Transverse Coherent Instabilities Research Articles

Imaginary tune split and repulsion single-bunch instability mechanism in the presence of a resistive transverse damper and its mitigation

A resistive transverse damper is often needed in particle accelerators operating with many bunches and it is usually very efficient as it can considerably reduce the necessary amount of nonlinearities needed to reach beam stability through Landau damping. In the CERN LHC for instance, the required current in the Landau octupoles is predicted to be reduced by an order of magnitude for zero chromaticity (for the beam and machine parameters used during the last year of Run 2, in 2018, this corresponded to $\ensuremath{\sim}2000\text{ }\text{ }\mathrm{A}$ without damper and $\ensuremath{\sim}200\text{ }\text{ }\mathrm{A}$ with damper, knowing that the maximum current available in the Landau octupoles is $\ensuremath{\sim}550\text{ }\text{ }\mathrm{A}$). However, a resistive transverse damper also destabilizes the single-bunch motion below the transverse mode coupling instability intensity threshold (for zero chromaticity), introducing a new kind of instability, which has been called ITSR instability (for imaginary tune split and repulsion). Until now, only one type of impedance-driven transverse coherent instability has been explained for a single bunch in a circular particle accelerator, at zero chromaticity and without a multiturn wake: the transverse mode coupling instability. A transverse mode coupling instability can also be observed in the presence of Landau damping, beam-beam, electron cloud or space charge. However, the ITSR instability exhibits a different mechanism, which is not due to mode coupling. The purpose of this article is to explain in detail both this new instability mechanism and its mitigation using a simplified analytical model, which has been carefully benchmarked, using the pyheadtail macroparticle tracking code, by Oeftiger (one of the code's developers).

Vlasov description of the effects of nonlinear chromaticity on transverse coherent beam instabilities

A theoretical analysis of transverse coherent beam instabilities in the presence of nonlinear chromatic effects.

Transverse beam instabilities in the presence of linear coupling in the Large Hadron Collider

In the past, transverse coherent instabilities have been observed at the Hadron-Electron Ring Accelerator (HERA) proton ring that were instigated by the presence of linear coupling. Linear coupling can also potentially explain some transverse instabilities that were observed in the Large Hadron Collider (LHC) in both run I and run II, however a detailed description of the destabilizing mechanism of linear coupling was not known at the time. A study into the effect of linear coupling on transverse beam stability was carried out, and a new mechanism that could incite transverse instabilities by causing a loss of Landau damping has been found. The study includes time domain simulations with PyHEADTAIL and frequency domain computations based on analytical approaches, and was then verified by measurements with a single proton bunch in the LHC.

Influence that the nekhoroshev criterion has on dynamical aperture of circular accelerators with octupole lens families

Russian mathematician N. Nekhorochev has shown that, if some conditions are valid (the Nekhoroshev criterion), the dynamical system describing isolated nonlinear resonance is stable (stability according to Nekhoroshev). Here we examine the influence of the Nekhoroshev criterion on the dynamical aperture (DA) of an accelerator ring that has two octupole lens families for increasing the spread of betatron frequencies and suppressing transverse coherent instabilities. We have designed rings with two lattices: one lattice with a strong modulation of the beta function (which allows us to satisfy to the Nekhoroshev criterion) and a second one which does not satisfy the Nekhoroshev criterion. For both rings we calculate the dependence of the DA on the current in the octupole lens families in the presence of systematic and random errors of a magnetic field. Calculations have shown that, in both rings, the DA is diminished with an increase in the current; however in the first ring this diminishment is slower than in the second one.

Fast transverse multibunch coherent instabilities in a beam with a quasi-uniform filling

We study effects of the long-range wakefield memory on multibunch transverse coherent instabilities of a beam in a storage ring. We assume that the oscillation rise times substantially exceed the frequency of small synchrotron oscillations of particles. Despite the eigensolution spectrum due to the wake memory and because of essential singularity in the oscillation frequency of the function defining the dispersion equation, the amplitudes of coherent oscillations of the beam bunches non-exponentially depend on time. Such beam break-up like instabilities are always suppressed by Landau damping, or by a single bunch feedback damping system. The instability threshold is determined by an acceptable level of coherent oscillations of the beam.

Transverse coherent instability of a bunch in a rectangular potential well

A theory of transverse instability of a bunch in a rectangular potential well is developed. A series of equations adequately describing the instability is derived and solved both analytically and numerically. The dependence of the instability growth rate and threshold on bunch factor is investigated for various beam coupling impedances. The theory is applied to the Fermilab recycler ring.

Simple model for multibunch transverse coherent instabilities in a beam containing a gap

We use the model with exponentially decaying wakes to study transverse multibunch instabilities in a beam where a uniformly filled train of bunches is followed by the gap which is empty of bunches. Stability of both betatron and synchrobetatron modes is inspected. Contrary to cases of uniformly filled beams, the amplitudes of multibunch eigenmodes in such a beam grow towards the end of the train. This amplification of oscillation amplitudes along the beam can limit the beam performance in high-current operation of accelerators.

Instability phenomena of electron-cooled ion beams at COSY

At the cooler synchrotron COSY electron cooling is used after stripping injection of H− or D− ions in order to prepare phase-space-dense ion beams before acceleration to a requested energy. The electron-cooled beam has been successfully applied for specific external experiments. In addition, stacking of an electron cooled beam at injection could significantly increase the stored beam intensity. Transverse coherent instabilities due to beam–wall interaction occurring at higher intensities could be cured through chromaticity correction either by introducing more Landau damping or by applying an active transverse feedback system. This led to an increase in intensity and stability of a cooled beam.

