Transverse Mode Coupling Instability Research Articles

Head-tail modes for strong space charge

The head-tail modes are described for the space charge tune shift significantly exceeding the synchrotron tune. A general equation for the modes is derived. The spatial shapes of the modes, their frequencies, and coherent growth rates are explored. The Landau damping rates are also found. The suppression of the transverse mode coupling instability by the space charge is explained.

Resistive wall wakefields in the extreme anomalous skin effect regime

Usual treatments of resistive wall effects in accelerators are limited to the normal skin effect regime of electrical conductivity in metals. Therefore they do not generally apply to the situations when beam-exposed metallic surfaces of the vacuum chamber are held at cryogenic temperatures, where simple metals exhibit anomalous skin effect behavior. These situations occasionally occur in accelerators with cold-bore devices, such as small-gap superconducting undulators. The amount of anomalous resistivity material can be substantial to significantly influence beam dynamics. To accurately estimate these effects, we expand the conventional treatment of resistive wall in accelerators into the extreme anomalous skin effect region. Starting with the surface impedance expressions, we derive resistive wall related quantities commonly used in accelerator physics, such as wake functions, wake potentials, loss factor, etc. in the extreme anomalous skin effect region. We follow with examples for resistive wall generated heat and transverse mode-coupling instability.

Mechanisms for suppressing the transverse mode coupling instability in a circular accelerator

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.

Simulation study of electron cloud induced instabilities and emittance growth for the CERN Large Hadron Collider proton beam

The electron cloud may cause transverse single-bunch instabilities of proton beams such as those in the Large Hadron Collider (LHC) and the CERN Super Proton Synchrotron (SPS). We simulate these instabilities and the consequent emittance growth with the code HEADTAIL, which models the turn-by-turn interaction between the cloud and the beam. Recently some new features were added to the code, in particular, electric conducting boundary conditions at the chamber wall, transverse feedback, and variable beta functions. The sensitivity to several numerical parameters has been studied by varying the number of interaction points between the bunch and the cloud, the phase advance between them, and the number of macroparticles used to represent the protons and the electrons. We present simulation results for both LHC at injection and SPS with LHC-type beam, for different electron-cloud density levels, chromaticities, and bunch intensities. Two regimes with qualitatively different emittance growth are observed: above the threshold of the transverse mode-coupling (TMC) type of instability there is a rapid blowup of the beam, while below this threshold a slow, long-term, emittance growth remains. The rise time of the TMC instability caused by the electron cloud is compared with results obtained using an equivalent broadband resonator impedance model, demonstrating reasonable agreement.

Theory of a feedback to cure transverse mode coupling instability

In this paper an analysis of Transverse Mode Coupling Instability (TMCI) with presence of feedback and chromaticity is performed. It has been clear that a combination of resistive feedback and negative chromaticity allows one to increase current threshold significantly without strong demands on feedback phase. For illustration suppression of TMCI at VEPP-4 and LEP has been investigated.

Transverse beam stability with an “electron lens”

This article is devoted to stability analysis of the antiproton beam interacting with an electron beam in an {open_quotes}electron lens{close_quotes} setup for beam-beam compensation in the Tevatron collider. Electron space charge forces cause transverse {open_quotes}head-tail{close_quotes} coupling within antiproton bunch which may lead to a transverse mode coupling instability (TMCI). We present a theory, analytical studies, and numerical simulations of this effect. An estimate of threshold longitudinal magnetic field necessary to avoid the instability is given. Dependence of the threshold on electron and antiproton beam parameters is studied. {copyright} {ital 1999} {ital The American Physical Society}

Increasing the transverse mode coupling instability threshold by RF quadrupole

Transverse mode coupling instability is one of the major limitations of a single bunch current in storage rings. Until now it has appeared in large electron-positron machines, while its presence in proton colliders has not been observed. This paper describes a theoretical analysis of the effect of longitudinal variation of the betatron tune on the transverse mode coupling instability. This variation can be introduced by an RF quadrupole. In the result, the instability threshold could be significantly increased when a modulation of the betatron frequency is comparable with the synchrotron tune.

