LEP Operation and Performance
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- Dwain Bailey
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1 LEP Operation and Performance Outline: Mike Lamont, CERN 1) Brief History ) Injection & TMCI 3) Beam-beam tune shift & Luminosity performance 4) Optimisation 5) Equipment 6) Operations, controls and instrumentation 6) Polarization 6) Other issues 7) Conclusion Will try and concentrate on physics & lessons that might be relevant to future machines. 1/5/1 Cornell October 1 1
2 LEP - The Largest Particle Accelerator to Date 1989 First operation The Z-years (precision studies) The W-years (precision studies) The Higgs-year (almost a discovery?) Nov Start of dismantling 1/5/1 Cornell October 1
3 Energy Peak luminosity Integrated luminosity 1/5/1 Cornell October 1 3
4 History YEAR OPTICS COMMENT BUNCH SCHEME /6 Commissioning 4 on /6 4 on /6 9/9 tested 4 on /9 Pretzel commissioned 4 on 4/ Pretzel /6 Pretzel /6 Pretzel /6 Tests at GeV Bunch trains /6 18/9 tested 4 on /6 18/9 & 1/9 tests 4 on /9 4 on /9 4 on 4 1/9 Higgs discovery mode 4 on 4 1/5/1 Cornell October 1 4
5 commissioning 14th July: first beam 3rd July: circulating beam 4th August: 45 GeV 13th August: colliding beams These people are to blame for what followed 1/5/1 Cornell October 1 5
6 199 operational teething troubles Luminosity: cm - s -1 Beam current around 3 ma Pretzel test Lots of waist scans BIG beam sizes 8.6 pb -1 Conclusion from Chamonix 91 a 7/76 team has been set up a dispersion team has been set up a dynamic aperture team has been set up a closed obit team has been set up an intensity limitation team has been set up a longitudinal oscillation team has been set up a crash pretzel team has been set up a beam-beam team already exists! 1/5/1 Cornell October 1 6
7 cruising 53 pb -1 BORING! 1/5/1 Cornell October 1 7
8 Performance Two distinct regimes: GeV characterised by working well into the soft beam-beam limit and approaching the hard limit. 8.5 GeV and above Staged installation of RF cavities Maximum collision energy (c.m.) raised to 9 GeV Accelerator physics regime of ultra-rapid damping Not beam-beam limited : Operational strategy to maximize discovery reach with operation in the regime of ultra-rapid damping 1/5/1 Cornell October 1 8
9 Injection A lot of effort in to pushing the bunch current in anticipation of high energy, Efficiency always variable, synchrotron injection used In the end limited way below maximum by RF system (power levels and stability) Fundamental limit at LEP TMCI which was eventually reached despite more practical problems coherent tune shift & resonances (in particular synchro-betatron) Increase injection energy Removal of copper RF cavities Increase of synchrotron tune wigglers Some evidence that long-range beam-beam reduced TMCI limit 1/5/1 Cornell October 1 9
10 Injection limits in 1998 Transverse mode coupling instability (TMCI): (ignore hardware, RF consideration Experimentally found 1998 to be around ~ 1 ma Influence from beam-beam: Lower TMCI threshold by ~ 1 % Synchro-betatron resonances (SBR): I th = π E f e β k % rev Qs ( σ ) Q v = n Q s with n = 1,, 3 (coherent and incoherent) s Raise Q s (also helps RF) Avoid SBR Longitudinal single-bunch instability: Not understood. Avoided with bunch lengthening. 1/5/1 Cornell October 1 1
