1. HLRF: KCS option Christopher Nantista SLAC ILC ML&SCRF Baseline Technical Review KEK, Tsukuba, JAPAN January 19, 2012. …… …… …… … ….

2. Is the nominal high-power beam current (2×10 10 e - )×(1.60218×10 -19 C/e - ) ÷ 369.23 ns = 8.6785 mA or (2.0741×10 10 e - )×(1.60218×10 -19 C/e - ) ÷ 369.23 ns = 9.0000 mA? 480 cycles  720 cycles = 553.85 ns Baseline beam current = 5.786 A or 6.000 A? Beam Current RDR: 3.7% difference

3. KLYSTRON CLUSTER BUILDING CTO ACCELERATOR TUNNEL ~2 km of linac powered per 2-cluster shaft. 12 shafts total for both linacs. Klystron Cluster System (KCS) Concept Main linac rf power is produced in several surface buildings and brought down to and along the tunnel in low-loss circular waveguide. Many modulators and klystrons are “clustered” to minimize surface presence and number of required shafts. Power from a cluster is combined and then tapped off in equal amounts at 3-cryomodule (RDR rf unit) intervals. equipment accessible for maintenance tunnel size smaller than for other options underground electrical power and heat load greatly reduced ADVANTAGES space for additional sources for high power upgrade

4. A novel waveguide device was developed for coupling into and out of the low-loss circular TE 01 mode waveguide without creating large surface fields. Combining and Dividing Power CTO (Coaxial Tap-Off) For combining, the tap-offs are used in reverse. Proper phase and relative amplitude needed for match (mismatched power goes to circulators). determines coupling Couplings ranging from ~1 to 1/33 are required. CTO’s of increasing coupling every ~38 m ~1/26~1/25 C = ~1/2 C = ~1 … Tunnel Cross-Section (initial concept) CTO Replace vacuum windows w/ smaller pressure windows. Eliminate combiner and add two high-power circulators. bend D =5m

5. -- main facilities shaft -- additional KCS shaft KCS Shafts and RF Units per KCS total:588 rf units (15+281 + 15+277) 1,764 cryomodules 15,288 cavities 25 e - beam 25 e + beam undulator 15 RTML2’s:10 GeV  (31.5 MeV/m×1.038 m/cav.) = ~306 cav. 306 cav.  26 cav./rf unit = 11.77 rf units, but 15 requested (running off-crest)  RTML2: 15 rf units Main Linacs: (250 GeV–15 GeV)  (31.5 MeV/m×1.038 m/cav.) = 7,187 cav.’s 7,187 cav.  26 cav./rf unit = 276.4 rf units  e + ML:277 rf units (9×25 + 2×26) e - ML:281 rf units* (5×25 + 6×26) 26 25 26 25 I.P. *4 more to restore up to 3.4 GeV loss in undulator. Latest Changes: Back to 9-8-9 (26 cavity) rf units. 2 nd stage bunch compression at 15 GeV  10 GeV moved from each main linac to an “RTML2”. Since the latter are in-line w/ the main linacs, we can power them with upstream KCS’s running past the BC’s from the first shaft at the start of each main linac proper, which is itself powered with the remaining 11 KCS’s. 1/6/12

6. Low Power (new baseline) Pulses KCS is very flexible. Combining tens of klystrons allows us to adjust installed power with relatively fine granularity. Simply eliminating every other bunch (halving f B ) maintains the beam duration and halves the current, cutting in half the required peak power. However, it also doubles the cavity fill time., thereby increasing the required rf pulse width at full gradient by 38%. It’s preferable to adopt parameters which allow use of the modulators and klystrons developed for full RDR beam specifications, i.e. to stay within the ~1.6 ms pulse width. This can be achieved by reducing the bunch spacing to increase the current to 0.69 I 0. The rf peak power required at the cavities is reduced from that for the full beam by this factor. Fixed t b : Fixed t rf : (P rf → ½ P rf0, t rf → 1.38 t rf0 ) (P rf → 0.69 P rf0, t rf → t rf0 ) (~9 mA)

