Ya. Derbenev

A Method to Overcome Space Charge at Injection

The transverse space charge forces in a high current, low energy beam can be reduced by mean of a large increase of the beams transverse sizes while maintaining the beam area in the 4D phase space. This can be achieved by transforming the beam area in phase space of each of two normal 2D transverse (either plane or circular) modes from a spot shape into a narrow ring of a large amplitude, but homogeneous in phase. Such a transformation results from the beam evolution in the island of a dipole resonance when the amplitude width of the island shrinks adiabatically. After stacking (by using stripping foils or cooling) the beam in such a state and accelerating to energies sufficiently high that the space charge becomes insignificant, the beam then can be returned back to a normal spot shape by applying the reverse transformation. An arrangement that can provide such beam gymnastics along a transport line after a linac and before a booster and/or in a ring with circulating beam will be described and numerical estimates will be presented. Other potential applications of the method will be briefly discussed.

Acceleration of polarized protons and deuterons in the ion collider ring of JLEIC

The figure-8-shaped ion collider ring of Jefferson Lab Electron-Ion Collider (JLEIC) is transparent to the spin. It allows one to preserve proton and deuteron polarizations using weak stabilizing solenoids when accelerating the beam up to 100 GeV/c. When the stabilizing solenoids are introduced into the collider’s lattice, the particle spins precess about a spin field, which consists of the field induced by the stabilizing solenoids and the zero-integer spin resonance strength. During acceleration of the beam, the induced spin field is maintained constant while the resonance strength experiences significant changes in the regions of “interference peaks”. The beam polarization depends on the field ramp rate of the arc magnets. Its component along the spin field is preserved if acceleration is adiabatic. We present the results of our theoretical analysis and numerical modeling of the spin dynamics during acceleration of protons and deuterons in the JLEIC ion collider ring. We demonstrate high stability of the deuteron polarization in figure-8 accelerators. We analyze a change in the beam polarization when crossing the transition energy. PRESERVATION OF ION POLARIZATION IN FIGURE-8 ACCELERATORS A characteristic feature of JLEIC [1] is its figure-8shaped rings [2]. Such a ring topology is transparent to the spin: the combined effect of arc fields on the spin in an ideal collider lattice reduces to zero after one particle turn on the design orbit, i.e. any orientation of the particle spin at any orbital location repeats from turn to turn. To preserve the polarizations of the proton and deuteron beams during acceleration from 8 GeV/c to 100 GeV/c in the ion collider ring, it is sufficient to use a weak solenoid with a field integral of 1.2 Tm, which does not perturb the design orbit and has practically no effect on the beam’s orbital parameters [3-10]. The solenoid then stabilizes longitudinal spin polarization at its location. A solenoid with the indicated field integral allows one to induce a spin tune � of 10-2 for protons and 310-3 for deuterons, i.e., when a particle with a vertical spin makes one turn on the design orbit, its spin tilts by an angle of �� from its initial orientation. For polarization stability, one must ensure that the spin tune � induced by the solenoid significantly exceeds [3-6] the strength of the zero-integer spin resonance �: � ≫ �. The resonance strength is the average spin field �⃗ (the zero-integer Fourier harmonic of the spin perturbation without a stabilizing solenoid) determined by deviation of the trajectory from the design orbit due to machine element errors and beam emittances. In the absence of a solenoid, the spin precesses by an angle of �� about the �⃗ direction in one particle turn. The resonance strength consists of two parts: a coherent part arising due to additional transverse and longitudinal fields on a trajectory deviating from the design orbit and an incoherent part associated with the particles’ betatron and synchrotron oscillations (beam emittances) [8, 9] �⃗ = �⃗ ��h + �⃗ ��� , ���h ≫ ���� In practice, the coherent part ���h significantly exceeds the incoherent one ���� . The coherent part does not cause beam depolarization and only results in a simultaneous rotation of the polarization about the field determined by the strength and alignment errors of collider elements. In principle, the direction and size of the coherent part of the resonance strength can be measured and taken into account for polarization control. To preserve the polarization, it is then sufficient to satisfy a weaker condition: � ≫ ���� . CALCULATION OF ZERO-INTEGER SPIN RESONANCE STRENGTH IN JLEIC Figure 1 shows  functions of the JLEIC collider lattice in the acceleration mode [11] used in our spin dynamics calculations. The origin of the coordinate frame is located at the colliders IP. Figure 1 also indicates the location of the solenoid stabilizing the spin during acceleration. The difference from the collision mode [12] where functions in the IP region reach 2.5 km is that, in the acceleration mode, the functions in the detector section do not exceed 150 m. Figure 1: functions of the ion collider ring. ___________________________________________ * Authored by Jefferson Science Associates, LLC under U.S. DOE Contracts No. DE-AC05-06OR23177 and DE-AC02-06CH11357. The U.S. Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce this manuscript for U.S. Government purposes. WEPIK038 Proceedings of IPAC2017, Copenhagen, Denmark ISBN 978-3-95450-182-3 3014 Co py rig ht

