Køling, emittans, colliders og CERN

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1 Køling, emittans, colliders og CERN Emittance, phase space, Liouville theorem and cooling Radiation damping in storage rings Emittance in electron storage rings. (ASTRID, ASTRID, MAX IV as examples) Low-emittance lattices. Other cooling methods: Stochastic, Electron, Laser and others (ionisation) Fixed target versus collider experiments, Luminosity in colliders CERN s ringcircus and antiprotons mv Wille kap. 6 samt ½ side af kap. 7 Introduction What is cooling? What is Temperature? 3 1 ( k) T mv // // v is the velocity relative to the reference particle moving with the average ion velocity. (internal temperature) Temperature is a measure of the disordered motion. Cooling is hence a reduction of the temperature, i.e. of the disordered motion. Clearly, other parts of the total system will get warmer. 1

2 Beam cooling cooling is not: collimation (loss of particles) adiabatic damping (see later) Since beamcooling is slow, it is mostly used in storage rings; however, ionisation and stochastic cooling has been or will be used for e.g. for muons in single-pass beamline Introduction What is cooling? What is Temperature? 3 1 ( k) T mv // // v is the velocity relative to the reference particle moving with the average ion velocity. Temperature is a measure of the disordered motion. In an accelerator T T // Mc p / p Mc 1 1 H V

3 Why beam cooling? Deep within the atomic supercollider, the search continues for the elusive elephantino Why beam cooling? Improve beam quality beam size, emittance energy spread intensity of beam, accumulation, stacking lifetime of beam Counteract degradation of beam quality due to interaction of beam particles with other particles (intrabeam scattering) rest-gas (internal targets) non-ideal fields, resonances, instabilities injection errors 3

4 current [ma] Stacking by cooling y septum x Stacking by cooling 00 ASTRID SR source: ~00 ma accumulated from many injections of ~5 ma Fermilab antiproton accumulator stacking for 1 hour 10 8 / sec pbar at 8 GeV shutter time [sec] injection stack tail core 4

5 Liouville formelt Et systembestående af N partikler beskrives i 6N dimensionalt faserum. Hvis partiklerne ikke vekselvirker kan systemet beskrives som i 6 dimensionalt faserum med såkaldte konjugered e koordinater p L / q, hvor L( q, q, t) T U er Lagrangefu nktionen. i F.eks. x,y,z og de tilhørende impulser p,p,p Hamiltonfunktion H H ( q, p, t) Hamiltons ligninger konservative eller Hamiltonske del, der kan udledes og Q er ikke Hamiltonske kræfter som friktion etc. Kontinuitetetsligning i siger d/dt 0 konstant p H / q Q d dt Qi p i x i y i z p q L q H / p, hvor H / q er den fra et potential, N partikler q, p, Liouville for konservative kræfter Liouville: Phase space and Liouville For hamiltonian systems, the phase space density is constant (when measured along a trajectory) The phase space volume (emittance) is conserved Often the two transverse and the longitudinal degrees of freedom are decoupled p x pdq constant q x Quadrupole focusing 5

6 Phase space, Liouville and cooling Liouvilles theorem means that cooling is not possible for Hamiltonian systems, that is systems with forces that can be derived from potentials. Hence particles cannot be injected into already filled areas of Phase space. All you can do is to change the form of phase space. However, with velocity-dependent forces drag, friction (dissipative) forces electron, radiation, Laser, ionisation cooling cooling is indeed possible!! Coffee, cream, Liouville and Stochastic cooling 6

7 Adiabatisk damping og normaliseret emittans Liouville : pdq constant Mc dx Mc x x dx dvs. xdx constant emittance ( ) Vi ser altså at under acceleration er den normaliserede emittans * konstant Under acceleration reduceres emittansen 1/, altså omvendt proportionalt med impuls. Medandre ord reduceres beam størrelse og divergens med 1/ Dettekaldes adiabatisk dæmpning impuls Radiation damping (W6) In principle: any charged particle in practise: only electrons/positrons since E/(U 0 /T 0 ) (U 0 ~ 1/M 4 ) RF This is Vertical betatron cooling Horisontally: also heating due to dispersion! Longitudinal: also heating due to dispersion! 7

8 Dæmpning af vertikale betatron oscillationer vertikal dæmpnings konstant a hvor energi udstrålet per omløb W horisontal dæmpnings konstant a longitudin al dæmpnings z W0 ET 0 0 J z E [ GeV ] R[ m] W0 ET W0 ET D D 1 (k ) ds R R, J D, J 1, J 1 D ds R konstant a s x s z 0 J 0 x x J s Læg mærke til J Læg også mærke til : Robinson teorem x J z J x, z, s s konstant 1/ x, z, s C[ m] [ m] 3 13.J E [ GeV ] x, z, s Man kan altså kun refordele den totale dæmpning! Separate-function synkrotroner er altid dæmpede i alle 3 dimensioner, da D << 1. For combined-function synkrotroner kan man også risikere antidamping, altså a x/s < 0 8

