This note finds results for the intrabeam scattering growth rates for a bi-gaussian distribution. The bi-gaussian distribution is interesting for studying the possibility of using electron cooling in RHIC. Experiments and computer studies indicate that in the presence of electron cooling, the beam distribution changes so that it developes a strong core and a long tail which is not described well by a gaussian, but may be better described by a bi-gaussian. Being able to compute the effects of intrabeam scattering for a bi-gaussian distribution would be useful in computing the effects of electron cooling, which depend critically on the details of the intrabeam scattering. The calculation is done using the reformulation of intrabeam scattering theory given in [1] based on the treatments given by A. Piwinski [2] and J. Bjorken and S.K. Mtingwa [3]. The bi-gaussian distribution is defined below as the sum of two gaussians in the particle coordinates $x,y,s,p_x,p_y,p_s$. The gaussian with the smaller dimensions produces most of the core of the beam, and the gaussian with the larger dimensions largely produces the long tail of the beam. The final result for the growth rates are expressed as the sum of three terms which can be interperted respectively as the contribution to the growth rates due to the scattering of the particles in the first gaussian from themselves, the scattering of the particles in the second gaussian from themselves, and the scattering of the particles in the first gaussian from the particles in the second gaussian.
The proposed High-Energy LHC project presents an unusual combination of strong synchrotron radiation (SR) damping and intrabeam scattering (IBS), which is not seen in present-day hadron colliders. The subject of investigation reported in this paper was the simulation of beam-beam effect for the HE-LHC parameters. Parameters of SR and IBS are calculated, and the luminosity evolution is simulated in the absence of beambeam interaction. Then, a weak-strong numerical simulation is used to predict the effect of beam-beam interaction on particle losses and emittance evolution.
In April 2000 the single bunch energy spread, bunch length, horizontal emittance, and vertical emittance were measured as functions of current in KEK's ATF damping ring. In this report the measurement results are analyzed in light of intrabeam scattering theory. The measurements are found to be relatively consistent with theory, although the measured effects appear to be stronger than theory. In addition, the factor of 3 growth in vertical emittance at a current of 3 mA does not seem to be supported.
Electron cooling that results when a bunch of electrons overlaps a bunch of ions , with both bunches moving at the same velocity, may be considered to be an intrabeam scattering process. The process is similar to the usual intrabeam scattering, where the ions scatter from each other and usually results in beam growth. An important difference is that in electron cooling the mass of the ion is different from and much larger than the mass of the electron. This difference considerably complicates the intrabeam scattering theory. It introduces a new term in the emittance growth rate, which vanishes…
At the Accelerator Test Facility (ATF) at KEK intrabeam scattering (IBS) is a strong effect for an electron machine. It is an effect that couples all dimensions of the beam, and in April 2000, over a short period of time, all dimensions were measured as functions of current. In this report we derive a simple relation for the growth rates of emittances due to IBS. We apply the theories of Bjorken-Mtingwa, Piwinski, and a formula due to Raubenheimer to the ATF parameters, and find that the results all agree (if in Piwinski's formalism we replace the dispersion squared over beta by the dispersion…
Intrabeam scattering studies with large-emittance-ratio ion beams in the Relativistic Heavy Ion Collider, and implications for the Electron-Ion Collider
Beginning with the general Bjorken-Mtingwa solution for intrabeam scattering (IBS) we derive an accurate, greatly simplified model of IBS, valid for high energy beams in normal storage ring lattices. In addition, we show that, under the same conditions, a modified version of Piwinski's IBS formulation (where dispersion squared over beta has been replaced by the dispersion invariant) asymptotically approaches the result of Bjorken-Mtingwa.
Beginning with the general Bjorken-Mtingwa solution, we derive a simplified model of intrabeam scattering (IBS), one valid for high energy beams in normal storage rings; our result is similar, though more accurate than a model due to Raubenheimer. In addition, we show that a modified version of Piwinski's IBS formulation (where eta squared over beta has been replaced by the dispersion invariant) at high energies asymptotically approaches the same result.
