Low-Emittance Beams and Collective Effects in the ILC Damping Rings And Wolski Lawrence Berkele National Laborator Super-B Factor Meeting, Laboratori Nazionali di Frascati November 1, 005
Comparison of parameters Circumference Beam energ Horizontal emittance Vertical emittance Bunch length Bunch charge e + / e - ILC Damping Rings 3 km 17 km 5 GeV 0.8 nm pm mm 10 10 / 10 10 Super B-Factor. km 3.5 GeV 0.1 nm 1 pm mm 4 10 10 / 8 10 10 Notes: Super B-Factor parameters from P. Raimondi, Eotic approach to a Super B-Factor, presented at Super B-Factor Workshop, Hawaii, April 005. Parameters are for the flat-beam case, L = 10 3 cm - s -1 Bunch length mm (in the ring) assumes factor 0 compression between ring and IP.
There are several common issues and concerns, including: Tuning for low vertical emittance Best achieved vertical emittance is ~ 4 pm (at KEK-ATF). ILC DR s require pm, Super B-Factor parameters assume 1 pm. Intrabeam scattering IBS causes emittance growth; growth rates scale strongl with energ, linearl with bunch charge, and inversel with beam sizes and bunch length. Touschek lifetime Space-charge tune shifts Can cause emittance growth and particle loss. Microwave instabilit Coupled-bunch instabilities Can be suppressed using bunch-b-bunch feedback sstems. Electron cloud, ion effects - see Yunhai s talk.
Damping ring configuration options Studies of a number of different damping ring configuration options have been performed over the past several months. The configuration studies have focused on beam dnamics issues in seven representative lattice designs: Lattice Name Energ [GeV] Circumference [m] Cell Tpe PPA 5.0 84 PI OTW 5.0 33 TME OCS 5.0 114 TME BRU 3.7 333 FODO MCH 5.0 15935 FODO DAS 5.0 17014 PI TESLA 5.0 17000 TME
Vertical emittance has a fundamental limit from SR Vertical opening angle of the snchrotron radiation places a fundamental lower limit on the vertical emittance. The fundamental limit depends on lattice design, and not on beam energ. In the ILC damping rings, the lower limit is of order 0.1 pm 1 pm looks ok from point of view of fundamental limits Radiation Limited Vertical Emittance 0.1 Vertical Emittance [pm] 0.10 0.08 0.0 0.04 0.0 0.00 KEK- ATF PPA OTW OCS BRU MCH DAS TESLA ε 13 Cq β = ds 55 J I ρ, SR 3
Vertical emittance is mostl generated b alignment errors Vertical emittance is generated b vertical dispersion and betatron coupling Dominant sources are: - vertical beam offset in setupoles - quadrupole tilts about the beam ais We can characterize the sensitivit of a lattice to magnet alignment errors, as the magnet misalignment, starting from a perfect machine, that will generate the nominal vertical emittance. Larger values are better (indicate a lower sensitivit to magnet misalignments) Sensitivit estimates do not take into account tuning and coupling correction. Sensitivit values should not be interpreted as tolerances on surve alignment. These sensitivit values simpl indicate the likel difficult of achieving a given emittance, and the frequenc with which tuning will need to be performed.
Damping Ring sensitivit to setupole misalignments ε Y set J 4J [ 1 cos( πν ) cos( πν )] J zσ δ ΣCε + Σ D [ cos( πν ) cos( πν )] 4sin ( πν ) coupling dispersion Σ = β D = β ( k L) Σ β ( k L) C η sets sets Sensitivities are tpicall of the order of a few tens of microns. Note: Horizontal emittance in Super-B Factor is 8 times lower than in damping rings, so a Super-B Factor could be less sensitive to setupole misalignment than the damping rings.
Damping Ring sensitivit to quadrupole tilts Θ ε quad J 4J [ 1 cos( πν ) cos( πν )] J zσ δ Σ1 Cε + Σ 1D [ cos( πν ) cos( πν )] 4sin ( πν ) coupling dispersion Σ1 C = β 1 1D = η quads β ( k L) Σ β ( k L) quads 1 Sensitivities are tpicall of the order of 100 µrad. Note: Horizontal emittance in Super-B Factor is 8 times lower than in damping rings, so a Super-B Factor could be less sensitive to setupole misalignment than the damping rings.
