Simulations for FCC-ee beam self-polarization

Transcription

1 Smulatons for FCC-ee beam self-polarzaton E. Ganfelce (Fermlab) Contents: - Sokolov-Ternov polarzaton n a 1 km rng - Polarzaton n presence of wgglers; parametrc studes - Smulatons at 45 and 8 GeV n presence of msalgnments - Some consderatons on energy calbraton - Summary FCC Week, Rome, Aprl 216 1/44 < >? P

2 Introducton Hgh precson beam energy measurement ( 1 kev) s needed for Z pole physcs at 9 GeV CM energy and W physcs at 16 GeV CM energy. If not at cost of lumnosty, longtudnal beam polarzaton mproves Z peak measurements, but t s not essental. Self-polarzaton through Sokolov-Ternov effect strongly depends on bendng radus and beam energy: not obvous for FCC. 2/44 < >? P

3 Sokolov-Ternov polarzaton Beam get vertcally polarzed n the vertcal gudng feld of the rng P = 92.3% τ 1 p = 5 3 r e γ 5 8 m C ds ρ 3 For FCC-e + e wth ρ 1424 m, fxed by the maxmum attanable dpole feld for the hh case, t s E U σ E /E τ pol (GeV) (MeV) (%) (h) /44 < >? P

4 Effect of wgglers τ p may be reduced by ntroducng wgglers: τ 1 p = F γ 5 [ dp ds ρ d 3 + wg ds ] ρ w 3 F r e m C Polarzaton P = ds ˆB ˆn ρ 3 ds 1 ρ 3 τ p [ dp ds ˆB d ˆn ρ d 3 + wg ds ˆB w ˆn ] ρ w 3 ˆn ŷ n a perfectly planar rng. Constrants: x = outsde the wggler wg ds B w = x = outsde the wggler wg ds sb w = (vanshng feld ntegral) (true for symmetrc feld) P large wg ds B3 w must be large 4/44 < >? P

5 The LEP polarzaton wgglers have been consdered wg ds 1 ρ 3 w = L + (1 1 ) ρ 3 + N 2 N L /L + = B + /B N should be large for keepng polarzaton hgh! 5/44 < >? P

6 4 such wgglers wth N = 6 and L + =1.3 m have been ntroduced n dsperson free regons of a smplfed FCC rng ( toy rng ). At 45 GeV: B + U E/E E ɛ x τ x P τ pol (T) (MeV) (%) (MeV) (µm) (s) (%) (mn) e e e /44 < >? P

7 LEP measured polarzaton (R. Assmann et al., SPIN2, Osaka) Polarzaton strongly dependng on energy and no polarzaton observed above 65 GeV! 7/44 < >? P

8 Sokolov-Ternov effect n the gudng dpole feld Polarsaton Perturbatons (v-bends, vertcal orbt n quads etc.) Depolarsaton Equlbrum polarsaton (< P ST ) 8/44 < >? P

9 Derbenev-Kondratenko expresson for equlbrum polarzaton wth P DK = ds < 1 ˆb (ˆn ˆn ρ 3 δ ) > [ ] ds < ρ 3 9 (ˆn ŝ) ( ˆn δ )2 > ˆb v v/ v v ˆn/ δ (δ δe/e) quantfes the depolarzng effects resultng from the trajectory perturbatons consequent to photon emsson. Perfectly planar machne: ˆn/ δ=. In presence of radal felds: ˆn/ δ and large when ν spn ± mq x ± nq y ± pq s = nteger ν spn aγ Usually the domnant hgher order resonances are the synchrotron sdebands of the frst order resonances. LEP lack of polarzaton at hgh energy s understood as due to the larger beam energy spread. Wgglers ncrease the energy spread of FCC-e+e- beams! 9/44 < >? P

10 Is t possble to mprove the wggler desgn to get lower energy spread at constant τ pol? The mportant nterconnected parameters are U loss = C γe 4 2π ds ρ 2 (σ E /E) 2 = C q J ɛ γ 2 ds ds ρ / 3 ρ 2 τ 1 p = F γ 5 [ dp ds ρ d 3 + wg ds ρ w 3 ] = F γ 5 [ dp ds ρ d 3 + L+ ρ + 3 ( N 2 ) ] P = 8F γ5 5 3 τ p [ dp ds ˆB d ˆn ρ d 3 + L+ ρ + 3 ( 1 1 N 2 ) ] ˆn ŷ n a planar rng 1/44 < >? P

