1. Christopher Nantista SLAC Project X Workshop November 12, 2007 Fermilab

2. BCD: linear ACD: semi-branched w/ VTO’s & no circulators? Fewer types of splitters (3 vs. 9) Power division adjustable by pairs Elimination of circulators possible Basic ILC RF Distribution Scheme (Baseline) (Alternate) 3 cryomodules per klystron 26 cavities (9-8-9)

3. Baseline RF Distribution System Alternative RF Distribution System Fixed Hybrid Tap-offs w/ various couplings Circulators Variable Tap-Offs (VTOs) 3 dB Hybrids 3-stub tuners phase shifters

4. SLAC Variable Tap-Off (VTO) Mode Rotator (Center): Polarization Selecting 3-Port Junction (Ends): oblong cross-section circular Full 4-Port Assembly: length = 64.924” machined aluminum; dip-brazed rotatable flanges Mechanical Design: Coupling is a function of center rotation angle: C = sin 2 (2 

5. angle (degrees)~0angle 1angle 2~45 coupling (dB / %)-51.4 / 0.0007-5.67 / 27.10-2.417 / 57.32-0.004 / 99.9 coupled phase (degrees)(57.496)-81.581-81.655-81.508 through phase (degrees)-22.165-22.208-21.547(32.256) reflection (dB / %)-40.34 / 0.012-48.39 / 0.001-48.16 / 0.002-36.84 / 0.02 loss (dB / %)-0.033 / 0.77 -0.026 / 0.61-0.028 / 0.65-0.025 / 0.57 VTO Cold Test Results Average attenuation: -0.028 dB / 0.65% Coupled phase variation: 0.15° Through phase variation: 0.66°

6. L-Band “Magic-H” 3-dB Hybrid 20.137” HFSS DesignMechanical Design Ports oriented for branching distribution (eliminate 2 bends) Design for high accuracy/isolation at 1.3 GHz. This is crucial for elimination of circulators. Don’t need broad bandwidth Fabricated by aluminum dip-brazing milled halves. Loss: 0.31% Match & Isolation: ~-43 dB Coupling: -3.031 dB (49.76%) Coupling Error: -0.0207 dB or Frequency Error: 4.4 MHz Cold Test Results:

7. SLAC is building VTOs and hybrids, using aluminum dip- brazing, and acquiring parts to assemble RF distribution systems for FNAL’s NML cryomodules. A VTO and hybrid have operated stably at 3 MW, 1.2 ms, 5 Hz at atmospheric pressure.

8. Other Components 1 MW load Circulator (also AFT) bidirectional coupler E-plane bendH-plane bend semi-flex waveguide = 6” S.P.A. Ferrite, Ltd. (St. Petersburg) DESY phase shifter

9. Input Power Baseline TTF-3 Coupler Design tunablity (Q L ) HV hold-off dual vacuum windows bellows for thermal expansion motorizable knob movable antenna (Q L adjustment) Design complicated by need for:

10. Cold WindowBias-ableVariable QextCold Coax Dia.# Fabricated TTF-3Cylindricalyes 40 mm62 KEK2Capacitive Diskno 40 mm3 KEK1Tristan Diskno 60 mm4 LAL TW60Diskpossible 62 mm2 LAL TTF5Cylindricalpossible 62 mm2 Baseline and Alternative Coupler Designs

11. beam RF Alternative ILC RF Distribution Layout with circulators: without circulators: VTO’s allow pair-wise adjustment of power distribution and thus more efficient use of power. Hybrid feeding of equal-Q cavity pairs directs reflected power into hybrid loads. RF beam loads hybrid VTO circulators flex guide load directional couplers H-plane bends

12. Case Not Sorted [%] Sorted [%] Individual P’s and Q’s 0.0 0.0 (Indiv. P control and Circ) P’s in pairs, individual Q’s 2.5  0.4 0.8  0.2 (VTO and Circ) 1 P, individual Q’s 2.7  0.4 2.7  0.4 (Circ but no VTO) P’s in pairs, Q’s in pairs 7.2  1.4 0.8  0.2 (VTO but no Circ) 1 P, Q’s in pairs 8.8  1.3 3.3  0.5 (no VTO, no Circ) G i set to lowest G lim 19.8  2.0 19.8  2.0 (no VTO, no Circ) Optimized 1  G  /  G lim  ; results for 100 seeds Consider uniform distribution of gradient limits (G lim ) i from 22 to 34 MV/m in a 26 cavity RF unit - adjust cavity Q’s and/not cavity power (P) to maximize overall gradient while keeping gradient uniform (< 1e-3 rms) during bunch train Gradient Optimization with VTOs and Circulators also more efficient power usage

13. 0 -  /2 P For cavity phasing: n=6 :  P=1.3260m = 52.205” Cavity Spacing and Phasing beam Reflections from identical cavities combine into hybrid load port. Type 3+ cryomodule has 1.3836m (= 6 0 ) spacing to allow energy recovery in X-FEL. Type 4+ cryomodule will have 1.326m (= 5.75 0 ) spacing to allow elimination of (most) ILC circulators. This won’t work in Project X with ILC cryomodules due to low  (wrong spacing) and varying cavity parameters (mismatched reflections). Even in the ILC-like last section of the high-energy linac, with an average  of 0.99, the cavity spacing is off by ~21° (reflections by 42°).  Circulators required in Project X linac. load from hybrid from beam transit RF

