Beam-Beam Interaction

Understanding beam loss in an accelerator is crucial to accelerator design and operation. Losses contribute to a shorter liftetime of a circulating beam, higher radiation doses to accelerator components, and backgrounds in experiments which use the beam. One source of beam loss is diffusion caused by effects such as beam scattering with residual gas in vacuum chamber, noise in the radio frequency acceleration system and power supplies, and beambeam collisions . We measure the diffusion rate in the Fermilab Tevatron using the flying wire beam profile monitor. We have developed a new technique for interpreting the flying wire data. Using this technique, we measure the proton horizontal diffusion rate for ten stores in the Tevatron during colliding beam operation.

A one-dimensional model was considered to study the effects of the beam-beam force on the coherent dynamics of colliding beams. The key ingredient is a linearized beam-beam kick. Only the quadrupole modes were studied, with the dynamical variables being the 2nd-order moments of the canonical variables q, p. The model is self-consistent in the sense that no higher order moments

Long-range beam-beam collisions may limit the dynamic aperture and the beam lifetime in colliders. Their effect can be compensated by a current-carrying wire mounted parallel to the beam. A compensation scheme based on this principle has been proposed for the Large Hadron Collider (LHC). To demonstrate its viability, a prototype wire was installed at the CERN SPS in 2002. First successful machine experiments explored the dependence of beam loss, beam size, and beam lifetime on the beam-wire distance and on the wire excitation. They appear to confirm the predicted effect of the long-range collisions on the beam dynamics. In 2004, two further wires will become available, by which we can explicitly demonstrate the compensation, study pertinent tolerances, and also compare the respective merits of different beam-beam crossing schemes for several interaction points.

Over the past 2 years the Tevatron peak luminosity steadily progressed and reached the level of 3.15 · 10³² cm² s¹ which exceeds the Run II Upgrade goal. We discuss the collider performance, illustrate limitations and understanding of beam-beam effects and present experimental results of compensation of the beam-beam effects by electron lenses--a technique of great interest for the LHC.

Many nonlinear beam dynamics experiments have been performed in the past year.' We studied motion near the 2-D nonlinear resonances given by v,-2v, =-6 and v, + 2v, = 13. The Hamiltonian for the accelerator operating near these nonlinear resonances can be expressed as

High fidelity charged particle beam dynamics, especially if collisional, require specialized numerical methods. The challenges include the ability to deal with very large particle numbers, long-range electromagnetic forces, and vast spatial and timescales. We developed a novel algorithm to address these challenges. The main characteristics of the algorithm are Strang splitting to separate near and far forces, the fast multipole method to lower the computational cost of the far region, and the Simò integrator to capture all close encounters efficiently in the near region. The algorithm is fully adaptive both in space and time, while maintaining symplecticity to machine precision. Its performance is illustrated with two challenging examples from nonlinear multiparticle beam dynamics, including the first electron cooling simulations based on first principles.

The SuperB project aims at the construction of an asymmetric very high luminosity B-Factory on the Frascati/Tor Vergata (Italy) area, providing a uniquely sensitive probe of New Physics in the flavour sector of the Standard Model. The luminosity goal of 10³ cm² s¹ can be reached with a new collision scheme with 'large Piwinski angle' (LPA) and the use of

In colliding-beam storage rings transverse and longitudinal beam halo is generated, or depleted, by the effect of head-on and long-range beam-beam collisions. Measurements from several past and present lepton or hadron colliders are compared with simulations and analytical models, highlighting a few halo-specific techniques. This overview concludes with an outlook on the future Large Hadron Collider (LHC), where long-range beam-beam collisions are the dominant perturbation of particle motion and beam-beam compensation schemes appear a promising remedy.

We present here the relevant space charge issues for long-term beam storage. The impact on the choice of the working point along with the prediction of the beam loss is discussed for the example of the SIS100. We present a first estimate on the effect of self consistency and discuss the equivalence of space charge, and electron clouds induced ”quasi” incoherent effect.