9 Beamst er givet Brilliance ørrelse af og emittansen divergens photons Flux F s 0.1%BW A Beam emittans / F F photons B 4 4 s 0.1%BW mm mrad Photon emittance / 4 x z x z x z A Jvf. Synch. Rad. lecture For at få en stor Brilliance af synkrotronstrålingen skal vi altså designe vores elektron synkrotron med en lille emittans Anderledes for ikke-elektroner: Her er emittansen bestemt af emittans af det injicerede beam: DOG: Adiabatisk dæmpning og køling Dæmpningstid og ligevægtsemittans Vi har altså set at et elektron beam bliver kølet dæmpet, men hvad er ligevægtsemittansen? 9

10 10 Equilibrium emittance Emittans bestemmes af ligevægt mellem dæmpning og eksitation fra kvantisering af synkrotronstrålingen og dispersionen. Derfor meget lille vertikal emittans da D z 0. I den horisontale plan Equilibrium emittance p p D x p p D x ) ( ) ' ( s p p D DD D p p x x x x i H

11 55 x 3 3 h mc Equilibrium emittance 1 R J 3 x H( s) 1 R E[ GeV ] mrad R[ m] 1 l l 0 H( s) ds FODO R konstant og J x 1 Model FODO NB: ε x for k Chromaticity Small emittance requires strong quadrupoles gives large chromaticities requires strong sextupoles gives small dynamical aperture!!! FODO 11

12 Minimum emittance lattices minimere H( s) D DD D / Mange celler! (1 ) / Chasman Green lattice HISOR 1.5 GeV Min 67 nm Actual 79 nm 1

13 ASTRID ASTRID álá Chasman-Green (double-bend achromat) 13

14 Small emittance lattices MAX IV i Lund Ø 58 m 0.5 nm ved 3 GeV 0 7 bend achromat Andre kølings metoder SR (radiation damping) - done Stokastisk køling Elektron køling Laser køling andre Kun kvalitativ beskrivelse 14

15 Stochastic cooling principle p p macroscopic emittance q q Maxwells demon Stochastic cooling Liouville: Cooling is not possible with electromagnetic forces deflecting the particles (continous fluid, og N=). When single particles can be observed, and a corresponding correction applied, cooling is possible! This is the secret of stochastic cooling! pick-up kicker N=10 8, =5mm /N=0.5m In reality W< 15

16 Stochastic cooling transverse pick-up transverse kicker pulse at pick-up t <x> s x n g Cooling time N/W g(<x> s + x n ) N S t pulse at kicker T s =1/W W bandwidth TS N T N WT Cooling Time 1 W Large bandwidth optimumcooling time N ( ) (W> GHz, N s ~10-3 N) mixing noise/signal-ratio pick-up kicker pick-up small mixing good mixing 16

17 Stochastic cooling Betatron cooling: systems (hor. and vert.) dist. PU kicker = odd number of /4 Momentum cooling: acc. gap instead of transverse kicker (i) PU in high-dispersion region x/x=d p/p (ii) detect f/f= p/p and correct p/p (Most) stochastic cooling facilities: ISR (1977), ICE, AA, AC, LEAR, CERN Fermilab TARN COSY, GSI Stochastic Cooling 17

18 FNAL antiproton source Stochastic Cooling AD at CERN Fermilab antiproton accumulator stacking for 1 hour 10 8 / sec pbar at 8 GeV shutter p/p (f/f) injection stack tail core p/p (f/f) 18

19 Ions Electron cooling ~10 8 /cm 3 e-gun (T e ~0. ev) collector Laboratory frame particle frame ( v ) I Electron Cooling Invented by Budker in Novosibirsk NAP-M ring at INP, 1974, 68 MeV p magnets: solenoids toroids 19

20 MSL in Stockholm MSL electron cooler Cryostat Superconducting solenoid Electron gun Ion beam Magnet winding (NC) Interaction region Cryopump Collector Correction dipole * Vacuum chamber Support frame Return yoke NEG pump 0

21 1 ASTRID electron cooler Electron cooling Initially i e e I I i I e i T mv v M T v v 1 1 Finally rms e rms e I I rms I f e f I v N Z v M m v v T T ) ( no heating

22 Electron cooling drag force Electron cooling time 1 v I dvi dt 1 Mv F I 1 PF 3 rms PF 4 ( vi ) ( vi ve ) Mm 1 4 Z e nl{ T 3/ 3 e rms PF ( vi ve ) m Typically ~tens of seconds ( Z=1) L ln( b b msx/ min Coulomb logarithm )

23 Electron cooling LEAR, ICE, CERN CRYRING, CELSIUS TSR, COSY, SIS, ESR IUCF, Fermilab Electron cooling at AD TARN,.. ASTRID ELENA på CERN 5 MeV 100 kev pbar Beam i efterår

24 Virtues of electron cooling Versatile cooling technique Longitudinal and transverse cooling Cooling times 0.1-1secA/Q T // << 0.1 ev T 0.1 ev in addition: adiabatic expansion T // B Ions Laser cooling h hv Ion recoil : Mv r q c v0 Doppler hv' hv(1 cos ) c Laser 4