The motivation for the treatment of intrabeam scattering theory given in this paper was to find results which would be convenient for computing the intrabeam scattering growth rates for particle distributions which are more complicated than a simple gaussian. It was shown by A. Piwinski that beam growth rates due to intrabeam scattering can be expressed as a multidimensional integral [1]. It was pointed out by J. Bjorken and S. Mtingwa [2] that the reduction of the multidimensional integral to a 3-dimensional untegral is made easier by writing the integral so that its relativistic transformati…
Intrabeam scattering (IBS) limits the emittance and single-bunch current that can be achieved in electron or positron storage ring colliders, damping rings, and light sources. Much theoretical work on IBS exists, and while the theories have been validated in hadron and ion machines, the presence of strong damping makes IBS in lepton machines a different phenomenon. We present the results of measurements at CesrTA of IBS dominated beams, and compare the data with theory. The beams we study have parameters typical of those specified for the next generation of wiggler dominated storage rings: low…
A beam loss in the superconducting part of the SNS linac has been observed during its commissioning and operation. Although the loss does not prevent the SNS high power operation, it results in an almost uniform irradiation of linac components and increased radiation levels in the tunnel. Multi-particle tracking could neither account for the magnitude of the observed loss nor its dependence on machine parameters. It was recently found that the loss is consistent with the intrabeam particle collisions resulting in stripping of H- ions. The paper describes experimental observations and correspon…
Interplay of space charge and intrabeam scattering in the LHC ion injector chain
European Organization for Nuclear Research (CERN)（欧洲核子研究组织（CERN））；University of Crete（克里特大学）；Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de Santiago de Compostela（圣地亚哥-德孔波斯特拉大学加利西亚高能物理研究所）
We derive a simple relation for estimating the relative emittance growth in x and y due to intrabeam scattering (IBS) in electron storage rings. We show that IBS calculations for the ATF damping ring, when using the formalism of Bjorken-Mtingwa, a modified formalism of Piwinski (where eta squared divided by beta has been replaced by the dispersion invariant), or a simple high-energy approximate formula all give results that agree well. Comparing theory, including the effect of potential well bunch lengthening, with a complete set of ATF steady-state beam size vs. current measurements we find r…
As part of the R\&D for the 50 MeV ThomX Compton source project, we have studied the effect of several beam dynamics processes on the evolution of the beam in the ring. The processes studied include among others Compton scattering, intrabeam scattering, coherent synchrotron radiation. We have performed extensive simulations of a full injection/extraction cycle (400000 turns). We show how each of these processes degrades the flux of photons produced and how a feedback system contributes to recovering most of the flux.
At the Large Hadron Collider (LHC), the interplay between a series of effects, including intrabeam scattering (IBS), synchrotron radiation, longitudinal beam manipulations, two beam effects (beam-beam, e-cloud) and machine non-linearities, can change the population of the core and tails and lead to non-Gaussian beam distributions, at different periods during the beam cycle. By employing generalised distribution functions, it can be demonstrated that the modified non-Gaussian beam profiles have an impact in the beam emittance evolution by itself and thereby to the collider luminosity. This pape…
The ability of laser cooling for relativistic ion beams is investigated. For this purpose, the excitation of relativistic ions with a continuous wave and a pulsed laser is analyzed, utilizing the optical Bloch equations. The laser cooling force is derived in detail and its scaling with the relativistic factor $γ$ is discussed. The cooling processes with a continuous wave and a pulsed laser system are investigated. Optimized cooling scenarios and times are obtained in order to determine the required properties of the laser and the ion beam for the planed experiments. The impact of beam intensit…
Negative hydrogen ions are often used for injecting protons from linacs to storage rings via charge-exchange injection. In this process, the two electrons are stripped by a foil or laser to produce protons which can be merged with an existing beam without significantly affecting its dynamics, allowing high intensities of protons to be accumulated. However, this capability comes with the drawback that the outer electron of an H$^-$ ion has a low binding energy and can easily be stripped away prior to injection. This paper addresses the following stripping mechanisms: interactions with residual …
The evolution of the phase space density of particle beams in external fields is found proceeding from the continuity equation in the six-dimensional (6D) phase space (mu-space). The Robinson theorem, which includes the Liouville theorem as a special case, was proved in a more simple and consistent alternative way valid for arbitrary external fields, averaged fields of the beam (self-generated electro-magnetic fields except intrabeam scattering) and arbitrary frictional forces (linear, nonlinear). It includes particle accelerators as a special case. The limits of the applicability of the Robin…
In storage rings, horizontal dispersion in the rf cavities introduces horizontal-longitudinal (xz) coupling, contributing to beam tilt in the xz plane. This coupling can be characterized by a "crabbing" dispersion term ζa that appears in the normal mode decomposition of the 1-turn transfer matrix. ζa is proportional to the rf cavity voltage and the horizontal dispersion in the cavity. We report experiments at the Cornell Electron Storage Ring Test Accelerator (CesrTA) where xz coupling was explored using three lattices with distinct crabbing properties. We characterize the xz coupling for each…
The emittance growth in the HL-LHC due to beam-beam effects is examined by virtue of strong-strong computer simulations. A model of the transverse damper and the noise level have been tuned to simulate the emittance growth in the present LHC. Simulations with projected HL-LHC beam parameters and crab cavities are discussed. It is shown that with the nominal working point, the large beam-beam tune shift moves the beam into a resonance that causes substantial emittance growth. Increasing the working point slightly is demonstrated to be very beneficial.
