Transition Wakes in the 3.9 GHz Cryomodule Andrei Lunin, Arun Saini, Nikolay Solyak 11 July 2016

Geometry of the LCLS-II 3.9 GHz Cryomodule LCLS-II 3.9 GHz CM Wake 11/18/2018

CM in L0, with cryogens feed cap and end cap (FC1) Presenter | Presentation Title 11/18/2018

Differential Pumping system (LCLSII-1.1-EN-0658) Ltot=1.2m Ø 34.8 mm 320 mm 490 mm Ltot=2.14 m Ø 34.8 mm 440 mm 440 mm MADDECK file FC-3 CAVC028 cavity #8 center 115.18739 3917.0   CMBH2 BPM 115.68376 4413.39 CMH2END manual gate valve d/s flange face 115.84825 4577.88 FC3 FC-3 feed cap feed cap plate face 117.60357 6333.20 beamline flange 117.69247 MSC1D MSC space d/s end 119.43257 1.8290 PSC1D differential pumping space 121.33862 1.9060 ENDL1B end of L1B linac Diff Pump Length of SS pipe pipe ~3.73m (we use 2.5m) Presenter | Presentation Title 11/18/2018

End Cups EC-D EC-U Presenter | Presentation Title 11/18/2018

FC6 (F10040900) FC2, FC4 (F10040671) FC1 (F10040670) FC3,5 (F10040895) Presenter | Presentation Title 11/18/2018

Wakefield simulation summary (ECHO-2D) Loss-factor in 3.9 GHz Cryomodule (V/pC) Bunch length (sigma) 0.5mm 1mm 2mm 8 x Cavities only - 113.9 8x (Cavities + bellow) 135.5 All elements but gaps 142.7 Full CM geometry with gaps 204.9 150.4 105.5 CM with gaps + extra bellow 205.2 151.64 107.2 CM with long spool transition 148.3 CM_ 78mm spool-piece 151.58 Wakefield power, generated by 300µA; σ=1mm beam is 13.65 W per 3.9GHz CM, and only 9.4 W above beam pipe cut-off frequency (the rest will be in cavity as beam loading) Presenter | Presentation Title 11/18/2018

Wake Functions of LCLS-II 3.9 GHz Cryomodule Longitudinal wake functions of a point like charge* 𝑤 ∥ 0 𝑠 =−𝐻 𝑠 𝐴 𝑒 − 𝑠/ 𝑠 0 +0.9 cos⁡(5830 𝑠 0.83 ) 𝑠 +195𝑠 +𝐵𝛿(𝑠) , [V/pC] s0= 8.4*10-4 , A = 784, B= 1098 * I. Zagorodnov, T. Weiland, “Wake Fields Generated by the LOLA-IV Structure and the 3rd Harmonic Section in TTF-II”, TESLA Report 2004-1 LCLS-II 3.9 GHz CM Wake 11/18/2018

Wake Potential of LCLS-II 3.9 GHz Cryomodule Longitudinal wake potential of Gaussian bunch σz= 1 mm* 𝑞 𝑠 = 1 2𝜋 𝜎 𝑧 𝑒 − 𝑠 2 2 𝜎 𝑧 𝑊 ∥ 0 (𝑠)= 1 𝑄 −∞ 𝑠 𝑤 ∥ 0 𝑠− 𝑠 ′ 𝑞 𝑠 ′ 𝑑 𝑠 ′ 𝑘 ∥ = 1 𝑄 −∞ ∞ 𝑊 ∥ 0 (𝑠)𝑞 𝑠 𝑑𝑠 * Coefficients of the wake function are adjusted for best fit with numerical (ECHO 2D) wake simulation in the 3.9 GHz LCLS-II cryomodule LCLS-II 3.9 GHz CM Wake 11/18/2018

