Transverse mode coupling instability of bunched beam is investigated in the paper at different form of the bunches with space charge included. Equation of transverse motion of the bunch in parabolic potential well of synchrotron oscillations is derived and analysed. The bunch of constant density (flat bunch) is examined in detail to make comparison with the square well model. It is shown that both models result in very close instability thresholds of the flat bunch. Then different form bunches are investigated in the parabolic potential well. It is shown that decrease of the bunch r.m.s length leads to the growth of its threshold, that is the flat bunch model gives only a minimal estimation of the threshold. The results are treated in terms of Landau damping due to spread of the space charge tune shift.
Transverse mode-coupling instability (TMCI) is known to limit bunch intensity. Since space charge (SC) changes coherent spectra, it affects the TMCI threshold. Generally, there are only two types of TMCI with respect to SC: the vanishing type and the strong space charge (SSC) type. For the former, the threshold value of the wake tune shift is asymptotically proportional to the SC tune shift, as it was first observed twenty years ago by M. Blaskiewicz for exponential wakes. For the latter, the threshold value of the wake tune shift is asymptotically inversely proportional to the SC, as it was s…
Transverse mode coupling instability of a bunch with space charge and wake field is considered within the frameworks of the boxcar model. Eigenfunctions of the bunch without wake are used as a basis for the solution of the equations with the wake field included. A dispersion equation for constant wake is presented in the form of an infinite continued fraction and also as the recursive relation with an arbitrary number of the basis functions. Realistic wake fields are considered as well including resistive wall, square, and oscillating wakes. It is shown that the TMCI threshold of the negative …
Transverse mode coupling instability of a bunch with space charge is considered in frameworks of the boxcar model. Presented results demonstrate a monotonous growth of the TMCI threshold at increasing space charge tune shift, and do not support the supposition that the monotony can be violated at a higher SC.
Transverse mode-coupling instability (TMCI) with a high-frequency resonator wake is examined by the Nested Head-Tail Vlasov solver (NHT), where a Gaussian bunch in a parabolic potential (GP model) is represented by concentric rings in the longitudinal phase space. It is shown that multiple mode couplings and decouplings make impossible an unambiguous definition of the threshold, unless Landau damping is taken into account. To address this problem, instead of a single instability threshold, an interval of thresholds is suggested, bounded by the low and high intensity ones. For the broadband imp…
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…
The transverse instability of a bunch in a circular accelerator is elaborated in this paper. A new tree-modes model is proposed and developed to describe the most unstable modes of the bunch. This simple and flexible model includes chromaticity and space charge, and can be used with any bunch and wake forms. The dispersion equation for the bunch eigentunes is obtained in form of a third-order algebraic equation. The known head-tail and TMCI modes appear as the limiting cases which are distinctly bounded at zero chromaticity only. It is shown that the instability parameters depend only slightly…
We examine the stability of intense flat bunches in barrier buckets used in the Recycler. We consider some common stationary distributions and show that they would be unstable against rigid dipole oscillations. We then discuss an analytical model for the line density that best describes measured bunch profiles. We include space charge in this model to predict the bunch intensity at which Landau damping would be lost. The dependence of this threshold on the bunch length is studied and related to the results of an experimental study with shorter bunch lengths. The threshold for the microwave ins…
Transverse mode coupling instability of a single bunch caused by oscillating wake field is considered in the paper. The instability threshold is found at different frequencies of the wake with space charge tune shift taken into account. The wake phase advance in the bunch length from 0 up to $4π$ is investigated. It is shown that the space charge can push the instability threshold up or down dependent on the phase advance. Transition region is investigated thoroughly, and simple asymptotic formulas for the threshold are represented.
