FUNCTIONAL REQUIREMENT SPECIFICATION PROJECT NICA/MPD. Passport of the NICA accelerator complex

Transcription

1 FUNCTIONAL REQUIREMENT SPECIFICATION PROJECT NICA/MPD Passport of NICA accelerator complex Dubna, 2015

2 Page 1of 19 Prepared by: Date 01 February 2015 Editors/Authors: Igor Meshkov Scientific Leader of NICA Accelerator complex Project Grigory Trubnikov Leader of Nuclotron-NICA Project Anatoly Sidorin Deputy Leader of Nuclotron-NICA Project Organization JINR Telephone, +7 (496) (496) (496) Co-authors: N.N. Agapov, V.S. Aleksandrov, O.I. Brovko, A.V. Butenko, E.D. Donets, E.E. Donets, D.E.. Donets, A.V. Eliseev, A.A. Fateev, V.V. Fimushkin, A.R. Galimov, E.V. Gorbachev, A.I. Govorov, E.V. Ivanov, V.N. Karpinsky, V.D. Kekelidze, H.G. Khodzhibagiyan, V.V. Kobets, O.S. Kozlov, S.A. Kostromin, A.D. Kovalenko, G.L. Kuznetsov, R. Lednicky, N.I. Lebedev, V.A. Matveev, V.A. Mikhailov, V.A. Monchinsky, Yu.K. Potrebenikov, A.V. Philippov, S.V. Romanov, P.A. Rukoyatkin, N.V. Semin, N.A. Shurkhno, A.I.. Sidorov, V.M. Slepnev, A.V. Smirnov, A..S. Sorin, N.D. Topilin, A.V. Tuzikov, V.I. Volkov

3 Page 2of 19 TABLE OF CONTENTS 1. Introduction Mission Statement Project Goals 4 4. Key Assumptions, Interfaces and Constraints Additional Project Goals Facility Scope 6 7. Functional Requirements References 19

4 Page 3of Introduction: Project NICA/MPD (Nuclotron based Ion Collider facility and Multi Purpose Detector) is an accelerator facility conceived to implement a world-leading program in particle physics at JINR.A description of physics program envisioned is available on web. Project NICA/MPD is a part of JINR Roadmap for is described in JINR 7-years Program. It is approved by Scientific Council of JINR and The Committee of Plenipotentiaries of JINR in That is a flagship project of JINR presently. The project comprises experimental studies of fundamental character in fields of following directions of experimental research: 1. Relativistic nuclear physics search for mixed phase, phase transitions and critical phenomena in strongly interacting baryonic matter; 2. Spin physics in high and middle energy range of interacting particles; 3. Radiobiology. Applied researches based on particle beams generated at NICA are dedicatedd to development of novel technologies in material science, environmental problems resolution (like radioactive waste transmutation), energy generation (accelerator driven nuclear reactors), particle beam rapy and ors. Education program using facility for performance of research works having goal of teaching of young specialists. Project NICA/MPD can serve wide researchers community in different fields of science and technology where intense and high energy particle beams are required. 2. Mission Statement: Project NICA/MPD, a modern accelerator facility, will support world-leading programs in long base line relativistic nuclear physics and particle spin physics, radiobiology, applied research and education. It willl be unique among accelerator facilities worldwide in its flexibility to support multiple research programs based on particle beams of frontier parameters. The main goal of project is a study of hot and dense strongly interacting matter in heavy ion (up to Au) collisions at centre-of-mass energies up to 11 GeV. Two modes of operation are foreseen, collider mode and extracted beams, with two detectors: MPD and BM@N. An average luminosity in collider mode is expected as cm 2 s 1 for Au 79+. Extracted beams of various nuclei species with maximum momenta of 13 GeV/c (for protons) will be available. A study of spin physics with extracted and colliding beams of polarized deuterons and protons at energies up to 27 GeV (for protons) is foreseen with NICA facility. The proposed program allows to search for possible signs of phase transitions and critical phenomena as well as to shed light on problem of nucleon spin structure.

