Overview of Acceleration R B Palmer, Scott Berg, Steve Kahn (presented by Steve Kahn) Nufact-04 RF Frequency Acc types and System Studies Linacs RLA s FFAG s Injection/Extraction US Study 2a acceleration costs Conclusion Appendix on Cost Model 1
Acceleration Frequency Compare two choices: 1. Very Low frequency e.g. 5MHz (Studied in Japan) Gradient restricted to e.g. 0.5 MeV/m Allows the largest longitudinal acceptance in a single bunch e.g. for: p=0.2 GeV/c, rms dp/p=10% and dφ= 0.2: ɛ = β v γλ dφ 2π dp p 0.4 (pi m rad) 2. Higher frequency e.g. 200 MHz (Studied in US) Iris diam. for trans. acceptance sets this max frequency Allows higher acceleration gradients e.g. 10 MeV/m allows efficient superconducting RF Small single bunch acceptance overcome by many bunches made from single proton pulse (e.g. 40): For same: p, dp/p and dφ: ɛ = 0.01 ( λ) 40 (bunches) = 0.4 (pi m rad) 2
Conclusions on frequencies 5 and 200 MHz solutions have similar longitudinal acceptance Higher gradient of 200 MHz will give less decay loss But 200 MHz, if vacuum, does not allow frequency variation more isochronous acceleration required And 200 MHz, if superconducting, has added requirement of very small stray magnetic fields 3
Accelerator types for muon acceleration in different energy regimes 1. Linac Fastest of all Works for low γ where β v is varying with z But RF expensive per GeV 2. RLA About 1/2 acceleration rate of linac Finite number of turns ( 4) gives 1/4 RF cost Min injection energy ( 1 GeV) from phase slip in linac 3. FFAG About 1/4 acceleration rate of linac More turns (e.g. 15) gives about 1/15 RF cost Min energy from cost comparison with RLA 5 GeV Limited momentum swing (e.g. 1:2 or 1:3) 4
Systems studied 1. Japanese A sequence of Scaling FFAG s :.3 to 1 GeV, 1 to 3 GeV, 3 to 10 GeV, 10 to 20 GeV All with trans. acceptance 30,000 π mm mrad (30 π mm rad) No cooling in the published study, but the addition of cooling is not ruled out 2.CERNandUSStudy-2 Linac from 0.3 to about 2.5 GeV 4 pass RLA from 2.5 to 20 GeV In US Study-2 case: transverse acceptance of RLA, but not the linac, was 30,000 π mm mrad Same as Japan 3. US Study-2a (To be part of APS neutrino study) Linac from 0.3 to about 1 GeV 4passRLAfrom1to5GeV 2 Non-scaling FFAG s: 5-10 GeV, 10-20 GeV All acceptance = 30,000 π mm mrad Same as Japan 5
Study 2a Linac Design for 30,000 pi mm mrad If Superconducting, RF then stray field requires cavity to nearest quadrupole 60 cm If 200 MHZ, Cavity length 80 cm, & maximum iris radius 23 cm So minimum required gap for RF 2m This is just ok at the initial energy. At higher energies, longer gaps and more RF/cell can be used, giving better ave. gradient. 0.5to1.0GeV/c 0.38 to 0.5 GeV/c 0.27 to 0.38 GeV/c 6
Study 2a RLA Design for 30,000 pi mm mrad Dog-bone and Racetrack RLA s, with same number of passes through the Linac, have: slightly less total arc length much easier switch-yards For the larger acceptance of Study 2a, Dog-bone is probably the required solution For phase slip reasons, injection is half way along linac Cost optimization probably prefer more passes 7
Discussion of FFAG types 1. Scaling FFAG (MURA & now Japanese Effort) Tunes independent of E All orbits exactly similar in shape Non-Isochronous: orbits r p k+1 Significant % of reverse bend Larger circumference 2. Non-Scaling FFAG (Carol Johnstone et al) Isochronous at central momentum Less reverse bending more compact than scaling But tunes vary a lot acceleration through integer resonances Requires rapid acceleration More RF 3. New: Quasi-Scaling FFAG (Sandro Ruggiero) Tunes constant, or nearly so, Avoids crossing integer tunes allows slower acceleration less RF Interesting for protons Not suitable for muons (will not discuss further) 8
