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An Introduction to the Physics and Technology of e+e- Linear Colliders Lecture 1: Introduction and Overview Nick Walker (DESY) Nick Walker DESY DESY Summer Student Lecture th USPAS Santa Barbara 16 June,st2003 31 July 2002 Course Content Lecture: 1. 2. 3. 4. 5. 6. 7. 8. 9. Introduction and overview Linac part I Linac part II Damping Ring & Bunch Compressor I Damping Ring & Bunch Compressor II Final Focus Systems Beam-Beam Effects Stability Issues in Linear Colliders the SLC experience and the Current LC Designs This Lecture • Why LC and not super-LEP? • The Luminosity Problem – general scaling laws for linear colliders • A introduction to the linear collider sub-systems: – – – – – main accelerator (linac) sources damping rings bunch compression final focus during the lecture, we will introduce (revise) some important basic accelerator physics concepts that we will need in the remainder of the course. Energy Frontier e+e- Colliders LEP at CERN, CH Ecm = 180 GeV PRF = 30 MW Why a Linear Collider? Synchrotron Radiation from an electron in a magnetic field: B 2 P e c 2 2 2 CE B 2 Energy loss per turn of a machine with an average bending radius : E / rev CE 4 Energy loss must be replaced by RF system Cost Scaling $$ • Linear Costs: (tunnel, magnets etc) $lin • RF costs: $RF E E4/ • Optimum at $lin = $RF Thus optimised cost ($lin+$RF) scales as E2 The Bottom Line $$$ L E P -II S u p e r-L E P E cm G e V 180 L km 27 E G eV 1 .5 9 $ to t 1 0 S F 2 500 H yp e rLEP 2000 The Bottom Line $$$ L E P -II S u p e r-L E P E cm G e V 180 500 L km 27 200 E G eV 1 .5 12 2 15 9 $ to t 1 0 S F H yp e rLEP 2000 The Bottom Line $$$ L E P -II S u p e r-L E P E cm G e V 180 500 H yp e rLEP 2000 L km 27 200 3200 E G eV 1 .5 12 240 2 15 240 9 $ to t 1 0 S F solution: Linear Collider No Bends, but lots of RF! e+ e5-10 km • long linac constructed of many RF accelerating structures • typical gradients range from 25-100 MV/m Note: for LC, $tot E A Little History A Possible Apparatus for Electron-Clashing Experiments (*). M. Tigner Laboratory of Nuclear Studies. Cornell University - Ithaca, N.Y. M. Tigner, Nuovo Cimento 37 (1965) 1228 “While the storage ring concept for providing clashingbeam experiments (1) is very elegant in concept it seems worth-while at the present juncture to investigate other methods which, while less elegant and superficially more complex may prove more tractable.” A Little History (1988-2003) • • • • • • • SLC (SLAC, 1988-98) NLCTA (SLAC, 1997-) TTF (DESY, 1994-) ATF (KEK, 1997-) FFTB (SLAC, 1992-1997) SBTF (DESY, 1994-1998) CLIC CTF1,2,3 (CERN, 1994-) Over 14 Years of Linear Collider R&D Past and Future SLC LC E cm 1 00 5 00 - 100 0 G eV P bea m 0 .0 4 5 - 20 MW *y 5 00 (5 0) 1-5 nm E /E bs 0 .0 3 3 - 10 % L 0 .0 003 ~3 10 generally quoted as ‘proof of principle’ 34 but we have a very long way to go! 2 ? -1 cm s LC Status in 1994 1994 Ecm=500 GeV f [GHz] L1033 [cm-2s-1] Pbeam [MW] PAC [MW] ey [10-8m] y* [nm] TESLA SBLC JLC-S JLC-C JLC-X NLC VLEPP CLIC 1.3 3.0 2.8 5.7 11.4 11.4 14.0 30.0 6 4 4 9 5 7 9 1-5 16.5 7.3 1.3 4.3 3.2 4.2 2.4 ~1-4 164 139 118 209 114 103 57 100 100 50 4.8 4.8 4.8 5 7.5 15 64 28 3 3 3 3.2 4 7.4 LC Status 2003 2003 Ecm=500 GeV TESLA f [GHz] L1033 [cm-2s-1] Pbeam [MW] PAC [MW] ey [10-8m] y* [nm] SBLC JLC-S JLC-C JLC-X/NLC VLEPP CLIC 1.3 5.7 11.4 30.0 34 14 20 21 11.3 5.8 6.9 4.9 140 233 195 175 3 4 4 1 5 4 3 1.2 The Luminosity Issue (cm-2 s-1) Collider luminosity approximately given by is 2 L n b N f rep A HD where: Nb N frep A HD = bunches / train = particles per bunch = repetition frequency = beam cross-section at IP = beam-beam enhancement factor 2 For Gaussian beam distribution: L n