Wake Power Spectrum of 1.3&3.9 GHz LCLS-II Cryomodules 𝒅𝑷 𝒅𝝎 = 𝒒 𝟎 𝟐 𝒇 𝒃 𝒁 ∥ 𝒆 − 𝝎 𝝈 𝒛 𝒄 𝟐 𝒁 ∥ = 𝟏 𝝅𝒄 𝑹𝒆( 𝟎 ∞ 𝒘 ∥ 𝟎 𝒔 𝒆 − 𝒊𝝎𝒔 𝒄 𝒅𝒔) q0= 300 pC , fb = 1 MHz , σz= 1 mm 𝑃 𝑇𝑀01 =8 1 4 R Q 𝜔 𝑞 0 2 𝑓 𝑏 ≅ 0 𝜔 𝑐 𝒅𝑷 𝒅𝝎 𝑑𝜔 Wakes below the beam pipe cut-off frequency is deposited to the operating modes! LCLS-II 3.9 GHz CM Wake 11/18/2018

Integrated Wake Power in 1.3&3.9 GHz LCLS-II Cryomodules max 9.4 W/CM max 12.8 W/CM q0= 300 pC , fb = 1 MHz , σz= 1 mm 𝑃(𝜔)= 𝑞 0 2 𝑓 𝑏 𝜔 𝑐𝑢𝑡𝑜𝑓𝑓 𝜔 𝑍 ∥ 𝑒 − 𝜔 𝜎 𝑧 𝑐 2 𝑑𝜔 Propagating wake power: LCLS-II 3.9 GHz CM Wake 11/18/2018

Wake Power Deposition (Transition Model) Pinp TM01 Prad A single monopole mode at the input is almost equally mixed up with others propagating TM0n modes after a transmission through the cavity ! LCLS-II 3.9 GHz CM Wake 11/18/2018

Wake Power Deposition (Transition Model) dP/df, [W/GHz] F, [GHz] TM01 TM02 TM03 Total Wake F, [GHz] P, [W] Wake Monopole TM-modes Decomposition: 𝐏 𝒇 = 𝒏=𝟏 𝑵( 𝒇𝒄 𝒏 ) 𝑷_𝑻𝑴 𝟎𝒏 𝑵( 𝒇𝒄 𝒏 ) , where N(fcn) is number oTM0n modes below the cut off frequency Transition model approaches wake power deposition by a direct calculation of monopole modes transitions through beam line components (BLA, FPC, HOMC, Gate Valves): 𝑃≈ 𝑛=1 𝑁 𝑓 𝑐 ∞ 𝑑 𝑃 𝑇𝑀 0𝑛 𝑑𝑓 (1− 𝑆 12 2 )𝑑𝑓 LCLS-II 3.9 GHz CM Wake 11/18/2018

Beam Line Absorber properties 𝜀.𝑟𝑒 𝑓 ≈73 𝑒 −0.66 𝑓 0.25 tan ∆ =0.4=𝑐𝑜𝑛𝑠𝑡 LCLS-II 3.9 GHz CM Wake 11/18/2018

Wake transmission (single pass) through beam line components BLA wake loss is ~ 42% FPC wake loss is ~ 20% BLA FPC HFSS Driven Modal (20 GHz) Prad Pinp TM01 Pinp TM01 LCLS-II 3.9 GHz CM Wake 11/18/2018

Wake Power Deposition (Transition Model) Wake transmission (single pass) through beam line components HOMC Gate Valve Prad HFSS Driven Modal (20 GHz) Prad Pinp TM01 Pinp TM01 HOMC wake loss is ~ 1.6% Gate Valve wake loss is ~ 2.7% LCLS-II 3.9 GHz CM Wake 11/18/2018

Wake Power Deposition (Transition Model) Wake transmission (single pass) through beam line components 9-cell structure End Pipe (Ø 32mm) HFSS Driven Modal (20 GHz) Pinp TM01 Prad Pinp TM01 Prad wake radiation is ~ 41% wake transmission is ~ 50% LCLS-II 3.9 GHz CM Wake 11/18/2018