In this article we present results of emittance growth measurements in the Tevatron beams. Several mechanisms leading to transverse and longitudinal diffusions are analyzed and their contributions estimated.
We derive evolution equations for the first and second moments of an initially mismatched, coupled, and displaced arbitrary Gaussian phase-space distribution under the influence of decoherence due to amplitude-dependent tune shift. Moreover, we find expressions for the asymptotic values of the beam matrix and the emittance and use them to evaluate error tolerances for injection.
The successful operation of a Two-Beam accelerator based on extended relativistic klystrons hinges upon decreasing the cumulative dipole BBU growth from an exponential to a more manageable linear growth rate. We describe the theoretical scheme to achieve this, and a new experiment to test this concept. The experiment utilizes a 1-MeV, 600-Amp, 200-ns electron beam and a short beamline of periodically-spaced rf dipole-mode pillbox cavities and solenoid magnets for transport. Descriptions of the beamline are presented, followed by theoretical studies of the beam transport and dipole-mode growth.
In order to ensure proper SASE lasing of a fourth Generation light source, one of the goal is to produce an electron beam of small emittance and to conserve it until its used in the machine undulator. One of the non recoverable emittance increase is the collision of the electron beam during its transport with the residual gas. Based on previous work by others, we have derived a useful expression of emittance increase for electrons of any energy and cross check its validity for energies above 100 MeV with an analytical formula.
In a Low Energy Beam Transport line (LEBT), the emittance growth due to the beam's own space charge is typically suppressed by way of neutralization from either electrons or ions, which originate from ionization of the background gas. In cases where the beam is chopped, the neutralization pattern changes throughout the beginning of the pulse, causing the Twiss parameters to differ significantly from their steady state values, which, in turn, may result in beam losses downstream. For a modest beam perveance, there is an alternative solution, in which the beam is kept un-neutralized in the porti…
The Dual-Axis Radiographic Hydrotest (DARHT) facility uses bremsstrahlung radiation source spots produced by the focused electron beams from two linear induction accelerators (LIAs) to radiograph large hydrodynamic experiments driven by high explosives. Radiographic resolution is determined by the size of the source spot, and beam emittance is the ultimate limitation to spot size. Some of the possible causes for the emittance growth in the DARHT LIA have been investigated using particle-in-cell (PIC) codes, and are discussed in this article. The results suggest that the most likely source of e…
In a Low Energy Beam Transport line (LEBT), the emittance growth due to the beam's space charge is typically suppressed by way of neutralization from either electrons or ions, which originate from ionization of the background gas. In cases where the beam is chopped, the neutralization pattern usually changes throughout the beginning of the pulse, causing the Twiss parameters to differ significantly from their steady state values, which, in turn, may result in beam losses downstream. For a modest beam perveance, there is an alternative solution, in which the beam is kept un-neutralized in the p…
Using a particle-in-cell (PIC) code, we investigated the possibilities for emittance growth through the quadrupole magnets of the system used to transport the high-current electron beam from an induction accelerator to the bremsstrahlung converter target used for flash radiography. We found that even highly mismatched beams exhibited little emittance growth (< 6%), which we attribute to softening of their initial hard edge current distributions. We also used this PIC code to evaluate the accuracy of emittance measurements using a solenoid focal scan following the quadrupole magnets. If the bea…
The effect of the transverse self-force in a relativistic beam has been studied in the earlier paper of the author [1]. However, the analysis of [1] missed an important observation and has lead to an incorrect estimate of the emittance growth of the beam when it passes through a long bending magnet. Here we correct that analysis. In particular, we conclude that the emittance growth due to the transverse self-force in a long bend is always much smaller than the emittance growth due to the longitudinal coherent synchrotron radiation (CSR) wake.
