M. A. Kondratenko

Calculation of spin resonance strength at COSY accelerator

The influence of RF dipole on spin motion at the COSY accelerator was studied in [1, 2]. The discrepancy between the theoretically calculated spin resonance strength for the deuteron beam and the experimentally observed value were discovered [2]. In this work it is shown that the calculation using the response function makes explaining the discrepancy between experimental data and theoretical calculations of spin resonance strengths induced by modulated radial magnetic dipole possible.

Polarized deuterons and protons at NICA@JINR

The novel scheme of proton and deuteron polarization control in the NICA collider at Dubna is proposed. By means of two Siberian Shakes with solenoid magnetic field the beam spin tune is shifted to the “zero” spin resonance vicinity, whereas manipulation of the polarization is realized by “weak” field solenoids. The scheme makes it possible to obtain any desired direction of the polarization in the both MPD and SPD detectors for any sort of the particles. The possibility of the beam polarization control in the orbit plane at any azimuth of the collider magnetic arcs exists also. The last gives necessary flexibility of optimal matching the beam polarization at injection into collider and at the polarimetery monitor points.

Program of Polarization Studies and Capabilities of Accelerating Polarized Proton and Light Nuclear Beams at the Nuclotron of the Joint Institute for Nuclear Research

A program of polarization studies is presented; this program can enhance our understanding of the constituents from which the spin of hadrons and lightest nuclei is constructed. Beams of polarized lightest nuclei at Nuclotron are required to complete this program. Calculations of linear resonance strengths at Nuclotron, which may result in depolarization effects, are presented. The application of a new method for conserving particle beam polarization at crossing these resonances at Nuclotron is discussed.

High-precision measurement of the polarized hadron beam energy in circular accelerator

A method for the high-precision measurement of the hadron polarized beam energy in circular accelerators by measuring the spin precession frequencies is offered. The problem of the particles energy measurement with accuracy better, than the beam energy spread, first of all, is connected with influence of synchrotron oscillations on spin motion. The given method develops the well-known method of high-precision measurement of electron-positron beams mean energy in case of a wide spin frequency spread.

On Compensation of Beam Depolarization at Crossing of a Spin Resonance

The method of beam polarization preservation at crossing of a spin resonance in cyclic accelerators is offered. The known methods do not compensate depolarization degree, but only reduce it by means of fast or adiabatic resonance crossing. Our method is based on control the spin precession axis and the spin rotation phase inside of the resonance region. The conditions of restoration beam polarization after resonance crossing are given with the help of the spin adiabatic invariant conception. Results are essential for production of the intensive polarized beams of high energy particles. Numerical examples are presented.

Spin Transparency Mode in the NICA Collider with Solenoid Siberian Snakes for Proton and Deuteron Beam

Two solenoid Siberian Snakes are required to obtain ion polarization in spin transparency mode of the NICA collider. The snake solenoids with a total field integral of 2×50 Tm are placed into the straight sections of the NICA collider. It allows one to control polarization of protons and deuterons up to 13.5 GeV/c and 4 GeV/c respectively. The snakes introduce a strong betatron oscillation coupling. The calculations of orbital parameters of proton and deuteron beams in the NICA collider with solenoid Snakes are presented.

First results on the measurements of the proton beam polarization at internal target at Nuclotron1

The spin program at NICA using SPD and MPD requires high intensity polarized proton beam with high value of the beam polarization. First results on the measurements of the proton beam polarization performed at internal target at Nuclotron are reported. The polarization of the proton beam provided by new source of polarized ions has been measured at 500 MeV using quasielastic proton-proton scattering and DSS setup at internal target. The obtained value of the vertical polarization of ~35 % is consistent with the calculations taking into account the current magnetic optics of the Nuclotron injection line.

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

Superconducting racetrack booster for the ion complex of MEIC

The current design of the Medium-energy Electron-Ion Collider (MEIC) project at Jefferson lab features a single 8 GeV/c figure-8 booster based on super-ferric magnets. Reducing the circumference of the booster by switching to a racetrack design may improve its performance by limiting the space charge effect and lower its cost. We consider problems of preserving proton and deuteron polarizations in a superconducting racetrack booster. We show that using magnets based on hollow high-current NbTi composite superconducting cable similar to those designed at JINR for the Nuclotron guarantees preservation of the ion polarization in a racetrack booster up to 8 GeV/c. The booster operation cycle would be a few seconds that would improve the operating efficiency of the MEIC ion complex.

NICA Facility in Polarized Proton and Deuteron Mode

NICA project at JINR is aimed at the experiments with polarized protons and deuterons at both as fixed target and colliding mode over beam momentum range from 2 to 13.5GeV/c. Polarized beams are injected into collider from the Nuclotron-superconducting synchrotron. Dynamic solenoid “Siberian snakes” are proposed to prevent resonance depolarization of proton beam during acceleration in the Nuclotron up to momentum of 6 GeV/c and further in the collider up to the maximum momentum after storage and stochastic cooling of necessary number of particles in each ring. By means of pair of the Snakes placed in the opposite collider straight sections “spin transparency” mode is provided. Stabilization and control of the polarization is reached due to “weak field” solenoids integrated in the lattice. The proposed scheme of the polarization control is universal and can be used for different ion spices (p, d, t, He3…).