Wake Power Deposition (Diffusion Model) TM-mode Loss in the Circular Pipe: dPn (ω) = 𝑷 𝟎 (𝟏− 𝒆 −𝟐𝜶𝒏𝒍 ) 𝜶 𝒏 (𝝎)= 𝒁(𝝎) 𝒁 𝟎 𝒓 𝟏− 𝝎𝒄 𝒏 𝝎 𝟐 −𝟏 HFSS Simulations 𝐝𝐏 𝝎 = 𝒏=𝟏 𝑵 𝝎𝒄 𝒏 𝒅𝑷 𝒏 (𝝎) 2𝜋𝑟 𝑙 𝑛 = 𝑆 𝑛 where, Sn is the area of lossy (radiating) surface and ln is the length of a beam pipe with an equivalent impedance Z(ω) We can derive the equivalent surface impedance Z(ω) for beam line components ! LCLS-II 3.9 GHz CM Wake 11/18/2018

Wake Power Deposition (Diffusion Model) Impedances of Beam Line Components LCLS-II 3.9 GHz CM Wake 11/18/2018

Wake Power Deposition (Diffusion Model) 3rd harmonic section Variant A CM1 CM2 BLA SS Beam Pipe (L=2.5m) Variant B CM1 CM2 BLA BLA BLA SS Beam Pipe (L=2.5m) Each CM contains: 9 bellows, 1 spool pipe, 2 gate valves, 16 HOMC, 8 FPC Diffusion Model Approaches: 1. Wake power is uniformly distributed and fully absorbed within the section. 2. Power deposition is proportional to the surface impedance and the surface area LCLS-II 3.9 GHz CM Wake 11/18/2018

Wake Power Deposition (Transition Model) 3rd harmonic section Variant A open CM1 CM2 BLA2 BLA1 SS Beam Pipe (L=2.5m) Power radiated from single CM (to each side): 𝑃𝐶𝑀 𝑟𝑎𝑑 ≈ 𝑃 0 16 𝑖=1 8 1− 𝑆𝑃 𝐹𝑃𝐶 + 2×𝑆𝑃 𝐻𝑂𝑀 + 𝑆𝑃 𝐵𝐸𝐿𝐿𝑂𝑊𝑆 𝑖 =1.7 𝑊 where SP is a single pass wake loss in the FPC, HOMC and bellows Power absorbed in CM: 𝑃𝐶𝑀 𝑙𝑜𝑠𝑠 = 𝑃 𝑤𝑎𝑘𝑒 − 2×𝑃𝐶𝑀 𝒓𝒂𝑑 =6.0 [𝑊] Power absorbed in BLA: 𝑃 𝐵𝐿𝐴1 ≈ (𝑃𝐶𝑀 𝑟𝑎𝑑 − 𝑃 𝐺𝑉1 )×0.42=0.7 [𝑊] 𝑃 𝐵𝐿𝐴2 ≈2 (𝑃 𝐵𝐿𝐴1 + 𝑃𝐶𝑀 𝑟𝑎𝑑 − 𝑃 𝐵𝐿𝐴1 − 𝑃 𝐺𝑉2 ∗0.5∗0.42+…)=1.9 [𝑊] Power radiated to Gate Valves: 𝑃 𝐺𝑉1 = 𝑃 𝐺𝑉4 ≈ 𝑃𝐶𝑀 𝑟𝑎𝑑 ×2×0.027=0.09 [𝑊] 𝑃 𝐺𝑉2 = 𝑃 𝐺𝑉3 ≈2∗ 𝑃 𝐺𝑉1 =0.18 [𝑊] LCLS-II 3.9 GHz CM Wake 11/18/2018

