Xband linac for Swiss FEL Athos energy vernier
X-band linac for Swiss. FEL Athos energy vernier Alexej Grudiev, CERN 30/10/2015
Outline • Motivation • Short range wakefields in Aramis Linac 3 and in Athos energy vernier – Introduction to very short range wakes in tapered structures – Very short range wake in Swiss. FEL C-band linac – Energy chirp compensation in Athos Vernier using X-band linac • X-band linac proposals – minimization total klystron peak power – Possible layouts for different X-band klystrons: 50 and 6 MW – Cost estimates • Conclusions
Outline • Motivation • Short range wakefields in Aramis Linac 3 and in Athos energy vernier – Introduction to very short range wakes in tapered structures – Very short range wake in Swiss. FEL C-band linac – Energy chirp compensation in Athos Vernier using X-band linac • X-band linac proposals – minimization total klystron peak power – Possible layouts for different X-band klystrons: 50 and 6 MW – Cost estimates • Conclusions
Motivations from Hans Braun
Outline • Motivation • Short range wakefields in Aramis Linac 3 and in Athos energy vernier – Introduction to very short range wakes in tapered structures – Very short range wake in Swiss. FEL C-band linac – Energy chirp compensation in Athos Vernier using X-band linac • X-band linac proposals – minimization total klystron peak power – Possible layouts for different X-band klystrons: 50 and 6 MW – Cost estimates • Conclusions
Short range wake critical (“catch-up”) distance In order to estimate critical number off cells: To calculate the wake of infinitely long periodic structure at w we need more than Ncrit cells Image courtesy of R. B. Palmer, Particle Accelerators, vol. 25, 1990
Validity of Karl Bane model: WL K. Bane et al. , ‘Calculation of the short-range longitudinal wakefields in the NLC linac’, ICAP 98, 1998 For const impedance periodic structure: NLC structure at 1998 was tapered over 206 cells. On the other hand, for this structure: Ncrit = amax 2/2 Lσz = 14 << Nc = 206, what justifies averaging the wake of periodic structure over the 206 cells proposed by Karl Bane: • However in CLIC for nominal σz = 44 um , Ncrit = amax 2/2 Lσz = 14 ≈ Nc = 26 in CLIC_G, • Furthermore taking shorter bunch like for example in X-FELs: σz = 10 or 2 um Ncrit => ~60 or ~300 which is bigger or much bigger than Nc. Eq. (2) does not apply • In the extreme case,
Wakefield simulation using ECHO 2 D* *Zagorodnov I. A, Weiland T. , ‘TE/TM Field Solver for Particle Beam Simulations without Numerical Cherenkov Radiation’, PRST-AB, 8 (2005) 042001 Geometry of the tapered structure: L=10 mm, g=9 mm, a=4 ->2 mm, N c=26 Number of structures Ns was increased by x 2 till the loss factor change δk. L < 1 e -3: • For σz = 10 um, Ns = 32 • For σz = 5 um, Ns = 200 • • For σz = 2 um, too long for simulations σz = 10 um k. LKB/k. LE 2 D 20% σz = 5 um k. LKB/k. LE 2 D 30 %
Very short wake in LCLS S-band linac Novokhatski A. , ‘A New Green’s Function for the Wake Potential Calculation of the SLAC S-band Constant Gradient Accelerating Section’, NIM-A, 684 (2012) 46 -51 amax = 13. 11 mm Nc = 86; L=35 mm • For σz = 10 um , Ncrit = amax 2/2 Lσz = 246 >> Nc = 86; wake has to be simulated over 4 -5 accelerating sections, indeed we are in very short range wake regime ----- • The loss factor in simulations is higher by 18% than predicted by Karl Bane model So it is not about X or C or S-band, it is about bunch length amin = 9. 62 mm
A new model for very short range wakes in tapered structures m M 0 lower limit: M 1 upper limit: Model shows better agreement with ECHO 2 D both for loss factor and wake derivative at s=0
Very short wake in Swiss. FEL C-band linac Linac 3 parameters amax, amin [mm] 7. 257, 5. 612 Nc, Ns, Nc*Ns 113, 52, 5876 Operating mode Long pulse Short pulse Bunch charge Qb [p. C] 200 10 Bunch length RMS [fs(μm)] 25(7. 5) 2(0. 6) Ncrit 201 > Nc Nc*Ns > 2508 >> Nc We should see the effect in short pulse mode
Long pulse operating mode 32 -100% 0 -3% Chirp: Non-linear wake: 0 -2% no difference in loss factor and chirp. Big difference in non-linear wake.
