# Summary of MLI Studies Chris Adolphsen GDE Meeting

Summary of MLI Studies Chris Adolphsen GDE Meeting at Sendai, 3/14/08 On Axis Wake Kicks (I. Zagorodnov, V Yakovlev, Z. Li and K. Bane) Detailed view of FM and HM couplers - note protrusion of couplers End on view of coupler geometry (from downstream end) y [mm] Edge of irises (r= 35 mm) 30 mm fm-ds 39 mm hm-ds hm-us (fmfundamental, hmhigher mode, dsdownstream, usupstream) x [mm] On-Axis Wake Due to Coupler Asymmetry Numerical calculations performed in 3 steps: couplers in beam pipe, cavity with couplers, multiple cavities with couplers (I. Zagorodnov) Wake varies along bunch; (kx, ky) are kicks averaged over beam; in calculations z= 1 mm (due to mesh limitations)

One set of couplers in beam pipe: (kx, ky) = (-21, -19) V/nC; agrees well with analytical optical model with all elements at same z: (-21, -17) V/nC One cavity with couplers: (kx, ky) = (-11, -10) V/nC; agrees well with a zindependent optical model with iris shadowing with all elements at same z: (-13, -7) V/nC. Periodic solution: (kx, ky) = (-7.6, -6.8) V/nC/m (reached after 2 cavities) V. Yakovlev has also performed numerical calculations for 1 mm bunches that agree reasonably well (e.g. periodic solution ~-5 V/nC/m) V. Yakovlevs Gdfidl Results For z= 0.3 mm the mesh needs to be finer, and more cavities are needed to reach periodic solution (~6) => large computer resources needed Expectation is that the kick for the short bunch ~0.3 times the kick for z= 1 mm T. Weilands group is also working on this calculation Symmetrizing Couplers y [mm] rotated coupler hm-us fm-ds hm-ds x [mm] Z. Li proposes rotating upstream coupler by 180 to reduce wake => For one cavity with couplers, optical model + iris shadowing: (kx, ky)= (-2.5, 1.2) V/ nC [was (-13, -7) V/nC] Effect on Beam Wake has two terms: an offset term and a slope term Offset: A constant driving term to the equation of motion generates a kind of dispersion => the closed orbit depends on (longitudinal) position in bunch; model: y + y/2= e2N W(s)/E has solution

y= 2e2N W(s)/E + betatron oscillation(s) Particles will perform free betatron oscillation about different centers, depending on s; projected emittance will oscillate; no real wake effect; average emittance will increase due to energy spread (filamentation) and normal cavity wake Slope: Numerical results for 3 couplers in beam pipe, Wav~ 2.4 V/nC/mm/m; for periodic case should reduce a factor 2~3 to ~1 V/nC/mm/m, which is a factor 20 smaller than the normal cavity wake, so can be ignored Estimated Emittance Growth (analytical approximation) Let eN = 3.2 nC, <>= 68 m, y = 2*10-8 m. k [V/nC/m] (/0)max (/0)final 20 3.1 1.03 5 1.23 1.02 2 1.04

1.003 Bottom Line: For periodic solution the wake due to coupler asymmetry should not be a problem; with Z. Lis modification, the effect will be even less Summary of RF Kicks (Z Li) Average over cavity pair Eacc = 35 MV/m, I_Beam = 0.011A, Qext ~3.4E6 Accelerating Gradient = 31.5MV/m Head-tail: +- 1 sigma_z Kick unit: Volt X-centroid Y-centroid X-head-tail Y-head-tail -2106 -785 33 3.5 TDR-M 761

2621 24 4 TDR,TDR-RotX 609 -739 20 0.3 TDR-M,TDR-M-RotX 664 2606 11 ~0 TDR-M,TDR-M-MirrorZ 664 15 11 4

TDR M = TDR with 180 deg rotation of HOM on non-FPC end RotX = TDR rotated about x axis by 180 so FPC switches from up-stream to down-stream end and power feed direction changes. MirrorZ = Up/Down end groups interchanged, power feed direction unchanged Summary of RF Kicks (K Bane) SLAC [V] krms [V] x y ZLi_x ZLi_y FNAL [V] krms [V] -2000 17. -3320 18. -670 2.7 -230 2.9

-650 13. -1020 16. -2490 1.8 -2810 4.6 Average and rms of rf kicks experienced by the beam, according to SLAC and FNAL calculations. Here we assume Vacc= 31.5 MV/m and z= 0.3 mm. Given are the total kicks due to all couplers in one cavity as is, and also after Z. Lis symmetrization (the upstream coupler is rotated by 180 deg). Beamline Absorber Study Using T3P 1. Application (ILC, XFEL, ERL,); 2. Simulation method (T3P); 3. Simulation results; (3D one TESLA cavity with couplers, 2D one cavity/two-cavity/three-cavity..) 4. Going to simulate multi-cavity with short bunch and taking account into dispersive medium; Liling Xiao Monopole Single Passage Losses for three cavities without couplers One bunch Q=3.2nc, bunch length=10mm Loss factor (V/pc)=9.96V/pc

