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NICA (Nuclotron-based Ion Collider fAcility) is a new accelerator complex being assembled at JINR to search for the mixed phase of baryonic matter and to investigate the nature of nucleon/particle spin. The polarized proton beams will be operated at the energy range of 5-12.6 GeV, the beam intensity in each ring of 2.2x10¹³ and the luminosity of 1x10³² cm⁻² s⁻¹. The conception of formation of high intensive proton beams is discussed for two different schemes. In first scheme the protons are injected from Nuclotron to Collider at an energy of 2-2.5 GeV to provide the cooling and the storage at this energy and then they are accelerated up to energy of experiments. In the second scheme the cooling of protons is realized in one from accelerators of the injection chain and the protons are injected from Nuclotron to Collider at energy of experiments, where they are stored up required intensity., Proceedings of the 13th International Particle Accelerator Conference, IPAC2022, Bangkok, Thailand

To implement the polarization program at the NICA complex (Dubna, Russia) the novel mode of ion polarization control - the transparent spin mode - is planned to use. To set up the transparent spin mode in the NICA collider two solenoidal snakes will be placed in straights of the Multi Purpose Detector (MPD) and the Spin Physics Detector (SPD). The beam polarization at SPD will be controlled by means of ‘‘weak’’ solenoids. The main characteristic of the transparent spin mode is the spin resonance strength, which consists of two parts: a coherent part arising due to additional transverse and longitudinal fields on the beam trajectory deviating from the design orbit and an incoherent part associated with the particles’ betatron and synchrotron oscillations (beam emittances). The resonance strength allows one to formulate requirements on the magnitudes of the control solenoids’ fields. The theoretical analysis, calculation and spin tracking simulation of the spin resonance strength in the whole momentum range of the NICA collider are presented., Proceedings of the 10th Int. Particle Accelerator Conf., IPAC2019, Melbourne, Australia

The transparent spin mode has been proposed as a new technique for preservation and control of the spin polari-zation of ion beams in a synchrotron. The ion rings of the proposed Jefferson Lab Electron-Ion Collider (JLEIC) adopted this technique in their figure-8 design. The transparent spin mode can also be setup in a racetrack with two identical Siberian snakes. There is a proposal to test the predicted features of the spin transparent mode in Relativistic Heavy Ion Collider (RHIC), which already has all of the necessary hardware capabilities. We have earlier analytically estimated the setup parameters and developed a preliminary experimental plan. In this paper we describe simulation setup and benchmarking for the proposed experiment using a Zgoubi model of RHIC., Proceedings of the North American Particle Accelerator Conference, NAPAC2019, Lansing, MI, USA

In the Spin Transparency (ST) mode of RHIC, the axes of its Siberian snakes are parallel. The spin tune in the ST mode is zero and the spin motion becomes degenerate: any spin direction repeats every particle turn. In contrast, the lattice of a conventional collider determines a unique stable periodic spin direction, so that the collider operates in the Preferred Spin (PS) mode. Contributions of perturbing magnetic fields to the spin resonance strengths in the PS mode are usually calculated using the spin response function. However, in that form, it is not applicable in the ST mode. This paper presents a response function formalism expanded for the ST mode of operation of conventional colliders with two identical Siberian snakes in the highly-relativistic limit. We present calculations of the spin response function for RHIC in the ST mode., Proceedings of the 10th Int. Particle Accelerator Conf., IPAC2019, Melbourne, Australia

High electron and ion polarizations are some of the key design requirements of a future Electron Ion Collider (EIC). The transparent spin mode, a concept inspired by the figure 8 ring design of JLEIC, is a novel technique for preservation and control of electron and ion spin polarizations in a collider or storage ring. It makes the ring lattice "invisible" to the spin and allows for polarization control by small quasi-static magnetic fields with practically no effect on the beam’s orbital characteristics. It offers unique opportunities for polarization maintenance and control in Jefferson Lab’s JLEIC and in BNL’s eRHIC. The transparent spin mode has been demonstrated in simulations and we now plan to test it experimentally. We present a design of an experiment using a polarized proton beam stored in one of the RHIC rings. In the experiment, one of the RHIC rings is configured in the transparent spin mode by aligning the axes of its two Siberian snakes. The experiment goals, procedures, hardware requirements and expected results are presented., Proceedings of the 10th Int. Particle Accelerator Conf., IPAC2019, Melbourne, Australia

The spin response function is determined by a collid-er's magnetic lattice and allows one to account for con-tributions of perturbing fields to spin resonance strengths. The depolarizing effect of an incoming beam depends significantly on the response function value at the interaction point (IP). We present an analytic calcula-tion of the response function for protons and deuterons at the IP of Jefferson Lab Electron Ion Collider (JLEIC) over its whole momentum range. We find a good agreement of the analytic calculation with our numerical modeling results obtained using a spin tracking code, Zgoubi., Proceedings of the 9th Int. Particle Accelerator Conf., IPAC2018, Vancouver, BC, Canada

The superconducting synchrotron Nuclotron allows one to accelerate proton and deuteron beams up to 13.5 GeV/c. The beam depolarization occurs at the crossing of spin resonances. For deuterons, the vertical polarization is preserved almost to the maximum momentum. Tens of spin resonances are crossing during the proton acceleration. The proton polarization will be preserved by a solenoidal 5% snake up to 3.4 GeV/c at the field ramp rate of 1 T/s. It is planned to use a partial 50% snake to eliminate the resonant depolarization of the proton beam in the total momentum range of the accelerator. The results of simulations and experimental data are presented., Proceedings of the 8th Int. Particle Accelerator Conf., IPAC2017, Copenhagen, Denmark