Beam instability due to higher-order modes of APS cavities in the Tristan accumulation ring

Shifts of resonant frequencies of the APS cavity were measured as a function of the tuner position and cavity temperature. From this measurement we found that cavity temperature warm-up plays an important part concerning coherent instability. There was evidence that the accumulation current was limited by resonance with higher-order modes. We could identify which cavity mode was responsible for the transverse coherent instability.

Tackling Transverse Coherent Instabilities of Co- and Counter-Rotating Bemis in the CERN Antiproton Accumulator

In the CERN Antiproton Accumulator, transverse instabilities set in at circulating intensities as low as 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sup> p(p), mainly because of the unusually small variation of Q vs. momentum. The bunched p "test" beam is lost due to head-tail instabilities, and vertical coasting beam modes of the p stack lead to an intolerable emittance growth. Based on estimated AA transverse impedances, a fairly simple feedback system was built. Particular features are (i) low power requirements (10 W); (ii) housing the electronics outside the tunnel; (iii) a "double damper" arrangement enabling the system to tackle simultaneously the p stack and the counter-rotating p test beam; (iv) the system's use for controlled beam blow-up to determine machilne apertures. Whereas the measured growth rates match the resistive wall impedance, significantly higher damping rates are required to eliminate all coasting beam modes, for yet unknown reasons.

Characteristics of Magnetic Focusing and Chromaticity Correction System for TARN

TARN is designed by a separated function F-D- lattice. Its main magnet system consists of eight dipole and sixteen quadrupole magnets. The relatively lower injection energy of TARN (ß ≃ 0.134) leads to large transverse coupling impedance and the relatively smaller intensity limit from transverse coherent instability (6 × 108 ions/pulse). In order to surmount the instability by Landau damping, a chromaticity control system with twelve sextupole magnets are designed and fabricated. The field properties of all the magnets are measured precisely before alignment and the result is taken into account by the calculation with the computer code SYNCH. The closed orbit is obtained by iteration and the nonlinear elements such as sextupole magnets are linearized in the neighbourhood of the closed orbit. The work line is also experimentally studied by an RF knock-out method. The chromaticities of TARN without correction sextupole magnets were measured at -1.59 and -0.47 in horizontal and vertical directions, respectively.

The 50 MEZ Transverse Feedback System in the CERN ISR

One of the intensity limits in the ISR is imposed by the transverse coherent instability. The intensity at which the instability occurs may be raised by Landau damping, i.e. increasing the tune spread of the stacked beam. However, due to non linear resonances, the maximum tune spread is limited. A vertical feedback system which detects and damps the first eight modes of the instability has succeeded in increasing the intensity limit by a factor of ~1.6. Recently this factor has once again become insufficient due to the increase in intensity resulting from improvements in the longitudinal density and vacuum system. A new 50 MHz feedback system has now been installed which damps the first 166 modes of the instability. Hence at low chromaticity values the critical intensity is raised by around another factor of two. The electronic gain of this system decreases with frequency in order to limit the blow-up of vertical oscillations due to electronic noise and to reduce phase errors at high frequencies. The 50 MHz system has been used to explore the ISR vacuum limit to intensities of 39 A.

Stabilization of the transverse coherent resistance instability by automatic correction

Stabilization of the transverse coherent resistance instability by automatic correction

Operation and Performance of the University of Wisconsin - Physical Sciences Laboratory Electron Storage Ring

A 240 MeV electron storage ring has been in operation at the Physical Sciences Laboratory of the University of Wisconsin for one year. The storage ring injector is a 50 MeV FFAG electron synchrotron. The bunched beam from the synchrotron is injected into the storage ring in a single turn. Radio-frequency capture is accomplished by using the signal from the bunched beam as the master oscillator during capture. Using this method, high capture efficiency is achieved. A useful consequence of the method of radio-frequency capture is the damping of the coherent synchrotron oscillation instability. The beam may be accelerated, or decelerated, to any energy within the capability of the ring - 10 MeV to 240 MeV. The vacuum system operates at a pressure in the mid 10-10 range allowing lifetimes of many hours for low intensity beams. During the first year of operation several interesting effects have been observed. Among these were photo etching of metal from the vacuum chamber by synchrotron radiation and enhanced beam loss due to scattering from ions trapped in the electron beam. The beam also exhibits a transverse coherent instability that violates the Courant-Sessler criteria for stability.

Transverse Coherent Resistive Instabilities of Azimuthally Bunched Beams in Particle Accelerators

The transverse electromagnetic coupling of bunches of particles with each other is investigated theoretically, and shown to incorporate the possibility (due to the effect of imperfectly conducting vacuum chamber walls) of coherent instability even when the longitudinal distance between bunches is much larger than the transverse dimensions of the vacuum tank. The modes of oscillation in which the bunches move rigidly are investigated; criteria for stability, and expressions for the small amplitude growth rates under unstable conditions are presented. The case of a single bunch is considered in detail and demonstrated to be stable (even in the absence of Landau damping) provided v lies between an integer and the next higher half-integer, where v is the number of transverse free betatron oscillations occurring in one revolution; for many bunches which are sensibly different in intensity (a criterion for this is presented), all modes are stable provided v satisfies the same restriction. For equally spaced bunches of equal numbers of particles, approximately half the modes are unstable without Landau damping. Numerical examples are presented covering some intermediate situations.

Transverse coherent instability of a charged particle bunch

Transverse coherent instability of a charged particle bunch