5 Page 4of Project Goals: The global scientific goal of NICA/ /MPD Project is to explore phase diagram of strongly interacting matter in region of highly compressed baryonic matter. Such matter exists in neutron stars and in core of supernova explosions, while in early Universe we meet opposite conditions of very high temperature and vanishing baryonic density. In terrestrial experiments, high-density nuclear matter can transiently be created in some reaction volume in relativistic heavy ion collisions. In se collisions a large fraction of beam energy is converted into newly created hadrons and excitation of resonances whose properties may noticeably be modified by surrounding hot and dense medium. At very high temperatures or densities, this hadron s mixture melts and its constituents, quarks and gluons, form a new phase of matter, quark-gluon plasma. The heavy-ion experiments at CERN-SPS and BNL-RHIC as well as coming CERN- where circumstantial evidence has been obtained for a new phase of matter existing above a LHC experiments probe region of high temperatures and low net baryon densities temperature of about MeV. At lower temperature and moderate baryonic density, GSI-SIS experiments definitely show no hint at a phase transition but certainly ree are in-mediumm modification effects. At very high densities and very low temperatures matter is deconfined and, as predicted, correlated quark-antiquark pairs form a color superconductive phase. Such phase may be created in interior of neutron stars. The NICA/MPD project is dedicated to search at intermediate values of temperature and densities, wheree essential evidences were obtained by NA49 collaboration within low-energy CERN-SPS program that system enters a new phase at beam energy of about 30 GeV/u. The importance of this finding was well understood at GSI, wheree CBM (Compressed Baryon Matter) experiment is under development within FAIR project, and by BNL-RHIC, where a limited statistics of Au + Au collisions has already been collected at decreased beam collider energies to study this domain of phase diagram. The studies of nucleon spin structure is first priority task for scientific program of The Spin Physics Detector (SPD) project at NICA facility. Since famous spin crisis in 1987, this problem of nucleon spin structure remains one of most intriguingg puzzle of high energy physics. The central component of this problem attracting for many years enormous both oretical and experimental efforts, is a search for answering questions, how spin of proton is built up from spins and orbital momenta of its constituents.the searches brought up a concept of Parton Distribution Functions (PDF) in nucleon. Now we know that must be about 50 different PDF for a complete description of nucleon structure. Some of m can be consideredd as sufficiently well known, when ors eir are absolutely unknown, or poorly known, especially spin dependent ones. Fixed target experiments at proton and ion beams delivered (up to 2001) by Synchrophasotron and (after 2001) by Nuclotron is long-lived research program at. It will be continued at beams from upgraded Nuclotron having goal of studies in all particle physics fields proposed for NICA/MPD and SPD, but in lower energy range. Thus, se studies will be complementary to those performed at NICA Collider. The Nuclotron beams will be used also for tests of MPD and SPD elements.

6 Page 5of 19 The new NICA acceleratorr facility will provide numerous particle beams of wide parameterr spectrum. That allows one to perform both applied and fundamental research in different fields of science and technology. Among m one can point out: radiobiology and cosmic medicine; cancer rapy; development of accelerator driven reactors ( energy generation with subcritical plutonium blankets) and radioactive waste transmutation; test of radiation proof electronics. Education program is one of first priority activities at JINR, as formulated in JINR Roadmap. The proposed NICA facility offers various possibilities for teaching and qualification procedures including practice at experimental set ups and test benches, preparation of diploma works, PhD, and doctoral (corresponding to habilitierter Doktor in Germany) ses. 4. Key Assumptions, Interfaces and Constraints: NICA facility is constructed on site and will utilize upgraded Nuclotron. The Nuclotron upgrade is in progress and will be completed in frames of Nuclotron-NICA project. Project NICA/MPD is JINR flagship project being international collaboration. That involves Institutions from or countries. fulfilled by world-wide JINR member-states and Project NICA/MPD technology choices will exploit experience and activity of laboratories dealing with accelerator and particle detectors development like CERN, Budker INP, GSI, Fermilab, BNL, and ors. Project NICA/MPD represents a large long-term investment for JINR high energy physics and hence must be robust, flexible, and designed with significant upgrade potential. The facility physics program is suggested to be implemented during three stages: At first stage of operation it will provide ion-ion collisionss with same ion species in both rings. The second stage will require an upgrade of beam interaction region in order to accomplish collisions of beams with different ion species at same energy per nucleon of both beams (in this case collider rings have to be operated at different magnetic rigidities) ). The spin physics program will be realized at third stage, when ring will be equipped with required spin control and diagnostic devices. The project realization presumes required development of liquid helium facility, constructionn of a control system and development of infrastructure.