25 Kick from one photon absorption-emission 100 kev Li Å (.3 ev) =4ns 1ss 1sp Change in momentum : p h / Change in energy : E pv 1meV At saturation (stimulated r ½ 10 in m : r m/ v 15 change in m :0. ev 7 s -1 Ultimate limit :single recoil 1meV spontaneous)(1mw in Ø3mm) F(v) Laser cooling v 5

26 Laser cooling in ASTRID Laser cooling Virtues of laser cooling: Laser cooling is fast However: Only effective for longitudinal cooling Not versatile: Li +, Be +, Mg +, 6

27 Ionisation cooling Slowing down in matter Friction force F v Not hadrons due to large inelastic cross section Not electrons due to short radiation length Can only be used in in -collider/ -factory s produced by decaying s s produced from decaying s s produced by p s on target Since s do not live forever (τ 0 =. s) cooling has to be fast (even when is large: τ = τ 0. Also emittances are very large! Ionisation cooling principle Transverse cooling: muons lose energy by de/dx and longitudinal momentum is restored by RF To minimize heating from Coulomb scattering: Small (high-field solenoids) Large L R (low-z absorber): Liquid H 7

28 Ionisation energy cooling Ionisation energy cooling using a wedge and dispersion R F possible -factory at CERN 8

29 MICE at RAL Other cooling methods Stimulated radiation cooling Radiative cooling 9

30 Conclusions on cooling methods Stochastic Electron Radiation Laser Ionisation Species all ions e - /e + some ions muons Favoured beam velocity Favoured beam intensity high medium 0.01< <0.1 very high >100 any (but Doppler) any low any any any any Cooling time N10-8 s s >10-3 s s 10-6 s Favoured beam temperature high low any low any Hvorfor bygger man colliders? Intersecting Storage Ring CERN Large Hadron Collider p+p p+p Pb+Pb 30

31 Why Colliders? E b m b m t Fixed target (pp) E cm =m b +m t +E b m t E b =1 TeV m b =m t =0.938 GeV E cm =43.3 GeV Symmetrical Collider E cm =E b +E t E b =E t = 1 TeV E cm = TeV m b E b E t m t Colliders Twin-ring / single-ring colliders Anti-particles: e + e -, pp,

32 How Colliders? Event Rate = Lσ 1 L 4e f rev I b 1 * x I * z Luminosity I 1 I average current b number of bunches f rev revolution frequency σ * x σ * z beam size at crossing point Thus intense bunched beams with tiny beam spots at the interaction points Beam-beam tune shift limits the luminosity Lepton collisions versus hadron collisions m q m p /10 since p quarks gluons 3

33 Intersection Storage Rings GeV protons, ~10 A of beam, L =10 3 /cm /s Super Proton Synchrotron 450 GeV protons (~1975 today) Converted into a proton-antiproton collider at 5 GeV (1980 ~1990) But where to get the antiprotons? 33

34 Antiproton Collector and Accumulator (3.5 GeV/c) 34

35 Fermilab Tevatron proton antiproton collider Rubbia, van der Meer (Nobelprize 1984) W og Z blev først fundet ved p-pbar collideren på CERN p-pbar kollisioner blev indtil for nylig stadig studeret ved Tevatronen ved Fermilab med håb om at se Higgs før LHC, men Tevatronen lukker nu 35

36 LHC LHC på CERN Synkrotron 7 km omkreds 50 m under jorden p energi på 7 TeV Dipol mag: 13 Magnetfelt: 8.3T Superledende ~10 mia. 36

37 LHC in tunnel Detektor Person 37

38 Large Hadron CERN 7 TeV 8 km circumference dipole field: 8.3T Stored energy: 700 MJ T=1.7K LHC σ when E, hence high luminosity needed: cm - s -1 38

39 Hvorfor bygge LHC? Jeg tror jeg har fundet en Higgs partikel! Higgs fundet på CERN (01) 39

40 e-p collider at DESY Twin-ring collider (one above the other!) 30 GeV e colliding 80 GeV p RHIC at Brookhaven One next-to-the-other 100 GeV/u Au+Au: A=197 Quark-gluon plasma 40

41 Large Electron Positron collider på CERN Først 45+45GeV e + e - for at lave Z 0 Dernæst 80+80GeV for at lave W + og W - Til sidst op til GeV Ved 100 GeV, W~3 GeV, E c ~ 90 kev 88 SC RF cavities Current ma MW i rf power Max luminosity 10 3 /cm /s? LEP Beton magneter E [ GeV ] U0[ kev ] [ m] 41

42 LEP cm (atomare tværsnit ~ cm SLAC Linear Collider Første linear collider Billig, hurtig, genbrug af SLAC Linac Opdagede før LEP bredden af Z, dvs antal familier i standard modellen (3) 4

43 Fremtiden indenfor højenergifysik acceleratorer?? Se sidste forelæsning What particle collider physicists do in their spare time. 43