11 MD-results by P. Collier, G. Roy, R. Assmann and K. Cornelis, M. Lamont, M. Meddahi) 998 standard working oint (SWP): Q h =.8 Q v =.3 Q s =.13 (chromaticities ~ 1-) 78 µa per bunch reached with two beams LEP working Points: Extended up to ~ 94 µa in single electron bunch MD 1/5/1 Cornell October 1 11
12 High Q v working point: Q h =.9 Q v =.3 Q s =.14 (lowered chromaticities by.5) 13 µa per bunch in 4 bunches (limited by TMCI). New working point (Cornelis, Lamont, Meddahi): (single beam, separators off) Q s >.144 inconclusive. Q s =.16,.166,.174 with 85 µa per bunch. (low injection efficiency %, injection would require re-optimisation). 1/5/1 Cornell October 1 1
13 Overview of Luminosity and Energy Performance /5/1 Cornell October 1 13
14 Why was high energy so good for LEP? With the strong transverse damping (6 turns at 14 GeV) second beam-beam limit (tails, resonances) is overcome beam-beam limit is pushed upwards we then profit from smaller IP spot size and higher currents 1/3 resonance can be jumped beams can be ramped in collision with collimator closed but also no radiative spin polarization above 61 GeV (energy calibration) Unique experience with ultra-strong damping at LEP 1/5/1 Cornell October 1 14
15 Vert. beam-beam parameter: * re me β y ib L ξ y = π e f E σ σ i Observed in LEP (1994-): Energy ξ y (max) Damping [GeV] per IP [turns] Beam-beam limited Beam-beam limit not reached rev x y b ξ 1/ E y Strong damping 3 naively Beam-beam limit pushed upwards σ x σ y from 45.6 GeV to 98 GeV: Reduced by factor ~ 1.6 (factor ~ in σ y ) Peak luminosity: 1 3 cm - s -1 1/5/1 Cornell October 1 15
16 Luminosity Performance at High Energy Beam behavior at high energy: Larger emittances / energy spread (ε ~ E, σ E /E ~ E) Less luminosity Higher backgrounds Solenoid coupling is weaker (θ ~ 1/E with B=const) Residual coupling contributes less to vertical emittance Strong transverse damping (τ ~ 1/E 3, 6 turns at 14 GeV) Second beam-beam limit (tails, resonances) is overcome Higher beam-beam tune shifts with higher beam-beam limit 1/3 resonance can be jumped Beams can be ramped in collision 1/5/1 Cornell October 1 16
17 orizontal beam size: rms σ = βε β / J D E x x x x x x ompensate increase with energy (smaller luminosity, larger background): ) High Q x optics with smaller D rms x (D. Brandt et al, PAC99) ) Smaller β x* (. m m m) ) Increase damping partition number J x via RF frequency Automatic control J x = function (U RF ) For highest energy reach: Reduce J x. RF frequency [Hz] 11 GeV :4 1: 1: 1:4 : : :4 3: Time J x = 1.6 (smaller σ J x = 1.4 Safety setting J x = 1.4 (larger σ 1/5/1 Cornell October 1 17
18 What Is the Energy Dependence of the Beam-beam Limit? Scaling empirically fitted by Keil, Talman, Peggs, Several points in a given machine, similar configuration for LEP. Independent cross-check of previous results, however: Beam-beam limit reached at 45.6 GeV Beam-beam limit not reached Can we infer the beam-beam limit at high energy? Look at functional dependence of beam-beam parameter on bunch current 1/5/1 Cornell October 1 18
19 imple model used to fit unperturbed mittance and beam-beam limit: y 1 = i A+ ( B i ) wo fit parameters A and B: * π e f γ β x A = ε * x ε re β y B = 1 ξ ( i ) y b b b y Vertical Beam-beam Blow-up Vertical beam-beam parameter GeV 5 Limited gain 15 in luminosity 1 ξ y (asymp) =.115 with ε y : 5 ε y (no BB) =.1 nm No BB blow-up Luminosity [1 3 cm - s -1 ] Bunch current [µa] No BB limit Vertical emittance [nm] With BB limit 1/5/1 Cornell October 1 19
