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11.11.09 Marcel Schuh CERN-BE-RF-LR CH-1211 Genève 23, Switzerland marcel.schuh@cern.ch 3rd SPL Collaboration Meeting at CERN on November 11-13, 2009 Higher Order Modes In The SPL, Transverse And Longitudinal Effects
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Outline HOM Bunch Tracking Simulation Code Simulation input parameters Simulation results Chopping Conclusions & Outlook 2 mschuh@cern.ch 11.11.09 3 rd SPL Collaboration Meeting
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Basic LINAC Simulation Model Drift kick model with exact cavity spacing (not transverse) E 0 T(β) via field integration (only sync. particle) Phase and field controlled individually for each cavity Transfer matrix between cavities (transverse) using phase advance per period (no magnets modeled) Longitudinal and transverse plane are independent Bunch (point charge)/particle tracking without space charge effects 3 mschuh@cern.ch 11.11.09 3 rd SPL Collaboration Meeting
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Basic HOM Model One HOM per cavity (monopole or dipole) Gaussian or Uniform HOM frequency distribution ( σ = 1MHz ) with no change over time R/Q(β) applied in each cavity according to beam β Global Q ex Load HOM via bunch tracking (Bunch ⇔ HOM interaction) 4 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Beam Input Parameters 5 ParameterMeanVarianceSimulation Bunch period [ns]1/f b ≈30.00315long Pulse length [ms]1.00both Period length [ms]200both Beam current [mA]40...4003%both W Input [MeV]1600.078long Tr. position [mm]00.3trans Tr. momentum [mrad]00.3trans Basic beam settings used in all simulations: https://twiki.cern.ch/twiki/bin/view/SPL/SplHom mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
![Beam Input Parameters 5 ParameterMeanVarianceSimulation Bunch period [ns]1/f b ≈ long Pulse length [ms]1.00both Period length [ms]200both Beam current [mA] %both W Input [MeV] long Tr.](http://images.slideplayer.com/32/10064703/slides/slide_5.jpg "position [mm]00.3trans Tr. momentum [mrad]00.3trans Basic beam settings used in all simulations: rd SPL Collaboration Meeting")
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HOM Parameter Compare phase space (ε) of one pulse (350.000 bunches) with (loaded HOM) and without HOM interaction at the exit of the linac. 6 LongitudinalTransversal Section Parameter Medium βHigh βMedium βHigh β f HOM [MHz]1783±11330±11015±1915±1 R/Q(β) [Ω*] (avg) 121146048 * linac def. mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Longitudinal - General Case 7 mschuh@cern.ch3 rd SPL Collaboration Meeting Longitudinal Bunch Center Emittance Growth Rate σ I = 3% σ f = 1MHz 11.11.09
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Transversal - General Case 8 mschuh@cern.ch3 rd SPL Collaboration Meeting σ I = 3% σ f = 1MHz Transversal Bunch Center Emittance Growth Rate 11.11.09
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Chopping Modes 9 mschuh@cern.ch3 rd SPL Collaboration Meeting New machine lines (created by chopping): N ci /N cb : x/8 : f mc1 = 44.025MHz y/80 : f mc1 = 4.4025MHz z/800 :f mc1 = 0.44025MHz T cb = 8 · T b T ci = 5 · T b PULSE T p = N · T b N.B.: Charge per pulse stays const. charge per bunch increases 11.11.09
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Effect Of Chopping Analytically (Longitudinal) 10 mschuh@cern.ch3 rd SPL Collaboration Meeting Voltage induced by one pulse: Voltage induced by one pulse with substructure: Further details: S. Kim et al., Higher-order-mode (HOM) power in elliptical superconducting cavities for intense pulsed proton accelerators 11.11.09
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5/8 Chopping 11 mschuh@cern.ch3 rd SPL Collaboration Meeting V HOM after one pulse (5/8 chopping) 11.11.09 f HOM [MHz]