Intrinsic fourth order space charge resonances may occur in linear as well as in circular accelerators. The fourth order difference resonance ("emittance exchange" or "Montague" coupling-resonance) and the fourth order structure resonance lead to emittance degradation depending on the strength of space charge, the crossing rate through the resonance and the lattice. Based on fully self-consistent simulation with a 2D code in the coasting beam limit, we present scaling laws for the "Montague" resonance and for the fourth order structure resonance in terms of simple power law expressions.

During the recent years of LHC operation, we analysed the situation of beam instrumentation and the need to optimize it for beam-beam studies. The most important beam instrumentation devices will be highlighted and modifications or optimizations will be suggested. A complete wish list will be presented to make sure we will be ready after LS1 (Long Shutdown 1) to study the beambeam effect in a more complete way.

The structure under consideration represents a set of long thin parallel wires which are placed in a plane with fixed spacing. The wires can exhibit a limited conductivity. If the period of the structure is much less than the typical wavelength, the structure's influence can be described with help of the averaged boundary conditions [1]. The main attention is given to the case when the bunch flies through the grid in the orthogonal direction. Radiation of charged particle bunch which have small transversal size and limited longitudinal one is studied. Analytical expressions for volume and surface waves are given for the bunches with arbitrary longitudinal profile. A separate analysis is performed for the particular case of the plane which is ideally conducting in only one direction. It is shown that the surface wave is similar, in some way, to the radiation field of the bunch moving in a wire metamaterial [2]. It is demonstrated that the detection of surface waves can be used to estimate the longitudinal sizes of bunches. Typical numerical results for bunches of different shapes and structures with different parameters are given.

We report on first experience with colliding electron and proton beams in HERA (see also [2]). In 1992, the first year of operation, HERA has delivered some 60(nb)-' of e-p Luminosity to the experiments Hl and ZEUS. The beam energies amounted to 26GeV and 820GeV. A maximum luminosity of 2.2. 102gcm-2s-1 has been achieved by colliding a train of nine electron bunches against nine proton bunches. A complete collection of data is contained in reference[l]. The beams could be brought into and held in collision without problems. The lifetime of the proton beam in collision is as long as 50h. This requires both careful matchingof the electron and proton beam cross sections and also that the two orbits coincide within N 0.2a beam size at the interaction point. The proton beam suffered a beam-beam tune shift of up to AQz N 0.0018. This is close to the limit which was assumed in the design of HERA. Nonetheless, there is only little degradation in the proton beam quality in collision. Under these conditions, the proton beam fills could be stored and be made available for collision for some 24h in HERA.

A transverse coherent amplitude growth is occasionally detected in the HERA proton ring for small negative values of the chromaticities. This phenomenon has been carefully studied, and the characteristic behaviour of an headtail instability has been evidenced. The overall transverse impedance of the machine is now under investigation. Systematic growth rate measurements were performed during the machine studies of November 1994; they were repeated in December 1995 also in the presence of controlled linear coupling which, in the mean time, had shown to be a crucial ingredient for the instability to occur. The results of these measurements will be shown: they were found reasonably consistent among each other, therefore allowing us to give an estimate of the effective transverse impedance of HERA-p.

In high brightness colliders the tune spread due to the collisions has a significant impact on the quality of the beams. The impact of the working point on emittance growth and beam lifetime has been observed in beam experiments in LHC. Strong-strong beam-beam simulations that were accomplished to better understand such observations are shown. Compared to experiments, wide ranged parameter scans can be done easily. Tune footprints and scans of the emittance growth obtained from simulations are discussed. Three cases are considered: Very high intensity, moderate intensity and collisions with separated beams.