7. Attenuation loss along tunnel: ~ 6.86% Shaft waveguide (~75 m?) power transmission: 0.9899 3 Bends + tapers power transmission: 0.9922 TOTAL KCS waveguide ohmic loss  ~8.52% power flow at each CTO: condition for equal rf unit powers: CTO couplings: power/rf unit normalized to P 1 : 3.582%  total: 93.14% N = 26, e -2  L = 0.9944 TE 01 :  = 2.459  10 7  -1 m -1 (6061-T6 Al) f = 1.3 GHz (k 0 = 27.246 m -1 )  s = (  0  f  -1/2 R s = 1/(  s ) =  0  f/  = 0.0144 a = 0.24 m  0,1 = 3.8317 For a = 0.1746 m: = 6.771  10 -5 m -1 = 2.404  10 -4 m -1 rf unit waveguide lengthWC1890: 37.956m - 1.326m = 36.63 m WC1375: 1.326m Power attenuation per rf unit length (6061 Al): e -2(  L1+  L2) = 0.9944 (~0.558% ) KCS Main Waveguide Loss

8. Mean: 4.0509 MW Std: 126.30 kW 2  (mean+2std) = 8.607 MW (0.307% more) Mean: 8.1018 MW Std: 239.45 kW mean + 2std (97.5%) = 8.5807 MW Mean: 5.89% over nominal (294.3 kW) Mean+2std (97.5%): 12.49 % over (12.15% w/ feed division adjustment)  5.9% reflected, 6.6% into end loads Needed Power at Cavities With the given distribution of cavities and sorting prescription, there will still be some statistical spread in how much power each rf unit needs. Since the CTO’s will not be adjustable, excess power will have to be provided to accommodate most (97.5%?) units. With no adjustment to the split between halves of an rf unit, the statistics are over 13 cavity feeds, or 1/2 rf units. The difference is marginal. from BAW1 Sept. 2010

9. Effect of Tunnel CTO Coupling Errors Errors in the coupling coefficients of CTO’s will lead to a spread in the total peak power available at each rf unit. With a flat distribution of random errors between ±0.2 dB, an extra ~5% power is needed to guarantee nominal power available at each rf unit.

10. Effect of Combining CTO Coupling Errors Assume 2.5m CTO spacing (WC1375),  e -2  l = ~0.998799 Also assume equal klystron powers and perfect phasing. Nominal ohmic combining loss: ~1.898% CTO couplings for equal power: 33 KCS Klystrons One Klystron Off and ±0.2 dB Errors 1 st off mean: 0.9234 min: 0.9203 (vs. 0.94) One off factor, no attn.: (32/33) 2 = 0.9403 Another ~2% effectively lost due to combining errors of this scale. Nominal CTO Couplngs Statistical Distribution

11. Achieving Flat Gradient Flat acceleration across the beam pulse is important for maximizing gradient. With control of power, Q e, and fill time, a steady state match can be achieved at the desired gradient in a cavity, giving constant acceleration with no power is reflected during the beam pulse. With KCS, 748 cavities are locked to a common source timing. With power and Q e adjustable, a steady state constant gradient is still achievable, but there will generally be some level of power reflected. Normalized to 31.5MV/m × 1.0377m × 9mA = 294.2kW Mean: 1.0426 Mean: 1.0533  20% spread example For a given distribution of gradients, the timing can be set so as to minimize the average reflected power, not necessarily at the point where the center gradient is matched. Power Needed for Flat Acceleration from BAW1 Sept. 2010 Blue: timing set for zero reflection at center gradient Red: timing set for zero reflection 5% below center gradient For upstream(downstream) KCS systems, the effective spread in fill time is ~7.64(0.40)  s. This is roughly 1.28%(.07%) of the nominal fill time and has little effect on efficiency.

12. 189.3 kW(nominal to beam per cavity = 31.5 MV/m  1.038m  5.79mA) × 1.059 (for flat gradient w/ cavity gradient spread and common timing) × 1.062 (for statistical spread in feed/rf unit requirements w/ fixed couplings) × 26 (cavities/rf unit) ÷ 0.92(8% local distribution losses) = 6.017 MW/rf unit @ CTO × 26 (rf units) ÷ 0.931 (6.9% main waveguide losses) = 168.03 MW @ beginning of linac run ÷ 0.982(shaft and bends) ÷ 0.981(1.9% combining CTO circular waveguide losses) ÷ 0.965(input circulator and WR650 losses) ÷ 0.977(CTO coupling/klystron amplitude mismatches) 185.00 MW from klystrons ~9.1% klystron-to-tunnel Peak RF Power Required from Klystrons per KCS feeding 26 26-Cavity RF Units (Low Current)