20 Model of Beam-beam Parameter Versus Bunch Current: Dependence of vertical beam-beam tune param. on bunch current I (in the regime of strong 1 ξ y = i A+ B i synchrotron radiation, K. Cornelis): ( ) Two fit parameters A and B: A * π e f γ β x = ε * x ε re β y y B = 1 ξ ( i ) y Knowing all other parameters, A is just given by the unperturbed vertical emittance. Without a beam-beam limit: B gives the asymptotic beam-beam limit of the vertical beam-beam parameter: 1 ξ y = i A Beta beat due to beam-beam not included Tune dependent resonances are not included Beam-beam tune shift might see other limits 1/5/1 Cornell October 1
21 Example from 98 GeV: Vertical beam-beam parameter GeV Bunch current [µa] Unperturbed vertical emittance ε y = 18 pm Beam-beam limit ξ y =.115 1/5/1 Cornell October 1 1
22 Emittance blow-up for fill in 1998: Vertical emittance [nm] Luminosity BEXE (e - ) Fitted single bunch emittance Bunch current µa Clear beam-beam blowup of 5-1%! (consistently observed from x-ray synchrotron radiation and luminosity) 1/5/1 Cornell October 1
23 Example From 11 GeV Vertical beam-beam parameter GeV Bunch current [µa] Unperturbed vertical emittance ε y = 8 pm Beam-beam limit ξ y =.111 1/5/1 Cornell October 1 3
24 Similar Asymptotic Limits Suggested.14.1 Fitted asymptotic ξ y limit ξ y October July August Bunch current ma 1/5/1 Cornell October 1 4
25 Predictions Energy Damping decrement δ BB-limit 45.6 GeV 3.5e GeV 3.8e Scaling: ξ y δ.4 Exponent.4 instead of.7! VLLC33 (δ =.1): ξ y.17 (.56 for VLLC34 with δ = 6e-4) Total tune shift still smaller than in LEP (4 IP s) 1/5/1 Cornell October 1 5
26 Use model to predict luminosity: From model get the luminosity incl BB: L nb γ i = e re β B b * y A + ( ib ) In the BB limit: L nb γ = ξ * y i e re β y b For a given BB limit, the increase of luminosity with current is proportional to the energy γ (el.-magn. field of beam scales as 1/γ) 1/5/1 Cornell October 1 6
27 Compare BB fit to luminosity data: 98 GeV Luminosity [1 3 cm - s -1 ] Bunch current [µa] Very well described Simple squared scaling not adequate 1/5/1 Cornell October 1 7
28 hat happens for emittance (unperturbed) improvement: Luminosity [1 3 cm - s -1 ] DFS limit No BB limit Vertical emittance [nm] (unperturbed) (6 ma current) With BB limit Luminosity [1 3 cm - s -1 ] (8 ma current) 3 5 No BB limit 15 1 With BB limit Vertical emittance [nm] (unperturbed) LEP luminosity limit due to beam-beam:. 1 3 cm - s -1 (expected at maximum possible current) 1/5/1 Cornell October 1 8
29 Optimisation Horizontal beam size given by synchrotron radiation and optics Working point beam-beam Vertical emittance Coupling, global & local Residual dispersion - golden orbits and dispersion free steering Vertical beam size at interaction point: β * X and β * y Dispersion at IP Thereafter: Reproducibility 1/5/1 Cornell October 1 9
30 ertical emittance: ( rms ε ) 1999/: β y* = 5 cm y C Dy E + K ε +K Initial tuning of coupling, chromaticity, orbit, dispersion, Vertical orbit to get smallest RMS dispersion } Coupling to get smallest global coupling Local dispersion, coupling, β-function at IP } Golden orbit strategy for optimization: rial and error! Complement with: 1/5/1 Cornell October 1 3 x E Peak luminosity Luminosity balance (solenoids) ispersion-free steering (DFS): 1) Measure orbit and dispersion ) Calculate correctors to minimize both Note: Global correction generally also improves local dispersion/coupling!