The figure-8 JLEIC collider ring opens wide possibilities for manipulating proton and deuteron spin directions during an experiment. Using 3D spin rotators, one can, at the same time, efficiently control the polarization direction as well as the spin tune value. The 3D spin rotators allow one to arrange a system for reversals of the spin direction in all beam bunches during an experiment, i.e. a spin-flipping system. To preserve the polarization, one has to satisfy the condition of adiabatic change of the spin direction. When adjusting the polarization direction, one can stabilize the spin tune value, which completely eliminates resonant beam depolarization during the spin manipulation process. We provide the results of numerical modeling of a spin-flipping system in the JLEIC ion collider ring. The presented results demonstrate the feasibility of organizing a spin-flipping system using a 3D rota-tor. The figure-8 JLEIC collider provides a unique capability of doing high-precision experiments with polarized ion beams., Proceedings of the North American Particle Accelerator Conf., NAPAC2016, Chicago, IL, USA

The scheme for preservation and control of the ion polarization in the Medium-energy Electron-Ion Collider (MEIC) has been under active development in recent years. The figure-8 configuration of the ion rings provides a unique capability to control the polarization of any ion species including deuterons by means of "weak" solenoids rotating the particle spins by small angles. Insertion of "weak" solenoids into the magnetic lattices of the booster and collider rings solves the problem of polarization preservation during acceleration of the ion beam. Universal 3D spin rotators designed on the basis of "weak" solenoids allow one to obtain any polarization orientation at an interaction point of MEIC. This paper presents the baseline scheme for polarization preservation and control in the MEIC ion complex., Proceedings of the 6th Int. Particle Accelerator Conf., IPAC2015, Richmond, VA, USA

Ion polarization in the Medium-energy Electron-Ion Collider (MEIC) is controlled by means of universal 3D spin rotators designed on the basis of “weak” solenoids. We use numerical calculations to demonstrate that the 3D rotators have negligible effect on the orbital properties of the ring. We present calculations of the polarization dynamics along the collider’s orbit for both longitudinal and transverse polarization directions at a beam interaction point. We calculate the degree of depolarization due to the longitudinal and transverse beam emittances in case when the zero-integer spin resonance is compensated., Proceedings of the 6th Int. Particle Accelerator Conf., IPAC2015, Richmond, VA, USA

Two solenoid Siberian snakes are placed in the opposite collider’s straight sections are used to control deuteron’s and proton’s polarization in the NICA collider. Solenoid snakes substantially reconstruct beam’s orbital motion. The change of the polarization direction in the vertical plane of MPD and SPD detectors occurs due to insertion of polarization control (PC) solenoids in the magnetic lattice of the collider. The solenoids rotating particle’s spin by small angels practically do not influence on the beam’s orbital motion parameters. The dynamic of the polarization vector as function of the orbit length for cases of longitudinal and vertical polarization in the MPD and SPD detectors are presented., Proceedings of the 6th Int. Particle Accelerator Conf., IPAC2015, Richmond, VA, USA

The Medium-energy Electron-Ion Collider (MEIC) proposed by Jefferson Lab is designed to provide high polarization of both colliding beams. One of the unique features of JLab’s MEIC is figure-8 shape of its rings. It allows preservation and control of polarization of all ion species including small-anomalous-magnetic-moment deuterons during their acceleration and storage. The figure-8 design conceptually expands the capability of obtaining polarized high-energy beams in comparison to conventional designs because of its property of having no preferred periodic spin direction. This allows one to control effectively the beam polarization by means of magnetic insertions with small field integrals. We present a complete scheme for preserving the ion polarization during all stages of acceleration and its control in the collider’s experimental straights., Proceedings of the 5th Int. Particle Accelerator Conf., IPAC2014, Dresden, Germany

Different aspects of the NICA facility operation in polarized proton and deuteron modes aimed at reaching the highest possible luminosity and polarization degree as well are analysed. The main aim is to provide average luminosity L ≥ 1•1032 cm⁻² s^{−1} at √sNN ≥ 26-27 GeV for single-spin proton collisions. Optimal schemes of the Siberian Snake insertions to the Nuclotron and NICA collider rings were proposed. The results of simulations are presented and discussed., Proceedings of the 5th Int. Particle Accelerator Conf., IPAC2014, Dresden, Germany

The influence of solenoids on spin is very efficient, but beam focusing is determined mainly by structural quadru-poles. The condition of stable orbital motion of particles does not require compensation of the betatron oscillation coupling. To reduce the influence of the Snake on orbital motion it is desirable to exclude compensating quads completely. The design of solenoid Siberian snake for the Nuclotron lattice is presented. The orbital functions of the lattice were calculated and the results are discussed., Proceedings of the 5th Int. Particle Accelerator Conf., IPAC2014, Dresden, Germany

The Medium-energy Electron Ion Collider (MEIC) at JLab is designed to provide high luminosity and high polarization needed to reach new frontiers in the exploration of nuclear structure. The luminosity, exceeding 1033 cm⁻²s^{−1} in a broad range of the center-of-mass (CM) energy and maximum luminosity above 1034 cm⁻²s^{−1}, is achieved by high-rate collisions of short small-emittance low-charge bunches made possible by high-energy electron cooling of the ion beam and synchrotron radiation damping of the electron beam. The polarization of light ion species (p, d, 3He) can be easily preserved and manipulated due to the unique figure-8 shape of the collider rings. A fully consistent set of parameters have been developed considering the balance of machine performance, required technical development and cost. This paper reports recent progress on the MEIC accelerator design including electron and ion complexes, integrated interaction region design, figure-8-ring-based electron and ion polarization schemes, RF/SRF systems and ERL-based high-energy electron cooling. Luminosity performance is also presented for the MEIC baseline design., Proceedings of the 6th Int. Particle Accelerator Conf., IPAC2015, Richmond, VA, USA