ILC Accelerator Physics 2008 09 Kiyoshi Kubo KEK

ILC Accelerator Physics 2008. 09. 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 ATF 2 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

What is Luminosity ? Instantaneous Luminosity determines event rate. 1. 5/5. 5

(Average) luminosity of beams of “rigid” Gaussian bunches Usually, x: horizontal, y: vertical coordinate Luminosity is proportional to transverse density, inverse of cross section of the beam 1. 5/7

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 Focal point Stronger focus shorter focal depth Lens: Quadrupole magnet. 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

Basics of (one dimensional) beam optics -2: drift space Emittance is invariant in quadrupole field and drift space (Determinant of the transfer matrix is 1. ) <> denotes average over particles in the beam 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. s We need small emittance beam for high luminosity. 2/16

In Phase Space, 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. weak quad long drift x’ x 2/18 Strong quad short drift

Another limit of Minimum beam size Quantum effect - Oide limit Radiation in the focusing magnet Uncertain energy loss uncertain orbit downstream Quad magnet Stronger focus More uncertainty 1. 5/19. 5

Quantum effect - Oide limit Ref. : K. Oide, PRL vol. 61, p 1713 (1988) • Supposing the bunch length is very small, s* should be as small as possible for high luminosity. • In classical electro-magnetic dynamics, s* 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 SKIP For small beam size, with a certain emittance, strong focus is required. weak x’ x 1/22 stronger focus beam size at focal point from classical dynamics

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

On collision parameters For large luminosity and small beamstrahlung, FLAT BEAM 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 d. BS. 2/26. 5

On collision parameters (continued) Limit of vertical beam size Hour-glass Luminosity per one bunch collision as function of vertical emittance and beamstrahlung Keeping beamstrahlung small, the only two ways to increase luminosity are • Increase number of particles (increase beam power) • Reduce the vertical emittance. Directly increase cost 1. 5/28

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

? Disruption parameter P I K S 1/30

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 -s Offset, 1

2 -s Offset, 2

2 -s Offset, 3

2 -s Offset, 4

2 -s Offset, 5

2 -s Offset, 6

2 -s Offset, 7

2 -s Offset, 8

2 -s 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 angle q (2 mrad in ILC) h. kick Crab crossing 2. 5/37 kick l. position kick

Luminosity vs. Crossing angle without crab ILC nominal parameter, by CAIN. 5/37. 5

Parameters at IP 1/38. 5 Number of particles/bunch 2 E 10 Normalized emittance, h 1 E-5 m-rad Normalized emittance, v 4 E-8 m-rad b*x 21 mm b*y 0. 4 mm s*x 655 nm s*y 5. 7 nm sz 0. 3 mm Dx 0. 16 Dy 19 d. BS 0. 022 crossing angle 14 mrad Luminosity 2 E 34 /cm^2/s

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 ATF 2 at KEK 2/47

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

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

Appendix: Expansion of vertical position at IP SKIP

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 tuning/feedback control correctors Luminosity tuning Monitors IP Final focus system Luminosity Monitor Deflected beam position monitor deflector IP Orbit feedback Monitoring is essentially important. IF we can measure anything, we can control them. 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 s 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 ATF 2 at KEK (see later slides) 1/55

Acceleration

Basics of Acceleration Electro-magnetic power of Radio Frequency (RF) is fed to resonator (RF Cavity). The power is accumulated in the cavity. Lcell Standing wave, p mode, 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 Input coupler: feed RF power Le. He HOM coupler: Extract HOM coupler: Tuner: change length of cavity for adjusting resonance frequency Slow and large stroke : motor, Fast and small stroke : piezo 1. 5/59. 5

Two parameters expressing Performance of Cavity • Field Gradient • Quality factor (Q 0) Specification of ILC before installing in cryomodule. Necessary cooling capacity depends on Quality factor strongly depends on smoothness and purity of cavity’s inner surface. ILC RDR 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 • 1/62. 5 Avoid contaminations

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

History of highest gradients achieved in single cell cavities. 1/65. 5 from Kenji Saito

Beam parameter of ILC (superconducting LC) in Main Linac, compare with normal conducting LC Super (rough) Normal (very rough) Particles/bunch 2 E 10 1 E 10 Bunches/pulse 3000 100 Charge/pulse 10 m. C 160 n. C Bunch spacing 300 ns 3 ns Pulse length 0. 9 ms 300 ns Beam current in pulse 10 m. A 500 m. A 5 Hz 100 Hz 50 m. A 16 m. A Rep. rate Average beam current 1/66. 5

Time structure of ILC beam Bunch length: RMS 0. 3 mm (1 ps) pulse Bunch to bunch spacing ~ 300 ns Bunch number ~3000 Pulse length ~ 0. 9 ms (270 km) 0. 9 ms 200 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 Assuming matched condition. Beam loading = input power voltage = constant beam Power on 2/70 Bunches

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) put bunch center slightly off-crest minimize energy spread bunch tail 1/71

Transient behavior of power to/from cavity Reflection Input 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. Roughly, For high efficiency, total charge/pulse should be large. 1/74

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. This is the reason why Superconducting LC has a long beam pulse and large number of bunches per pulse. 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 T 1 Cryogenics Need to be dumped to environment, at T 2 Need to add energy from outside (Power to cryogenics) From fundamental law (total entropy cannot be reduces), dumped heat > Q x (T 2/T 1) Entropy has to be dumped, not only heat. 1. 5/78. 5

Simple Summary of Beam Parameter Choice Three independent parameters out of four: Ib: Average beam current T: Pulse length Limited by RF system Limited by Cryogenics Nb: Number of bunches Limited by Damping Ring q: Bunch charge Determined by luminosity/beam-beam force Q=q x Nb = Ib x T : Total charge The larger the better for RF power efficiency There must be some compromise. 1. 5/80

In the case of normal conducting LC (not so simple though ) input power Power loss 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) 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 • 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. Tuner: change length of cavity for adjusting resonance frequency Slow and large stroke : motor, Fast and small stroke : piezo 1/84. 5

Dynamic Lorentz Detuning Mechanical oscillation, long time range Results at TTF　 compensation by piezo tuner DPkly < 10 % →　Detuning angle < 12 deg. , Df < 46 Hz S. Nogichi, ILC School 2006, Hayama 1. 5/86

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