Short pulse operating mode 8 -14% • Small difference in loss factor and chirp. • Huge difference in non -linear wake. 5 -12% 925 -559%
X-band linac for Athos energy vernier • Total active length 8 * 2 m = 16 m • The aperture of a const impedance X-band linac has to be optimized to have ~80% of the chirp of the C-band Linac 3 in the long pulse mode (Sven proposed a_XB=2. 7 mm) • The other 20% will have to be compensated with a dedicated de-chirper which will be ~5 times shorter than in the case of a C-band energy vernier
Energy chirp for a_XB=2. 7 mm, L_XB=16 m 2. 7 mm const impedance X-band structure will compensate 83% of the chirp compared to C-band linac 3 in long pulse mode. It will compensate 86% in short mode The new model predict more chirp in the C-band linac 3 compared to the Karl Bane model depending on the operating mode. In this case, X-band will compensate smaller part of the C-band linac 3 chirp Long pulse mode -17% -14% Short pulse mode
Non-linear wake for a_XB=2. 7 mm, L_XB=16 m 2. 7 mm const impedance X-band structure will have about 30% percent more non-linear wake compared to the C-band linac 3 wake according to Karl Bane model. According to the new model X-band linac will have more or much more linear wake compared to the C-band linac 3 depending on the operating mode Long pulse mode 31% 33% Short pulse mode
Conclusions about wakes • According to the new model of a very short range wakes in tapered structures, C-band linac 3 generates different wake when predicted by Karl Bane model for the very short bunches used in Swiss. FEL – In long pulse mode, it is 30 -100% more non-linear. Chirp and loss factor are similar within few percents. – In short pulse mode, it is about factor 5 -to-10 more non-linear. Chirp and loss factor are also higher by ~15% • X-band energy vernier for Athos with constant aperture of a=2. 7 mm and length of 16 m generates chirp which is 83 % of the C -band linac 3 chirp in the long pulse mode • The X-band wake is only 30% more non-linear compared to the Cband according to the Karl Bane model. • However, according to the new model the C-band linac 3 may have higher or much higher non-linear wake than the proposed X-band energy vernier depending on the bunch length
Outline • Motivation • Short range wakefields in Aramis Linac 3 and in Athos energy vernier – Introduction to very short range wakes in tapered structures – Very short range wake in Swiss. FEL C-band linac – Energy chirp compensation in Athos Vernier using X-band linac • X-band linac proposals – minimization total klystron peak power – Possible layouts for different X-band klystrons: 50 and 6 MW – Cost estimates • Conclusions
Pulse compression model Analytical expression for the pulse shape with 180 degree phase flip Example at 12 GHz: Q 0 = 180000; Qe = 20000 tk = 1500 ns klystron pulse length tp = 100 ns compressed pulse length Average power gain = = average power in compressed pulse / input power = 5. 6 Average power efficiency = = compressed pulse energy / input pulse energy = 34. 7 %
Minimization of the total klystron peak power • Effective shunt impedance of the full system (pulse compressor + accelerating structures) is introduce for total klystron peak power minimization • Analytical expressions have been derived both for constant impedance (CI) and for constant gradient (CG) structures with 180 degree phase flip pulse compression * i. e. A. Lunin, V. Yakovlev, A. Grudiev, PRST-AB 14, 052001, (2011) ** R. B. Neal, Journal of Applied Physics, V. 29, pp. 1019 -1024, (1958)
Normalized Effective Shunt impedance and optimum attenuation in CIAS and PCCIAS No pulse compression: CIAS Rs 0/R With pulse compression PCCIAS Rs/R τs 0 = 1. 2564 => Rs 0 /R = 0. 8145 For Q = 8128; Q 0 = 180000; Qe = 20000 τs 0 = 0. 6078 => Rs 0 /R = 3. 3538 But in general it is function of all three Qfactors: Q, Q 0, Qe and the klystron pulse length
Optimum Qe for PCCIAS Q 0 = 180000; tk = 1500 ns Optimum attenuation: τs 0 Point from slide above Q 0 ↓ t k → 1500 ns (50 MW CPI tube) s 0/R Normalized REffective Shunt Impedance Rs 0/R Point from slide above 5000 ns (6 MW Toshiba tube) 180 000 (Xbox) Qe=21147; τs 0=0. 624; Rs 0/R=3. 38 Qe=39684; τs 0= 0. 796; Rs 0/R=3. 98 220 000 (BOC) Qe=21398; τs 0=0. 628; Rs 0/R=3. 46 Qe=42484; τs 0= 0. 916; Rs 0/R=4. 18 Small (2%) gain from higher Q 0 Very similar structure 18% gain from longer tk, 5% gain from higher Q 0 Different structure design Q = 8000
Case 1: tk=1500 ns, Q 0=180000 a=2. 7 mm With pulse compression, CI (left) and CG (right) structure show the same performance in terms of total klystron peak power (red). From now on, we will limit our study only to CI structures.