Lossy dielectric conductivity eff=0.6(s/m) Total Energy Generated by Beam (J) 10.208e-5 Energy propagated into beam pipe (J) 4.44e-6 Energy dissipated in the absorber (J) 7.0e-7 Energy loss on the Non SC beampipe wall (J) around absorber 9.3e-10 Energy loss in intersection between two cavities (J) 1.3e-9 (cold copper conductivity=3500e6Simm/m) Dielectric constant r=15, within 80ns Ratio of Dissipated Energy and Propagated Energy to Total HOM Energy 1-cavity+absorber @200ns 1-cavity+absorber @80ns

2-cavity+absorber @80ns 3-cavity+absorber @80ns left beampipe 14.1% 12.4% 8.9% 6.6% right beampipe 11.3% 10.3% 6.0% 4.5% absorber 2.6% 2.1% 1.8% 1.7%

Total 28.0% 24.8% 16.7% 12.8% Absorber fraction 9.4% 8.5% 10.8% 13.5% Beam Pipe Total for 3-cavity CM = 1.3e-9 * 2800 * 5 / ( 0.128 * 0.135) = 1.1 mW Worse case for 8-cavity CM and 300 um bunch = 1.1 * (8/3) * (10/0.3) = 100 mW E-Field Strength at TTF3 Cold Coupler Window Region Lixin Ge, ACD Group at SLAC Model E magnitude red is window

1 2 3 4 5 E amplitude along y axis TTF HOM Measurement Data Analysis with Curve Fitting Method Shilun Pei with Chris Adolphsen, Zenghai Li, Karl L. Bane, et al. SLAC, Feb. 27, 2008 Steering setup Module ACC4 BPM18 BPM17 2007-01-22T091106.mat Modal Analysis of Dipole Signals Real Im

Amp Fit frequency spectrum near 1.7 GHz to sum of complex Lorentzians Derive frequency and Q of two polarizations from simultaneous fit to 36 orbits Cavity Freq in ACC3/ACC4/ACC5 2007-01-22T091106 Two cavities with largest mode splitting ACC3 ACC4 ACC5 Cavity Q in ACC3/ACC4/ACC5 2007-01-22T091106 ACC3 ACC4 ACC5 Fit of Amplitudes to BPM X and Y Ignoring the small out-of-phase (angle) contributions, the resulting mode amplitudes correlate well with the x and y positions inferred from the bpm data Mode Polarizations 2007-01-22T091106, ACC4 CAV #

Mode 1 Pol. Angle Mode 2 Pol. Angle 2 3.03o 92.70o 4 21.62o 111.27o 5 2.85o 94.29o 6 4.10o 93.68o 7 -15.01o

72.47o 8 -23.76o 68.77o S-Band RF BPM Signal Simulations Johnny Ng RF Distribution Module Cold Test load VTO 2 1 load 4 window circulator 3 hybrid phase shifter turned for visibility

The first (of 4) 2-cavity module of our RF power distribution system for Fermilabs first NML cryomodule is assembled and cold tested and ready for high-power testing. It incorporates: SLAC VTO and hybrid IBFM window (for pressurization of high-power volume) S.P.A. Ferrite isolators and loads Mega bends and flex guides (and dir. cplrs. while awaiting S.P.A. pieces) C. Nantista VTO set for 2nd to last cavity pair (~3 dB). COLD TEST RESULTS: S11 = -43.0 dB (0.005%) S21 = -2.948 dB (50.72%) POWER 2.36% of power missing (-0.104 dB) Pair power division equal to within 1%. Slightly more than power sent through to allow for downstream losses. Expect roughly: S31 = -6.318 dB (23.35%) S41 = -6.276 dB (23.57%) Bends: VTO: Window: 0.4930.088% =