13. With 21 klystrons and 20 on, we have 190.5 MW available (~4% short). However, we need 7% (5% usable) overhead for LLRF to be harnessed via phase control of the rf drives, oppositely dephased in pairs, such that the combined power is reduced as P = P max cos 2 , with  nominally 15˚. Klystrons Needed per KCS (Low Current) We also want to be robust against a single klystron failure per system. With N sources combined in a passive network, failure of one source leaves combined the equivalent of (N-1) 2 /N sources. The calculation/estimate suggests we need generate ~185 MW worth of klystron power for a 26 rf unit KCS at I b = 5.79 mA. The maximum power requirement rises to 185 MW/0.933 = ~198.3 MW. With 22 klystrons and one off, we have 200.45 MW (~1% to spare). 21 klystrons for the 25 unit KCS (need ~190.7 MW) 14 klystrons for the 15 unit KCS (need ~114.4 MW) TOTAL: 8×22 + 14×21 + 2×14 = 498 klystrons installed (474 on)

14. However, we need 7% (5% usable) overhead for LLRF to be harnessed via phase control of the rf drives, oppositely dephased in pairs, such that the combined power is reduced as P = P max cos 2 , with  nominally 15˚. Klystrons Needed per KCS (High Current) We also want to be robust against a single klystron failure per system. With N sources combined in a passive network, failure of one source leaves combined the equivalent of (N-1) 2 /N sources. The calculation/estimate suggests we need generate ~277.3 MW worth of klystron power for a 26 rf unit KCS at I b = 8.68 mA. The maximum power requirement rises to 277.3 MW/0.933 = ~297.2 MW. With 32 klystrons and one off, we have 300.3 MW (~1% to spare). 31 klystrons for the 25 unit KCS (need ~285.8 MW) 20 klystrons for the 15 unit KCS (need ~171.5 MW) TOTAL: 8×32 + 14×31 + 2×20 = 730 klystrons installed (706 on)

15. 9/2010 (BAW1) 3/2011 (ALCPG11) 9/2011 (LCWS11) TDR (LCWS11) 1/2012 (BTR) # of shafts / main linac56666 # of KCS systems / main linac1011 1211 + 1(RTML) # of rf units / main linac (e + /e - )280/284290/294314/319 277+15 / 281+15 # of rf units (CTO’s) / KCS28272927 (22) 25  26, 15 linac length fed per KCS (km)1.0641.0261.0240.994 0.950  0.988*, 0.57 # of cryomodules / KCS84818781 75  78, 45 # of cavities / KCS728702696648 650  676, 390 # of klystrons/mod.’s / KCS3433 22 (18) 21  22, 14 peak rf power / system (MW)340 installed 330 gen. 320 into sys. 330 inst. 320 gen. 310 in 330 inst. 320 gen. 310 in 220 inst. 210 gen. 200.5 in 220 installed 210 generated 200.5 into system Evolving KCS Parameters rf units added from RTML 9-8-9  8-8-8 half bunches 10 GeV  RTML but included, 8-8-8  9-8-9 * plus end box lengths, etc.

16. Source Failure in Combining Circuit Using the junction in reverse for combining, the normalized input powers of n-1 and 1 respectively in ports 2 and 3 combine as n out of port 1 with no reflections. If the port 3 input drops out, a normalized output power of 1 - 1/n is seen in port 3. As the power balance at all downstream combining junctions will be thrown off, there will also be some reflection into port 1, which will affect the port 3 output. Then, if one source fails, we’re left with: With one unit less power going in, this means 1 - 1/N is misdirected, primarily toward the failed klystron, which no longer has its self-reflected field to cancel the field from the pipe. 1 2 3 The scattering matrix for an ideal, lossless, 1/n-coupling matched 3-port junction (e.g. a CTO) is of the form: Looked at another way, if each input junction ultimately contributes equally to the final combined output field: So, with N large, on the order of 5 MW reverse power can be expected in each feed arm of a failed klystron. 1 2 3

17. Klystron to CTO Connection 5 MW circulators (isolators) protect klystron during operation and prevent reflection into system of mismatched/emitted fields from KCS waveguide. Remote-controlled mechanical rf switches can provide additional isolation from KCS waveguide power in case of klystron (or circulator) failure, allowing maintenance/replacement during operation (with spare klystron turned on to maintain power). CTO KLY switch + 5 MW load 5MW circulator window