b N f rep 4 x y HD The Luminosity Issue: RF Power Introduce the centre of mass energy, Ecm: L E cm n b N f rep N 4 x y E cm HD n b N f rep E cm Pbeam s R F beam PR F RF is RF to beam power efficiency. Luminosity is proportional to the RF power for a given Ecm L R F PR F N 4 x y E cm HD The Luminosity Issue: RF Power L Some numbers: Ecm N nb frep = 500 GeV = 1010 = 100 = 100 Hz R F PR F N 4 x y E cm HD Pbeams = 8 MW Need to include efficiencies: RFbeam: Wall plug RF: range 20-60% range 28-40% linac technology choice AC power > 100 MW just to accelerate beams and achieve luminosity The Luminosity Issues: storage ring vs LC LEP frep = 44 kHz L LC frep = few-100 Hz (power limited) R F PR F N 4 x y E cm factor ~400 in L already lost! Must push very hard on beam cross-section at collision: LEP: xy 1306 mm2 LC: xy (200-500)(3-5) nm2 factor of 106 gain! Needed to obtain high luminosity of a few 1034 cm-2s-1 HD The Luminosity Issue: intense beams at IP L 1 4 E cm R F PR F choice of linac technology: • efficiency • available power N HD x y Beam-Beam effects: • beamstrahlung • disruption Strong focusing • optical aberrations • stability issues and tolerances see lecture 2 on beam-beam The Luminosity Issue: Beam-Beam 3000 2000 Ey (MV/cm) • strong mutual focusing of beams (pinch) gives rise to luminosity enhancement HD • As e± pass through intense field of opposing beam, they radiate hard photons [beamstrahlung] and loose energy • Interaction of beamstrahlung photons with intense field causes copious e+e- pair production [background] x y 1000 0 1000 2000 3000 6 4 2 0 y/y 2 4 6 see lecture 2 on beam-beam The Luminosity Issue: Beam-Beam beam-beam characterised by Disruption Parameter: z fbeam Dx, y = bunch length, = focal length of beam-lens for storage rings, f beam 2 re N z x , y x z y and D x , y z f beam 1 In a LC, D y 1 0 - 2 0 hence f beam z Enhancement factor (typically HD ~ 2): H Dx , y 3 D x, y 1/ 4 1 Dx,y 1 D3 x, y ln Dx,y 0.8 x , y 1 2 ln z ‘hour glass’ effect see lecture 2 on beam-beam 3 3 2 2 1 1 Y Y The Luminosity Issue: Hour-Glass 0 0 1 1 2 2 3 3 2 1 0 Z 1 = “depth of focus” reasonable lower limit for is bunch length z 2 2 1 0 Z 1 2 The Luminosity Issue: Beamstrahlung see lecture 2 on beam-beam 2 E cm N 0.86 2 2 2 m 0 c z ( x y ) 3 RMS relative energy loss BS ere we would like to make xy small to maximise luminosity BUT keep (x+y) large to reduce SB. Trick: use “flat beams” with x y BS E cm N 2 2 z x Now we set x to fix SB, and make y as small as possible to achieve high luminosity. For most LC designs, SB ~ 3-10% The Luminosity Issue: Beamstrahlung Returning to our L scaling law, and ignoring HD L R F PR F N 1 E cm From flat-beam beamstrahlung hence L RF PRF 3/2 cm E x N x BS z y y z BS E cm The Luminosity Issue: story so far L RF PRF 3/2 Ecm BS z y For high Luminosity we need: • • • • • high RF-beam conversion efficiency RF high RF power PRF small vertical beam size y large bunch length z (will come back to this one) could also allow higher beamstrahlung BS if willing to live with the consequences Next question: how to make a small y The Luminosity Issue: A final scaling law? L RF PRF 3/2 cm E BS z y y ye n, y where en,y is the normalised vertical emittance, and y is the vertical -function at the IP. Substituting: L RF PRF 3/2 cm E BS z e n, y y RF PRF BS z Ecm e n,y y hour glass constraint y is the same ‘depth of focus’ for hour-glass effect. Hence y z The Luminosity Issue: A final scaling law? L • • • • • RF PRF BS Ecm e n,y HD y z high RF-beam conversion efficiency RF high RF power PRF small normalised vertical emittance en,y strong focusing at IP (small y and hence small z) could also allow higher beamstrahlung BS if willing to live with the