11 For energy calbraton the actual mportant parameter s the tme, τ 1%, needed to reach P 1% rather than τ p τ 1% = τ p ln(1.1/p ) depends upon P The energy spread may wrtten as (σ E /E) 2 = C qc γ E 4 2πJ ɛ F γ 3 1 τ p U loss.e. small σ E and τ p are at the prce of hgher U loss. 11/44 < >? P

12 Effect of one wggler - 45 GeV B + (T) N = 2 N = 4 N = 6 N = τ p (h) P (%) N = 2 N = 4 N = 6 N = τ p (h) nb: L =NL +, wth L + =1.3 m τ 1% (h) N = 2 N = 4 N = 6 N = τ p (h) 12/44 < >? P

13 σ Ε (Μες) N = 2 N = 4 N = 6 N = τ p (h) U loss (MeV) N = 2 N = 4 N = 6 N = τ p (h) 13/44 < >? P

14 Fxng σ E =5 MeV (LEP σ E at 6 GeV) B + 1 T for any value of N. L =NL +, wth L + =1.3 m N B + U loss σ E P τ pol τ 1% (T) (MeV) (MeV) (%) (h) (h) For such feld only N=2 should be avoded because of the larger τ 1%. 14/44 < >? P

15 Keepng L + + L =L + (1 + N)=9.3 N B + U loss σ E P τ pol τ 1% (T) (MeV) (MeV) (%) (h) (h) /44 < >? P

16 Effect of number of wgglers B + (T) # = 1 # = 4 # = 8 # =12 # = τ p (h) P (%) # = 1 # = 4 # = 8 # =12 # = τ p (h) nb: L =NL +, wth L + =1.3 m and N=6 τ 1% (h) # = 1 # = 4 # = 8 # =12 # = τ p (h) 16/44 < >? P

17 σ Ε (Μες) # = 1 # = 4 # = 8 # =12 # = τ p (h) U loss (MeV) # = 1 # = 4 # = 8 # =12 # = τ p (h) 17/44 < >? P

18 Fxng σ E =5 MeV # B + U loss σ E P τ pol τ 1% (T) (MeV) (MeV) (%) (h) (h) No mraculous set of parameters, but larger number of wgglers s better: polarzaton tme decreases n- losses ncrease but they are better dstrbuted; however wth 16 wgglers P RF creases from 51 to 7.5 MW for I=145 ma (U loss =35 MeV w/o wgglers) 18/44 < >? P

19 8 GeV case For curosty... E U σ E /E σ E τ pol τ 1 (GeV) (MeV) (%) (MeV) (h) (h) Do we need wgglers? No, as polarzaton s not needed for physcs. 19/44 < >? P

20 B + (T) # = 1 # = 4 # = 8 # =12 # = τ p (h) P (%) # = 1 # = 4 # = 8 # =12 # = τ p (h) L =NL +, L + =1.3 m 8 GeV beam energy τ 1% (h) # = 1 # = 4 # = 8 # =12 # = τ p (h) 2/44 < >? P

21 σ Ε (Μες) # = 1 # = 4 # = 8 # =12 # = τ p (h) U loss (MeV) # = 1 # = 4 # = 8 # =12 # = τ p (h) 21/44 < >? P

22 Parameter values for halvng τ 1% # B + U loss σ E P τ pol τ 1% (T) (MeV) (MeV) (%) (h) (h) No advantage from large number of wgglers, a part from better dstrbuted losses. 22/44 < >? P

23 Resonances are awakened by mperfectons! Queston: how perfect the rng must be for keepng resonances sleepng? Smulatons n presence of realstc errors and correctons are needed. MAD-X used for smulatng quadrupole msalgnments and orbt correcton SITROS (by J. Kewsh) used for computng the resultng polarzaton. It s a trackng code wth 2th order orbt descrpton and non-lnear spn moton. It has been used for HERA-e n the verson mproved by M. Böge and M. Berglund. HERA-e lke Harmonc Bumps optmzaton for δˆn correcton n the FCC-e+erng mplemented. SLIM by A. Chao s used for lnear calculatons. SLICKTRACK by D. Barber s avalable too, but t needs extra work to avod usng the costly NAG lbrary. 23/44 < >? P