The plasma wakefield accelerator may accelerate particles to high energy in a future linear collider with unprecedented acceleration gradients, exceeding the GeV/m range. Beams for this application would have extremely high brightness and, subject to the intense plasma ion-derived focusing, they would achieve densities high enough to induce the plasma ions to collapse into the beam volume. This non-uniform ion density gives rise to strong nonlinear focusing which may lead to deleterious beam emittance growth. The effects of ion collapse and their mitigation has been investigated recently throu…
An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. A new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensi…
Currently, Fermilab Booster accelerates ~4.5E12 protons per pulse (ppp) in 81 bunches from 400 MeV to 8 GeV at 15 Hz to provide beam to multiple HEP experiments and is being upgraded to handle higher beam intensity >6.7E12 ppp at a repetition rate of 20 Hz. In the current mode of operation, we control longitudinal coupled bunch instabilities (LCBI) using combination of passive and active dampers. The issues with LCBI are expected to worsen at higher beam intensities. Here, we would like to investigate at what time in the beam cycle a particular mode is going to originate and how much it contri…
The Dual-Axis Radiographic Hydrotest (DARHT) facility uses bremsstrahlung radiation source spots produced by the focused electron beams from two linear induction accelerators (LIAs) to radiograph large hydrodynamic experiments driven by high explosives. Radiographic resolution is determined by the size of the source spot, and beam emittance is the ultimate limitation to spot size. On the DARHT Axis-II LIA we measure an emittance higher than predicted by theoretical simulations, and even though this axis produces sub-millimeter source spots, we are exploring ways to improve the emittance. Some …
The interaction of the witness beam with the surrounding plasma particles and wakefields was studied. The impli- cations of the elastic scattering process on beam emittance and, emittance evolution under the focusing and acceleration provided by plasma wakefields were discussed. Simulations results from GEANT4 are presented in this paper.
In the framework of the earlier derived dispersion equation, we study induced Smith Purcell (SP) radiation of relativistic electron beam in the absence of a resonator. We offer a new method for calculation of coefficients for partial amplitudes in the case of rectangular grating. Using this method we calculate the growth rate of the SPFEL with a rectangular grating. The growth rate dependences on harmonic number, beam current, observation angle and relativistic factor are presented.