Hybrid: 0.4930.42% = Circulators: 0.4931.78% = Phase shifters: 0.4930.55% = Flex guides: 0.62% + 0.4930.62% = PHASE 0.41% 0.446% 0.043% 0.207% 0.878% 0.271% 0.926% ~3.18% Phases of S31 and S41 initially within 1.7 of each other (adjustable with phase shifter). Module through phase error = ~-6.7 (easily absorbed in next modules phase shifters). SPACING Feed spacing measures ~1.3827m, compared to 1.3837m coupler spacing. Module length measures ~2.7674m, exact to measurement resolution. C. Nantista Simulation of Cavity Pair Coupling Through Hybrid w/o Circulators Individual Cavity Gradients 1.005 Assumed identical cavities 1 and lossless,

symmetric 0.995 coupling network with equal coupling 0.99 but imperfect 0.985 port isolation. 0.98 0.5 0: black -40 dB: blue & red -30 dB: cyan & magenta 0.6 0.7 1 Normalized Acceleration Through Pair Normalized Gradients in Cavity Pair =0 |S23| = 0.96 |S23| = 0.94 -40 dB: blue & red -30 dB: cyan & magenta

0.92 0.9 0.5 0: black 0.6 0.7 0.8 0.9 -201 dB: & yellow 1.1 green 1.2 1.3 1.4 1.5 Time (ms) 0.992 0.99 0.988 0.6 0.7 0.8

0.9 1 1.1 Time (ms) 1.2 1.3 1.4 1.5 1.001 Normalized Acceleration Through Pair Normalized Gradients in Cavity Pair 0.98 0: black -40 dB: blue -30 dB: cyan -20 dB: green 0.994 1.002 =/4 1 |S23| =

0.996 0.5 Time (ms) 1.02 is the phase length from the hybrid ports to the cavities (with S23 set to 0). 0.998 0.986 -20 dB: green & yellow 0.9 1 1.1 1.2 1.3 1.4 1.5 0.8 1.04

Net Pair Acceleration 1.002 1 0.999 |S23| = 0.998 0: black -40 dB: blue -30 dB: cyan -20 dB: green 0.997 0.996 0.995 0.994 0.993 0.5 0.6 0.7 0.8 0.9 1 1.1 Time (ms)

1.2 Typical measured isolation: -4248 dB gradient variation << 0.1% 1.3 1.4 1.5 C. Nantista ILC Positron Capture Cavity Prototype Goal: Power with 5 MW, 1 msec pulses to produce 15 MV/m gradient Faya Wang RF waveforms are calibrated in these cases Breakdown in Cavity Normal Off 0 Hard Events -15 -20 Normalized power: dB -5

-10 -25 -10 -15 -20 -25 -30 -30 -35 -35 992 994 996 Time: us 998 1000 Klystron output Soft Events -15 -20 -25

Normalized power: dB -10 Reflect pow er from cavity Stored energy Change -25 -30 -35 -40 -45 210 215 Time: us 220 225 332 -20 -35 205 330 -15 -30

200 328 Time: us Input power to cavity Reflect power from cavity Stored energy Change -5 Input pow er to cavity -10 326 0 0 -5 324 1002 Breakdown in Waveguide Normalized power: dB Normalized power: dB -5

Input power to cavity Reflect power from cavity Stored energy Change 0 Input power to cavity Reflect power from cavity Stored energy Change 95 100 105 110 115 Time: us 120 125 130 Breakdown Data During Processing Rate (1/hr) vs Time (hr) Breakdown rate: 1/hr 40 30

20 10 0 0 100 200 300 Time: hr 400 500 600 1 Fraction of Hard and Soft Events vs Time (hr) Hard breakdown rate percent Soft breakdown rate percent 0.8 0.6 0.4 0.2

0 0 100 200 300 Time: hr 400 500 600 0 10 10 Possibility Distribution of Time Between Breakdowns for Different Processing Periods 0~135hrs-5Hz 135~270hrs-5Hz 270~405hrs-1Hz 405~528hrs-1Hz -1

-2 10 -3 10 -4 10 0 0.5 1 1.5 2 2.5 Breakdown time interval: hr 3 3.5 4 F. Wang Temperature vs Cavity Input Power (with 28 gpm cooling)

Cavity Detuning vs Temperature (slope near that expected) 35 114.5 Temperature of Cavity: degF 113.5 113 Cavity deturned frequency: kHz Input Coupler-upward Input Coupler-backward Cell 1 Cell 2 Cell 3 Cell 4 Cell 5 114 112.5 112 111.5 111 110.5 110 30 25 df = 16.78*dT + 0.5771 20

15 10 5 0 0 2 4 6 8 10 Average Power into cavity: kW 12 14 data fit 0 0.5 1 1.5 Average Temperature rise: degC 2 Cavity Gradient Measurements with Beam (Worlds first L-band cavity operation in an X-band Linac) 14 12

100us RF pulse and beam at 85us G=7.34*sqrt(P) 1100us RF pulse and beam at 85us G=7.49*sqrt(P) 1100us RF pulse and beam at 900us G=7.23*sqrt(P) Predict value G=7.6*sqrt(P) Gradient: MV/m 10 8 6 4 2 0 0 0.5 1 1.5 Power: MW 2 2.5

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