One of the main advantages of proposed by P. Raimondi "Crab Waist" collision scheme is a strong suppression of betatron resonances excited by beam-beam interaction. Some qualitative explanations with numerical examples, describing beam-beam resonances for different collision schemes, were given in arXiv:physics/0702033. This paper can be considered as an "appendix" (additional illustration) to that one. We performed a number of full 2D betatron tune scans (beam-beam simulations) for different collision schemes, so one can easily see how the beam-beam resonances appear and disappear, depending on the colliding conditions.
This document presents in detail the derivation of the formulas that describe the resonance driving terms and the tune spread with amplitude generated by the beam-beam long range interactions and the DC wire compensators in cyclical machines. This analysis make use of the weak-strong approximation.
A blowup of vertical emittance has been observed in particle tracking simulations with beam-beam and lattice misalignments. It was somewhat unexpected, since estimation without lattice errors did not predict such a blowup unless a residual vertical dispersion at the interaction point (IP) is larger than a certain amount. Later such a blowup has been seen in a tracking of lattices without beam-beam effect. A possible explanation of the blowup is given by a Vlasov model for an equilibrium of quadratic transverse moments in the synchrotron phase space. This model predicts such a blowup as a synch…
The diffusion process near low order synchro-betatron resonances driven by beam-beam interactions at a crossing angle is investigated. Macroscopic observables such as beam emittance, lifetime and beam profiles are calculated. These are followed with detailed studies of microscopic quantities such as the evolution of the variance at several initial transverse amplitudes and single particle probability distribution functions. We present evidence to show that the observed diffusion is anomalous and the dynamics follows a non-Markovian continuous time random walk process. We derive a modified mast…
As an extension of previous theoretical study on the coherent structure resonance due to space charge effects [Chao Li and R. A. Jameson, Phys. Rev. Accel. Beams 21, 024204, 2018], this paper aims to demonstrate how the beam, as a whole, is spontaneously affected when the predicted mixed coherent 2nd/4th order structure resonance stop band around $90^{\circ}$ phase advance is crossed. The beam characteristics during the structure resonance crossing, such as the rms emittance growth and the appearance of 2-fold/4-fold structure in phase space, are well explained by the mixture characteristic of…
In DAΦNE, the Frascati e+/e- collider, the crab waist collision scheme has been successfully implemented in 2008 and 2009. During the collision operations for Siddharta experiment, an unusual synchrotron damping effect has been observed. Indeed, with the longitudinal feedback switched off, the positron beam becomes unstable with beam currents in the order of 200-300 mA. The longitudinal instability is damped by bringing the positron beam in collision with a high current electron beam (~2A). Besides, we have observed a shift of \approx 600Hz in the residual synchrotron sidebands. Precise measur…
In this paper we present a quantitative measurement of the change in frequency (tune) with intensity of four transverse resonances in a high intensity Gaussian beam. Due to the non-linear space charge forces present in high intensity beams, particle motion cannot be analytically described. Instead we use the Simulator of Particle Orbit Dynamics (S-POD) and the Intense Beam Experiment (IBEX), two linear Paul traps, to experimentally replicate the system. In high intensity beams a coherent resonant response to both space charge and external field driven perturbations is possible, these coherent …
A formula for the collider luminosity is derived for a head-on collision of two beams with different parameters. Three particular cases are presented: the collision of two identical axially symmetric bunches, the collision of a bunch with a coasting beam, and the collision of two coasting beams. The colliding beams have coinciding longitudinal axes. The formula is valid for colliding both counter propagating and co-propagating ("merging") beams.
For modern high-intensity linear accelerators, the well-known envelope instability and recently reported fourth-order particle resonance impose a fundamental operational limit (i.e., zero-current phase advance should be less than 90 deg). Motivated by the stability of spinning flying objects, we propose a novel approach of using spinning beams to surpass this limit. We discovered that spinning beams have an intrinsic characteristic that can suppress the impact of the fourth-order resonance on emittance growth and the associated envelope instability.