Feedback system for elimination of the transverse mode coupling instability

Transverse mode coupling (TMC) instability [1] is one of the major limitations of a single bunch current in large storage rings. This paper is devoted to a theoretical analysis of the effect of transverse feedback systems on TMC thresholds. It presents a space-time formalism for a hollow beam model and time-independent collective interaction. Then, in the framework of a simplified model, the principle of eliminating the TMC by means of a special transverse feedback system is outlined. This approach is then generalized in the form of an algorithm.

Simple model with damping of the mode-coupling instability

Abstract In this paper we use a simple model to study the suppression of the transverse mode-coupling instability. Two possibilities are considered. One is due to the damping of particular synchrobetatron modes, and another due to Landau damping, caused by the nonlinearity of betatron oscillations.

Optimal control of transverse mode coupling instability based on the two particle model

The optimal regulator design technique is applied to asymptotically stabilize the transverse mode coupling instability of a storage ring. The state equations are based on the two particle model. These are a pair of equation sets, one for the first and one for the second half of the synchrotron phase. Each set consists of first-order difference equations in vector-matrix form, with time step equal to the revolution time of the ring. Solution of the discrete Riccati equation gives the optimal gain matrix of the transverse feedback. Computer simulations are carried out to verify its effectiveness. Some modifications necessary to apply it to the real accelerator operation are made. The old methods, the classical output feedback and the reactive feedback, are interpreted from the viewpoint of the optimal control.

Effect of Reactive Feedback on the Transverse Mode Coupling Instability Using the Few-Particles Model and Simulation

For short bunches in electron storage rings the onset of the transverse mode coupling instability usually occurs when the frequency shift of the coherent dipole mode (mode zero) equals around three quarters of the synchrotron frequency. A reactive feedback system has been proposed which maintains the coherent dipole frequency constant and may thereby delay the onset of instability. The influence of this feedback system on the threshold of instability is studied using matrix eigenvalue analysis (few particles model) and a computer simulation code. This analysis shows that for a single localised transverse impedance, the reactive feedback system increases significantly the threshold for instability, provided the betatron phase shift between the kicker and the impedance is properly chosen. Results are also shown for the more realistic case of many localised sources of transverse impedance.

Transverse Instabilities Due to Wall Impedances in Storage Rings

RF voltages are induced by charged particle beams in the impedances of surrounding metallic or dielectric structures. These voltages may reinforce perturbations of the charge distribution and cause instabilities of a beam. Transverse oscillations are particularly dangerous, as the usually small transverse apertures of the vacuum chamber often lead to loss of part or all of the particle beam. In this review, we limit ourselves to a transverse instability of single bunches which has been observed rather recently in large electron positron storage rings and which has become known as transverse turbulence, fast head-tail effect or transverse modecoupling instability.

The Effect of Radiation Damping and Noise on the Transverse Mode Coupling Instability Due to Localized Structures

The transverse mode coupling instability due to localized structures of a storage ring, like RF-cavities, is investigated in presence of radiation damping and quantum excitation for both synchrotron and betatron oscillations. Replacing the Vlasov equation by the Fokker-Planck equation, the longitudinal dynamics can only be described in terms of transition probabilities, whereas the transverse motion of the bunch barycenter remains deterministic. By a numerical solution of the associated integral equation, we obtain better estimates of the instability growth rates and we show the disappearence of the stop-bands associated with very high order dipole modes, which turn out to be damped proportionally to their mode number.

Feedback to Suppress Beam Insiabiiliiies in Future Proton Rings

Criteria for the design of feedback systems to suppress coherent beam instabilities are presented. These address starting amplitudes, diffusion from noise during damping or long storage, and choice of kicker. As a model for future accelerators, specifications of the proposed 20 leV SSC are used to calculate parameters of systems to control expected instabilities. A scenario and hardware to stabilize the transverse mode-coupling instability is examined. The scale of the systems is large but not out of scale with the large ring.