The SuperB project aims at the construction of an asymmetric very high luminosity B-Factory on the Frascati/Tor Vergata (Italy) area, providing a uniquely sensitive probe of New Physics in the flavour sector of the Standard Model. The luminosity goal of 10 36 cm-2 s-1 can be reached with a new collision scheme with "large Piwinski angle" (LPA) and the use of "crab waist sextupoles" (CW) [1]. A LPA&CW Interaction Region (IR) has been successfully tested at the DA NE-Factory at LNF-Frascati in 2008 [2]. The LPA&CW scheme, together with very low *, will allow for operation with relatively low beam currents and reasonable bunch length, comparable to those of PEP-II and KEKB. In the High Energy Ring (HER), two spin rotators will bring longitudinally polarized beams into collision at the IP. The lattice has been designed with a very low intrinsic emittance and is quite compact, less than 2 km long. The tight focusing requires the final doublet quadrupoles to be very close to the IP and very compact. A Conceptual Design Report was published in March 2007 [3], and beam dynamics and collective effects R&D studies are in progress in order to publish a Technical Design Report by the end of 2010.

Parameters have been studied for a high luminosity e+e-collider operating at the Upsilon 4S that would deliver a luminosity of 1 to 4 x 10 36 /cm 2 /s. This collider, called a SuperB Factory, would use a combination of linear collider and storage ring techniques. In this scheme an electron beam and a positron beam are stored in lowemittance damping rings similar to those designed for a Linear Collider (LC) or the next generation light source. A LC style interaction region is included in the ring to produce sub-millimeter vertical beta functions at the collision point. A large crossing angle (+/-24 mrad) is used at the collision point to allow beam separation. A crab-waist scheme is used to reduce the hourglass effect and restore peak luminosity. Beam currents of 1.8 A at 4 x 7 GeV in 1251 bunches can produce a luminosity of 10 36 /cm 2 /s with upgrade possibilities. Such a collider would produce an integrated luminosity of about 10,000 fb-1 (10 ab-1) in a running year (10 7 sec) at the Υ(4S) resonance. Further possibilities include having longitudinally polarized eat the IR and operating at the J/Psi and Psi' beam energies.

We describe features of the soft-gaussian beam-beam simulation code "TRS" and present sample results for the PEP-II e + e − collider. 1 DESCRIPTION OF THE CODE A basic experimental observation in e + e − colliders in stable operation is that the particle distribution density at the beam core is approximately gaussian, while the density at large amplitudes (a few σ's away from the center) is not gaussian and is much larger than the extrapolation from a gaussian fit to the core [1, 2]. The code TRS (Two-Ring Simulation) [3] is geared to study the beam core of colliding e + e − beams. Although it can be used to study large-amplitude tail distributions, it is very inefficient at doing so, since the vast majority of the CPU time is spent simulating the gaussian core. The "engine" of this code is similar to that in other codes [4, 5, 6, 7]. The code is written in FORTRAN 77, and is yet to be documented in detail.

We consider the combined effects of the beam-beam interaction and the lattice nonlinearities for one specific design of the muon collider ring. The beam-beam interaction is represented by a thick gaussian lens, and the ring is described by a 9th-order Taylor map. At the single-particle level we compare the tune footprints and the dynamic aperture with and without the beam-beam

We present a summary of a fairly extensive study of beam-beam issues that arise in the design of PEP-II. Most of these studies are carried out with "strong-strong" multiparticle tracking simulations. We focus on: choice of nominal beam- beam parameter, strength of the parasitic collisions, injection issues, performance and tradeoffs with unequal beam-beam parameters. We comment only briefly on beam

The electron-positron collider DAÈNE, the Italian È factory, has been recently upgraded in order to implement an innovative collision scheme based on large crossing angle, small beam sizes at the crossing point, and compensation of beam-beam interaction by means of sextupole pairs creating a ''crab-waist'' configuration in the interaction region. Experimental tests of the novel scheme exhibited an increase by a factor of 3 in the peak luminosity of the collider with respect to the performances reached before the upgrade. In this Letter we present the new collision scheme, discuss its advantages, describe the hardware modifications realized for the upgrade, and report the results of the experimental tests carried out during commissioning of the machine in the new configuration and standard operation for the users.