Conditions for the existence, uniqueness and stability of self-consistent bunch steady states are considered. For the existence and uniqueness problems, simple algebraic criteria are derived for both the action and Hamiltonian domain distributions. For the stability problem, van Kampen theory is used. The onset of a discrete van Kampen mode means the emergence of a coherent mode without any Landau damping; thus, even a tiny couple-bunch or multi-turn wake is sufficient to drive the instability. The method presented here assumes an arbitrary impedance, RF shape, and beam distribution function. …
Electron accelerators and synchrotrons can be operated to provide short emission pulses due to longitudinally compressed or sub-structured electron bunches. Above a threshold current, the high charge density leads to the micro-bunching instability and the formation of sub-structures on the bunch shape. These time-varying sub-structures on bunches of picoseconds-long duration lead to bursts of coherent synchrotron radiation in the terahertz frequency range. Therefore, the spectral information in this range contains valuable information about the bunch length, shape and sub-structures. Based on …
In order to study the single bunch longitudinal instability in BEPCII, experiments on the positron ring (BPR) for the bunch lengthening phenomenon were made. By analyzing the experimental data based on Gao's theory, the longitudinal loss factor for the bunch are obtained. Also, the total wake potential and the beam current threshold are estimated.
We have performed bunch lengthening and microwave instability threshold measurements on the positron ring of the Frascati electron-positron Phi-factory DAPhNE. The results are in a good agreement with earlier analytical predictions and numerical simulations.
Transverse instability of a bunched beam is investigated with synchrotron oscillations, space charge, and resistive wall wakefield taken into account. Boxcar model is used for all-round analysis, and Gaussian distribution is invoked for details. The beam spectrum, instability growth rate and effects of chromaticity are studied in a wide range of parameters, both with head-tail and collective bunch interactions included. Effects of the internal bunch oscillations on the of collective instabilities is investigated thoroughly. Landau damping caused by the space charge tune spread is discussed, an…
Longitudinal collective modes of a bunched beam with a repulsive inductive impedance (the space charge below transition or the chamber inductance above it) are analytically described by means of reduction of the linearized Vlasov equation to a parameter-less integral equation. For any multipolarity, the discrete part of the spectrum is found to consist of infinite number of modes with real tunes, which limit point is the incoherent zero-amplitude frequency. In other words, notwithstanding the RF bucket nonlinearity and potential well distortion, the Landau damping is lost. Hence, even a tiny c…
The paper focuses on two issues important for design and operation of bunch-by-bunch transverse damper in a very large hadron collider, where fast damping is required to suppress beam instabilities and noise induced emittance growth. The first issue is associated with kick variation along a bunch which affects the damping of head-tail modes. The second issue is associated with affect of damper noise on the instability threshold.
We have directly measured THz wakefields induced by a subpicosecond, intense relativistic electron bunch in a diamond loaded accelerating structure via the wakefield acceleration method. We present here the beam test results from the first diamond based structure. Diamond has been chosen for its high breakdown threshold and unique thermoconductive properties. Fields produced by a leading (drive) beam were used to accelerate a trailing (witness) electron bunch which followed the drive bunch at a variable distance. The energy gain of a witness bunch as a function of its separation from the drive…
In this paper, we study single-bunch instabilities observed in the CERN Super Proton Synchrotron (SPS). According to the linearized Vlasov theory, radial or azimuthal mode-coupling instabilities result from a coupling of bunch-oscillation modes, which belong to either the same or adjacent azimuthal modes, respectively. We show that both instability mechanisms exist in the SPS by applying the Oide-Yokoya approach to compute van Kampen modes for the realistic longitudinal impedance model of the SPS. The results agree with macroparticle simulations and are consistent with beam measurements. In pa…
Linear theory of the parametric beam instability or the self-amplification of parametric x-ray radiation (PXR) from relativistic electrons in a crystal is considered taking into account finite emittance of the electron beam and absorption of the radiation. It is shown that these factors change essentially the estimation of threshold parameters of the electron bunches for the coherent X-ray generation. The boundary conditions for the linear theory of the effect is analyzed in details and it is shown that the grazing incidence diffraction geometry is optimal for the growth of instability. Numeri…
Transverse mode coupling instability of a bunch with space charge and wake field is considered in frameworks of the boxcar model. Eigenfunctions of the bunch without wake are used as the basis for solution of the equations with the wake field included. Dispersion equation for the bunch eigentunes is obtained in the form of an infinite continued fraction. It is shown that influence of space charge on the instability essentially depends on the wake sign. In particular, threshold of the negative wake increases in absolute value until the space charge tune shift is rather small, and goes to zero a…
An analytical model of transverse convective instability of a bunch at transition crossing is presented for the microwave case, when the wake is sufficiently short compared with the bunch length. The space charge is assumed to be strong, as it typically is for the low and medium energy synchrotrons. A simple formula for the intensity threshold is obtained and its prediction is compared with available CERN PS data; without a single fitting parameter, a good agreement is demonstrated.