Orbit jitter is also a concern Quadrupole jitter sensitivit is the rms quadrupole misalignment that will generate an orbit distortion equal to the beam size. amplification factor β Σ 1O Σ1 O = β ( k1l) 8sin ( πν ) quads Quadrupole Jitter Sensitivities are tpicall of the order of 00 nm. 350 Sensitivit [nm] 300 50 00 150 100 50 0 1 4 70 19 7 197 00 85 Analtical Simulation KEK-ATF PPA OTW OCS BRU MCH DAS TESLA
IBS increases the emittance with increasing bunch charge Intrabeam scattering (IBS) can be a strong effect in low-emittance machines at low energ and high bunch charge. Measurements from KEK-ATF have been used to benchmark the theories. Accurate measurements with beam sizes ~ few µm are hard to make. Beam size at 4.5 pm is around 5 µm, and comparable to the size of the laser-wire itself. Measurements do not allow for beam jitter, but this should be small. Y. Honda et al, Phs. Rev. Lett. 9, 05480-1 (004). Y. Honda et al, Phs. Rev. Lett. 9, 05480-1 (004).
IBS will increase emittance in the ILC damping rings Horizontal emittance vs bunch charge 3.7 GeV
IBS will increase emittance in the ILC damping rings Vertical emittance vs bunch charge 3.7 GeV
IBS growth is less severe longitudinall than transversel 3.7 GeV Bunch length vs bunch charge Energ spread vs bunch charge 3.7 GeV
Intrabeam scattering scales strongl with energ Emittance growth is largest in horizontal plane Growth mechanism is analogous to quantum ecitation: energ change resulting from particle scattering at locations of high dispersion leads to large betatron oscillations. Growth rates ~ 1/E (for fied bunch length and vertical emittance): IBS could make it ver difficult to achieve 0.1 nm horizontal emittance with high bunch charge, low vertical emittance and short bunch length. IBS effects in the ILC damping rings are suppressed to some etent b relativel fast radiation damping. ( ) ( ) 4 1 4 3 3 0 1 (log) 1 H z g N c r T β β ε β ε β σ σ σ σ ε ε γ δ δ δ δ δ ε σ T H T 1 1,,
Touschek lifetime can be epected to be short (~ ½ hour) A rigorous calculation of the Touschek lifetime requires a detailed model of the energ acceptance at ever point around the lattice. We can make a simple estimate, assuming a fied energ acceptance of 1%. Touschek lifetime scales as the square of the energ acceptance. Using the formulae from Wiedemann ( Particle Accelerator Phsics II ): 3 1 re cn0δ ma = τ 8πγ σ σ σ D( ε ) 3 ε 1 ln u u 1 D( ε ) = ε e + ε e du + ( 3ε ε lnε + ) u ε β δ ma ε = γ mcσ z u ε e u du PPA OTW OCS BRU MCH DAS TESLA Lifetime [min] 1 17 33 18 8 44 50 dogbone lattices have large beam sizes in the long straights
Space-charge tune shifts are large in the dogbone rings We can estimate the incoherent space-charge tune shift using a simple linearfocusing approimation: C [m] γ ε [pm] σ z [mm] PPA 84 9785.04 ν = OTW 33 9785.04 r e N 0 β + 3 3 ( π ) σ γ σ ( σ σ ) z OCS 114 9914.00 Studies for the TESLA TDR suggested significant emittance growth from particles crossing resonance lines in the tune plane. Coupling bumps in the long straights were proposed as a solution. More detailed studies to understand the full impact of space-charge effects are in progress. BRU 333 7319.5 ds 15935 1.9 17014 1.7 17000 N 0 [10 10 ].4. ν -0.0-0.04-0.05-0.1-0.17-0.30-0.37 9 MCH 9785 9 DAS 9785 TESLA 9785 1.45
Space-charge effects ma also be large for Super B-Factor We can estimate the incoherent space-charge tune shift using a simple linearfocusing approimation: ν Circumference = r e N 0 β + 3 3 ( π ) σ γ σ ( σ σ ) z ds. km Number of particles, N 4 10 10 0 Bunch length, σ z mm Beam energ, γ Horizontal emittance, ε Vertical emittance, ε Horizontal beta function, β Vertical beta function, β Incoherent tune shift, ν 850 (3.5 GeV) 0.1 nm 10 pm 50 m 50 m -0.59 In general, tune shifts should be kept below ~ 0.1
A ver simple estimate for the microwave threshold We can use the Keill-Schnell-Boussard criterion to estimate the impedance (Z/n) at which we epect to see an instabilit: Z n = Z 0 π γα pσ δσ z N r 0 e PPA OTW OCS BRU MCH DAS TESLA γ 9785 9785 9914 7319 9785 9785 9785 α p [10-4 ].83 3. 1. 11.9 4.09 1.14 1. σ δ [10-3 ] 1.7 1.3 1.9 0.973 1.30 1.30 1.9 σ z [mm] 9 9 N 0 [10 10 ].4. Z/n [mω] 187 99 134 510 94.8 100 Compare with measured values: APS: measured Z/n ~ 500 mω (40 mω from impedance model) Y.-C. Chae et al, Broadband Model Impedance for the APS Storage Ring, PAC 001. DAΦNE: measured Z/n ~ 530 mω in electron ring (0 mω from impedance model), and Z/n ~ 1100 mω in positron ring A. Ghigo et al, DAΦNE Broadband Impedance, EPAC 00.