1 Permanent address: LPP JINR, Dubna 141980 Russia Abstract ν′y Under certain circumstances such as large chromatic tune modulation, bunch length comparable with the betafunction, crossing at an angle or finite dispersion at the interaction points the beam-beam interaction can be a source of the synchro-betatron coupling. In the present report the effect of these factors on the p-bar stability in the Tevatron Run II configuration is considered. ν′x

In recent years several measurements of the SPS nonlinear chromaticity have been performed in order to determine the non-linear optics model of the SPS machine at injection energy for different cycles. In 2006 additional measurements have been performed at injection and during the ramp for the cycle used to accelerate the LHC beam. New and more robust matching algorithms have been developed in 2006 to fit the model to the measurements up to arbitrary chromatic order. In this paper we describe the algorithms used in the analysis of the data and we summarize and compare the results from all experiments.

Deuteron and gold beams have been accelerated to a collision energy of √ s = 200 GeV/u in the Relativistic Heavy Ion Collider (RHIC), providing the first asymmetric-species collisions of this complex. Necessary changes for this mode of operation include new ramping software and asymmetric crossing angle geometries. This paper reviews machine performance, problems encountered and their solutions, and accomplishments during the 16 weeks of ramp-up and operations.

Colliding beams with equal intensities and close tunes in either plane can give rise to coherent beam-beam modes. If the beam-beam interaction is the dominant source for transverse nonlinearities, the frequencies of the coherent modes can be outside the continuous frequency spectrum, and are therefore not Landau damped. Coherent beam-beam modes were observed in RHIC in a dedicated experiment and in routine operation. We describe the machine and beam conditions that gave rise to these modes.

During Run-8, the Relativistic Heavy Ion Collider (RHIC) provided collisions of spin-polarized proton beams at two interaction regions. Helical spin rotators at these two interaction regions were used to control the spin orientation of both beams at the collision points. Physics data were taken with different orientations of the beam polarization. We present recent developments and improvements as well as the luminosity and polarization performance achieved during Run-8.

The hourglass effect arises due to a coupling between the longitudinal and transverse bunch planes. This coupling will result in a charge density distribution that will vary parabolically through the Interaction Point (IP). Here a method of analytically determining the electric field a particle receives from a charge density distribution which varies parabolically when centred at the IP, is derived for a 2D transverse model of a Gaussian bunch.

An intra-beam scattering (IBS) is the limiting factor of the luminosity lifetime for RHIC operating with heavy ions. In order to suppress the IBS we designed and implemented new lattice with higher betatron tunes. This lattice had been developed during last three years and had been used for gold ions in yellow ring of the RHIC during d-Au part of the RHIC Run-8. The use of this lattice allowed both significant increases in the luminosity lifetime and the luminosity levels via reduction of betastars in the IPs. In this paper we report on the development, the tests and the performance of IBSsuppression lattice in RHIC, including the resulting increases in the peak and the average luminosity. We also report on our plans for future steps with the IBS suppression.

A proposal for the new high luminosity L=10 scm polarized electron proton/3He and other un-polarized heavy ions eRHIC based on Electron Recovery Linac (ERL), assumes a location in the existing tunnel of the operating Relativistic Heavy Ion Collider (RHIC). Requests of the experiments for the interaction region are very challenging: allow detection of neutrons, allow deep virtual scattering for protons-electron collisions, detection of partons with lower momentum, etc. We present an interaction region (IR) design with a vey high focusing where at the collision point IP of 5 cm, and a 10-mrad collision angle between electrons and ions using the crab cavities. We are introducing a combined function magnet for the first element in the high focusing triplet configuration to provide neutron and the lower energy parton detection, and allow at 4.5 cm distance passage of electrons through free magnetic field region. The 200 T/m gradient quadrupoles provide very small beam size at the IP and ...