24 Washngton week: 45 GeV case wth 4 wgglers effect of quadrupole vertcal ms-algnment for varous wggler feld strength was consdered n absence of BPMs errors polarzaton was not a msson mpossble In ths talk: 45 GeV lmt E=5 MeV (extrapolatng from LEP) 4 wgglers wth B + =.7 T 1% polarzaton n 2.9 h for energy calbraton 8 GeV no wgglers 1% polarzaton n 1.6 h for energy calbraton BPMs errors added to quadrupole msalgnments 24/44 < >? P

25 Toy rng, 4 wgglers wth B + =.7 T Smulatons at 45 GeV Q x =.1278 Q y =.285 Q s =.1174 (U rf =9 MV, f RF =4 MHz) Closed orbt correcton scheme: BPM ntroduced close to each quadrupole one vertcal corrector ntroduced close to each vertcal focusng quadrupole orbt corrected ether by SVD usng all 196 correctors or 11 correctors (MICADO algorthm) polarzaton axs ˆn (s) dstorton corrected by 8 Harmonc Bumps à la HERA-e 25/44 < >? P

26 Quadrupole vertcal msalgnments δ Q y = 2 µm y rms δˆn,rms (mm) (mrad) SVD Wgglers B+=.7 T - Q s =.1 Polarzaton [%] Lnear SITROS a*γ 26/44 < >? P

27 δ Q y = 2 µm BPMs errors δ M y = 2 µm 1% calbraton errors y rms δˆn,rms (mm) (mrad) SVD bumps.9 2. Polarzaton [%] Wg. B + =.7T Lnear SITROS Polarzaton [%] Wg. B + =.7T Lnear SITROS a*γ a*γ SVD SVD + harmonc bumps 27/44 < >? P

28 Increasng wggler strength and keepng errors/correctors (orbt and δˆn are unchanged), e 4 wgglers wth B + =3.9 T ( E=247 MeV at 45 GeV!) δ Q y = 2 µm BPMs errors δ M y = 2 µm Polarzaton [%] Wgglers OFF - Q s = Lnear SITROS % calbraton errors a*γ SVD correcton + hb 28/44 < >? P

29 y rms δˆn,rms (mm) (mrad) MICADO bumps Polarzaton [%] Wg. B + =.7T Lnear SITROS Polarzaton [%] Wg. B + =.7T Lnear SITROS a*γ a*γ MICADO MICADO + harmonc bumps 29/44 < >? P

30 Effect of quadrupole roll angle. 1.8 Dsperson θ Q rms =.25 mrad D(m) ɛ x ɛ y rato (µ) (µ) (%) D x D y.148e-2.27e s(km) 1 4 Wg. B + =.7T Polarzaton [%] Lnear SITROS a*γ 3/44 < >? P

31 Smulatons at 8 GeV no wgglers δ Q y = 2 µm no BPMs errors orbt correcton by SVD y rms =.5 mm ɛ y /ɛ x Polarzaton [%] Wgglers OFF Lnear SITROS δˆn,rms =3 mrad at GeV a*γ 31/44 < >? P

32 Increasng Q s to.3 a Correctng δˆn,rms =2.5 mrad Wgglers OFF - Q s =.33 Polarzaton [%] Lnear SITROS Wgglers OFF - Q s =.1 Polarzaton [%] Lnear SITROS a*γ a*γ a Enhancement factor ξ = ( aγ E ) 2 Q s E 32/44 < >? P

33 Addng BPMs errors 6 Harmonc Bumps no wgglers 4 2 δ Q y = 2 µm BPMs errors δ M y = 2 µm 1% calbraton errors y(mm) s(km) orbt correcton by SVD Wgglers OFF - Q s =.1 y rms =.8 mm ɛ y /ɛ x =.2% δˆn,rms =19.8 mrad at GeV wth harmonc bumps Polarzaton [%] Lnear SITROS δˆn,rms =8.6 mrad ɛ y /ɛ x =2% a*γ /44 < >? P

34 Polarzaton [%] Lnear - w/o harmonc bumps P P x P y P s Polarzaton [%] Lnear - wth harmonc bumps P P x P y P s a*γ a*γ 34/44 < >? P