consequences Above result is for the low beamstrahlung regime where BS ~ few % Slightly different result for high beamstrahlung regime Luminosity as a function of y L ( cm - 2 s - 1 ) 34 5 10 z 100 m m BS 1 z 34 4 10 34 z 300 m m 2 1034 500 m m 3 10 nb N 2 f L 4 x y 700 m m 900 m m 1 1034 200 400 600 y (m m ) 800 1000 The ‘Generic’ Linear Collider pre-accelerator few GeV source KeV damping ring few GeV few GeV bunch compressor 250-500 GeV main linac extraction & dump final focus IP collimation Each sub-system pushes the state-of-the-art in accelerator design The Linear Accelerator (LINAC) Ez see lectures 3-4 on linac c z travelling wave structure: need phase velocity = c (disk-loaded structure) bunch sees constant field: Ez=E0 cos(f ) Ez ct 2 c c standing wave cavity: z bunch sees field: Ez =E0 sin(wt+f )sin(kz) =E0 sin(kz+f )sin(kz) The Linear Accelerator (LINAC) Travelling wave structure Circular waveguide mode TM01 has vp>c No good for acceleration! Need to slow wave down using irises. see lectures 3-4 on linac see lectures 3-4 on linac The Linear Accelerator (LINAC) • Gradient given by shunt impedance: – PRF – RS Ez RF power /unit length shunt impedance /unit length • The cavity Q defines the fill time: – vg = group velocity, ls = structure length • For TW, t is the structure attenuation constant: • RF power lost along structure (TW): dPRF dz - E 2 z Rs power lost to structure t fill PRF R s 2Q / w 2 t Q /w ls / v g PR F , o u t PR F , in e SW TW - 2t RF - ib E z beam loading would like RS to be as high as possible Rs w The Linear Accelerator (LINAC) see lectures 3-4 on linac • Steady state gradient drops over length of structure due to beam loading unloaded av. loaded E z ,u - E z , l 1 ib rs 2 2t 0 e 1- e - 2t - 2t 0 0 1 assumes constant (stead state) current The Linear Accelerator (LINAC) see lectures 3-4 on linac • Transient beam loading – current not constant but pulses! (tpulse = nb tb) – for all LC designs, long bunch trains achieve steady state quickly, and previous results very good approximation. – However, transient over first bunches needs to be compensated. V unloaded av. loaded t The Linear Accelerator (LINAC) Single bunch beam loading: the Longitudinal wakefield NLC X-band structure: Ez bunch 700 kV /m The Linear Accelerator (LINAC) Single bunch beam loading Compensation using RF phase wakefield RF Total f = 15.5º The Linear Accelerator (LINAC) Single bunch beam loading: compensation RMS E/E Ez> fmin = 15.5º Transverse Wakes: The Emittance Killer! tb V (w , t ) I (w , t ) Z (w , t ) Bunch current also generates transverse deflecting modes when bunches are not on cavity axis Fields build up resonantly: latter bunches are kicked transversely multi- and single-bunch beam breakup (MBBU, SBBU) Damped & Detuned Structures N LC RD DS1 bunch spacing t 2Q H O M w Slight random detuning between cells causes HOMs to decohere. Will recohere later: needs to be damped (HOM dampers) Single bunch wakefields Effect of coherent betatron oscillation - head resonantly drives the tail head eom: 2 d yh ds tail k yy 0 2 tail eom: head 2 d yt ds k yt k wf y h 2 Wakefields (alignment tolerances) cavities tail performs oscillation bunch accelerator axis tail y head tail head head tail 5 km 0 km E YR M S 1 NW f -3 E N z 10 km higher frequency = stronger wakefields Z -higher gradients -stronger focusing (smaller ) -smaller bunch charge The LINAC is only one part pre-accelerator few GeV source KeV damping ring few GeV few GeV bunch compressor 250-500 GeV main linac extraction & dump final focus IP collimation • Produce the electron charge? Need to understand how to: • Produce the positron charge? • Make small emittance beams? • Focus the beams down to ~nm at the