31 easured single beam performance of DFS in LEP: ORBIT DISPERSION CORR. KICKS D y [cm] θ y [µrad] BPM number BPM number Corrector number DFS: Simultaneously optimize orbit, disp., corr D y [cm] θ y [µrad] BPM number BPM number Corrector number (same algorithm as implemented for the SLC linac) 1/5/1 Cornell October 1 31
32 Vertical optimization (simulated) 1.8 Reduction of RMS dispersion (DFS + change of separation optics) (Data 5-55 µa) 1999 εy [nm] E [GeV] D y (rms) [cm] 98 GeV Reduction of vertical emittance Emittance ratio:.5% Fill number 1/5/1 Cornell October 1 3
33 (ii) Choice of RF frequency: Damping partition number J x used to reduce horizontal beam size σ x : σ rms = βε β / J D E x x x x x x Increase with beam energy. Good for luminosity and backgrounds in experiments J x controlled with RF frequency f RF. f RF = Hz J x = 1. f RF = 1 Hz J x = 1.55 E max = -.7 GeV Pay with reduction of maximum beam energy. In : Keep RF frequency shift small (~ -5 to + Hz). 1/5/1 Cornell October 1 33
34 LEP lifetime without surprises: (E.g. H. Burckhardt, R.Kleiss. Beam Lifetimes in LEP. EPAC94) ifferent regimes: ) Without collision: Lifetime [h] Lifetime without collision Putting into collision Lifetime τ due to particles lost in Compton scattering on thermal photons, beam-gas scattering. We assume 3 hours. ) In collision: Lifetime due to particles lost in radiative Bhabha scatt. or beam-beam bremsstrahlung. 18: 19: : 1: Time Electrons Positrons Lifetime during collision (increase with current decrease) 1/5/1 Cornell October 1 34
35 Lifetime at High Energy Used As Fastest Luminosity Signal: Formulas in convenient units for LEP parameters (94.5 GeV): L[1 3 cm s 1 ] = 671. i bunch 1 [ ma] τ [ h] 1 τ [ h] Lum. [1 3 cm - s -1 ] 55 5 Luminosity decay BCT 45 Correct Optimize 4 orbit vert. tune drift 35 Load new orbit + cancel 3 19: 19:5 19:1 19:15 19: 19:5 19:3 BCT ξ y 1 3 τ [ h] 6 ALEPH DELPHI OPAL Lum. [1 3 cm - s -1 ] No effect from tails, resonances, 4 19: 19:5 19:1 19:15 19: 19:5 19:3 Time 1/5/1 Cornell October 1 35
36 Operations Standard techniques: Measure & correct beta* Beta beating, coupling Essential, of course, good diagnostics, established measurement techniques: Q-loop, Fast displays of lifetimes, beam sizes, Orbit feedback, Bunch current equalisation First years: Lack of basic high-level control facilities Poor data management Interfaces to crucial beam instrumentation missing in control room Poor and unreliable, incoherent data acquisition systems 1/5/1 Cornell October 1 36
37 Optimization of Turn-around Year Recover [min] Filling [min] Ramp / Squeeze [min] Adjust [min] time Total [min] # fills Difference Faster degauss, optimize procedure Less current Twice the ramp speed BFS Average turn-around time improved by ~ 8 minutes! Typical turn-around: ~ 45 minutes Reproducibility 1/5/1 Cornell October 1 37
38 Hardware Specialised groups: power converters, RF, beam instrumentation, kickers, separators, vacuum, dedicated expertise (electronics, controls, hardware) Over designed? Possibly but all hardware managed to withstand the extremely hard push to high energy Good availability with experience Access system always a problem - Hardware performance Vacuum system Magnets Power supplies Instrumentation etc excellent without major worries - Effects from LHC civil engineering No limiting effect on LEP operation (some realignment) 1/5/1 Cornell October 1 38
39 RF voltage (design and actual): 4 35 Available RF voltage Beam energy 15 [GeV] RF voltage [MV] Nominal RF voltage Cryogenics upgrade Jul-95 Feb-96 Aug-96 Mar-97 Sep-97 Apr-98 Nov-98 May-99 Dec-99 Jun- Jan-1 Date Beam energy follows available RF voltage Beam energy Improvements: Progressive installation of additional RF cavities Increase accelerating gradient 1/5/1 Cornell October 1 39
40 ) Other issues: - Background in the experiments: Higher beam energy RF frequency shift reduced for optimization of energy reach Larger horizontal beam size Potentially larger backgrounds New optics in P4 and P8 to help reducing background Steady state conditions: Occasional spikes: Very good. Required continuous follow-up o collimators, orbit, tunes, Q h >.33 required RF trips with negative RF frequency shift Related current loss 1/5/1 Cornell October 1 4
