Workshop on SPS-LEP Performance Chamonix IX Mismatch, damping and emittance growth o r LHC beam emittance preservation in SPS L. Vos 1 Boundary conditions 2 Quasi static errors (time scale : many machine cycles) 2.1 dipole mismatch 2.2 dispersion mismatch 2.3 betatron mismatch 2.4 multipole errors, etc. 3 Dynamic errors (time scale : turns to machine cycle) 3.1 transverse feedback : basic specs for stability 3.2 optimum correction injection errors 3.3 correction of injection errors 3.4 blow-up of circulating beam 4 Conclusion
Workshop on SPS-LEP Performance Chamonix IX 1 Boundary conditions 3.0 µ mrad input emittance : 3.5 µ mrad output emittance : Total blow-up budget attributed to SPS : 0.5 µ mrad many contenders to have a piece of the cake - 2-
Workshop on SPS-LEP Performance Chamonix IX 2 Quasi static errors 2.1 dipole mismatch or dipole injection error Transverse feedback (see later) can only handle errors below some limit ■ measure and correct static steering required when limit exceeded (injection error watch dog) these errors do not contribute to emittance blow-up if treated correctly - 3-
Workshop on SPS-LEP Performance Chamonix IX 2.2 dispersion mismatch Off momentum particles of a well injected beam (dipole) will be subjected to oscillations, filamentation and beam blow up. 2 βγ δ D p ∆ ε = ∆ β 2 p y emittance increase 0.08 / µ mrad for δ p/p = 10 -3 0.06 0.04 0.02 0 0 0.1 0.2 0.3 0.4 0.5 error in D / m ■ measure and correct measure trajectory of beam with small momentum spread (pencil beam, long bunches) - 4-
Workshop on SPS-LEP Performance Chamonix IX 2.3 betatron mismatch λ 1 1 ( ) ε = λ + λ ε − 2 2 0 2 Emittance increase due to quadrupole errors is multiplicative - 5-
Workshop on SPS-LEP Performance Chamonix IX µ mrad 3.7 3.6 3.5 3.4 3.3 3.2 3.1 3 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 mismatch factor λ - 6-
Workshop on SPS-LEP Performance Chamonix IX PS, transfer line PS-SPS, SPS optics well known and stable ejection/ injection SPS injection trajectory clear of machine magnet gaps PS ejection trajectory more difficult to model (off-centered beams, stray-fields) some uncertainty on the exact optics persists ■ measure and correct ■ install multiturn interceptive high resolution profile monitor in SPS ■ develop and install non interceptive quadrupole BPM ( watch dog function ) - 7-
Workshop on SPS-LEP Performance Chamonix IX 2.4 multipole errors, etc. ■ Avoid non-linear resonances HF single bunch instabilities ■ measure and correct =====> need a precise tune control and good betatron coupling compensation (much easier for LHC beam than for pbar-p beam : only zero order since no tune split as for low β optics !) - 8-
Workshop on SPS-LEP Performance Chamonix IX 3 Dynamic errors Only dipole errors considered 3.1 transverse feedback : basic specs for stability Stability against RW imposes a minimum gain that rolls off from a min frequency to fb/2 ( 20 MHz). R Q = G E e Z i ⊥ max G for ultimate intensity : 0.08 occurs at ~ 3 f rev due to non-uniform filling - 9-
Workshop on SPS-LEP Performance Chamonix IX 3.2 optimum correction injection error In principle observation and correction can be done at any harmonic of fb . OK for observation but not for correction : correction amplitude ideal correction correction at <f> correction at <f>/2 0 0 time Comparison between base-band and high frequency corrections deflector frequency below <f>/2 = 80 MHz choice of base band is good! - 10-
Workshop on SPS-LEP Performance Chamonix IX 3.3 correction of injection errors 3.3.1 errors • fast kickers γ normalised deflection CERN kickers ∆ x β = 0 1 . m e K = 0 5 . σ ====> total for kickers : fast kickers upstream SPS rise time < 100 ns ⇒ power bandwidth of 5 MHz. • bending magnets and septa ripple in transfer line e B = 0 5 . σ bendings in injection line e S = 0 25 σ . septa in injection line γ γσ 2 ( ) = 1 = + + ⇒ ε 2 2 2 2 e e e e 0 375 . β β inj K B S 2 [ assumed similar H and V !] e inj = 2.3 mm - 11-
Workshop on SPS-LEP Performance Chamonix IX 3.3.2 correction by feedback 2 2 1 1 1 1 ∆ ε = = 2 2 e e + τ τ + ∆ inj inj 2 1 2 1 2 5 . G Q dc d sc ε γ ˆ 2 i R Q Z R ∆ Q = − ε = σ 2 sc 0 ( ) σ π γ sc 2 2 direct space charge 2 E e R Q (ultimate intensity) 0.8 emittance increase / µ mrad 0.6 0.4 0.2 0 0 0.05 0.1 0.15 0.2 Gain - 12-
Workshop on SPS-LEP Performance Chamonix IX ε 2 θ = G total ∫ E dl ⇒ β γ ⊥ kic ker µ mrad allowed blow-up 0.3 µ mrad 2 1.5 e inj gain (RW) 0.08 gain (injection) 0.1 total gain 0.18 deflection ( β= 45 m) µ rad 6.3 ∫ kV 165 E dl ⊥ power band-width MHz 5 Gain and deflection requirements for SPS - 13-
Workshop on SPS-LEP Performance Chamonix IX Note Commissioning beam • 10x less intensity • √ 10 less emittance • same errors • fortunately √ 10 less ∆ Q sc ∆ε ~ 0.06 µ mrad for same G - 14-
Workshop on SPS-LEP Performance Chamonix IX 3.4 blow-up of circulating beam ε γ 2 d x = ∆ Q β x is the r.m.s. noise level dt T µ V noise level 40 Ω/ m effective monitor Z 40 A• µ m resolution 1 average coast time sec 7.2 µ mrad max blow-up 0.1 µ mrad/s max rate 0.014 µ m max x for max rate 4 dynamic(digital) 5300 µ m analog x for ultimate 0.9 (1.09 A) µ m analog x for nominal 1.5 (0.64 A) Resolution and emittance blow-up in SPS - 15-
Workshop on SPS-LEP Performance Chamonix IX 4 Conclusion 3.0 µ mrad input emittance : 3.5 µ mrad output emittance : Total blow-up budget attributed to SPS : 0.5 µ mrad Tight but it can be done Final quality control with high precision wire scanner beyond and above any suspicion - 16-
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