Comments on microwave threshold Z/n is a ver crude characterization of the impedance. Much more detailed analsis is needed to understand the instabilities properl. The impedance found from beam-based measurements in a storage ring are often several times larger than the impedance epected from a model of the individual components. A significant safet margin is highl advisable between the nominal working point and the point at which instabilities are epected to occur. Z/n for KEK-B is of the order 100 mω or less, but still several times larger than that epected from the design model. SLC eperience suggests that ver small effects in the damping rings, which ma not be an real concern to other machines, could have a significant impact on ILC operation and performance.
Feedbacks will be needed to suppress multibunch instabilities We can make an estimate of the growth rates from the resistive-wall impedance. A number of assumptions are needed: Uniforml filled ring Homogeneous lattice (i.e. constant beta function around ring) Uniform circular aperture for the vacuum chamber Time domain simulations show that these assumptions are good, even in the dogbone damping rings. Simulations of Resistive-Wall Instabilit in the ILC Damping Rings, A.Wolski, J.Brd, D.Bates (PAC 005). For our calculations, we assume an aluminum vacuum chamber, with radius: 0 mm in the arcs 49 mm in the long straights 8 mm in the wigglers We also assume a uniform fill with the nominal bunch charge.
Resistive-wall growth times are fast Γ = 4π β c A Z c 4γ I I C 1 ( 1 frac( )) 0 A ν A = 0 C 3 π 1 b Z c c 4π σ Lattice PPA OTW OCS BRU MCH DAS TESLA Chamber 40/1/100 5 1 1 9 Shortest growth time Note: chamber sizes are diameters in arcs/wigglers/straights Chamber 50/3/100 155 8 9 3 1 1 3 Feedback sstems look challenging in some cases. Growth times of 0 turns are state-of-the-art. There is a potential concern with bunchto-bunch jitter that can be induced on the beam from the feedback sstem, because of limited pick-up resolution. Higher-order modes in the RF cavities, and other long-range wakes, will contribute to the growth rates, and make the feedback sstems still more challenging.
Summar and Conclusions for Super-B and ILC DRs Super-B Factor parameters could be more challenging than the ILC damping rings Tuning for low vertical emittance ~ 1 pm will be difficult Best achieved so far is ~ 4 pm at KEK-ATF. Vertical emittance will likel not be limited b snchrotron radiation opening angle. Vertical emittance will be sensitive to setupole motion at the level of ~ 10 µm. Orbit stabilit will be important Quadrupole jitter should be kept < 100 nm. Collective effects look particularl challenging All get worse at lower energ and higher bunch charge. Variet of smptoms can be epected: emittance growth; coherent single-bunch and coupled-bunch modes; particle loss
Summar and Conclusions: Collective Effects Intrabeam scattering Could be a limiting effect on low emittance (horizontal and vertical) at high bunch charge. IBS growth rates scale strongl with energ. Touschek lifetime Could be as short as ½ hour. A lattice with a large energ acceptance will help. Space-charge tune shifts Large tune shifts are epected, because of high charge, short bunch and low emittance. Tracking studies are needed to see if space-charge is reall a problem. Microwave threshold As alwas, ver careful design and construction of vacuum chamber will be needed to keep impedance as low as possible. Coupled-bunch instabilities Bunch-b-bunch feedbacks will almost certainl be needed. Increasing the chamber aperture helps a lot with the resistive-wall impedance. The bottom line: mabe not impossible but ver challenging.