1. 1 Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake Yu.N. Filatov 1,3, A.D. Kovalenko 1, A.V. Butenko 1, A.M. Kondratenko 2, M.A. Kondratenko 2 and V.A. Mikhaylov 1 1 Join Institute for Nuclear Research, Dubna, Russia 2 Science and Technique Laboratory Zaryad, Novosibirsk, Russia 3 Moscow Institute of Physics and Technology, Dolgoprydny, Russia July 7 –13, 2013, Prague, Czech Republic "ADVANCED STUDIES INSTITUTE – SYMMETRIES AND SPIN" (SPIN-PRAHA-2013 AND NICA-SPIN-2013)

2. 2 Polarized proton and deuteron in Nuclotron B. Issinskii et al., “Deuteron Resonance Depolarization Degree in JINR Nuclotron,” in Proc. of VI Workshop on HESP, Protvino, 1996 N. I. Golubeva et al., “Study of Depolarization of Deuteron and Proton Beams in Nuclotron Ring,” Preprint JINR R9-22-289 (Dubna, 2002) S.Vokal et al. “Program of Polarization Studies and Capabilities of Accelerating Polarized Proton and Light Nuclear Beams at the Nuclotron of the Joint Institute for Nuclear Research”, Physics of Particles and Nuclei Letters, 2009, Vol. 6, No. 1, pp. 48–58. I.Meshkov and Yu.Filatov, “ Polarized hadrons beams in NICA project”, 19th International Spin Physics Symposium, 2010 Jülich, Germany A.Kovalenko et al. The NICA Facility in polarized proton operation mode, IPAC’11 Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake Yu. Filatov et al., Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake, SPIN-Praha 2013, July 7- 13, 2013, Prague

3. 3 lg(w/w D ) E p, GeV w D = 7.3  10-4 lg(w/w D ) w D = 7.3  10 -4 E p, GeV 2.Integer res. spin = k Spin resonances at Nuclotron lg(w/w D ) 3. Nonsuperperiodic res. spin = m  Q y, m  kp E p, GeV lg(w/w D ) 4. Coupling res. spin = m  Q x, m  kp w D = 7.3  10 -4 E p, GeV w D = 7.3  10 -4 1.Intrinsic res. spin = kp  Q y 1 4 5 16 1 4 1 2 Dangerous resonances are marked with red caps dB/dt = 1 T/s An option: acceleration up to 6 GeV and extraction into NICA collider for further acceleration up to 12 GeV max. Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake Yu. Filatov et al., Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake, SPIN-Praha 2013, July 7- 13, 2013, Prague

4. 4 Full and Partial Siberian Snake Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake Yu. Filatov et al., Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake, DSPIN-2012, Sep 17- 22, 2012, Dubna Spin tune in accelerator with Partial Siberian Snake eliminate integer resonances eliminate intrinsic resonances Full Siberian Snake

5. 5 Solenoid Siberian Snake in Nuclotron (E kin =5GeV) Total longitudinal field integral: ( B || L) max = 22 T  m Full Siberian Snake Partial Siberian Snake ( B || L) max =11 T  m, (  z =  /2), |k- y,x |<0.25 (B || L) max =5,5 T  m, (  z=  /4), |k- y,x |<0.125 (z=)(z=) Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake Yu. Filatov et al., Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake, SPIN-Praha 2013, July 7- 13, 2013, Prague It is appropriate to apply partial Siberian Snake in Nuclotron for proton polarization preservation during acceleration (acceleration time  acc ~1 sec). It allows to use free space of Nuclotron more efficiently. is angle between polarization and vertical axis

6. 6 Conventional coupling compensation scheme Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake Yu. Filatov et al., Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake, SPIN-Praha 2013, July 7- 13, 2013, Prague Two free spaces of Nuclotron for installation of the partial Siberian Snake Compensation quadrupoles for any spin rotation angle of solenoids Conventional scheme allows to compensate the solenoids coupling, but it significantly changes the orbital characteristics of Nuclotron ring. Conventional coupling compensation schemes with optical transparency condition are unfeasible in Nuclotron. Solenoid parameters: Structural quadrupole:

7. 7 7 Coupling Compensation 0 L sol  1 z1z1 sol  2 z2z2 q 1,  1 q 2,  2 … sol  i zizi q i,  i … Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake Yu. Filatov et al., Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake, SPIN-Praha 2013, July 7- 13, 2013, Prague Consider a system of weak solenoids and quadrupoles in a straightsection Coupling compensation and optical transparency conditions Conventional scheme uses strong quadrupoles are angles between quadrupole normal and vertical accelerator axis where is net orbit angle in solenoids

8. 8 8 Coupling Compensation (section with one structural quadrupole) Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake Yu. Filatov et al., Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake, SPIN-Praha 2013, July 7- 13, 2013, Prague 0 L sol  1 z1z1 sol  2 z2z2 q 1,  1 q 2,  2 … sol  i zizi q i,  i … z0z0 q 0,  0 = 0 … Structural quadrupole allows to reduce strengths of compensating quadrupoles additionally

9. 9 The optical transparency scheme of coupling compensation are angles between quadrupole normal and vertical accelerator axis is quadrupole gradient L S, mL 1, mL 2, m  L, m 0,550,51,00,15  B ||, Tk 1, m -2 k 2, m -2 G 1, T/mG 2, T/mG 0, T/m  /4 2,50,2 3,9 14,7  /2 50,460,49,07,814,7 is the structural defocusing quadrupole G0G0 Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake Yu. Filatov et al., Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake, SPIN-Praha 2013, July 7- 13, 2013, Prague E kin = 5 GeV

10. 10 Summary & Outlook  The class of optical transparency schemes for solenoidal inserts is presented. Usage of structural quadrupole allows to reduce strengths of compensating quadrupoles additionally. Such inserts do not change orbital characteristics of the Nuclotron.  Partial Siberian Snakes open possibility to use Nuclotron as the polarized protons injector for NICA collider and for fix target experiments too.  Similar schemes of partial Siberian Snake can be used to preserve proton polarization in the Booster. Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake Yu. Filatov et al., Polarized Proton Beam Acceleration at Nuclotron with the use of the Solenoid Siberian Snake, SPIN-Praha 2013, July 7- 13, 2013, Prague

11. Thank you for your attention!