29202817
Electron cooling in the presence of undulator fields
The design of the higher-energy cooler for Relativistic Heavy Ion Collider (RHIC) recently adopted a non-magnetized approach which requires a low temperature electron beam [1]. However, to avoid significant loss of heavy ions due to recombination with electrons in the cooling section, the temperature of the electron beam should be high. These two contradictory requirements are satisfied in the design of the RHIC cooler with the help of the undulator fields. The model of the friction force in the presence of an undulator field was benchmarked vs direct numerical simulations with an excellent agreement. Here, we discuss cooling dynamics simulations with a helical undulator, including recombination suppression and resulting luminosities.
55044187
VLASOV AND PIC SIMULATIONS OF A MODULATOR SECTION FOR COHERENT ELECTRON COOLING
Next generation ion colliders will require effective cooling of high-energy hadron beams. Coherent electron cooling (CEC) can in principle cool relativistic hadron beams on orders-of-magnitude shorter time scales than other techniques [1]. We present Vlasov-Poisson and delta-f particlein-cell (PIC) simulations of a CEC modulator section. These simulations correctly capture the subtle time and space evolution of the density and velocity wake imprinted on the electron distribution via anisotropic Debye shielding of a drifting ion. We consider 1D and 2D reduced versions of the problem, and compare the exact solutions of Wang and Blaskiewicz [2] with Vlasov-Poisson and delta-f PIC simulations. We also consider interactions under non-ideal conditions where there is a density gradient in the electron distribution, and present simulations of the ion wake. COHERENT ELECTRON COOLING Coherent electron cooling (CEC) is an exciting new technique for rapidly cooling high-energy hadron beams [1]. CEC begins in the same way as conventional electron cooling, with hadrons (in this case ions) and electrons co-propagating at matched mean velocities. The proposed Brookhaven CEC consists of three sections: a modulator, where the ion imprints a density wake on the electron distribution, an FEL, where the density wake is amplified by an FEL, and a kicker, where the amplified wake interacts with the ion, resulting in dynamical friction for the ion. In this paper we consider only the modulator section. We calculate the wakes in the electron distribution due to the presence of the ions. In the modulator section the ions drift in a nearly uniform distribution of electrons. Although these beams are highly relativistic in the laboratory frame, all velocities are non-relativistic in the “beam frame” drifting with the mean speed of the particles. The response of the electrons is classical Debye shielding, with a few complications. Accelerated electrons have a non-isotropic velocity distribution, and the electron density may also be non-uniform.
37838867
Numerical algorithms for modeling electron cooling in the presence of external fields
The design of the high-energy cooler for the Relativistic Heavy Ion Collider (RHIC) recently adopted a nonmagnetized approach. To prevent recombination between the fully stripped gold ions and co-propagating electrons, a helical undulator magnet has been proposed. In addition, to counteract space-charge defocusing, weak solenoids are proposed every 10 m. To understand the effect of these magnets on the cooling rate, numerical models of cooling in the presence of external fields are needed. We present an approach from first principles using the VORPAL parallel simulation code. We solve the n-body problem by exact calculation of pair-wise collisions. Simulations of the proposed RHIC cooler are discussed, including fringe field and finite interaction time effects.
118415064
Fringe field simulations of a non-scaling FFAG accelerator
Fixed-field Alternating Gradient (FFAG) accelerators offer the potential of high-quality, moderate energy ion beams at low cost. Modeling of these structures is challenging with conventional beam tracking codes because of the large radial excursions of the beam and the significance of fringe field effects. Numerous tune resonances are crossed during the acceleration, which would lead to beam instability and loss in a storage ring. In a non-scaling FFAG, the hope is that these resonances can be crossed sufficiently rapidly to prevent beam loss. Simulations are required to see if this is indeed the case. Here we simulate a non-scaling FFAG which accelerates protons from 31 to 250 MeV. We assume only that the bending magnets have mid-plane symmetry, with specified vertical bending field in the mid-plane (y=0). The magnetic field can be obtained everywhere using a power series expansion, and we develop mathematical tools for calculating this expansion to arbitrary order when the longitudinal field profile is given by an Enge function. We compare the use of a conventional hard-edge fringe with a more accurate, soft-edge fringe field model. The tune 1/3 resonance is the strongest, and crossing it in the hard-edge fringe model results in a 21% loss of the beam. Using the soft-edge fringe model the beam loss is less than 6%.