IP? e+e- Sources Requirements: • produce long bunch trains of high charge bunches • with small emittances • and spin polarisation (needed for physics) 100-1000s @ 5-100 Hz few nC enx,y ~ 10-6,10-8 m mandatory for e-, nice for e+ Remember L scaling: L n N2 b en e- Source • laser-driven photo injector • circ. polarised photons on GaAs cathode long. polarised e• laser pulse modulated to give required time structure • very high vacuum requirements for GaAs (<10-11 mbar) • beam quality is dominated by space charge (note v ~ 0.2c) la r se ph o s to n = 8 4 0 nm e lectro ns 20 m m G aA s cath od e 1 20 kV e n 10 - 5 m factor 10 in x plane factor ~500 in y plane e- Source: pre-acceleration E = 76 M eV E = 12 M eV K K K SHB to D R in e cto r lin ac so le n o id s la se r SHB = sub-harmonic buncher. Typical bunch length from gun is ~ns (too long for electron linac with f ~ 1-3 GHz, need tens of ps) e Source e Photon conversion to e± pairs in target material e- e Standard method is ebeam on ‘thick’ target (em-shower) e- eei- e- e Source :undulator-based 250GeV e- to IP e+e- pairs from e- linac N S N S N S N S N S S N S N S N S N S N ~30MeV photons undulator (~100m) 0.4X target • SR radiation from undulator generates photons • no need for ‘thick’ target to generate shower • thin target reduces multiple-Coulomb scattering: hence better emittance (but still much bigger than needed) • less power deposited in target (no need for mult. systems) • Achilles heel: needs initial electron energy > 150 GeV! ~ 30 MeV 0.4X0 10-2 m 5 kW see lecture 5 Damping Rings • (storage) ring in which the bunch train is stored for Tstore ~20-200 ms • emittances are reduced via the interplay of synchrotron radiation and RF acceleration initial emittance (~0.01m for e+) e f e eq ( e i - e eq ) e final emittance -2T /t D damping time equilibrium emittance see lecture 5 Damping Rings: transverse damping p replaced by RF such that pz = p. y’ not changed by photon (or is it?) dipole since (adiabatic damping again) y’ = dy/ds = py/pz, RF cavity we have a reduction in amplitude: y’ = -p y’ p p Must take average over all -phases: tD 2E P where P c C E 4 2 2 and hence tD 2 E 3 LEP: E ~ 90 GeV, P ~ 15000 GeV/s, tD ~ 12 ms see lecture 5 Damping Rings: Anti-Damping u 1 E -u ecB 0 E ecB u a r ecB particle now performs -oscillation about new closed orbit 1 increase in emittance dex dt dex Equilibrium achieved when Q dt 0Q- 2 td ex Damping Rings: transverse damping tD 2 E 3 suggests high-energy and small ring. But required RF power: PR F E 4 2 equilibrium emittance: e n , x an example: • • • • see lecture 5 nb N E 2 Remember: 8tD needed to reduce e+ vertical emittance. Store time set by frep: t s ntrain / f rep radius: Take E 2 GeV ntrain nb tb c Bbend = 0.13 T 50 m 2 <P> = 27 GeV/s [28 kV/turn] hence tD 148 ms - Few ms required!!! Increase <P> by 30 using wiggler magnets see lecture 5 Damping Rings: limits on vertical emittance • Horizontal emittance defined by lattice • theoretical vertical emittance limited by – space charge – intra-beam scattering (IBS) – photon opening angle • In practice, ey limited by magnet alignment errors [cross plane coupling] • typical vertical alignment tolerance: y 30 mm requires beam-based alignment techniques! see lecture 6 Bunch Compression • bunch length from ring ~ few mm • required at IP 100-300 mm E /E long. phase space E /E z RF E /E z E /E z dispersive section E /E z z see lecture 6 The linear bunch compressor u z,0 initial (uncorrelated) momentum spread: initial bunch length compression ration beam energy RF induced (correlated) momentum spread: RF voltage RF wavelength longitudinal dispersion: Fc=z,0/z E c VRF RF = 2 / kRF R56 c u 2 conservation of longitudinal emittance