Mitglied der HelmholtzGemeinschaft Acceleration of Polarized Protons and

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Mitglied der Helmholtz-Gemeinschaft Acceleration of Polarized Protons and Deuterons at HESR/FAIR 28 -30 May

Mitglied der Helmholtz-Gemeinschaft Acceleration of Polarized Protons and Deuterons at HESR/FAIR 28 -30 May 2009 | Andreas Lehrach

Content Introduction Spin dynamics Methods for preserve polarization Acceleration of Polarized Beams Spin resonances

Content Introduction Spin dynamics Methods for preserve polarization Acceleration of Polarized Beams Spin resonances in SIS 18 and HESR Measures for polarized protons and deuterons Extension for Polarized Beams 12 March 2021 A. Lehrach, Common ENC/EIC Workshop at GSI 2

Spin Dynamics in Circular Accelerators Thomas-BMT Equation (Thomas [1927], Bargmann, Michel, Telegdi [1959]): Lab

Spin Dynamics in Circular Accelerators Thomas-BMT Equation (Thomas [1927], Bargmann, Michel, Telegdi [1959]): Lab system Number of spin rotations per turns: Imperfection resonance: Intrinsic resonance: P: Super-periodicity Qy: Vertical tune k: integer Field and positioning errors of magnets Vertical focusing fields Resonance strength ~ yrms Resonance strength ~√εy Vertical closed orbit correction Partial Snake Vertical tune jump Vertical coherent betatron oscillation 12 March 2021 A. Lehrach, Common ENC/EIC Workshop at GSI 3

Methods for Polarization Preservation • < 5 Ge. V: Conventional methods Correcting dipoles Tune-jump

Methods for Polarization Preservation • < 5 Ge. V: Conventional methods Correcting dipoles Tune-jump quadrupoles ZGS, COSY, ELSA, … • 5 - 10 Ge. V: Adiabatic spin-flip Partial snake AC dipole AGS • > 10 Ge. V: Full Siberian snake RHIC 12 March 2021 A. Lehrach, Common ENC/EIC Workshop at GSI 4

Siberian Snake cos(180 νsp) = cos( /2) · cos(180 γG) • Full: = 180°

Siberian Snake cos(180 νsp) = cos( /2) · cos(180 γG) • Full: = 180° νsp = ½ All spin resonances except snake resonances • Partial: < 180° νsp ≠ k Imperfection resonances • Magnet system for snakes: Longitudinal fields (solenoids) for low energies Transversal fields (dipoles) for higher energies 12 March 2021 A. Lehrach, Common ENC/EIC Workshop at GSI 5

Preliminary Scheme for ENC at FAIR Scheme of the ENC@FAIR for electron-proton collisions Contribution

Preliminary Scheme for ENC at FAIR Scheme of the [email protected] for electron-proton collisions Contribution to the Particle Accelerator Conference, Vancouver, 2009 12 March 2021 A. Lehrach, Common ENC/EIC Workshop at GSI 6

Proton Spin Resonances in SIS 18 Acceleration to HESR injection: 369 Me. V/c (70

Proton Spin Resonances in SIS 18 Acceleration to HESR injection: 369 Me. V/c (70 Me. V) – 3. 8 Ge. V/c (3. 0 Ge. V) • Imperfection: 6 2 (464 Me. V/c) , 3 (1. 26 Ge. V/c), 4 (1. 87 Ge. V/c), 5 (2. 44 Ge. V/c), 6 (3. 00 Ge. V/c), 7 (3. 51 Ge. V/c) Correction: • Intrinsic Acceleration rate 1 Ge. V/c per 0. 05 s 3% partial snake (0. 5 Tm solenoid) (P=12, Qy=3. 28): 1 0+ (1. 44 Ge. V/c) 12 - (4. 47 Ge. V/c) Correction: 12 March 2021 Depending on beam emittance 20 mm mrad (norm. ): R = 3· 10 -3 AC dipole 1 mm mrad (norm. ): R < 10 -3 Tune-jump quadrupole A. Lehrach, Common ENC/EIC Workshop at GSI 7

Proton Spin Resonances in HESR • Imperfection: 25 4, 5, 6, . . .