At the Cornell Electron-Positron Storage Ring Test Accelerator (CesrTA) experiments have been studying the interaction of the electron cloud (EC) with 2.1 GeV stored electron and positron beams. These experiments are intended to characterize the dependence of beam–EC interactions on various beam parameters, such as bunch spacing and vertical chromaticity. Most experiments were performed with 30 or 45-bunch trains, at a fixed current of 0.75 mA/bunch. Earlier experiments with positrons had varied the bunch spacing between 4 and 56 ns at three different vertical chromaticity settings. More recent measurements have included electron-bunch trains to contrast the build up of EC between electron and positron beams. The dynamics of the stored beam was quantified using: a gated Beam Position Monitor (BPM) and spectrum analyzer to measure the bunch-by-bunch frequency spectrum of the bunch trains; an x-ray beam size monitor to record the bunch-by-bunch, turn-by-turn vertical size of each bunc...

A cw high power linear accelerator can only work with very low particle losses and structure activation. At low energy, the radio frequency quadrupole (RFQ) is an accelerator element that is very sensitive to losses. To design this structure, a good understanding of the beam dynamics is required. Generally, the reference code PARMTEQM is enough to design the accelerator. TOUTATIS has been written with the goals of cross-checking results and obtaining more reliable dynamics. This paper relates the different numerical methods used in the code. It is time based, using multigrids methods and adaptive mesh for a fine description of the forces without being time consuming. The field is calculated through a Poisson solver and the vanes are fully described, allowing it to properly simulate the coupling gaps and the RFQs extremities. Theoretical and experimental tests are also described and show a good agreement between simulations and reference cases.

Proton beam stability when in collision with high current electron bunches was of foremost concern during the design stages of the HERA collider[l]. In initial commissioning the beam-beam interaction proved to be a key factor in determining the lifetime of the proton beam. It was quickly ascertained[2] that the proton beam lifetime in collision could be substantially increased by both matching the electron and proton beam sizes (a) at the interaction points (IPs) and by carefully centering the beams. Presently, proton beam life times of hundreds of hours are routinely observed. In the near future, the accelerators will be upgraded[3] to include new low-/3 insertions and to allow for yet higher beam currents. Key factors affecting the stability of colliding proton beams will be described as well as recent experiments performed to explore at high electron beam currents new regimes of the proton beam-beam limit* at HERA.

The Factories'03 ICFA Beam Dynamics Workshop was held at SLAC from October 13 to 16, 2003. The workshop was organized in three working groups. In this report, I summarize the highlights of the working group on interaction-region (IR) design, beam-beam interaction and optics, emphasizing the suggestions for future studies and pointing out the open questions.

Charged particle beams in high energy, high luminosity particle colliders are accompanied by strong and highly nonlinear electromagnetic fields. When two counterrotating beams pass each other these fields give rise to so called ``beam-beam interactions'' with a wide spectrum of negative consequences for the beam dynamics resulting e.g. in particle loss and emittance blow up. In the Large Hadron Collider (LHC) such crossings will occur each turn four times ``head-on'' (once at each interaction point, IP) and fifteen times ``long-range'' on each side of each IP with a small transverse offset. In order to correct for the resulting perturbations a wire compensator is foreseen. In the framework of this thesis the tracking code ``BBTrack'' has been developed and employed to investigate long-range beam-beam interaction and its wire compensation in the CERN LHC (nominal and upgraded). Complementary experimental studies at RHIC at BNL and the CERN SPS ...

The LHC, its luminosity upgrade (HL-LHC), the upgrade of its injectors (LIU), and other high performance storage rings around the world are facing challenging requirements for optics measurements, correction and modelling. This workshop aims to do a review of the existing techniques to measure and control linear and non-linear optics parameters. The precise optics determination has proven to be a key ingredient to improve the performance of the past and present accelerators. From 20 to 22 June 2011 an international workshop, "OMCM," was held at CERN with the goal of assessing the limits of the present techniques and evaluating new paths for improvement.