35 Wgglers OFF - Q s =.1 no wgglers δ Q y = 2 µm BPMs errors δ M y = 2 µm 5% calbraton errors Polarzaton [%] Lnear SITROS orbt correcton by SVD a*γ y rms =.6 mm ɛ y /ɛ x =.3% δˆn,rms =14.4 mrad at GeV δˆn,rms =6.9 mrad wth harmonc bumps ɛ y /ɛ x =2.5% y(mm) Harmonc Bumps s(km) 35/44 < >? P

36 Polarzaton [%] Lnear - no harmonc bumps P P x P y P s Polarzaton [%] Lnear - wth harmonc bumps P P x P y P s a*γ a*γ The large vertcal bumps ncrease the vertcal emttance! 36/44 < >? P

37 Wgglers OFF - Q s =.1 no wgglers δ Q y = 2 µm BPMs errors δ M y = µm Polarzaton [%] Lnear SITROS % calbraton errors a*γ orbt correcton by SVD y rms =.4 mm δˆn,rms =11.5 mrad at GeV 2 1 Harmonc Bumps δˆn,rms =5 mrad wth harmonc bumps ɛ y /ɛ x =1.2% y(mm) s(km) 37/44 < >? P

38 Idea: use 5 cols to get dsperson-free bumps. no wgglers δ Q y = 2 µm BPMs errors δ M y = 2 µm Polarzaton [%] Lnear - wth harmonc bumps P P x P y P s % calbraton errors a*γ orbt correcton by SVD y rms =.8 mm ɛ y /ɛ x =.2% δˆn,rms =19.9 mrad at GeV wth harmonc bumps δˆn,rms =9.7 mrad Polarzaton [%] Wgglers OFF - Q s = Lnear SITROS ɛ y /ɛ x =.2% a*γ 38/44 < >? P

39 Some consderatons on energy calbraton through resonant depolarzaton It s based on the relatonshps ν spn = aγ a gyromagnetc anomaly Requred precson: better than 1 KeV. To be taken nto account beam energy dependence upon orbt length contnuous montorng poston along the rng short lumnosty lfetme (1-3 hours) calls for top-up njecton use of non-colldng bunches for polarzaton non-colldng bunches may have a dfferent energy One more basc problem s t always ν spn = aγ? 39/44 < >? P

40 The relatonshps ν spn = aγ holds for a purely planar rng Effect of radal felds depends upon energy and unperturbed spn tune. For the toy rng, averagng over 1 seeds a E (KeV) 45 GeV 6.3 ± 3. 8 GeV 2. ± 9.4 Effect of RF electrc feld (term β E RF n BMT-equaton) b E (KeV) 45 GeV α rms 43 8 GeV α rms 76 α angle between orbt and electrc feld (mrad). a Usng formulas from R. Assmann thess b From Yu. I. Edelman et al. formulas 4/44 < >? P

41 The spn tune changes as computed by SITF (lnear) for the actual cases presented here (wth BPMs errors) gve E (KeV) svd +hb 45 GeV GeV The effect seems to be larger than expected; t should be better nvestgated! 41/44 < >? P

42 Summary and outlook. Studes for the 45 GeV and 8 GeV case have been presented. The large bendng radus requres wgglers for reducng the polarzaton tme at low energy keepng a hgh asymptotc polarzaton level n absence of errors. In presence of errors, n partcular the vertcal msalgnment of quadrupoles, depolarzng resonances appear. Synchrotron sde-bands become more dangerous wth ncreasng energy spread. Ther mportance can be quantfed only by non-lnear calculatons, lke n SITROS. Mantanng acceptable level of polarzaton calls for well planned correcton schemes, n partcular at 8 GeV. Wth the proposed scheme t seems that mantanng polarzaton for energy calbraton at 45 GeV s not a msson mpossble, but space must be provded n the FODO cells for BPMs and correctors! 42/44 < >? P

43 At larger energy ɛ x ncreases larger effect of couplng and δˆn At 8 GeV, δˆn due to the same msalgnments ncreases and although the energy spread s the same as at 45 GeV wth wgglers, the polarzaton s lower! The LEP lmt shouldn t be appled to lower energes. The large bumps requred for the correcton cause a even larger vertcal emttance ncrease. A more effcent δˆn correcton has been consdered, lkely there s stll space for mprovements. The reach of beam-based algnments technques should be nvestgated. Effect of solenods (δˆn and couplng) must be compensated, better wth antsolenods at proper locatons. The planned soluton s hghly recommended! 43/44 < >? P

44 End of the 3th Epsode Thanks! 44/44 < >? P