With the help of the linearized perturbation theory, the collective beam instability due to the space charge, modelled by the Vlasov-Poisson equation, is well studied in the former research theoretically in a general sense [Chao Li and R. A. Jameson PRAB, 21, 024204 (2018)], where the related instability is depicted by the "structure resonance". As an extension of the theoretical study, this paper aims to verify the validity of the structure resonance with numerical simulations and to show the basic principles which interpret the interaction between structure resonance and beam in a general se…
We recently used an rf solenoid to study the widths of rf spin resonances with both unbunched and bunched beams of 2.1 GeV_c polarized protons stored in the COSY synchrotron. A map, with unbunched beam at different fixed rf-solenoid frequencies, showed a very shallow possible depolarization dip at the resonance. Next we made frequency sweeps of 400Hz, centered at similar frequencies, which greatly enhanced the dip. But, with a bunched proton beam, both the fixed-frequency and frequency-sweep techniques produced similar maps, and both bunched maps showed full beam depolarization over a wide reg…
We applied Frequency Map Analysis (FMA) - a method that is widely used to explore dynamics of Hamiltonian systems - to beam-beam effects study. The method turned out to be rather informative and illustrative in the case of a novel Crab Waist collision approach, when "crab" focusing of colliding beams results in significant suppression of betatron coupling resonances. Application of FMA provides visible information about all working resonances, their widths and locations in the planes of betatron tunes and betatron amplitudes, so the process of resonances suppression due to the beams crabbing i…
The buildup of low energy electrons in an accelerator, known as electron cloud, can be severely detrimental to machine performance. Under certain beam conditions, the beam can become resonant with the cloud dynamics, accelerating the buildup of electrons. This paper will examine two such effects: multipacting resonances, in which the cloud development time is resonant with the bunch spacing, and cyclotron resonances, in which the cyclotron period of electrons in a magnetic field is a multiple of bunch spacing. Both resonances have been studied directly in dipole fields using retarding field an…
Ion extraction from DECRIS-PM source is simulated by using initial distributions of ions at the extraction aperture obtained with NAM-ECRIS code. Three-dimensional calculations of plasma emissive surface are done and ions are traced in the extraction region. The ion beam profiles show strong aberrations due to shape of plasma meniscus; hollow beam features are reproduced, as well as changes in profiles for different focusing conditions.
In high energy physics, the luminosity is one useful value to characterize the performance of a particle collider. To gain more available data, we need to maximize the luminosity in most collider experiments. With the discussions of tune shift involved the beam dynamics and a recently proposed "crabbed waist" scheme of beam-beam collisions, we present some qualitative analysis to increase the luminosity. In addition, beam-beam tune shifts and luminosities of $e^{+}e^{-}$, $pp$/$p\bar{p}$, and $μ^{+}μ^{-}$ colliders are discussed.
A method proposed to preserve the electron beam polarization at the VEPP-4M collider during acceleration with crossing the integer (imperfection) spin resonance at energy E=1763 MeV has been successfully applied. It is based on full decompensation of the $ 0.6\times3.3$ Tesla$\times$meter integral of the KEDR detector longitudinal magnetic field due to the anti-solenoids 'switched-off'.
We show that the difference resonance driven by the space charge pseudo-octupole of high-intensity beams not only couples the beam core emittances; it can also lead to emittance exchange in the beam halo, which is of relevance for beam loss in high intensity accelerators. With reference to linear accelerators the "main resonance" kz/kxy =1 (corresponding to the Montague resonance 2Qx-2Qy=0 in circular accelerators) may lead to such a coupling and transfer of halo between planes. Coupling of transverse halo into the longitudinal plane - or vice versa - can occur even if the core (rms) emittance…
Beam-beam forces and collision optics can strongly affect beam lifetime, dynamic aperture, and halo formation in particle colliders. Extensive analytical and numerical simulations are carried out in the design and operational stage of a machine to quantify these effects, but experimental data is scarce. The technique of small-step collimator scans was applied to the Fermilab Tevatron collider and to the CERN Large Hadron Collider to study the effect of collisions on transverse beam halo dynamics. We describe the technique and present a summary of the first results on the dependence of the halo…
Space charge is typically one of the performance limitations for the operation of high intensity and high brightness beams in circular accelerators. In the Proton Synchrotron (PS) at CERN, losses are observed for vertical tunes above $Q_y=6.25$, especially for beams with large space charge tune shift. The work presented here shows that this behaviour is associated to structure resonances excited by space charge due to the highly symmetric accelerator lattice of the PS, typical for first generation alternating gradient synchrotrons. Experimental studies demonstrate the dependency of the losses …