RF cavity c k R F V R F z ,0 E Fc V RF u E c k R F z ,0 2 c u E u k R F z ,0 Fc - 1 2 Fc - 1 2 The linear bunch compressor see lecture 6 chicane (dispersive section) z R56 R 56 - z 2 - c z ,0 F u 2 2 2 k R F V R F z ,0 1 2 E F u z ,0 2 m m u 0.1% 2% z 100 m m Fc 20 f R F 3 G H z k R F 62.8 m E 2 G eV V RF 3 1 8 M V -1 R 5 6 0 .1 m Final Focusing final doublet (F D ) f1 f1 f2 IP f2 f2 (=L*) Use telescope optics to demagnify beam by factor m = f1/f2= f1/L* Need typically m = 300 putting L* = 2m f1 = 600m see lecture 7 Final Focusing L* 2 - 4 m y e n,y y / y 2 - 5 nm y 100 - 300 μm remember y ~ z f L* at final lens y ~ 100 km short f requires very strong fields (gradient): dB/dr ~ 250 T/m pole tip field B(r = 1cm) ~ 2.5 T normalised quadrupole strength: K 1 1 Br o B 0 where B = magnetic rigidity = P/e ~ 3.3356 P [GeV/c] see lecture 7 Final Focusing: chromaticity 1 for a thin-lens of length l: y quad - K 1l y quad f 1 K 1l - K 1l y quad y IP f y quad y quad y IP y quad 2 f L* for rms ~ 0.3% y IP 2 2 2 quad e y rm s 2 20 - 40 nm y IP y rm s 2 more general: is chromaticity y 2 K 1 ( s ) ( s ) ds chromaticity must be corrected using sextupole magnets Final Focusing: chromatic correction see lecture 7 magnetic multipole expansion: 1 1 1 2 3 By ( x) B K1x K 2 x K3x 2 3! dipole quadrupole sextupole octupole 2nd-order kick: introduce horizontal dispersion Dx - k1 y y - k 2 xy quadrupole kn l 0 K nds sextupole x x D x y - k 2 xy - k 2 D x y geom etric chromatic correction when k2 - chrom aticity Dx k1 need also to cancel geometric (xy) term! (second sextupole) see lecture 7 Final Focusing: chromatic correction dipole IP Dx sextupoles m 0 R 0 0 0 0 1/ m 0 0 m 0 0 0 0 0 1 / m FD L* Final Focusing: Fundamental limits see lecture 7 Already mentioned that y z At high-energies, additional limits set by so-called Oide Effect: synchrotron radiation in the final focusing quadrupoles leads to a beamsize growth at the IP minimum beam size: 1.83 re occurs when 2.39 re 7 F e e n 1 7 en 2 F e 5 7 3 7 F is a function of the focusing optics: typically F ~ 7 (minimum value ~0.1) independent of E! Stability • Tiny (emittance) beams • Tight component tolerances – Field quality – Alignment • Vibration and Ground Motion issues • Active stabilisation • Feedback systems Linear Collider will be “Fly By Wire” see lecture 8 see lecture 8 Stability: some numbers • • • • Cavity alignment (RMS): Linac magnets: FFS magnets: Final “lens”: parallel-to-point focusing: ~ mm 100 nm 10-100 nm ~ nm !!! see lecture 8 LINAC quadrupole stability NQ y * k NQ Q ,i i 1 gi i 1 0.5 i sin( f i ) * * 0.5 1 0 for uncorrelated offsets y *2 * Y 2 * 1 NQ i k Q ,i i sin ( f ij ) 2 2 i 1 2 *2 y N Q kQ 500 1000 1500 2000 100nm RMS random offsets 0.5 0 * * e / Dividing by *2 y y ,n and taking average values: yj sing1e quad 100nm offset 0 i Yi g i k Q Yi g i 1 0.5 1 0 500 1000 1500 2000 2 2e y ,n Y 0.3 2 2 take NQ = 400, ey ~ 610-14 m, ~ 100 m, k1 ~ 0.03 m-1 ~25 nm see lecture 8 Beam-Beam orbit feedback e - IP bb y FDBK kicker BPM e use strong beambeam kick to keep beams colliding Generally, orbit control (feedback) will be used extensively in LC Beam based feedback: bandwidth 10 5 1 0.5 g = 0.01 g = 0.1 g = 0.5 g = 1.0 0.1 0.05 0.0001 0.001 0.01 0.1 f / frep f/frep Good rule of thumb: attenuate noise with ffrep/20 1 Ground motion spectra see lecture 8 Long Term Stability understanding of ground motion and vibration spectrum important 1 minute 1 hour 1 day 10 days 1 0.9 0.8 beam-beam feedback + upstream orbit control relative luminosity 0.7 No Feedback 0.6 0.5 0.4 0.3 beam-beam feedback 0.2 0.1 example of slow 0 0.1 diffusive ground motion (ATL law) 1 10 100 1000 tim e /s 10000 100000 1000000 Here Endeth the First Lecture