119104094
Modulator simulations for coherent electron cooling using a variable density electron beam
Increasing the luminosity of relativistic hadron beams is critical for the advancement of nuclear physics. Coherent electron cooling (CEC) promises to cool such beams significantly faster than alternative methods. We present simulations of 40 GeV/nucleon Au+79 ions through the first (modulator) section of a coherent electron cooler. In the modulator, the electron beam copropagates with the ion beam, which perturbs the electron beam density and velocity via anisotropic Debye shielding. In contrast to previous simulations, where the electron density was constant in time and space, here the electron beam has a finite transverse extent, and undergoes focusing by quadrupoles as it passes through the modulator. The peak density in the modulator increases by a factor of 3, as specified by the beam Twiss parameters. The inherently 3D particle and field dynamics is modeled with the parallel VSim framework using a $\delta$f PIC algorithm. Physical parameters are taken from the CEC proof-of-principle experiment under development at Brookhaven National Lab.
53999449
Advances in Coherent Electron Cooling
Cooling techniques are required for improving the quality of hadron beams and increasing the luminosity in hadron- and electron-hadron-colliders. In contrast to light leptons that have very strong radiation damping via synchrotron radiation, the hadrons radiate very little (even in a 7-TeV LHC) and require an additional cooling mechanism to control the growth or reduce their emittances. In this paper, we focus on the advances in, and challenges of Coherent Electron Cooling (CeC) that promises to be an effective method of cooling of high-energy hadron beams, and potentially even ultra-relativistic muon beams. Specifically, we describe the underlying physics principles, and the advances in this revolutionary, but yet untested, technique: viz., CeC. While we described physics principles in an earlier paper [1], our comprehensive studies revealed several other important factors affecting the CeC’s performance [2-5]. In this paper, we summarize our main findings as well as presenting current advances and novel CeC schemes. We also briefly describe the CeC demonstration experiment under preparation at Brookhaven National Laboratory; its detailed description is part of these proceedings [6].
119143806
Higher order QCD corrections in exclusive charmless B decays
We discuss exclusive charmless B decays within the Standard Model of particle physics. In particular we compute part of the NNLO corrections for hadronic two-body decays in the framework of QCD Factorization. We also present a conceptual analysis of heavy-to-light form factors at large recoil.
118509342
Master integrals for the two-loop penguin contribution in non-leptonic B-decays
A bstractWe compute the master integrals that arise in the calculation of the leading penguin amplitudes in non-leptonic B-decays at two-loop order. The application of differential equations in a canonical basis enables us to give analytic results for all master integrals in terms of iterated integrals with rational weight functions. It is the first application of this method to the case of two different internal masses.
56450914
NNLO corrections to semileptonic and hadronic B decays
We review recent progress in the perturbative calculations for semileptonic and hadronic B meson decays with an emphasis on the phenomenological implications of the next-to-next-to-leading order (NNLO) corrections. Specifically, we consider CP-averaged branching ratios of tree-dominated B -> pi pi/pi rho/rho rho decays and the inclusive determination of |V_ub| from B -> X_u l nu.
53121491
Transverse-momentum spectra of electroweak bosons near threshold at NNLO
A bstractWe obtain the next-to-next-to-leading order corrections to transverse-momentum spectra of W, Z and Higgs bosons near the partonic threshold. In the threshold limit, the electroweak boson recoils against a low-mass jet and all radiation is either soft, or collinear to the jet or the beam directions. We extract the virtual corrections from known results for the relevant two-loop four-point amplitudes and combine them with the soft and collinear two-loop functions as defined in Soft-Collinear Effective Theory. We have implemented these results in a public code PeTeR and present numerical results for the threshold resummed cross section of W and Z bosons at next-to-next-to-next-to-leading logarithmic accuracy, matched to next-to-leading fixed-order perturbation theory. The two-loop corrections lead to a moderate increase in the cross section and reduce the scale uncertainty by about a factor of two. The corrections are significantly larger for Higgs production.
17920247
NNLO vertex corrections in charmless hadronic B decays: Real part
Abstract We compute the real part of the 2-loop vertex corrections for charmless hadronic B decays, completing the NNLO calculation of the topological tree amplitudes in QCD factorization. Among the technical aspects we show that the hard-scattering kernels are free of soft and collinear infrared divergences at the 2-loop level, which follows after an intricate subtraction procedure involving evanescent four quark operators. The numerical impact of the considered corrections is found to be moderate, whereas the factorization scale dependence of the topological tree amplitudes is significantly reduced at NNLO. We in particular do not find an enhancement of the phenomenologically important ratio | C / T | from the perturbative calculation.