Wake Power Deposition (Transition Model) 3rd harmonic section Variant A open CM1 CM2 BLA2 BLA1 SS Beam Pipe (L=2.5m) Power absorbed in bellows: 𝑃 𝐵𝐸𝐿𝐿 ≈0.007 [𝑊] Power radiated to FPC: 𝑃 𝐹𝑃𝐶 ≈0.75 [𝑊] Power radiated to HOMC: 𝑃 𝐻𝑂𝑀𝐶 ≈0.05 [𝑊] Power absorbed in 2.5 m SS Beam Pipe (1st pass & 2nd pass): 𝑃 𝑆𝑆1 ≈ (𝑃𝐶𝑀 𝑟𝑎𝑑 − 𝑃 𝐺𝑉1 )∗0.11=0.18 [𝑊] 𝑃 𝑆𝑆2 ≈ (𝑃𝐶𝑀 𝑟𝑎𝑑 − 𝑃 𝐺𝑉1 −𝑃 𝑆𝑆1 − 𝑃 𝐸𝑁𝐷2 )∗0.11=0.1 [𝑊] Power radiated to Beam Line: 𝑃 𝑈𝑃 ≈ (𝑃𝐶𝑀 𝑟𝑎𝑑 − 𝑃 𝐺𝑉1 − 𝑃 𝐵𝐿𝐴1 )=0.9 [𝑊] 𝑃 𝐷𝑂𝑊𝑁1 ≈ (𝑃𝐶𝑀 𝑟𝑎𝑑 − 𝑃 𝐺𝑉4 − 𝑃 𝑆𝑆1 )∗0.41=0.6 [𝑊] 𝑃 𝐷𝑂𝑊𝑁2 ≈ (𝑃𝐶𝑀 𝑟𝑎𝑑 − 𝑃 𝐺𝑉4 − 𝑃 𝑆𝑆1 − 𝑃 𝐷𝑂𝑊𝑁1 − 𝑃 𝑆𝑆2 − 2𝑃 𝐺𝑉4 )∗0.41=0.3 [𝑊] LCLS-II 3.9 GHz CM Wake 11/18/2018

Wake Power Deposition in the 3rd Harmonic Section Components # Surface Area, [mm2] Power Deposition, [W] Transition Diffusion A B BLA 2(3) 1.4e4 2.6 3.6 10 12 End Pipe (SS) 1 6.2e5 0.3 0.16 0.8 0.6 End Pipe (Rad) 2 804 1.8 1.2 - Bellows (Cu&SS) 18 3.7e4 0.14 0.12 Gate Valve 4 2.0e2 0.55 1.4 Spool Pipe (Cu) 1.0e5 0.01 HOMC 32 3.1e2 1.7 FPC 16 7.1e2 11.6 11.5 5.7 4.5 Total Wake Power 18.9 Transition model predicts much higher wakefields radiation to FPC & HOMC Over 65% of wake power is absorbed within the cryomodule itself! LCLS-II 3.9 GHz CM Wake 11/18/2018

Cryogenic Heat Loads in the 3rd Harmonic Section Both models show a significant amount of radiated wakefields, up to 65%, going to FPC and HOMC ports of the 3.9 GHz cryomodule. The major part of the total wakefield power (85%) is a source for the 50 K cryogenic heat load, while the rest is resulted in about 10% and 1% of the power deposition going to 5 K and 2 K circuits respectively. Without HOM absorber at the end of 3.9GHz cryomodule, power from wakes will be redistributed between SS tube and HOM absorber installed in upstream CM. Power going to the SS pipe (2.5m) will be <1 W maximum. LCLS-II 3.9 GHz CM Wake 11/18/2018

Back-up slides Andrei Lunin | LCLS-II BPM Final Design Review 12/12/2014

CM-End Modeling: Upstream End A2 gap 0.4mm A4=A2 A6 gap after valve 2mm A7 Transitional Area AI3mm AH 3mm A3 Cu pipe A1=A5 SS pipe CM Gate Valve

CM-End Modeling: Downstream End A8 3mm A9 transition Area A10=A6 A11 178 mm A10 A11 A12 A21 Absorber 50 x 45 mm + Bellows

Intercavity Bellows Modeling Bellow Physical Length = 128.2 mm. Bellow Effective Length (including convolutions): 317.33 mm. Bellow 3.5mm

Absorber Bellow Sketch