1) Scaling FFAG r 1/p k+1 drift for rf Orbits at different momenta are similar B r k bend outward bend inward POPFFAGatKEK Low Momentum Mid Momentum High Momentum Fixed tune: no resonant crossing p limited only by aperture But apertures large only 1:2 for Japan s 10-20 GeV Non-isochronous Low Frequency Non-superconducting RF 9
2 Non-Scaling FFAG (Proposed by Carol Johnstone) Combined function strongly focusing lattices without sextupoles e.g. from Dejan Trbojevic Note Orbits are not similar, as in scaling They are closer together than in scaling smaller apertures more isochronous 10
Non-scaling more isochronous than Scaling Design can set chromaticity=0 at center of momentum range: Compare 10-20 GeV Scaling and Non-scaling FFAG s dct/turn (m) 1.25 Scaling (10-20) 1.00 0.75 0.50 0.25 Non-scaling (10-20) Less path length difference for same energy range Non-monotonic Allows 200 MHz (vs. 25 MHz for scaling) 0.00 10.0 Momentum 12.5 15.0 (GeV) 17.5 20.0 dct/turn (m) 1.25 1.00 0.75 0.50 0.25 0.00 Non-Scaling (6-20) Non-scaling (10-20) 7.5 10.0 Momentum 12.5 15.0 (GeV) 17.5 20.0 More difference for larger energy range Fix by increasing circumference expensive Essentially restricts momentum range to 2:1 11
But Non-scaling has huge chromaticity Tunes cross many integer resonances (right scale) But if 1. All cells essentially identical 2. Reasonably small magnet errors 3. Rapid acceleration Initial simulations indicate negligible emittance growth 12
Choice of Non-Scaling Lattice in Study 2a Triplet, FODO and Doublet lattices can all be designed to the same requirements on: Energy swing, minimum magnet spacing, length for RF, isochonicity, acceptance, and maximum allowed initial tune. S. Berg has cost optimized each style using a costing algorithm For 10-20 GeV rings he obtains: FODO triplet Doublet c.f.rla magnets 315 255 186 circumference m 681 521 486 1300 Decay loss % 10.4 10.1 8.5 5.0 cost per GeV $M 10.2 9.0 8.7 20.5 The differences are not large, but the doublet lattice is smaller, cheaper, and gives less decay losses. Doublets appear favored Note all 10-20 GeV FFAG s less than half RLA cost per GeV 13
Injection/Extraction Kickers for FFAG s Minimum required kicker stored energy and Voltage for A n (acceptance) =.03 m, L (length) =1 m, τ (rise time) = 1 µs U = V = m 2 µ 8 µ o c 2 4 m µ c A n τ A 2 n L = 700 (J) = 70, 000 (V) The Voltage is high but may be reasonable The stored energy is alreadyvery very large (Largest (antiproton) kickers have 10-20 J) In practice, they will both be even larger because: horiz ap Horizontal aperture > final beam size: beam size = σ 1+dp/p D σ 2 Extra Kicker aperture required to accept the deflecting beam Kick must go past the finite septum thickness The flux return µ is finite, and other inefficiencies If critically damping required (e.g. for injection), U is doubled 14
Extraction Example for 10-20 GeV FFAG 0.75 x limits 0.50 0.25 F D F S1 S2 0.76 T Kicker 1.8 T Septum S4 S3 F F D F 0.00 U=3400 J V=200 kv (2 orders of magnitude larger than normal) & will be higher for lower energy smaller rings 15
Possible power source: Magnetic Amplifier Used to drive Induction Linacs e.g. ATA or DARHT Switch low Amp long pulse Mag-Amp compresses pulse to high Amp short pulse Stored energy 1500 J (2 units required) Rise time 100 nsec (faster than required) 16
US Study 2a Acceleration Costs Choices of Linac, RLA, & two FFAGs was driven by costing With the assumptions used : Acceleration cost of Study 2a is about 67% of Study 2 Acceptance of the full system was increased 15 30 π mm Study 2 Study 2a GeV $M $M/GeV GeV $M $M/GeV Linac 0.3-2.5 132 60 0.3-1 70 100 RLA 2.5-20 355 20.3 1-5 82 20.5 FFAG 1 5-10 80 16 FFAG 2 10-20 98.3 9.8 Totals 544 363 Note falling FFAG cost per GeV at higher energies Costs exclude management overheads and are in unspecified year values. The numbers are given for comparison rather than actual amounts. Scott Berg calls the units Palmer Bucks 17