7 Page 6of Additional Project Goals: The NICA injector, Booster and Nuclotron should have provisions for delivering ion beam in range 3 MeV/u 4.5 GeV/u for various experimental studies in radiobiology, medicine, nuclear technology, material science, etc. 6. Facility Scope: The NICA facility (Fig. 6.1) includes: injectionn complex, Nuclotron and two storage rings with two interaction points (IP). booster, upgraded Fig Schematics of NICA layout: 1 injector facility, Booster and Nuclotron, 2 existing building for fixed target experiments, 3 collider rings, 4, 5 MPD and SPD detectors, 6 electron cooling system. The injection complex provides a wide set of ion species up to heaviest one, Au, at energy of 3.5 MeV/u with an expected intensity of particles per cycle. The facility contain also source of polarized ions (SPI) with linac accelerating light ions up to 5 MeV/u that provide direct injection of polarized deuterons and protons (proton beam energy is 20 MeV) into Nuclotron and n to Collider. The Booster synchrotron should accelerate ions up to 600 MeV/u (for ions with Z/A = 1/3). The magnetic ring of 211 m long is placed inside window of Synchrophasotron yoke. The upgraded Nuclotron should provide proton, deuteron (including polarized) and multi charged ion beams with maximum energies: 5.8 GeV/u for (A = 2, Z = l); 3.3 GeV/u for Xe (A = 124, Z = 42); and 4.5 GeV/u for Аu (А = 197, Z = 79). The ions are fully stripped before injectionn into Nuclotron. The two storage rings with two interaction points (IP). The major parameters of NICA Collider are following: Bρ = 45 T m; vacuum in a beam chamber: Torr; maximumm dipole field 1.8 T; ion kinetic energy range from 1 GeV/u to 4.5 GeV/u for Au 79+ ; zero beam crossing angl luminosity L = cm 2 s le at IP; 9 m space for detector allocations at IP s; average 1 for gold ion collisions at s NN = 9 GeV. The Collider ring m long (twice large as Nuclotron ring) has a racetrack shape and is based on double-aperture (top-to-bottom) superferric magnets dipoles and quadrupoles.

8 Page 7of Functional Requirements: 7.1. Injector facility The injector facility consists of following elements: cryogenic heavy ion source KRION of Electron String Ion Source (ESIS) type, laser source, duoplasmatron source, source of polarized protons and deuterons, modernized linac LU-20 (existing), new heavy ion linear accelerator (HILac), transfer channels. All particle sources (Table 7.1.1) are placed on own platforms suspended at positive potential of kev to provide injection into linacs (Table 7.1.2). The injector facility has two independent parts: 1. injector for light ions; 2. injector for heavy ions. The injector for light ions contains ion sources (laser, duoplasmatron sources, source of polarized protons and deuterons), modernized LU-20 and existing beam injection channel into synchrotron Nuclotron. The injector for heavy ions contains ion source KRION, HILac and two new beam transfer channels (Table 7.1.3).

9 Page 8of 19 Table Parameters of Particle Sources of NICA Injection Facility. Source Particles Particles per cycle ~ Repetition, Hz KRION-6T Au (3 pulses for 5 s) Laser source Duoplasmatron Light ions 10+ up to Mg Н +, D +, Не 2+ ~ Н +, D + ~ Не ~ *) SPI = Source of Polarized Ions Table Parameters of Linear Accelerators of NICA Injection Facility. Linac LU-20 HILac Acceleration structure (section number) RFQ + Alvarez type RFQ (1) + IH DTL (2) Mass to charge ratioa/z Injection energy, kev/u 150 for A/ZZ = Extraction energy, MeV/u Input current, ma 5 (A/Z = 1 3) up to ( (A/Z = 6) up to 10 Particle transmission, % Operating frequency, MHz Length, m Acceptance, π mm mrad Output emittance (effective), π mm mrad Table Parameters of Beam Transfer Channels of NICA Injection Facility. Beam transfer channel LEBT HILac Booster Length, m Channel composition 2 dipoles; 2 solenoids; 10 quadrupoles; 2D steerer; 1 debuncher; 2 focusing electrodes; 1 chopper; 1 accelerating tube (fore- beam diagnostics; injector) steerers Sort of ions entry); Au Au 30+, Au 31+, Au 32+ (at and several neighbor charge states Au 31+ (at exit) Ion energy, kev/u 1.6 (at entry); 17 (at exit) 3.2 Beam intensity ~ (Au ); ~ (Au 31+ ); up to (total) up to 6 10 (total) Particle transmission, % Output emittance (effective), π mm mrad 90 up to SPI *) Н +, D D +