18. Old RDR Power Distribution System

19. Phase shifter range of 0°–90°, the above arrangement allows full range power division. If  1 and  2 are moved equally in opposite senses, the output phases are unaffected. Phase Shifter for Local Power Tailoring Assembly incorporating 2 phase shifters + 2 hybrids can replace VTO. Pressurizable U-Bend Trombone Phase Shifter Folded Magic-T cold tests: transmission: -.03 .01 dB reflection: -50  36 dB high-power test: No breakdown in 8 hours at ~2 MW in 1bar N 2. Mega Industries combine with more compact longitudinally than VTO (for individual cavity feeding) motorizable for remote adjustment (crucial with cavity degradation) BENEFITS:

20. New Fully Adjustable Local PDS Unit To accommodate optimal power division among sets of cavities with a sustainable gradient spread of ±20%, not necessarily knowable before installation in CM and susceptible to degradation over time, we opt for a fully and remotely adjustable local power distribution scheme. We thus hope to make maximal use of the cavities at the cost of a more expensive PDS. The need for pre-sorting into matched pairs, introduced by a previous approach aimed at eliminating the need for circulators, has been removed. However sorting to produce more uniform power requirements per feed may still be useful Reorient to eliminate a bend. end-on views flex guide to cavity coupler bi-directional coupler phase shifter Pairs of folded magic-T’s and motorized U-bend phase shifters provide coupling adjustment, while preserving phase. dummy load circulator window

21. By splitting CTO outputs through asymmetric (-5.12 dB) “hybrids”, as in the RDR, we can physically decouple cryomodules and limit variable coupler cascading. Local PDS Circuit 994 Q 4 CTOKCS waveguide Use circulators and r.c. switches (as in combining circuit) respectively to shield KCS from reflections and, if necessary, to depower 1½ CM’s.

22. RDR-Like Option (Low Power) With the “kamaboko” tunnel design offering a virtual return to the 2-tunnel scenario, an RDR-like layout w/ 10 MW klystrons, modulators, etc. is now a serious option. For the new low power (half bunches) baseline beam, one could double the bunch spacing and install half the modulators and klystrons, each feeding 6 CM’s, rather than 3. However, this would double the fill time, increasing the required rf pulse width by 38%. The installed modulators and klystrons would then be overspec.ed for the upgrade. FULL BEAM HALF BEAM P rf → ½ P rf0 t rf → 1.38 t rf0 every other klystron omitted kamaboko tunnel

23. Alternatively, one could install 2/3 of the rf production equipment, with each klystron feeding 4 ½ CM’s. This would reduce the available power per cavity, and thus the acceleratable beam current or bunch frequency, by a factor of ~2/3 vs. RDR. The beam pulse duration (  n B /I b → ½ / 2/3) is then shortened by a factor of ¾, and the fill time increased by a factor of 3/2, yielding an rf pulse width increase of only ~3.5%. every 3 rd klystron omitted P rf → 2/3 P rf0 t rf → 1.035 t rf0 As this seems acceptable, we adopt 2/3 current, rather than 69%, as the new baseline for both HLRF options (KCS and RDR-like).

24. RDRTDR particles/bunch 2.074  10 10 *2.074  10 10 bunch spacing369.23 ns (480 cycles) 535.4 ns (696 cycles) 553.8 ns (720 cycles) beam current9.0 mA6.207 mA6.000 mA rf pulse cavity power294.3 kW202.94 kW196.2 kW cavity fill time 596  s864.2  s894.0  s bunches/pulse26251312 † bunch train length 968.9  s701.9  s726.1  s rf pulse length1.565 ms1.566 ms1.620 ms cavities per rf unit2624 *adjusted slightly for consistency from published value of 2  10 10.. Relevent Changes from RDR  33.3%  5.6% P b  50% 9/2011  3.5%  33.3%  25%

25. 250 GeV/beam # of bunches bunch spacing beam current beam duration rf peak power fill time, t i rf pulse duration full beam2625369.2 ns 480 cycles 9 mA0.969 ms294.3 kW0.596 ms1.565 ms ½ bunches A1313738.5 ns 960 cycles 4.5 mA0.969 ms147.1 kW (down 50%) 1.192 ms2.161 ms (up 38%) ½ bunches B KCS? 1313535.4 ns 696 cycles 6.207 mA0.7019 ms203.0 kW (down 31%) 0.864 ms1.566 ms ½ bunches B RDR-like 1313553.8 ns 720 cycles 6 mA0.7261 ms196.2 kW (down 33%) 0.894 ms1.620 ms (up 3.5%) -- full beam 0% -- ½ bunches A 40.6% -- ½ bunches B (KCS) 1.9% -- ½ bunches B (RDR) 5.5% @ 31.5 MV/m cryo load increase * * Only includes dynamic load of fundamental rf in cavity. Additional contributions come from coupler (linear w/ power and time) and HOM (current dependent). Parameter Summary Parameter choice also impacts cryogenic load. from Jan./Feb. 2011 460.6 J 317.9 J 317.8 J 69%