At strong space charge, transverse modes of the bunch core may effectively couple with those of the halo, leading to instabilities well below the core-only transverse mode-coupling threshold.
In laser illuminated dielectric accelerators (DLA) high acceleration gradients can be achieved due to high damage thresholds of the materials at optical frequencies. This is a necessity for developing more compact particle accelerator technologies. The Accelerator on a CHip International Program (ACHIP) funded by the Gordon and Betty Moore Foundation is researching such devices. DESY Hamburg is part of the collaboration. The dedicated accelerator research facility SINBAD is particularly well suited for DLA experiments at relativistic electron energies. High quality beams and short bunch length…
The strength of the electromagnetic fields in the bunch collision at a linear collider will have a significant effect, yielding large numbers of beamstrahlung photons and associated coherent pair production. These effects are limited in the proposed ILC beam parameters which limit the strength of the bunch field to $Υ_{\text{ave}}=0.27$. The CLIC 3 Tev design by comparison has a $Υ_{\text{ave}}=3.34$ yielding huge number of coherent pairs. In terms of the precision physics programs of these proposed colliders there is an imperative to investigate the effect of the strong bunch fields on higher…
The numerical solution of the Vlasov-Fokker-Planck equation is a well established method to simulate the dynamics, including the self-interaction with its own wake field, of an electron bunch in a storage ring. In this paper we present Inovesa, a modularly extensible program that uses OpenCL to massively parallelize the computation. It allows a standard desktop PC to work with appropriate accuracy and yield reliable results within minutes. We provide numerical stability-studies over a wide parameter range and compare our numerical findings to known results. Simulation results for the case of c…
Transverse instabilities of the antiproton beam have been observed in the Recycler ring soon after its commissioning. After installation of transverse dampers, the threshold for the instability limit increased significantly but the instability is still found to limit the brightness of the antiprotons extracted from the Recycler for Tevatron shots. In this paper, we describe observations of the instabilities during the extraction process as well as during dedicated studies. The measured instability threshold phase density agrees with the prediction of the rigid beam model within a factor of 2. …
Here we will derive the general theory of the beam-breakup instability in recirculating linear accelerators, in which the bunches do not have to be at the same RF phase during each recirculation turn. This is important for the description of energy recovery linacs (ERLs) where bunches are recirculated at a decelerating phase of the RF wave and for other recirculator arrangements where different RF phases are of an advantage. Furthermore it can be used for the analysis of phase errors of recirculated bunches. It is shown how the threshold current for a given linac can be computed and a remarkab…
Landau damping of head-tail modes in bunches due to spreads in the tune shift can be a deciding factor for beam stability. We demonstrate that the coherent tune shifts due to reactive impedances can enhance the space-charge induced damping and change the stability thresholds (here, a reactive impedance implies the imaginary part of the impedance of both signs). For example, high damping rates at strong space-charge, or damping of the $k=0$ mode, can be possible. It is shown and explained, how the negative reactive impedances (causing negative coherent tune shifts similarly to the effect of spa…
Producing high-brightness and high-charge (>100 pC) electron bunches at blowout regime requires ultrashort laser pulses with high fluence. The effects of laser pulse heating of the copper photocathode are analyzed in this paper. The electron and lattice temperature is calculated using an improved two-temperature model, and an extended Dowell-Schmerge model is employed to calculate the thermal emittance and quantum efficiency. A time-dependent growth of the thermal emittance and the quantum efficiency is observed. For a fixed amount of charge, the projected thermal emittance increases with decr…
Synchronization of Synchrotron Radiation Bursts during a spatio-temporal Instability in accelerator-Based source
Univ. Lille, CNRS, UMR 8523 - PhLAM - Physique des Lasers Atomes et Molécules（里尔大学）；Inria, Univ. Lille, CNRS, UMR 8524 - Laboratoire Paul Painlevé（法国国家信息与自动化研究所，里尔大学）；Synchrotron SOLEIL（SOLEIL同步辐射中心）
