Simulations for FCC-ee beam self-polarization E. Gianfelice - PowerPoint PPT Presentation

Simulations for FCC-ee beam self-polarization E. Gianfelice (Fermilab) Contents: - Sokolov-Ternov polarization in a 100 km ring - Polarization in presence of wigglers; parametric studies - Simulations at 45 and 80 GeV in presence of misalignments - Some considerations on energy calibration - Summary FCC Week, Rome, April 2016 1/44 < > � � ⊖ ? i P ≪ ≫ �

Introduction • High precision beam energy measurement ( ≪ 100 keV) is needed for Z pole physics at 90 GeV CM energy and W physics at 160 GeV CM energy. • If not at cost of luminosity, longitudinal beam polarization improves Z peak mea- surements, but it is not essential. • Self-polarization through Sokolov-Ternov effect strongly depends on bending radius and beam energy: not obvious for FCC. 2/44 < > � � ⊖ ? i P ≪ ≫ �

Sokolov-Ternov polarization Beam get vertically polarized in the vertical guiding field of the ring √ r e γ 5 � = 5 3 ds � τ − 1 P ∞ = 92 . 3% p | ρ | 3 8 m 0 C For FCC- e + e − with ρ ≃ 10424 m, fixed by the maximum attainable dipole field for the hh case, it is E U 0 σ E /E τ pol (GeV) (MeV) (%) (h) 45 35 0.038 256 80 349 0.067 14 3/44 < > � � ⊖ ? i P ≪ ≫ �

Effect of wigglers τ p may be reduced by introducing wigglers: √ ds ds F ≡ 5 3 r e � = F γ 5 �� � � τ − 1 | ρ d | 3 + p | ρ w | 3 8 m 0 C dip wig Polarization ˆ B · ˆ n 0 � ˆ ˆ ds 8 B d · ˆ n 0 B w · ˆ n 0 �� � � | ρ | 3 P ∞ = ∝ τ p ds + ds √ ds 1 � | ρ d | 3 | ρ w | 3 5 3 dip wig | ρ | 3 n 0 ≡ ˆ ˆ y in a perfectly planar ring. Constraints: • x ′ = 0 outside the wiggler ⇒ � wig ds B w = 0 (vanishing field integral) � • x = 0 outside the wiggler ⇒ wig ds sB w = 0 (true for symmetric field) wig ds B 3 � • P large ⇒ w must be large 4/44 < > � � ⊖ ? i P ≪ ≫ �

The LEP polarization wigglers have been considered ds 1 = L + 1 � � � 1 − N ≡ L − /L + = B + /B − ρ 3 ρ 3 N 2 wig + w N should be large for keeping polarization high! 5/44 < > � � ⊖ ? i P ≪ ≫ �

4 such wigglers with N = 6 and L + =1.3 m have been introduced in dispersion free regions of a simplified FCC ring ( “toy ring” ). At 45 GeV: B + U 0 ∆ E/E ∆ E ǫ x τ x P τ pol (T) (MeV) (%) (MeV) ( µ m) (s) (%) (min) 0 37 .04 18 .8e-3 .82 92.4 14e3 1.3 64 .22 99 .5e-2 .48 87.6 247 2.6 144 .41 184 .070 .21 87.6 31 3.9 278 .55 247 .274 .11 87.6 9 5.2 466 .65 292 .691 .06 87.6 4 6/44 < > � � ⊖ ? i P ≪ ≫ �

LEP measured polarization (R. Assmann et al., SPIN2000, Osaka) Polarization strongly depending on energy and no polarization observed above 65 GeV! 7/44 < > � � ⊖ ? i P ≪ ≫ �

Sokolov-Ternov effect Perturbations in the guiding dipole field (v-bends, vertical orbit in quads etc.) ↓ ↓ Polarisation Depolarisation ց ւ Equilibrium polarisation ( < P ST ) 8/44 < > � � ⊖ ? i P ≪ ≫ �

Derbenev-Kondratenko expression for equilibrium polarization | ρ | 3 ˆ n − ∂ ˆ n � 1 ds < b · (ˆ ∂δ ) > 8 P DK = √ � � s ) 2 + 11 5 3 18 ( ∂ ˆ n � 1 1 − 2 ds < 9 (ˆ n · ˆ ∂δ ) 2 > | ρ | 3 with ˆ v × ˙ v × ˙ b ≡ � � v/ | � v | � ∂ ˆ n/∂δ ( δ ≡ δE/E ) quantifies the depolarizing effects resulting from the trajectory perturbations consequent to photon emission. Perfectly planar machine: ∂ ˆ n/∂δ =0. In presence of radial fields: ∂ ˆ n/∂δ � = 0 and large when ν spin ± mQ x ± nQ y ± pQ s = integer ν spin ≃ aγ Usually the dominant higher order resonances are the synchrotron sidebands of the first order resonances. LEP lack of polarization at high energy is understood as due to the larger beam energy spread. Wigglers increase the energy spread of FCC-e+e- beams! 9/44 < > � � ⊖ ? i P ≪ ≫ �

Is it possible to improve the wiggler design to get lower energy spread at constant τ pol ? The important interconnected parameters are � ds � ds U loss = C γ E 4 ( σ E /E ) 2 = C q ds � γ 2 | ρ | 3 / ρ 2 ρ 2 2 π J ǫ L + ds ds ds 1 = F γ 5 �� � = F γ 5 �� � �� τ − 1 � | ρ d | 3 + | ρ d | 3 + 1 + p | ρ w | 3 | ρ + | 3 N 2 dip wig dip ˆ P ∞ = 8 F γ 5 + L + B d · ˆ n 0 1 − 1 �� �� � √ τ p ds n 0 ≡ ˆ ˆ y in a planar ring | ρ d | 3 | ρ + | 3 N 2 5 3 dip 10/44 < > � � ⊖ ? i P ≪ ≫ �

For energy calibration the actual important parameter is the time, τ 10% , needed to reach P ≃ 10% rather than τ p τ 10% = − τ p × ln(1 − 0 . 1 /P ∞ ) depends upon P ∞ The energy spread may written as ( σ E /E ) 2 = C q C γ E 4 1 2 πJ ǫ F γ 3 τ p U loss i.e. small σ E and τ p are at the price of higher U loss . 11/44 < > � � ⊖ ? i P ≪ ≫ �

Effect of one wiggler - 45 GeV 95 4.5 90 4 3.5 85 3 80 P ∞ (%) B + (T) 2.5 75 2 70 N = 2 N = 2 1.5 N = 4 65 N = 4 N = 6 1 N = 6 60 N = 8 0.5 N = 8 55 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 τ p (h) τ p (h) 12 10 8 τ 10% (h) 6 nb: L − = NL + , with L + =1.3 m 4 N = 2 N = 4 2 N = 6 N = 8 0 0 10 20 30 40 50 60 70 τ p (h) 12/44 < > � � ⊖ ? i P ≪ ≫ �

240 120 220 110 200 100 180 90 U loss (MeV) 160 σ Ε (Μες) 80 140 120 70 100 60 N = 2 N = 2 80 N = 4 50 N = 4 60 N = 6 N = 6 40 40 N = 8 N = 8 20 30 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 τ p (h) τ p (h) 13/44 < > � � ⊖ ? i P ≪ ≫ �

Fixing σ E =50 MeV (LEP σ E at 60 GeV) ⇒ B + ≃ 1 T for any value of N . L − = NL + , with L + =1.3 m B + N U loss σ E P τ pol τ 10% (T) (MeV) (MeV) (%) (h) (h) 2 1.03 40.4 50.1 59.1 25.5 4.7 4 1.08 39.9 50.0 82.6 25.8 3.3 6 1.09 39.7 50.1 87.9 26.0 3.1 8 1.09 39.5 50.0 89.8 26.0 3.1 For such field only N =2 should be avoided because of the larger τ 10% . 14/44 < > � � ⊖ ? i P ≪ ≫ �

Keeping L + + L − = L + (1 + N ) =9.3 B + N U loss σ E P τ pol τ 10% (T) (MeV) (MeV) (%) (h) (h) 2 0.78 42.4 50.0 59.0 24.3 4.5 4 0.96 40.6 50.0 82.6 25.5 3.3 6 1.08 39.7 50.0 87.9 26.0 3.1 8 1.18 39.2 50.0 89.8 26.3 3.1 15/44 < > � � ⊖ ? i P ≪ ≫ �

Effect of number of wigglers 90 4.5 4 89.5 3.5 3 89 2.5 P ∞ (%) B + (T) 88.5 2 # = 1 # = 1 1.5 88 # = 4 # = 4 1 # = 8 # = 8 # =12 87.5 0.5 # =12 # =16 0 # =16 87 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 τ p (h) τ p (h) 16 14 12 10 τ 10% (h) 8 nb: L − = NL + , with L + =1.3 m 6 # = 1 # = 4 and N =6 4 # = 8 # =12 2 # =16 0 0 20 40 60 80 100 120 140 τ p (h) 16/44 < > � � ⊖ ? i P ≪ ≫ �

240 220 220 200 200 180 180 160 U loss (MeV) 160 140 σ Ε (Μες) 140 120 120 100 # = 1 # = 1 100 80 # = 4 # = 4 80 # = 8 # = 8 60 60 # =12 # =12 40 40 # =16 # =16 20 20 0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140 τ p (h) τ p (h) 17/44 < > � � ⊖ ? i P ≪ ≫ �

Fixing σ E =50 MeV B + # U loss σ E P τ pol τ 10% (T) (MeV) (MeV) (%) (h) (h) 1 1.09 39.7 50.1 87.9 26.0 3.1 4 0.71 42.8 50.0 87.9 24.2 2.9 8 0.57 45.3 50.0 87.8 22.8 2.8 12 0.51 47.1 50.0 87.8 22.0 2.7 16 0.47 48.6 50.0 87.8 21.3 2.6 No “miraculous” set of parameters, but larger number of wigglers is better: • polarization time decreases • losses increase but they are better distributed; however with 16 wigglers P RF in- creases from 51 to 70.5 MW for I =1450 mA ( U loss =35 MeV w/o wigglers) 18/44 < > � � ⊖ ? i P ≪ ≫ �

80 GeV case For curiosity... E U 0 σ E /E σ E τ pol τ 10 (GeV) (MeV) (%) (MeV) (h) (h) 45 35 0.038 17.1 256 29.0 80 349 0.067 53.6 14 1.6 Do we need wigglers? No, as polarization is not needed for physics. 19/44 < > � � ⊖ ? i P ≪ ≫ �

92.5 3 92 2.5 91.5 91 2 90.5 P ∞ (%) B + (T) 1.5 90 # = 1 89.5 # = 1 1 # = 4 89 # = 4 # = 8 # = 8 0.5 88.5 # =12 # =12 # =16 88 # =16 0 87.5 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 τ p (h) τ p (h) 1.8 1.6 1.4 1.2 τ 10% (h) 1 L − = NL + , L + =1.3 m 0.8 # = 1 0.6 # = 4 80 GeV beam energy 0.4 # = 8 # =12 0.2 # =16 0 0 2 4 6 8 10 12 14 16 τ p (h) 20/44 < > � � ⊖ ? i P ≪ ≫ �

300 650 600 250 550 U loss (MeV) 200 σ Ε (Μες) 500 150 # = 1 # = 1 450 # = 4 # = 4 # = 8 # = 8 100 400 # =12 # =12 # =16 # =16 50 350 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 τ p (h) τ p (h) 21/44 < > � � ⊖ ? i P ≪ ≫ �