Study cases: a=2. 7 mm • Case 1: tk=1500 ns, Q 0=180000 (50 MW klystron) – A) Energy 400 Me. V – B) Energy 500 Me. V • Case 2: tk=5000 ns, Q 0=180000 (6 MW klystron) – A) Energy 400 Me. V – B) Energy 500 Me. V • In all cases linac length is Ngirders*4 m*95% includes overhead in the filling factor for interconnection between X-band structures • Structure length is a fraction of 4 m*95%: 0. 475 m(8), 0. 543 m(7), 0. 6333 m(6), 0. 76 m(5), 0. 95 m(4) • Cells have two roundings like C-band structure cells
Case 1 A, B 6 AS/G 1 2 3 Ls [m] 0. 475 0. 543 0. 475 d [mm] 1. 226 1. 525 dphi [o] 135 120 Case 1 A: 400 Me. V, 15. 2 m, <G>=26. 3 MV/m 2 7 AS/G Pt [MW] 1 8 AS/G AS# 3 23. 2 Sc [W/um 2] 0. 66 22. 7 23. 7 0. 6 Case 1 B: 500 Me. V, 15. 2 m, <G>=32. 9 MV/m Pt [MW] 36. 3 35. 5 37. 0 Sc [W/um 2] 1. 03 1. 09 0. 94 Sc << 4 W/um 2, low gradient
Layout of C-band RF stations in Athos energy vernier R. Ganter (PSI)
Layout of X-band RF station in Athos energy Vernier, Case 1 CPI 50 MW klystron Operation value: 0. 66 40 MW L_WG 90=0. 66+3. 66+7. 00+9. 80+1. 38+4. 5+4. 0=31 m 3. 66 7. 00 9. 80 1. 38 4. 50 1. 38 4. 00 4. 50 4. 00 19 MW WR-90: Attenuation: -0. 098 d. B/m * 31 m = -3. 038 d. B = 0. 5; Losses: 50% Half of the power is lost. It is not acceptable Alternative layout using WC-50 mm TE 01 mode line: attenuation: -0. 0124 d. B/m L_WC 50=3. 46+6. 8+4. 3+5. 1+4. 3 = 23. 96 m; L_WG 90 = 7. 04 m 40 MW 0. 66 3. 66 7. 00 1. 38 4. 50 4. 0 5. 30 4. 50 4. 0 1. 38 4. 0 31. 9 MW • WR-90 Attenuation: -0. 098 d. B/m * 7. 04 m = -0. 69 d. B = 0. 853; Losses: 14. 7% • WC-50 Attenuation: -0. 0124 d. B/m* 23. 96 m = -0. 3 d. B = 0. 934; Losses: 6. 6% • Total power Attenuation: -0. 99 d. B = 0. 797; Losses: 20. 3% • Case 1 A is possible, even 450 Me. V looks feasible R. Ganter (PSI)
Complete Dog-leg test RF network layout (expected RF transfer efficiency ~0. 75) Mode converter type#2 An example of WC 50 use at 12 GHz Cost: ~1 k. CHF/m RF 6 m 50 mm circular waveguide Beam Igor Syratchev The number of 12 GHz new RF components were fabricated by CERN and CEA to re-adjust ‘old’ 30 GHz low losses transfer line to the new frequency.
Case 2 A, B 3 5 AS/G 2 4 6 AS/G 7 AS/G 1 5 8 AS/G AS# 1 2 3 4 5 Ls [m] 0. 475 0. 633 0. 76 0. 633 0. 543 d [mm] 1. 059 1. 090 1. 005 1. 401 1. 494 dphi [o] 150 135 120 135 Case 1 A: 400 Me. V, 15. 2 m, <G>=26. 3 MV/m Pt [MW] 20. 27 19. 37 18. 79 19. 93 20. 3 Sc [W/um 2] 0. 61 0. 72 0. 83 0. 67 0. 63 Case 1 B: 500 Me. V, 15. 2 m, <G>=32. 9 MV/m Pt [MW] 31. 67 30. 27 29. 36 31. 14 31. 72 Sc [W/um 2] 0. 95 1. 13 1. 05 0. 98 Sc << 4 W/um 2, low gradient
Layout of X-band RF stations (2) in Athos energy Vernier Case 2 Tested at 7. 5 MW 100 Hz Operation L_WG 90=0. 66+3. 66+7. 00+1. 38+4. 5+4. 0=21. 2 m value: 6 MW 3. 66 7. 00 1. 38 0. 66 4. 50 4. 00 + 7. 4 MW 6 MW WR-90: Attenuation: -0. 098 d. B/m * 21. 2 m = -2. 008 d. B = 0. 62; Losses: 38% Half of the power is lost. It is not acceptable Alternative layout using WC-50 mm TE 01 mode line: attenuation: -0. 0124 d. B/m 6 MW + 6 MW 0. 66 L_WC 50=3. 46+6. 8+4. 3 = 14. 56 m; L_WG 90 = 6. 64 m 3. 66 7. 00 1. 38 4. 50 4. 00 9. 9 MW WR-90 Attenuation: -0. 098 d. B/m * 6. 64 m = -0. 65 d. B = 0. 86; Losses: 14% WC-50 Attenuation: -0. 0124 d. B/m* 14. 56 m = -0. 18 d. B = 0. 96; Losses: 4% Total power Attenuation: -0. 83 d. B = 0. 823; Losses: 17. 7% With 4 klystrons, 400 Me. V is just on the limit of possible for AS 2, 3 and almost there for AS 4 from the table in the previous slide • Combining power from 3 klystrons per RF station in order to reach 500 R. Ganter. Me. V (PSI)with some margin seems to be not practical • 4 klystrons per RF station - too many • •
