. We see how the beam is lost to a value below the threshold one as the instability grows. In frequency domain, the interaction of the beam with the broadband impedance causes the frequency of the beta-
tron oscillations, mainly the 0th (coherent) mode, to be shifted. Figure 1b shows the computed frequency shift curves for
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