Crab crossing scheme is an essential collision scheme to achieve high luminosity for the future colliders with large crossing angles. However, when bunch length of one or both colliding beams is comparable with the wavelength of the crab cavity voltage, the nonlinear dependence of the crabbing kick may present a challenge to the beam dynamics of the colliding beams and impact the beam quality as well as the luminosity lifetime. In this paper, the results of nonlinear dynamics in the crab crossing scheme are presented, using both analytical and numerical studies. The result indicates that highe…
Various seeding configurations have being proposed for frequency up-conversion of the electron beam density distribution, in which the energy spread, may however hinder the harmonic generation efficiency. In this Letter, a method for cooling the electron beam energy spread by off-resonance seed laser modulation is described, using a transversely dispersed beam and a modulator undulator with proper transverse gradient. With this novel mechanism, it is shown that the frequency up-conversion efficiency can be significantly enhanced. We present theoretical analysis and numerical simulations for se…
Today's high-intensity laser facilities produce short pulses can, in tight focus, reach peak intensities of $10^{22}\,\mathrm{Wcm}^{-2}$ and, in long focus, wakefield-accelerate electrons to GeV energies. The radiation-reaction--dominated regime, where the recoil from stochastic photon emission becomes significant, can be reached in the collision of such an electron beam with an intense short pulse. Measuring the total energy emitted in gamma rays or the presence of a prominent depletion zone in the electron beam's post-collision energy spectrum would provide strong evidence of radiation react…
In order to measure the mass of the eta meson with high accuracy using the d+p -> 3He+eta reaction, the momentum of the circulating deuteron beam in the Cooler Synchrotron COSY of the Forschungszentrum Juelich has to be determined with unprecedented precision. This has been achieved by studying the spin dynamics of the polarized deuteron beam. By depolarizing the beam through the use of an artificially induced spin resonance, it was possible to evaluate its momentum p with a precision of dp/p < 10-4 for a momentum of roughly 3 GeV/c. Different possible sources of error in the application of th…
In the present paper we study the role of particle interactions on the evolution of a high energy beam. The interparticle forces taken into account are due to space charge alone. We derive the collision integral for a charged particle beam in the form of Balescu-Lenard and Landau and consider its further simplifications. Finally, the transition to the generalized kinetic equation has been accomplished by using the method of adiabatic elimination of fast variables.
Cooling of muon beams for the next-generation lepton collider is necessary to achieve its higher luminosity with fewer muons. In this paper we present an idea to combine ionization cooling with parametric resonances that is expected to lead to muon beams with much smaller transverse sizes. We describe a linear magnetic transport channel where a half integer resonance is induced such that the normal elliptical motion of particles in x-x' phase space becomes hyperbolic, with particles moving to smaller x and larger x' at the channel focal points. Thin absorbers placed at the focal points of the …
Spin resonances can depolarize or spin-flip a polarized beam. We studied 1st and higher order spin resonances with stored 2.1 GeV/c vertically polarized protons. The 1st order vertical (νy) resonance caused almost full spin-flip, while some higher order νy resonances caused partial depolarization. The 1st order horizontal (νx) resonance caused almost full depolarization, while some higher order νx resonances again caused partial depolarization. Moreover, a 2nd order νx resonance is about as strong as some 3rd order νx resonances, while some 3rd order νy resonances are much stronger than a 2nd …
Three methods for handling beam-beam effects in luminosity measurement at ILC are tested and evaluated in this work. The first method represents an optimization of the LEP-type asymmetric selection cuts that reduce the counting biases. The second method uses the experimentally reconstructed shape of the $\sqrt{s'}$ spectrum to determine the Beamstrahlung component of the bias. The last, recently proposed, collision-frame method relies on the reconstruction of the collision-frame velocity to define the selection function in the collision frame both in experiment and in theory. Thus the luminosi…
A novel scheme is proposed for generating a polarized positron beam via multiphoton Breit-Wheeler process during the collision of a 10 GeV, pC seeding electron beam with the other 1 GeV, nC driving electron beam. The driving beam provides the strong self-generated field, and a suitable transverse deviation distance between two beams enables the field experienced by the seeding beam to be unipolar, which is crucial for realizing the positron polarization. We employ the particle simulation with a Monte-Carlo method to calculate the spin- and polarization-resolved photon emission and electron-pos…
We demonstrate the possibility of probing for the first time the fully nonperturbative regime of quantum electrodynamics. By using tightly compressed and focused electron beams in a 100 GeV-class particle collider, beamstrahlung radiation losses can be mitigated, allowing the particles to experience extreme electromagnetic fields. Three-dimensional particle-in-cell simulations confirm the viability of this approach. The experimental forefront envisaged has the potential to establish a novel research field and to stimulate the development of a new theoretical methodology for this yet unexplored…