Proton Spin Resonances in HESR • Imperfection: 25 4, 5, 6, . . . , 28 Strong: 8, 16, 24 • Intrinsic (P=1, Qy=7. 61): 50 21 -, 22 -, . . . , 45 -3+, -4+, . . . , 11+ Strong: 0+, 44 - • Coupling: 50 21 -, 22 -, . . . , 45 -3+, -4+, . . . , 11+ Correction: Full Siberian Snake 12 March 2021 A. Lehrach, Common ENC/EIC Workshop at GSI 8

Magent System of the Electron Cooler Compensation Solenoids Skew Quadrupoles Cooler Solenoid Quadrupoles 4.

Magent System of the Electron Cooler Compensation Solenoids Skew Quadrupoles Cooler Solenoid Quadrupoles 4. 8 Tm 7. 5 Tm 24 m Correcting Dipoles Toroid Integral magnetic field : ~20 Tm Required for full Siberian snake: 60 Tm (Proc. of SPIN 2004) 12 March 2021 A. Lehrach, Common ENC/EIC Workshop at GSI In Collaboration with Y. M. Shatunov et al. (BINP Novosibirsk) 9

Siberian Snake for HESR RHIC Helix dipole snake 4 superconducting helix: 4 T, 2

Siberian Snake for HESR RHIC Helix dipole snake 4 superconducting helix: 4 T, 2 m length with almost 360 twist of conductors Helixdipol u nd Solenoid 12 March 2021 A. Lehrach, Common ENC/EIC Workshop at GSI 10

Siberian Snake for HESR Solenoid Helix dipole HESR: 4 helix dipole (2. 5 T)

Siberian Snake for HESR Solenoid Helix dipole HESR: 4 helix dipole (2. 5 T) and 15 Tm solenoid In Collaboration with A. U. Luccio, BNL 12 March 2021 A. Lehrach, Common ENC/EIC Workshop at GSI 11

HESR Layout § Momentum range: 1. 5 – 15 Ge. V/c § Straight sections:

HESR Layout § Momentum range: 1. 5 – 15 Ge. V/c § Straight sections: cooler and target section § Ring circumference: 574 m Siberian Snake Stochastic Cooling 12 March 2021 A. Lehrach, Common ENC/EIC Workshop at GSI 12

Polarized Protons vs. Deuterons Polarization states: (2 S+1) 3 states for Spin 1 Vector

Polarized Protons vs. Deuterons Polarization states: (2 S+1) 3 states for Spin 1 Vector polarization: Pz = (n+-n-) / (n++n-+n 0) P zmax = ± 1 Tensor polarization: Pzz = (1 -3 n 0) / (n++n-+n 0) P zzmax = 1, -2 Gyromagnetic anomaly: Gp / Gd = -12. 6 Spin tune: Spin resonance strength: γp Gp / γd Gd= -25. 2 13 (low energies) to 25 (high energies) times weaker 25 times further apart Strength of spin resonances: same for vector and tensor polarization Siberian snake: much stronger magnetic fields 12 March 2021 A. Lehrach, Common ENC/EIC Workshop at GSI 13

Deuteron Spin Resonances • SIS 18: 0 No imperfection resonance No intrinsic resonance One

Deuteron Spin Resonances • SIS 18: 0 No imperfection resonance No intrinsic resonance One weak gradient error resonance 3 - (3. 16 Ge. V/c) No Correction needed • HESR: 3 Imperfection resonance: – 1 (13. 0 Ge. V/c) Intrinsic resonances: – 8+ (4. 76 Ge. V/c), 7 - (7. 78 Ge. V/c) Two weak coupling resonances Correction: Partial snake, tune-jump quads No longitudinal polarized beam! 12 March 2021 A. Lehrach, Common ENC/EIC Workshop at GSI 14

Partial Snake for HESR Spin Tune with Partial Snake n n Full Siberian snake

Partial Snake for HESR Spin Tune with Partial Snake n n Full Siberian snake for protons ONLY 20% partial snake for deuterons Move working point close to integer . 90 < Qfrac <. 10 like in the AGS 12 March 2021 A. Lehrach, Common ENC/EIC Workshop at GSI 15

Extension for Polarized Protons and Deuterons • Polarized ion sources (CIPIOS-type) • Acceleration via

Extension for Polarized Protons and Deuterons • Polarized ion sources (CIPIOS-type) • Acceleration via p-Linac or UNILAC • Several polarimeter (at least three) • Systems for spin preservation Protons correction system for SIS 18 (space available? , 2 times 0. 5 m needed) Full Siberian snake for HESR (space reserved) Deuterons Partial snake and tune-jump quads for HESR No longitudinal polarized beam 12 March 2021 A. Lehrach, Common ENC/EIC Workshop at GSI 16