![5/8 Chopping 11 rd SPL Collaboration Meeting V HOM after one pulse (5/8 chopping) f HOM [MHz]](http://images.slideplayer.com/32/10064703/slides/slide_11.jpg "5/8 Chopping 11 rd SPL Collaboration Meeting V HOM after one pulse (5/8 chopping) f HOM [MHz]")
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5/8 Chopping 12 mschuh@cern.ch3 rd SPL Collaboration Meeting f HOM = f cml ± 1MHz I b = 400 ± 12mA 11.11.09 V HOM after one pulse (5/8 chopping) f HOM [MHz]
![5/8 Chopping 12 rd SPL Collaboration Meeting f HOM = f cml ± 1MHz I b = 400 ± 12mA V HOM after one pulse (5/8 chopping) f HOM [MHz]](http://images.slideplayer.com/32/10064703/slides/slide_12.jpg "5/8 Chopping 12 rd SPL Collaboration Meeting f HOM = f cml ± 1MHz I b = 400 ± 12mA V HOM after one pulse (5/8 chopping) f HOM [MHz]")
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5/8 Chopping 13 mschuh@cern.ch3 rd SPL Collaboration Meeting f HOM = f cml ± 1MHz I b = 400 ± 12mA 11.11.09 V HOM after one pulse (5/8 chopping) f HOM [MHz]
![5/8 Chopping 13 rd SPL Collaboration Meeting f HOM = f cml ± 1MHz I b = 400 ± 12mA V HOM after one pulse (5/8 chopping) f HOM [MHz]](http://images.slideplayer.com/32/10064703/slides/slide_13.jpg "5/8 Chopping 13 rd SPL Collaboration Meeting f HOM = f cml ± 1MHz I b = 400 ± 12mA V HOM after one pulse (5/8 chopping) f HOM [MHz]")
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Emittance growth - chopping mschuh@cern.ch3 rd SPL Collaboration Meeting 14 f HOM = f cml ± 1MHz I b = 400 ± 12mA Q ex = 10 7 11.11.09 Longitudinal Bunch Center Emittance Growth Rate f HOM [MHz]
![Emittance growth - chopping rd SPL Collaboration Meeting 14 f HOM = f cml ± 1MHz I b = 400 ± 12mA Q ex = Longitudinal Bunch Center Emittance Growth Rate f HOM [MHz]](http://images.slideplayer.com/32/10064703/slides/slide_14.jpg "Emittance growth - chopping rd SPL Collaboration Meeting 14 f HOM = f cml ± 1MHz I b = 400 ± 12mA Q ex = Longitudinal Bunch Center Emittance Growth Rate f HOM [MHz]")
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Emittance growth - chopping mschuh@cern.ch3 rd SPL Collaboration Meeting 15 f HOM = f cml ± 1MHz I b = 40 ± 1.2mA Q ex = 10 7 11.11.09 Longitudinal Bunch Center Emittance Growth Rate f HOM [MHz]
![Emittance growth - chopping rd SPL Collaboration Meeting 15 f HOM = f cml ± 1MHz I b = 40 ± 1.2mA Q ex = Longitudinal Bunch Center Emittance Growth Rate f HOM [MHz]](http://images.slideplayer.com/32/10064703/slides/slide_15.jpg "Emittance growth - chopping rd SPL Collaboration Meeting 15 f HOM = f cml ± 1MHz I b = 40 ± 1.2mA Q ex = Longitudinal Bunch Center Emittance Growth Rate f HOM [MHz]")
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Emittance growth - chopping mschuh@cern.ch3 rd SPL Collaboration Meeting 16 f HOM = f cml ± 1MHz I b = 40 ± 1.2mA Q ex = 10 5 11.11.09 Longitudinal Bunch Center Emittance Growth Rate f HOM [MHz]
![Emittance growth - chopping rd SPL Collaboration Meeting 16 f HOM = f cml ± 1MHz I b = 40 ± 1.2mA Q ex = Longitudinal Bunch Center Emittance Growth Rate f HOM [MHz]](http://images.slideplayer.com/32/10064703/slides/slide_16.jpg "Emittance growth - chopping rd SPL Collaboration Meeting 16 f HOM = f cml ± 1MHz I b = 40 ± 1.2mA Q ex = Longitudinal Bunch Center Emittance Growth Rate f HOM [MHz]")
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Effect Of Different Parameters 17 ParameterLONGTRANS Frequency Spread ➘➘ Charge Scatter ➚➙ Input Phase Space ➙➙ I∙R/Q ➚➚ Machine Lines ➚ (no op.) ➚ Chopping ➚ (critical) ➚ Klystron Errors ➙ (minor growth) - Cav. Alignment - ➙ (minor growth) Pulse Length ➙ (Q ex <10 6 ) mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Conclusions Tools developed to simulate influence of HOMs Simulations show HOM damping seeming to be necessary in order to provide a high brilliance beam! Chopping is a critical issue in the longitudinal plane Q ex <10 7 (in case of chopping Q ex <10 5 ) The limit of Q ex based on the presented results: Q ex <10 7 (in case of chopping Q ex <10 5 ) 18 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Outlook Open beam dynamic issues: Halo particles losses (activation issue) Interaction of several modes in one cavity e - in the SPL (used as recirculating e - linac) Can steel bellows provide enough damping? 