ILC Accelerator Physics Kiyoshi Kubo (KEK)

Note We concentrate on electron - positron Linear Colliders, especially ILC. There is nothing about proton machines, or LHC.

Contents Introduction Beam collision Luminosity and emittance Beam-beam force crossing angle Beam Delivery System (Final focus) Acceleration Basics Beam parameter and power efficiency For high gradient Low emittance Creation of low emittance - Damping Ring (Preservation of low emittance) Other system in ILC Bunch compression Spin rotation Major test facilities for ILC ATF and ATF2 1/1

Two important parameters of colliders Center of mass energy –Circular e+e- collider will be too expensive for higher energy than LEP (energy loss due to synchrotron radiation)  Linear Collider Luminosity (Compare with circular colliders) –Each particle bunch has only one collision chance. Collision rate is very low. –Do not have to care beams after collision.  Very strong focus and small beam size at collision. 2/3

ILC e- source  Damping ring  long transfer line  turn around  bunch compressor  Main linac (undulator for e+)  final focus system  collision  dump photons  e+ source e+ system is similar to e- system, except for the undulator 1/4

Beam Collision

Instantaneous Luminosity What is Luminosity ? Luminosity determines event rate. 1.5/5.5

(Average) luminosity of beams of “rigid” Gaussian bunches Luminosity is proportional to transverse density, inverse of cross section of the beam 1.5/7 Usually, x: horizontal, y: vertical coordinate

Limit of beam size at collision High luminosity needs small transverse beam size. But it is limited. Hourglass effect Oide limit Both effects require small emittance beam for high luminosity. 1/8

Beam Focusing Lens: Quadrupole magnet Focal point Stronger focus  shorter focal depth.5/8.5

Basics of (one dimensional) beam optics -1: quadrupole field gradient g s : distance along beam line 2/10.5

These are called “transfer matrix”. 1/11.5

Emittance is invariant in quadrupole field and drift space (Determinant of the transfer matrix is 1.) <> denotes average over particles in the beam Basics of (one dimensional) beam optics -2: drift space emittance ~ (beam size) x (angular divergence) 1/12.5

Beam size near focal point (focal point is in drift space) RMS beam size at distance s from the focal point : 1.5/14

Small beam size at s=0  rapid increase of beam size. (hourglass) Bunch length is finite and collisions at finite s contribute to luminosity. There should be optimum beam size for given emittance. We need small emittance beam for high luminosity. s 2/16

In Phase Space, x-x’ x-x’ (y-y’ ) plane is called “phase space”. Gaussian distribution can be expressed as an ellipse. Emittance can be regarded as the area of the ellipse. x x’ weak quad Strong quad long drift short drift 2/18

Another limit of Minimum beam size Quantum effect - Oide limit Quad magnet Radiation in the focusing magnet Uncertain energy loss  uncertain orbit downstream Stronger focus  More uncertainty 1.5/19.5

Quantum effect - Oide limit Ref.: K. Oide, PRL vol. 61, p1713 (1988) Supposing the bunch length is very small,  * should be as small as possible for high luminosity. In classical electro-magnetic dynamics,  * can be very small using very strong focusing magnetic field. But, Particles emit radiation in the strong magnetic field. –The energy loss is uncertain in quantum dynamics. – Inducing uncertain change of trajectory after the radiation. (Lower energy particles change angle in magnetic field more.) –This uncertainty affects the beam size at the focal point. The minimum beam size depends on emittance, AGAIN. 1.5/21

In Phase Space For small beam size, with a certain emittance, strong focus is required. x’ x stronger focus weak beam size at focal point from classical dynamics 1/22 SKIP

Beam-beam force Particles feel electro-magnetic field induced by the opposite beam Particles emit radiation (beamstrahlung) and lose energy. Energy spread is increased Particles are focused. Luminosity is enhanced. Particles are deflected and/or oscillate. Luminosity is reduced.. 1/23

beamstrahlung Particles feel strong electro-magnetic field induced by the opposite beam and emit radiation and lose energy e+ e-.5/23.5

beamstrahlung Induces energy spread during collisions (not only after collisions) and affect quality of experimental data. beamstrahlung parameter This should be several percent or less (depends on aimed physics) 1/24.5

For large luminosity and small beamstrahlung, FLAT BEAM On collision parameters Vertical beam size should be much smaller than horizontal. (Usually, Vertical emittance can be smaller than horizontal because: Vertical alignment is easier than horizontal. Damping ring is in a horizontal plane.) Horizontal beam size should not be so small for small  BS. 2/26.5

Limit of vertical beam size Luminosity per one bunch collision as function of vertical emittance and beamstrahlung On collision parameters (continued) Keeping beamstrahlung small, the only two ways to increase luminosity are Increase number of particles (increase beam power) Reduce the vertical emittance. Hour-glass Directly increase cost 1.5/28

Charges of two beams are opposite. In head on collision, particles are focused and luminosity increase. Luminosity enhancement due to beam-beam force Collisions with offset/angle error, Bunch oscillates during collision and Bunch is deflected. 1/29