26. High Power Upgrade The power upgrade would double the beam power at the same CoM energy. Double number of bunches/pulse. Change bunch spacing s.t. beam current increases only 50%. Add 47-50% more sources (klystrons, modulators, etc.). Modify rf “plumbing”:KCS – tie new sources into KCS’s w/ CTO’s. RDR-like – install penetration waveguides and remove splitters and feeds from neighboring rf units. Adjust cavity couplings and timing to new beam structure. Accommodate new AC (1.5/1.035   ~45%), water cooling (~40%) and cryogenic demand increases.

27. Cost Scaling The “economy of scale” cost reduction might vary significantly among components depending on such factors as the market size and the fabrication technology. Following the RDR, I initially used a “learning curve” factor of 0.95 per doubling. A major vendor has suggested that after ~100 units, the cost per unit no longer decreases, bottoming out at ~0.75×the cost for 4. In the following tables, I’ve largely applied this more conservative scaling. 0.95/doubling vendor’s projection 1 10 100 1,000 10,000 100,000

28. Itemnumberunit costReducedtotal cost 10 MW MBK’s498 Marx modulators498 CTO’s (26 types)1,086 5 MW circ.’s996 5 MW switch996 block windows2,172 TE 01 bends72 diam. tapers1,152 end caps48 WR650 dir. cplrs.996 E-plane bends (p)1,992? H-plane bends (p)996? flex guides1,992 8’ (2.44m) WC1890 pipes9,310 large TE 01 rf spring seals10,015 small TE 01 rf spring seals1,950 rubber O-rings11,965 WR650 gaskets8,964 8’ WR650 section (p)498 2’ WR650 section (p)1,494 Component Cost Estimate for KCS up to Tunnel CTO’s* 516 kly +633 rf units 26×(37.956m - 2×1.326m) + 50m = ~968m 21×(37.956m - 2×1.326m)+50m = ~791m 21×968m + 3×791m = 22.7 km 22.7km/8’ = ~9,310 2 per CTO 2×(633 + 72) = 1,410 Total * Hardware only.

29. Itemnumberunit costreducedtotal cost 2’ WR650 section (p)2,940 8’ WR650 section (p)2,940 E-plane bend (p)5,880 H-plane bend (p)1,176 5 MW loads2,352 5 MW switch1,176 5 MW circulators1,176 flex guides (p)4,704 1 MW loads17,640 folded magic-T’s (p)30,576 pressure windows15,288 H-plane bend15,288 400 kW circ.’s15,288 WR650 phase shifters15,288 E-plane U bends15,288 WR650 bi-dir. cplrs.15,288 flex guides15,288 WR650 gaskets232,848 U-bend phase shifter30,576 asymmetric hybrids (p)1,176 Component Cost Estimate for Local PDS* 15,288 cav.’s Total * Hardware only.

30. For both main linacs, including second RTML stage LOW POWER Average rf power: 474 klystrons×10MW×1.62ms×5Hz = 38.4 MW Average beam power: 5.79mA×490GV×726  s×5Hz = 10.3 MW (26.8%, 59.8% during beam -- 44.8% of pulse width) wall plug–modulator pulse efficiency: ~87% modulator pulse–HPRF efficiency: ~65%  wall plug – HPRF: ~57% 38.4MW / 0.57 = 67.4 MW AC 67.4MW(AC) – 10.3MW(beam) = 57.1 MW cooling HIGH POWER Average rf power: 706 klystrons×10MW×1.62ms×5Hz = 57.2 MW Average beam power: 8.68mA×490GV×969  s×5Hz = 20.6 MW (36%, 58% during beam – 61.9% of rf pulse width) wall plug – HPRF: ~57% 38.4MW / 0.57 = 100.35 MW AC 67.4MW(AC) – 10.3MW(beam) = 79.75 MW cooling AC Power and Cooling Requirements ( KCS)