Compensation of Chromaticity in the JLEIC Electron Collider Ring

The Jefferson Lab Electron-Ion Collider (JLEIC) is being designed to achieve a high luminosity of up to 10 cms. The latter requires a small beam size at the interaction point demanding a strong final focus (FF) quadrupole system. The strong beam focusing in the FF unavoidably creates a large chromaticity which has to be corrected in order to avoid a severe degradation of momentum acceptance. This has to be done while maintaining sufficient dynamic aperture. An additional requirement in the electron ring is preservation of a low beam emittance. This paper reviews the development of a chromaticity correction scheme for the electron ring.

Preservation and control of the proton and deuteron polarizations in the proposed electron-ion collider at Jefferson Lab

We propose a scheme of preserving the proton and deuteron beam polarizations during acceleration and storage in the proposed electron-ion collider at Jefferson Lab. This scheme allows one to provide both the longitudinal and transverse polarization orientations of the proton and deuteron beams at the interaction points of the figure-8 ion collider ring. We discuss questions of matching the polarization direction at all stages of the beam transport including the pre-booster, large booster and ion collider ring.

SPIN-COSY: Spin-Manipulating Polarized Deuterons and Protons

We studied spin manipulation of 1.85 GeV/c polarized deuteron beam stored in COSY obtaining a spin‐flip efficiency of 97±1%. We first discovered experimentally and then explained theoretically interesting behavior of the deuteron tensor polarization. We, for the first time, studied systematically spin resonance strengths induced by rf dipoles and solenoids. We found huge disagreements between the strengths measured in controlled Froissart‐Stora sweeps and the theoretical values calculated using the well‐known formulae. These data instigated re‐examination of these formulae. We tested Chao’s proposed new matrix formalism for describing the spin dynamics due to a single spin resonance, which may be the first fundamental improvement of the Froissart‐Stora equation in that it allows analytic calculation of the beam polarization’s behavior inside a resonance. Our measurements of the deuteron’s polarization near and inside the resonance agreed precisely with the Chao formalism’s predicted oscillations. We teste...

ELIC at CEBAF

We report on the progress of the conceptual development of the energy recovering linac (ERL)-based electron-light ion collider (ELIC) at CEBAF that is envisioned to reach luminosity level of 1033-1035/cm2s with both beams polarized to perform a new class of experiments in fundamental nuclear physics. Four interaction points with all light ion species longitudinally or transversally polarized and fast flipping of the spin for all beams are planned. The unusually high luminosity concept is based on the use of the electron cooling and crab crossing colliding beams. Our recent studies focused on the design of low beta interaction points, exploration on raising the polarized electron injector current to the level of 3-30 mA with the use of electron circulator-collider ring, forming a concept of stacking and cooling of the ion beams, and specifications of the electron cooling facility.

An electron-ion collider at CEBAF

Abstract Electron-ion colliders with a center of mass energy between 15 and 100 GeV, a luminosity of at least 1033 cm−2S−1, and a polarization of both beams at or above 80% have been proposed for future studies of hadronic structure. The scheme proposed here would accelerate the electron beam using the CEBAF recirculating linac with energy recovery. If all accelerating structures presently installed in the CEBAF tunnel are replaced by ones with a ∼20 MV/m gradient, then a single recirculation results in an electron beam energy of about 5 GeV. After colliding with protons/light ions circulating in a figure-of-eight storage ring (for flexibility of spin manipulation) at an energy of up to 100 GeV, the electrons are re-injected into the CEBAF accelerator for deceleration and energy recovery. In this report several layout options and their respective feasibilities will be presented and discussed, together with parameters which would provide a luminosity of up to 1 · 1035 cm−2s−1. The feasibility of combining such a collider at a center-of-mass energy √s of up to 43 GeV with a fixed target facility at 25 GeV is also explored.