10 Page 9of Booster synchrotron The main goals of Booster (Table 7.2.1) are following: accumulation of Au 31+ ions; acceleration of heavy ions up to energy required for effective stripping; forming of required beam emittance with electron cooling system; providing a fast extraction of accelerated beam for its injection into Nuclotron. The present layout makes it possible to place Booster having 211 m circumference and four fold symmetry lattice inside yoke of Synchrophasotron (Fig ). The Booster has working cycle of 4.02 s duration (Fig ). In case of necessity a technological pause between Booster cycles of 1 s duration is presumed. Fig The Booster layout.

11 Page 10of 19 Fig The Booster cycle diagram for heavy ion acceleration. Fold symmetry Number of DFO lattice cells per arc Number of large straight sections Length of large straight sections, m Length of small straight sections, m Betatron tunes Amplitude of β-functions, m Maximum dispersion function, m Momentum compaction factor γ tr Table Lattice parameters of Booster. Chromaticity Horizontal acceptance, π mm mrad Vertical acceptance, π mm mrad /0.85/ / / The Booster electron cooling system is aimed to form required phase bunch. The maximumm designed electron energy is 60 kev. volume of 7.3. The Nuclotron The Nuclotron SC proton operation modes: synchrotronn (Table and Fig below) has three 1. Acceleration of heavy ions for storage in Collider. 2. Acceleration of polarized protons and deuterons for feeding Collider. 3. Acceleration of both polarized and unpolarized protons and deuterons and heavy ions for internal target experiments or slow extraction to fixed target experiments.

12 Page 11of 19 In first mode Nuclotron is operated as an element of NICA Collider injection chain and has to accelerate single bunch of fully stripped heavy ions (U 92+, Pb 82+ or Au 79+ ) from 0.6 to GeV/u (Table ). The required bunch intensity is about ions. The particle losses during acceleration have to be minimized and do not exceed 10 %. The magnetic field ramp has to be 1 T/s. In second mode Nuclotron will be used for acceleration of polarized proton beam from 20 MeV up to 12 GeV kinetic energy and polarized deuteron beam from 5 MeV/u up to 5.6 GeV/u. The bunch intensity in this case is a few units of particles. In third mode Nuclotron is operated similarly to 1 st or 2 nd mode (depending on accelerating particles sort) with furrr slow extraction of particles to fixed target area instead of a beam transfer into Collider. Fig The operation cycles of Nuclotron. Table Nuclotron beam and RF system parameters at heavy ion acceleration (Au 79+ ). Time, s B, T V rf, kv f rf, khz Synchronous phase, deg Kinetic energy, MeV/u Number of bunches Rms bunch length, m Rms energy spread, MeV p/p (± 2 σ) Bucket height, MeV p/pp within bucket Synchrotron tune Injection ± ± Acceleration Extraction ,, ± ± ± ±

13 Page 12of The NICA synchrotrons Both NICA synchrotrons (Table ) when operated in ion storage mode are synchronized to provide an optimal storage rate (Fig and ). Table General parameters of NICA facility synchrotrons. Parameter Booster Nuclotron Type Particles Injection energy, MeV/u Maximum energy, GeV/u Magnetic rigidity, T m Circumference, m Fold symmetry Quadrupole periodicity Betatron tune Cycle duration for Collider mode, s Dipole field, T Radius of curvature, m Magnetic field ramp, T/s Beam injection Beam extraction Vacuum, Torr Aubeam intensity, ions/pulse Transition energy, GeV/u RF range, MHz Harmonics number of accelerating frequency Chromaticity hor. /vert. Spill duration of slow extraction, s SC synchrotron ions A/Z / (active); 5 (total) single turn;multi-turn; multiple single turn single turn (at injection) 1 (after cooling) 5.1/ 5.5 up to 10 SC synchrotron p, d, nuclei 5 (p, d ), (gold nuclei) (p ), 5.62 (d ), 4.38 (gold nuclei) (active); 5 (total) (p, d ) (nuclei) single turn single turn, slow extraction (p, d ) (nuclei) 5 (p, d ) 1 (nuclei) 7. 8/ 10.0 up to 10