Layouts of old and new Studies 2 Phase Rotation Cooling Pre-Acc RLA Study 2 Phase Rotation Cool Pre Acc Study 2a RLA FFAG 1 FFAG 2 Study 2a System significantly smaller than Study 2 Smaller accleration is major component of this 18
Conclusions Designs very dependent on RF Frequency, yet for longitudinal acceptance: 5 MHz with single bunch 200 MHZ with multiple bunches Superconducting initial linac with 30 pi mm designed Dog-bone RLA has easier switch-yards than race track Non Scaling FFAG s isochronous enough for fixed frequency Non-scaling crossing of integer resonaces seems ok Doublet non-scaling lattice appears most cost effective Injection/extraction of any 30 pi mm FFAG is serious, but probably possible Non-Scaling FFAG cheaper than RLA But only at energies above 5 GeV Study 2a acceleration system, with FFAG s, costs 2/3 of Study 2 19
Appendix on Cost Model Costs in 2004 M$, Lengths in m, Gradients in MV/m Linear Costs tunneling, access, cabling, diagnostics, survey, etc. Cost =.025 L 200 MHz superconducting RF costs cavities plus power suplies RF Cost = 30 (16/G) + 26.8 G 16 200 MHz conventional RF costs cavities plus power suplies RF Cost = 10 (16/G) + 150 G 16 20
Magnet Costs Al lengths in m, fields in T Require magnet IR R m for beam radius R b : R m = 1.3 R b Fields at inside edge of the magnet coils: B ± = B 0 ± B 1 R m ± for absolute maximum and minimum fields on two sides. If field gradient B 1, then maximum field : ˆB = B + + B 1 0.00247B + Coils finite thickness gives a larger radius: ˆR = R m +0.002 ˆB. Cost expression Cost = f B ( ˆB) f G ( ˆR, L) f S (B /B + ) f N (n). L is the length of the magnet and n is the number of magnets being produced. Field dependence Size dependence f B ( ˆB) = 101 + 16.78 ˆB 1.5 (M$/m) f G ( ˆR, L) = ˆR(L +36 ˆR). 21
Correction for combied function magnets For the same ˆB, ˆR, and L, it is assumed that the cost of a quadrupole (B = B + ) is equal to that of a dipole (B = B + ) But for combined function magnets, less conductor is required, and we assume that the cost is correspondingly less. f S (B /B + )= where and Q = 1 2 D = 1 2 Quatity dicount π 0 D cos θ + Q cos 2θ dθ π 0 cos θ dθ 1+ B B + 1 B =1 D, B + f N (n) = Relative Cost n 0 1/3, 1.0 0.9 0.8 0.7 0.6 0.00 0.25 0.50 0.75 1.00 Relative Dipole vs Quad n where n 0 = 300 is the number of magnets used to define the constants, and n is the number of magnets required. 22
Magnets used to fit constants n L k R R B 0,(B 1 ) cost m m T, (T/m) k$ RHIC Q 300 1.10 0.040 (91) 36.25 RHIC 300 10.00 0.040 4.30 143.0 Willen 300 18 0.02 5.6 193.0 LHC 300 2 15.0 0.028 8.30 708.0 All costs have been escalated to 2004 at 2.5% per year. The RHIC quadrupole cost is the quoted cold mass cost plus 25% to include a cryostat. The Willen example is a design based on RHIC costing experience,optimized to yield the lowest cost per Tesla meter. TheLHCmagnetshavetwoboreswithinasingleyokeand cryostat. This is represented by the magnet length entered as the total for both bores. The number of magnets listed (300) is the number made per manufacturer. 23
Comparison with Earlier Model Cost per magnet (k$) 0.75 0.50 0.25 Green 2 1.34 0.77 Ω(Tm 3 ) 0.631 This Model L= 3 m r=4 cm n=5 0.00 0.0 2.5 5.0 Dipole Field 7.5 Green #1 had poor fit to Green s dipole data Agreement with Green #2 good at lower fields, as in most Green data M. A. Green, R. Byrns, S.J.St. Lorant;Estimating the cost of superconducting magnets and refrigerators needed to keep them cold; LBNL-30824 & Advances in Cryo Eng. 37, Feb 1992 24
Estimates using different cost models Cost per E gain (M$/GeV) 30 20 10 0 RLA 2.5-20 left: This Paper mid: Green #1 right: Green #2 dashes: non-magnet Triplet FFAG 5-10 Triplet FFAG 10-20 Cost rankings are not sensitive to models used 25