1/30 SKIP ? Disruption parameter

Head on, 1 By computer code CAIN (developed by K.Yokoya) 3/33

Head on, 2

Head on, 3

Head on, 4

Head on, 5

Head on, 6

Head on, 7

Head on, 8

Head on, 9

2-  Offset, 1

2-  Offset, 2

2-  Offset, 3

2-  Offset, 4

2-  Offset, 5

2-  Offset, 6

2-  Offset, 7

2-  Offset, 8

2-  Offset, 9

Crossing angle Large crossing angle is desirable: Beam should be dumped safely after collision It is necessary to measure property of beam after collision for monitoring beam condition But, reduce luminosity ILC design has crossing angle 14 mrad..5/34.5

Crossing angle and crab crossing kick Crab crossing crossing angle  (2 mrad in ILC) l. position h. kick 2.5/37

Luminosity vs. Crossing angle without crab ILC nominal parameter, by CAIN.5/37.5

Parameters at IP Number of particles/bunch2E10 Normalized emittance, h1E-5 m-rad Normalized emittance, v4E-8 m-rad  *x 21 mm  *y 0.4 mm  *x 655 nm  *y 5.7 nm zz 0.3 mm Dx0.16 Dy19  BS crossing angle14 mrad Luminosity2E34 /cm^2/s 1/38.5

Beamstrahlung and Luminosity vs. bunch population Total luminosity and luminosity ECM energy reduction <1% 1.5/40

Luminosity vs. offset error at collision Normalized by geometrical luminosity 2/42

SUMMARY of Beam Collision High luminosity need small beam size at IP Beam size is limited by emittance (Hourglass, Oide-limit) Beam-beam force focuses opposite charge beams.  Enhance luminosity. Beam-beam force induce radiation and energy loss during collision. (beamstrahlung) Suppression of beamstrahlung requires flat beam. Luminosity is roughly proportional to Crossing angle and crab-crossing 2/44

Beam Delivery System Last part of Linear Collider Final Focus  luminosity Collimation  reduce back ground  machine protection 1/45

Final focus system optics design Quadrupole fields must be very strong for small beam size Beam has momentum spread  Different angle changes in magnetic fields  different trajectories  in crease beam size at IP (chromatic aberration) –Need to be compensated by sextupole magnetic field –This compensation induce higher order optics in addition to the linear optics. (geometric aberration) Imperfection of the magnetic field, misalignment, etc. cause additional geometric aberrations. ILC final focus method will be tested in ATF2 at KEK 2/47

Schematic view of simple (first order) chromatic aberration quadrupole Because horizontal beam size >> vertical beam size, we can concentrate on vertical direction. low energy particle high energy particle 1/48

Schematic view of correction of first order chromatic aberration sextupolequadrupole But this induces higher order aberrations. 1/49

SKIP Appendix: Expansion of vertical position at IP

Tuning and Control of collision Designing the system (what is the optimum beam optics, etc.) is one big issue. Make a real machine close to the design is another big issue. In actual operation, various errors will affect the design optics. Tuning (reducing errors or mitigating effects of errors) procedures have been studied, mainly by simulations. –if we do not have a machine Maintaining luminosity for reasonably long time will also need a lot of efforts. –Luminosity is affected by small fluctuations, movements of many parameters of the machine. –Need continuous feed back control. etc. 1/50

Tuning and feedback loops in Final focus Monitoring is essentially important. IF we can measure anything, we can control them. Final focus system IP Orbit feedback Luminosity Monitor deflector Luminosity tuning IP tuning/feedback control Monitors correctors Deflected beam position monitor 2/52

IP beam position feedback Measure deflected beam position after collision feedback to steering magnet (deflector) for the next bunch of the opposite beam –Feedback signal processing within bunch spacing (~300 ns). Deflection angle vs. offset at IP feedback works if offset error < 30  1/53 luminosity vs. offset at IP

Collimation Hallo, particles far from the core of the beam (energy and transverse position/angle), may hit materials near IP, (near the detector). –background Population and distribution of hallo cannot be well estimated. May be formed in the main linac. Post-linac collimation is necessary to prevent large hallo which induces detector background. Some failure may cause big orbit distortions If the beam hit a machine component, it will be broken. Failed beam must hit collimators. –Collimators may be broken in rare failures. 1/54

SUMMARY of BDS Beam optics design of final focus: suppression of (chromatic and geometrical) aberrations. Tuning and feedback –IP position feedback: relying on beam-beam deflection ILC final focus method will be tested in ATF2 at KEK (see later slides) 1/55

Acceleration

Basics of Acceleration Standing wave,  mode, Electro-magnetic power of Radio Frequency (RF) is fed to resonator (RF Cavity). The power is accumulated in the cavity. Lcell  particles pass all cells on the same phase Superconducting cavity is used in this mode. 1.5/56.5

RF unit of ILC Main Linac from ILC RDR 1/57.5

DESY.5/58

Super Conducting Cavity From ILC RDR Tuner: change length of cavity for adjusting resonance frequency Slow and large stroke : motor, Fast and small stroke : piezo Input coupler: feed RF power HOM coupler: Extract HOM HOM coupler: Le. He 1.5/59.5

