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EDM Ring, Five Quads lattice, orbit and spin tracking

EDM Ring, Five Quads lattice, orbit and spin tracking. Alfredo U Luccio 06JUN07. Three Thin Quads. Five Fat Quads. Sector Bends. Alternating gradient Bends to reduce dispersion. FFQ parameters (1).

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EDM Ring, Five Quads lattice, orbit and spin tracking

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  1. EDM Ring, Five Quadslattice, orbit and spin tracking Alfredo U Luccio 06JUN07

  2. Three Thin Quads

  3. Five Fat Quads

  4. Sector Bends Alternating gradient Bends to reduce dispersion

  5. FFQ parameters (1) pc = 1.5 [GeV] (deuterons) r = 2.5 [m] g = 1.3414 bS = 0.6665 Br = 5.003 [ Tm ] B0 = 2.00 [ T ]

  6. FFQ parameters(2) Ld= pr(p2/6 - 1)= 5.0653 [m] , drift length n = 1, bend field index K1B = -n/r2 [1/m2] , bend quad strength LQ = 0.32 [m], quad length LH = 0.08 [m], quad-to-bend

  7. FFQ parameters(3) • K1Q1 = 0.166512 [1/m2 ] • K1Q2 = 1.282920 • K1Q3 = -1.564187 • G1 = K1Q1Br = 0.833136 [T/m] • G2 = K1Q2Br = 6.41904 • G3 = K1Q3Br =-7.82635

  8. FFQ parameters(4) total length = 25.838564 [m] nx = 0.637806, hor. beta tune ny = 1.182998, vert. beta tune ap = 1.00001, mom. compaction bX,max = 16.8168 [m] by,max = 36.5071 [m] gtr = 0.999997, transition Dx,max = 20.6318, dispersion

  9. Tracking (1) Track polarized deuterons (magnetic), or, equivalent protons with energy close to an Intrinsic spin resonance Gg = n + ny To check limits of spin stability. Cross the resonance by slow acceleration

  10. Lattice (MAD)

  11. FFQ tracking (2) 1+Gg = 1.183; G = g/2-1 G(p) = 1.79285, G(d) = -0.14301 pc(p) = 1.3764 GeV: Gg(p) = [3].183 pc(d) = 1.4983 GeV: g(d) = 1.2796 Gg(d) = 0.183 search for spin resonance at n +/- 0.183 Accelerate in a RF cavity with V = 5 KV Code Spink based on the BMT equation, modified to add edm

  12. EDM base line

  13. Transverse phase space(to check symplecticity after many turns)

  14. Longitudinal Phase Space

  15. Track spin - resonance Cross spin resonance at Gg=3.183 Various speeds of crossing (for Froissart-Stora) Represented is the vertical component of spin vs. spin tune Gg

  16. Various long. phases -cDt Track particles at various longitudinal position in the bunch They cross the resonance differently, producing some depolarization

  17. Spin resonance- vary: -cDt Some more of the same……

  18. Various –cDt (2) Central part of the bunch. Particles up to 4 m away from the synchronous particle Particles within a 1 m long bunch behave coherently

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