41 5b) Energy increase of LEP from 1999 to : EP preparation: 15 GeV (optics, power supplies, etc checked) ain from 1999 physics to : Maximum energy: 11. GeV 14.4 GeV mprovements: 8 additional Cu RF units +.14 GeV Higher RF gradient +.96 GeV Less RF margin GeV Reduced RF frequency +.7 GeV Bending length +. GeV Total GeV RF system Operational procedures Reduced luminosity production, potentially higher backgrounds 1/5/1 Cornell October 1 41
42 LEP operated in discovery mode : : conclusions Beam energy increased by 3.4 GeV Increase of RF voltage (365 MV), excellent stability Change of operational strategy (ramp during physics fill, ) Reduced shift of RF frequency Increase of average bending radius Push beam energy on cost of luminosity Reduce beam current (5 ma instead of 6. ma) Run with small J x, large horizontal beam size Mini-ramp to quantum lifetime limit (zero margin in RF voltage) Lose all fills with RF trips Luminosity production rate lower than 1999 but still excellent (as in 199 Luminosity improvement in 1999 with better tuning: + % Price to pay for energy increase in : - % was the second productive LEP year 1/5/1 Cornell October 1 4
43 Unique at LEP: Transverse spin-polarization in LEP Large range of energies GeV to 14.5 GeV Polarization studied from 41 GeV to 98.5 GeV Explore spin dynamics in unique regime Bench marking of theoretical predictions P [%] VEPP4, DORIS II, CESR PETRA HERA TRISTAN LEP1 With... Without... Harmonic Spin Matching 5 SPEAR LEP Sharp drop-off! VEPP-M, ACO E [GeV] 1/5/1 Cornell October 1 43
44 Use of Polarization at LEP: recise determination of the LEP beam energy (1-5 relative accuracy, ~ 1 MeV) recise measurement of the Z mass and width E [MeV] November 199 Axis of earth rotation CERN, Geneva Moon -5 3: 3: 7: 11: 15: 19: 3: 3: Ecliptic E [MeV] 5 9. August October Small changes of energy accurately measured (energy change from 1mm circumference change) 11: 13: 15: 17: 19: 1: 3: 18: : : 4: : 4: 6: 8: Daytime 1/5/1 Cornell October 1 44
45 heory by Derbenev, Kontratenko, Skrinsky (With LEP Parameters): pin une ν = E MeV Polarization buildup rate 1 λ = τ p = ν Synchrotron tune ν γ pin tune pread σ E σν = ν ν E 6 Resonance strength w k ν Condition for correlated spin resonance passings: ν λ α = << 1 3 ν γ true P [%] MeV E [MeV] SITF SODOM simulations = ν km, w k Tm ( k m γ ) ( / ν ) ν ν ν γ γ N σ E = 31 MeV (LEP I) σ E = 51 MeV (DWIG) σ E = 15 MeV (LEP II) σ σ exp ν ν m = I m ν γ ν γ ν 1/5/1 Cornell October 1 45
46 Polarization [%] Energy Dependence of Polarization: SITF simulations (5 seeds) τ p /τ d = (ν/88) 4 τ p /τ d = (ν/95) Simulation confirms 1/E 4 dependence of polarization! Energy [GeV] First order theory: Includes spin resonances with k x, k y, k s =1 ν depol = k ± k ν ± k ν ± k ν, k, k, k x x y y s s x y s N Machine tunes Synchrotron sidebands determine polarization degree in LEP 1/5/1 Cornell October 1 46
47 Polarization Measurements in LEP: With 9/6, 6/6 and 1/45 optics. Goal for energy calibration: > 5% Polarization not always fully optimized. Polarization [%] 8 7 Measurements 6 Linear Higher order Energy [GeV] 998: Polarization and energy calibration has been extended to 6.6 GeV (P = 7% measured)! Drop in polarization degree consistent with higher-order theory 1/5/1 Cornell October 1 47
48 Higher-Order Theory also Confirmed with Wigglers: Equivalent E [GeV] P [%] 5 Linear 4 3 Higher-order Bl [Tm] Wigglers increase spin tune spread and thus allow simulating energy increase... 1/5/1 Cornell October 1 48
49 Evaluate Correlation Criteria for LEP: LEP enters uncorrelated regime with high energy and small Q s! If spin resonance passing is uncorrelated it is completely uncorrelated for LEP! We can stay in the correlated regime by increasing the value of Q s! With: σ ν = E.4465GeV /5/1 Cornell October 1 49