14 7.5. The Collider Page 13of 19 The Collider will be constructed in a tunnel with additional buildings for two detectors and electron cooler ( Fig ). Fig The NICA facility at JINR. Collider will be operated at a fixed energy, also possibility to have slow-ratof field acceleration of an injected beam is foreseen. To provide required linearity maximumm bending field is chosen to be of 1.8 T. Two collider rings are placed one above or and beam superposition/separation is provided in vertical plane. The distance between ring median planes is chosen to be 32 cm. That is achieved with dipole and quadrupole magnets having two apertures in one yoke. The ring has a racetrack shape with two arcs and two long straightt sections. The minimumm beta function in interaction point is 35 cm. The ring acceptance is limited by aperture of final focus lenses is not less than 40 π mm mrad. RMS bunch length in collision mode is 60 cm. The inter-bunch distance is larger than 21 m. The arc optic structure consisting of 12 regular cells of FODO type (Fig ). The possibility to achieve required luminosity level is illustrated by bunch parameters optimized for operation with Au 79+ ions (Table 7.5.1). The ring composition for ion mode of operation is shown in Fig

15 Page 14of 19 Table Parameters of Collider optic structure and beams. Circumference of ring, m Structure of bending arc Number of bunches RMS bunch length, m β-function in IP, m Betatron frequinces, Q x /Q y Chromaticities, Q x /Q y Acceptance, π mm mrad Momentum acceptance, p/p Critical energy factor, γ tr Energy of Au 79+, GeV/u Number of ions per bunch RMS momentum spread, p/p RMS emittance, πmm mrad 1 Luminosity, cm 2 s IBS growth time, s / FODO, 12 cells / / ± / / / Fig Scheme of FODO periodic cell: QF, QD focusing and defocusing quadrupoles, Dip dipole magnets, PU pick-up station, Corr corrector pack.

16 Page 15of 19 Fig Scheme of Collider ring with equipment and insertions. Description is given in text below. To provide beam storage and bunch formation in Collider 3 independent RF systems are used (Table 7.5.2): 1. RF barrier bucket system (RF1) at 5 kv of voltage amplitude, allowing storage of required beam intensity st narrow-band RF system (RF2) operating at harmonics of revolution frequency corresponding to bunch number; it provides beam bunching and bunch compression. Maximum voltage amplitude for this system is 100 kv nd narrow-band RF system (RF3) operating at harmonics number three times larger than 1 st one, thatt provides bunch length necessary for collision experiments. Maximum voltage amplitude for this system is 1 MV. Collider injectionn system consists of septum (MS) and kicker (K) which are placed in missing dipole cell of bending arc. The emittance of injecting beam from Nuclotron is ε x,y = 1. 2 π mm mrad. For luminosity preservation in heavy ion collision mode, electron (ECool) and stochasticc cooling systems (PU-X, PU-Y, PU-L are horizontal, vertical and longitudinal pick-ups, K-X, K-Y, K-L corresponding kickers) are used. The electron cooling system will be used in ion energy range from 1 to4.5 GeV/ /u, stochastic cooling from 3 to 4.5 GeV/u. The band of stochastic cooling system is from 2 to 4 GHz. The longitudinal degree of freedom will be cooled using Palmer method.

17 Page 16of 19 Table Main parameters of Collider RF system. RF1 RF2 RF3 Frequency, MHz Total voltage amplitude, kv Voltage per resonator, kv Number of resonators per ring BB SC magnets for Booster and Collider The Nuclotron-type design of SC magnets based on a window frame iron yoke and a saddle-shaped superconducting winding is chosen for both new rings of NICA facility: for Booster (Table 7.6.1) and for Collider (Table 7.6.2). Table Main characteristicss of Booster magnets. Characteristics Dipoles Quadrupoles Number of magnets in ring Maximum magnetic induction, T (T/m, field gradient) Effective magnetic length, m Ramping rate db/dt, T/s dg/dt, T/(m s) Field error B/B ( G/G) at R = 30 mm Beam pipe aperture hor./vert., mm/mmm Pole radius, mm Bending angle, deg Radius of curvature, m Yoke width, m Yoke height, m Overall weight, kg Current at maximum field (field gradient), ka Number of turns in winding Inductance, µh Vacuum shell outer diameter, mm Dynamic heat release, W Static heat leak (with non-structural element), W Cable cooling channel diameter, mm Helium pressure drop in winding, kpa Maximal temperature of helium in winding, K /