Two parameters expressing Performance of Cavity Field Gradient Quality factor ( Q 0 ) ILC RDR Specification of ILC before installing in cryomodule. Necessary cooling capacity depends on Quality factor. Quality factor strongly depends on smoothness and purity of cavity’s inner surface. 2/61.5

For high gradient of superconducting cavities (1) Smoothness and Cleanness of cavity inner surface. –Any defect may cause heating (reduction of Q 0 ), breakdown of superconductivity. Fabrication –Electron beam welding Treatment of surface –Chemical polishing –Electric polishing –Cleaning Avoid contaminations 1/62.5

Construction of Superconducting cavities in clean environment RDR.5/63

For high gradient of superconducting cavities (2) Design of cavity shape. High magnetic field causes breakdown of superconductivity. (Fundamental limit of gradient) [Saito’s hypothesis] Eacc (gradient felt by beam) / Hpeak (peak magnetic field) should be large. Three different designs 1/65

from Kenji Saito History of highest gradients achieved in single cell cavities. 1/65.5

Beam parameter of ILC (superconducting LC) in Main Linac, compare with normal conducting LC Super (rough)Normal (very rough) Particles/bunch2E101E10 Bunches/pulse Charge/pulse 10  C 160 nC Bunch spacing300 ns3 ns Pulse length0.9 ms300 ns Beam current in pulse10 mA500 mA Rep. rate5 Hz100 Hz Average beam current 50  A16  A 1/66.5

Time structure of ILC beam Bunch length: RMS 0.3 mm (1 ps) Bunch to bunch spacing ~ 300 ns Bunch number ~3000 Pulse length ~ 0.9 ms (270 km) Bunch pulse 200 ms 0.9 ms Repetition rate: 5 Hz Note: In damping rings, bunch space is compressed to ~6 ns  circumference ~ 6 km. 1.5/68

Transient behavior of cavity voltage beam Power on Bunches Assuming matched condition. Beam loading = input power voltage = constant 2/70

Accelerating field from short time range view (single bunch) Total field is field induced by input power + field induced by beam (beam loading, or, wakefiled) (deceleration) bunch tail put bunch center slightly off-crest  minimize energy spread 1/71

Transient behavior of power to/from cavity InputReflection beam power on fill time 2/73

RF Power efficiency RF power during beam pulse is given to beam, almost all. RF power during “fill time” is lost.  For high efficiency, total charge/pulse should be large. 1/74 Roughly,

This is the reason why Superconducting LC has a long beam pulse and large number of bunches per pulse. For high efficiency, High beam current increase RF peak power, then number of klystrons or power of klystrons. It increase construction cost. So, beam current is limited.  For increasing charge/pulse, increase pulse length. 2/76

Damping ring limits number of bunches/pulse Damping ring circumference = [Number of bunches] x [Bunch spacing] Bunch spacing is limited by extraction/injection kicker speed and instabilities. See later discussions. 1/77

Cryogenics limit pulse length Pulse length is limited by Power for Cryogenics –Cavity wall loss is negligible for RF power efficiency, But, cannot be ignored considering total power efficiency. Cooling cavity needs power. Q Heat from cavity at T1 Need to be dumped to environment, at T2 From fundamental law (total entropy cannot be reduces), dumped heat > Q x (T2/T1) Entropy has to be dumped, not only heat. Need to add energy from outside (Power to cryogenics) Cryogenics 1.5/78.5

Q=q x Nb = Ib x T : Total charge Simple Summary of Beam Parameter Choice T : Pulse length Ib : Average beam current q : Bunch charge Nb : Number of bunches Determined by luminosity/beam-beam force Limited by Cryogenics Limited by RF system Limited by Damping Ring The larger the better for RF power efficiency There must be some compromise. Three independent parameters out of four: 1.5/80

In the case of normal conducting LC input power Power is rapidly lost  Longer the beam pulse, larger the power loss.  High beam current, short pulse.  High RF frequency (most designs choose > 10 GHz) Power loss (not so simple though ) 2/82

Lorentz Detuning Electromagnetic field pull the surface of cavity (Lorenz force). Cavity is a mechanical spring. The force reforms the cavity  change resonance frequency: Detuning Time dependent field strength + cavity’s mechanical property  Determine resonance frequency as function of time. Keeping acc. voltage with detuning  need too large input RF power in high gradient operation 1.5/83.5

Cure of Lorentz Detuning Tuner: change length of cavity for adjusting resonance frequency Slow and large stroke : motor, Fast and small stroke : piezo Control piezo tuner to compensate Lorentz detuning. (can be pre-program since the behavior is the same for every pulse.) Residual small detuning can be cured by RF feedback. 1/84.5

Dynamic Lorentz Detuning Results at TTF  Pkly < 10 % → Detuning angle < 12 deg.,  f < 46Hz S.Nogichi, ILC School 2006, Hayama Mechanical oscillation, long time range compensation by piezo tuner 1.5/86

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