Plasma-based accelerators (PBAs), having demonstrated the production of GeV electron beams in only centimetre scales, offer a path towards a new generation of highly compact and cost-effective particle accelerators. However, achieving the required beam quality, particularly on the energy spread for applications such as free-electron lasers, remains a challenge. Here we investigate fundamental sources of energy spread and bunch length in PBAs which arise from the betatron motion of beam electrons. We present an analytical theory, validated against particle-in-cell simulations, which accurately …
The Integrable Optics Test Accelerator (IOTA) at Fermilab is a small machine dedicated to a broad frontier accelerator physics program. An important aspect of this program is to investigate the potential benefits of the resonance free tune spread achievable with integrable optics to store and accelerate high intensity proton beams for which space charge is significant. In this context, a good understanding of proton beam emittance growth and particle loss mechanisms is essential. Assuming nominal design parameters, simulations show that for a bunched beam, the bulk of emittance growth takes pl…
Beams injected into a linear focusing channel typically have some degree of space-charge nonuniformity. In general, injected particle distributions with systematic charge nonuniformities are not equilibria of the focusing channel and launch a broad spectrum of collective modes. These modes can phase-mix and have nonlinear wave-wave interactions which, at high space-charge intensities, results in a relaxation to a more thermal-like distribution characterized by a uniform density profile. This thermalization can transfer self-field energy from the initial space-charge nonuniformity to the local …
Axial-symmetric magnetic field is often used in focusing of particle beams. Most existing ion Low Energy Beam Transport lines are based on solenoid focusing. Modern accelerator projects utilize superconducting solenoids in combination with superconducting accelerating cavities for acceleration of high-intensity particle beams. Present paper discusses conditions for matched beam in axial-symmetric magnetic field. Analysis allows us to minimize power consumption of solenoids and beam emittance growth due to nonlinear space charge, lens aberrations, and maximize acceptance of the channel. Express…
The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory has been in operation since 2000. Over the past decade, the luminosity in the polarized proton (p-p) operations has increased by more than one order of magnitude. The maximum total beam-beam tune shift with two collisions has reached 0.018. The beam-beam interaction leads to large tune spread, emittance growth, and short beam and luminosity lifetimes. In this article, we review the beam-beam observations during the previous RHIC p-p runs. The mechanism for particle loss is presented. The intra-beam scattering (IBS) co…
In the SSRF Phase-II beamline project, a Superconducting Wiggler (SW) will be installed in the electron storage ring. It may greatly impact on the beam dynamics due to the very high magnetic field. The emittance growth becomes a main problem, even after a well correction of the beam optics. A local achromatic lattice is studied, in order to combat the emittance growth and keep the good performance of the SSRF storage ring, as well as possible. Other effects of the SW are simulated and optimized as well, including the beta beating, the tune shift, the dynamic aperture, and the field error effec…
Alternative acceleration technologies are currently under development for cost-effective, robust, compact and efficient solutions. One such technology is plasma wakefield acceleration, driven by either a charged particle or laser beam. However, the potential issues must be studied in detail. In this paper, the emittance growth of the witness beam through elastic scattering from gaseous media is derived. The model is compared with the numerical studies.
We present a theory that allows us to accurately calculate the distribution functions and the emittance growth of a thermal charged-particle beam after it relaxes to equilibrium. The theory can be used to obtain the fraction of particles, which will evaporate from the beam to form a halo. The calculated emittance growth is found to be in excellent agreement with the simulations.
The resonant generation of relativistic plasma waves and plasma wave guiding by two co-propagating laser pulses has been studied. By proper timing between guiding and driver pulses, a resonant interaction occurs, which generates a high-amplitude plasma wave over a longer length than is possible with either of the laser pulses individually. The growth of the plasma wave is inferred by the measurement of monoenergetic electron beams with low divergence that are not measured by using either of the pulses individually. This scheme can be easily implemented, and allows more control of the interacti…
Random fluctuations in the tune, beam offsets and beam size in the presence of the beam-beam interaction are shown to lead to significant particle diffusion and emittance growth in hadron colliders. We find that far from resonances high frequency noise causes the most diffusion while near resonances low frequency noise is responsible for the large emittance growth observed. Comparison of different fluctuations shows that offset fluctuations between the beams causes the largest diffusion for particles in the beam core.
The numerical noise inherent to particle-in-cell simulation of 3D high intensity bunched beams is studied with the TRACEWIN code and compared with an analytical model by Struckmeier. The latter assumes that entropy growth can be related to Markov type stochastic processes due to temperature anisotropy and the artificial collisions caused by using macro-particles and calculating the space charge effect. The resulting noise can lead to growth of the six-dimensional rms emittance and a suitably defined rms entropy. We confirm the dependence of this growth on the bunch temperature anisotropy as pr…
In this paper we discuss design considerations and beam dynamics challenges associated with laser-driven plasma-based accelerators as applied to multi-TeV-scale linear colliders. Plasma accelerators provide ultra-high gradients and ultra-short bunches, offering the potential for compact linacs and reduced power requirements. We show that stable, efficient acceleration with beam quality preservation is possible in the nonlinear bubble regime of laser-plasma accelerators using beam shaping. Ion motion, naturally occuring for dense beams (i.e., low emittance and high energy) severely damps transv…