14. XFEL RF Distribution 2-level splitting, like SLAC ILC ACD: First splitting done with customizable asymmetric shunt T’s of various coupling (eliminating hybrid loads). Second splitting also done with matched T’s, rather than hybrids, eliminating loads. This is a good idea if circulators are used. In-line Phase shifters incorporated into T’s, eliminating two flange joints. V. Katalev

15. Individual Cavity Control VTO’s can be used to optimize division of RF power between pairs. For changing  (thus transit factor and shunt impedance) and cavity-to-cavity phasing, greater control over individual cavity feeding may be needed. rejected power reflected power rejected power reflected power Assuming Q L control by adjustable couplers, there are two hardware configurations by which local phase and amplitude control can be achieved A) B) A) Requires an E-H Tuner or Magic-T w/ two reflective phase shifters as well as an additional circulator w/ load B) Requires two additional hybrids w/ loads and two in-line phase shifters

16. A is probably more compact. B is probably less lossy. A uses one fewer load. B uses only components already developed for TESLA/ILC/XFEL. A uses simpler phase shifters in which it is easier to incorporate electronically controlled active elements (e.g. ferrites) if fast control is required. One could also gain contol over power to individual cavities by incorporating a VTO for each cavity, but: The current VTO design is longer than the cavity spacing Changing the setting of one affects the power to all downstream (RF wise) cavities in the line. The current design is not remotely controlable and it would be difficult and expensive (if possible) to make it so. Pros & Cons:

17. Average Effective Cavity Gradient (MV/m)10.03 20.65 27.71 26.41 The Project X L-Band Linac* 603 MeV – 8 GeV  =.7933 –.9945 *favored design ILC-8  /9 ILC-1 ILC-2 ILC

18. ILC 8  /9 Cavities 00   pp v p =c v p =9/10c  -8  /98  /9 10  /9 +2  The reference linac design incorporated low-  “squeezed ILC” cavities in the standard  -mode with adjusted cell length. To avoid a new cavity development and modifications to the cryomodule, the “favored” design instead uses standard ILC cavities deformed just enough to bring the 8  /9 mode up to 1.3 GHz and operated in this highly non-standard mode. Stretch to increase frequency by 0.8 MHz

19. For the  mode since the TW components are indistinguishable (from each other and from the SW), they both contribute equally to acceleration. For a non-  mode then, in a field-limited cavity, we automatically take a hit of about a half in voltage V seen by a synchronous particle. In a SW mode, the cells all oscillate in phase, but with an amplitude modulation determined by the “phase advance” of the TW components. The stored energy U is thus also cut in half, as is the R/Q (=V 2 /  U). Q L (~= V/((R/Q)I b )) and t i (~=2Q L /w ln2)), however, remain roughly unchanged. 8  /9 mode AnAn n  mode

20. One takes a further hit at low  due to the transit time factor for the individual cells. P. Ostroumov, et al. Fig. 2.1 Project X document 8p/9 mode in 9-cell ILC cavity peak cavity field equivalent  -mode gradient of ~23.25 MV/m (~26.8 MV/m @ 30° off crest) 5.9–11.9 MV/m 57% spread in V for first RF station

21. peak cavity field equivalent  -mode gradient of ~23.25 MV/m (~26.8 MV/m @ 30° off crest) 5.9–11.9 MV/m 57% spread in V for first RF station Parameters for Flat Acceleration Along Bunch Train: for constant, cavity field limited stored energy. Energy and Gradient Profiles Along Linac Section: Exact Solution for flat acceleration and zero reflection during beam. But 21 cavities with a large spread in V share a common klystron and thus a common t i.

22. PROBLEM: If we relax the efficiency condition and allow steady state reflected power during the beam, can we achieve constant gradient along the bunch train in each cavity with varying V but uniform stored energy and a common injection time? Assume we can adjust both Q L (~= Q e ) and P for each cavity. Solve optimal case (see above) for highest gradient cavity to set t i. Determine and fix stored energy in cavities, U 0. The RF power required to achieve this stored energy at time t i is now determined as a function of Q L.

23. Now, for the cavity field /gradient to equilibrate at injection time, the power flowing into the cavity at t i must equal the power taken out by the beam (neglecting wall losses). condition for flat acceleration. The steady-state reflected power during the beam is given for each cavity by:

24. Conclusions L-Band high-power RF distribution development for TESLA/XFEL/ILC can be applied to Project X. The configuration and components used will depend on the degree of control required in setting the power, phase, and coupling at each individual cavity which, if any, of these parameters need to be changeable remotely whether and what fast (not mechanical) control is needed These requirements will be set by considerations of beam dynamics, LLRF, operations, etc. The changing  causes changing shunt impedances and creates a different problem than in ILC, where the anticipated spread in cavity limits is the chief concern, but it would appear to be solvable.