18 Page 17of 19 Characteristics Number of magnets in ring Maximum magnetic induction, T (field gradient, T/m) Effective magnetic length, m Ramp rate db/dt,, T/s Field error B/B ( G/G) at R = 30 mm Beam pipe aperture hor./vert., mm/mm Pole radius, mm Bending angle, deg Yoke width, m Yoke height, m Distance between beam orbits, m Overall weight, kg Current at maximum field (field gradient), ka Number of turns in winding Inductance, µh Vacuum shell outer diameter, mm Heat release, W Helium pressure drop in winding, kpa Maximal temperature of helium in winding, K Final focus quadrupoles have largest aperture (diameter 180 mm) due to maximal β-function. There are 12 (4 triplets) final focus single-aperture quadrupoles in rings. Maximal gradient is 19 T/m. Distance from first quadrupole to IP is 5.25 m. Multipole corrector of Collider contains up to 4 separatee coils with following characteristics: dipole (max T, correction of x, y-closed orbit), quadrupole ( 1 T/m, betatron tune shift), skew quadrupole (1 T/m, coupling correction), sextupole (150 T/m, chromaticity correction), octupole (400 T/m 3 second order control). Correcting elements of 0.3 m long are placed next to main quadrupoles in arc and straight sections (Fig ). Inner pole tip radius is 66 mm Beam transfer channels Table Main characteristics of Collider lattice magnets. Dipole Quadrupole / The transfer channel from Booster to Nuclotron has fully (Fig , 7.7.2). The channel has total length of about 24 m and includes: 4 dipole magnets, Lambertson magnet and 6 quadrupole lenses; target for ion stripping ( stripping efficiency is about 80 %); beam dumper for ions at charge state less than bare nuclei; steerers and beam diagnostic devices. 3D geometry

19 Page 18of 19 Fig The transfer channel from Booster to Nuclotron. View from above. Fig The transfer channel from Booster to Nuclotron. Vertical profile. The transfer channel from Nuclotron to Collider rings has common part for both beams and two branches (Fig ). The channel has total length of about 335 m and consists of 33 dipole magnets, 45 quadrupole lenses, steerers and beam diagnostic devices. It will be operated in pulsed mode. Fig The transferr channel from Nuclotron to Collider. E extraction point from Nuclotron; C1 end of common part; L1, L2 beginning and end of big arc in left branch; R1 end of big arc in right branch; R2 beginning of small arc in right branch; LI, RI injection points into collider rings from left and right branches correspondingly.

20 Page 19of References: 1. Conceptual Design Report of Nuclotron-based Ion Collider facility (NICA), JINR, Conceptual Design Report of MultiPurpose Detector, JINR, V.V. Fimushkin et al., Eur. Phys. J., Special Topics, 162, 275, 2008; V.P. Derenchuk, A.S. Belov, in Proceedings of Particle Accelerator Conference Chicago, 2001, p E.D. Donets et al.., Electron string source of highly charged ions:studies and first test on a synchrotron, in Proceedings of EPAC2002, Paris, June 3-7, 2002,pp V.V. Kobets, A.I. Govorov, G.V. Trubnikov, et al., Heavy ion injector for NICA/MPD project, Proceedings of LINAC08, Victoria, BC, Canada, 2008, pp H.G. Khodzhibagiyan and A.A. Smirnov, The concept of a superconducting magnet system for Nuclotron, Proc. of 12 th Int. Cryogen. Eng. Conf., 1988, pp ; A.M. Baldin et al.., Superconducting fast cycling magnets of Nuclotron, IEEE Trans. on Applied Superconductivity, Vol. 5, 2, 1995, pp A. Sidorin, V. Alexandrov, O. Brovko, et al., Status of Nuclotron. Nuclotron-M project, Proceedings of IPAC10, Kyoto, Japan, 2010, pp Concept of NICA Collider, JINR, S. Kostromin, O. Kozlov, I. Meshkov, V. Mikhailov, A. Sidorin, V. Lebedev, S. Nagaitsev, Yu. Senichev, Lattice of NICA Collider Rings, Proceedings of IPAC10, Kyoto, Japan, pp

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