50 pin une ν = Theory by Derbenev, Kontratenko, Skrinsky (with LEP parameters): E MeV Polarization buildup rate 1 λ = τ p = ν Synchrotron tune ν γ pin tune pread σ E σν = ν ν E 6 Resonance strength w k ν Condition for correlated spin resonance passings: ν λ α = << 1 3 ν γ true false σ >> ν ν true γ Condition for complete uncorrelation = ν km, w k Tm ( k m γ ) ( / ν ) ν ν ν γ γ true << 1 σ ν false σ σ exp ν ν m = I m ν γ ν γ 4 τ p 11 π 18 exp( σ ) ν = ν w[ ] 1 ν + 3 τ d π π ν λ τ τ p d π = w λ k 1/5/1 Cornell October 1 5
51 Search for Polarization at Highest LEP Energies: xpected polarization: Very low, but possible increase at high energies? ew polarization optics (11.5/45 degrees) for measurements at low AND high energy 6.6 GeV 4 % (7% with 6/6 optics) 7. GeV < 1% 9.3 GeV < 1% 98.5 GeV < 1% o indication of measurable polarization at highest LEP energies! first measurements in regime of uncorrelated crossings of spin resonances) 1/5/1 Cornell October 1 51
52 Achievements at LEP: ransverse spin polarization in igh energy regime measured. way above previously assessed regime) harp drop after LEP1 in agreement ith theory/simulations. P [%] VEPP4, DORIS II, CESR PETRA HERA TRISTAN LEP1 With... Without... Harmonic Spin Matching ransverse spin polarization crucial or precision measurements of the and Z properties (energy calibration) irst measurement in regime of ncorrelated spin resonance crossing. o sign of transverse polarization. ew varieties of Harmonic Spin atching gave up to 57% polarization. 5 SPEAR VEPP-M, ACO LEP E [GeV] We can trust the polarization theories in LEP regime! Precise predictions for future projects 1/5/1 Cornell October 1 5
53 heory by Derbenev, Kontratenko, Skrinsky (With VLLC33 Parameters) pin une ν = E MeV Polarization buildup rate 1 λ = = ν τ p 1 5 Synchrotron tune ν γ pin tune pread σ E σν = ν.4 1 ν E 6 Resonance strength w k ν Condition for correlated spin resonance passings: ν λ α = << 1 3 ν γ true Build-up time τ p : 1.9 h = ν σ km, w k Tm ( k m γ ) σ exp ν ν m = I m ν γ ν γ ( / ν ) ν ν ν γ γ Spin tune ν: Spin tune spread σ ν :.4 Synchrotron tune: 1/7 1/5/1 Cornell October 1 53
54 What does this mean for VLLC? Polarization [%] Energy [GeV] Linear LEP HO VLLC33 HO Measurements Large spin tune spread Enhancement of depolarization (as in LEP at high energy) 1/5/1 Cornell October 1 54
55 P [%] N MeV σ E = 31 MeV (LEP I) E [MeV].8.6 σ E = 51 MeV (DWIG) σ E = 15 MeV (LEP II) ν 1/5/1 Cornell October 1 55
56 High Q s for LEP Linear / higher-order theory for different Q s Raising Q s improves polarization for high energies! Why? Imagine Q s = 1 Q s satellites overlay integer resonances (ν = k + i Q s ) Q s =.: Expect sufficient polarization up to 8-85 GeV! 1/5/1 Cornell October 1 56
57 Polarization increase at Ultra-high energies: Polarization [%] Higher-order theory Q s = 1/5 1 5 % Energy [GeV] Ultra-high energy Uncorrelated passings of spin resonances (small Q s ) Spin tune spread σ ν >> 1 (probably not true at 1 GeV) Theory predicts: Polarization comes back at ultra-high energies! Why? Fast increase of polarization build-up, increase in depolarization slows down! Very uncertain regime (who knows what really happens) 1/5/1 Cornell October 1 57
58 Some preliminary thoughts: trong transverse damping: Very nice beam dynamics regime (performance) Less tails Less effects from resonances (we can jump them) Ramp colliding beams at high energy Higher beam-beam limit wo thirds of all LEP luminosity collected in the last 3 years (out of 1.5y) EP data would indicate a beam-beam limit of.17 for VLLC33. ptimization of vertical orbit to the limit (dispersion/coupling correction for LEP) eed operational overhead in RF voltage (>= 6 % in LEP) - optimize # klystron o not expect significant radiative spin-polarization (even linear level is very low 1/5/1 Cornell October 1 58
59 Sociology Good support from equipment groups, good motivation, close interaction with machine in-house expertise. Common control room operations as focus for machine physicists, equipment groups and experiments.regular informal contact at all levels. Comprehensive annual workshops - Chamonix. Cross-fertilisation from other labs. Stimulated by close contact with experimental physicists. Makeup of operations. Ph.Ds on shift 1/5/1 Cornell October 1 59
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