Very Preliminary Cost Model • One 50 MW tube + modulator unit: ~1300 k • One 7. 5 MW tube + modulator unit: ~400 k • X-band accelerating structures: 0. 6 k/cell + (16 k+25 k)/stricture – T 24_PSI disks+couplers: ~120 k = 1. 2 k*60 disks+12 k*4 couplers • tapered structures -> all disks are different, Expected cost reduction for CI structure mid-scale series production: x 2 • Couplers: 4 mode launcher type. Expected cost reduction for mid-scale series production: x 1. 5 – Assembly: ~25 k/structure • WG network: ~50 k/girder + ~50 k/RF station + 5 k/structure – Girder: distribution system – RF station: distribution system + pulse compressor – Structure: high power load + splitter
Preliminary Cost for 4 girder configuration Cost is about 4 M +- few percent. No big difference between different cases
Alternative 1: 3 girder linac • Increasing gradient in X-band linac and reducing its length may reduce the cost of the linac • The aperture of the 3 girder linac has to be reduced in order to compensate the same amount of wake as in the 4 girder linac • This will increase the fundamental mode shunt impedance per meter length
Long pulse mode for a_XB=2. 35 mm, L_XB=12 m It will have about 45% percent more non-linear wake compared to the C-band linac 3 wake according to Karl Bane model. But not according to the new model. 2. 35 mm const impedance X-band structure will compensate 80% of the chirp compared to C-band linac 3 in long pulse mode. Main question is a=2. 35 mm still OK for transverse stability ? ? ? Non-linear wake Energy chirp -20% 45%
Case 3: tk = 1500 ns, Q 0 = 180000 AS# 1 2 3 Ls [m] 0. 317 0. 38 0. 317 d [mm] 1. 0 1. 38 dphi [o] 135 120 Case 3 A: 400 Me. V, 11. 4 m, <G>=35. 1 MV/m Pt [MW] 28. 4 Sc [W/um 2] 0. 95 2 10 AS/G 3 12 AS/G 1 27. 55 29. 1 1. 05 0. 9 • Going to 425 Me. V is feasible • Sc << 4 W/um 2, low gradient
Case 4: tk = 5000 ns, Q 0 = 180000 AS# 1 2 3 Ls [m] 0. 38 0. 475 0. 38 d [mm] 1. 161 1. 008 1. 483 dphi [o] 135 120 Case 4 A: 400 Me. V, 11. 4 m, <G>=35. 1 MV/m Pt [MW] 24. 44 Sc [W/um 2] 0. 96 2 8 AS/G 10 AS/G 1 3 23. 52 25. 32 1. 1 0. 91 • Going to 400 Me. V requires at least 5 klystrons, difficult to combine • 6 klystrons (3 RF stations) would allow to go to ~435 Me. V • Sc << 4 W/um 2, low gradient
Preliminary cost for 3 girders configuration • Cost for 50 MW case is reduced by ~5% only. Shorter linac but more structure ! • Cost for 7. 5 MW case is increased by ~20% due to 1 more RF station, but energy reach is also increased by ~10%
Conclusions • • Cost is shared 50/50 between the klystron/modulator and the linac. This typically indicate that we are close to an optimum. Strangely enough gradient is rather low for an X-band linac. In order to profit from higher gradient in cost-effective way the cost of peak power must go down significantly. Cost is about the same for both 50 MW CPI and 4 x 7. 5 MW Toshiba klystron based systems 50 MW based system can potentially go up to 450 Me. V but it has not been tested at 100 Hz and in general it is probably less robust compared to 7. 5 MW based system Running 50 MW klystron at 32 MW in order to operate at 400 Me. V can improve reliability Reducing linac from 4 to 3 girders reduces the cost by ~5% for 50 MW based system and increases the cost by 20% for the 7. 5 MW based one For 5000 ns, one can gain 5% in Rs (5% less klystron power for the same energy) by increasing pulse compressor Q 0 from 180000 to 220000. This is something to consider for Case 2 …
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