After the design luminosity had been exceeded in the electron–proton collider HERA, the interaction regions have been rebuilt to boost the luminosity by roughly a factor 4 and are now being commissioned. While the specific luminosity is increased by a reduction of the beta functionsat the interaction point and by a reduced horizontal electron emittance, the beam-beam tune shift of the e-beam will be increased and the vertical proton beta function at the interaction point will become comparable to the proton bunch length. To analyze these new beam dynamical conditions, the beam-beam force's effect on the tune spread and on high order resonances under the presence of the hourglass effect has been investigated, and accelerator studies have been performed in conditions for which the tune spread and the resonance strength are comparable to the luminosity upgrade parameters. In these experiments the nominal beam-beam parameter per experiment has been pushed to a record high of 0.5. Ba...

The electron-positron collider DAÈNE, the Italian È factory, has been recently upgraded in order to implement an innovative collision scheme based on large crossing angle, small beam sizes at the crossing point, and compensation of beam-beam interaction by means of sextupole pairs creating a ''crab-waist'' configuration in the interaction region. Experimental tests of the novel scheme exhibited an increase by a factor of 3 in the peak luminosity of the collider with respect to the performances reached before the upgrade. In this Letter we present the new collision scheme, discuss its advantages, describe the hardware modifications realized for the upgrade, and report the results of the experimental tests carried out during commissioning of the machine in the new configuration and standard operation for the users.

Precision measurement and control of the betatron tunes and betatron coupling in the Relativistic Heavy Ion Collider (RHIC) are required for establishing and maintaining both good operating conditions and, particularly during the ramp to high beam energies, high proton beam polarization. While the proof-of-principle for simultaneous tune and coupling feedback was successfully demonstrated earlier, routine application of these systems has only become possible recently. Following numerous modifications for improved measurement resolution and feedback control, the time required to establish full-energy beams with the betatron tunes and coupling regulated by feedback was reduced from several weeks to a few hours. A summary of these improvements, select measurements benefitting from the improved resolution and a review of system performance are the subject of this report.

The performance of the Large Hadron Collider (LHC) and its minimum crossing angle are limited by long-range beam-beam collisions. Wire compensators can mitigate part of the long-range effects. We perform simulations to explore the efficiency of the compensation at possible wire locations by examining the tune footprint and the dynamic aperture. Starting from the weak-strong simulation code BBTrack we developed a new Lyapunov calculation tool, which seems to better diagnose regular or chaotic particle behavior. We also developed faster ways to execute the simulation and the post-processing. These modifications have allowed us to study different wire positions (longitudinal and transverse), varying wire currents, several wire shapes, and a range of beam-beam crossing angles, in view of a prototype wire installation in the LHC foreseen for 2014/15. Our simulations demonstrate that the wire can provide a good compensation, including for reduced crossing angle. Among the benefits of an L...

The electron-positron collider DAÈNE, the Italian È factory, has been recently upgraded in order to implement an innovative collision scheme based on large crossing angle, small beam sizes at the crossing point, and compensation of beam-beam interaction by means of sextupole pairs creating a ''crab-waist'' configuration in the interaction region. Experimental tests of the novel scheme exhibited an increase by a factor of 3 in the peak luminosity of the collider with respect to the performances reached before the upgrade. In this Letter we present the new collision scheme, discuss its advantages, describe the hardware modifications realized for the upgrade, and report the results of the experimental tests carried out during commissioning of the machine in the new configuration and standard operation for the users.

During the normal operation period in the Pohang Light Source (PLS) storage ring, the spontaneous bunch length oscillation or beating is generated by the nonlinear effects of the RF noise whose frequency is much lower than the bifurcation frequency. Due to the bunch length beating, we can not supply the uniform intensity beams to users. We have described the observed bunch length beating and its mechanism in the PLS storage ring with a simulation.

At KEKB, a dedicated machine experiment on crab crossing has been carried out for about 4.5 months this year. Some of the beam-beam effects observed with crab crossing, which include a beam lifetime issue, are discussed in comparison with those with a finite crossing angle of ±11mrad.

We introduce a symplectic method to handle a large and finite crossing angle in the beam-beam interaction. This method has been implemented in a parallel computer program to simulate three-dimensional effects in the beam-beam interaction. Our simulation results are compared with the known analytical solutions, the simulations using the Lorentz boost and experimental observations.