19 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Thank You! 20 HOM Questions? mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Emittance Growth – 5/8 Chopping mschuh@cern.ch3 rd SPL Collaboration Meeting 21 f HOM = f cml ±1 MHz I b = 40 ± 12mA Longitudinal emittance growth rate 11.11.09 f HOM [MHz]
![Emittance Growth – 5/8 Chopping rd SPL Collaboration Meeting 21 f HOM = f cml ±1 MHz I b = 40 ± 12mA Longitudinal emittance growth rate f HOM [MHz]](http://images.slideplayer.com/32/10064703/slides/slide_21.jpg "Emittance Growth – 5/8 Chopping rd SPL Collaboration Meeting 21 f HOM = f cml ±1 MHz I b = 40 ± 12mA Longitudinal emittance growth rate f HOM [MHz]")
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Induced HOM Voltage – 5/8 chopping 22 mschuh@cern.ch3 rd SPL Collaboration Meeting β= 0.65 cavitiesβ= 1.0 cavities f HOM = 1321 ±1 MHz, I b =0.4A, Q ex = 10 7 11.11.09
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Tr. Emittance growth – chopping mschuh@cern.ch3 rd SPL Collaboration Meeting Chopping: 500/800 50/80 5/8 1/1 500/800 50/80 5/8 1/1 I b = 0.4A f HOM ≈ 1050MHz 11.11.09
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R/Q(β) maps mschuh@cern.ch3 rd SPL Collaboration Meeting Mono- pole Dipole 11.11.09
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Statistic: 1000 linacs 25 Influence of input beam and cavity to cavity frequency distribution mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Long. charge scatter 26 mschuh@cern.ch3 rd SPL Collaboration Meeting Bunch Center Emittance Growth Rate 11.11.09
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Long. Machine Line 27 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Long. Klystron 28 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Long. Pulse length 29 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Long. Chopping 30 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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TR. charge scatter 31 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Tr. Frequency scatter 32 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Tr. Machine line 33 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Tr. Max mode per cavity 34 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Tr. Pulse length 35 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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TR. alignment 36 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Beam HOM Interaction 37 Each bunch sees half of its self-induced voltage V b : Energy error caused by HOM: Iteration over linac: Monopole modes: mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Longitudinal Beam Dynamic 38 Particle velocity: β < 1 Energy error causes arrival time / phase error: Phase error causes a different energy gain in next cavity: mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Transverse Beam Dynamic Transfer Matrix between cavities Bunch induce an imaginary voltage: HOM kicks bunch/particle - momentum change: 39 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Observed Dipole Kick 40 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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HOM voltage distribution (const R/Q) 41 Dipole: Mono- pole: mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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HOM voltage distribution (R/Q ┴ ( β )) 42 mschuh@cern.ch3 rd SPL Collaboration Meeting R1 R2 Dipole mode – 1000 simulations: I b =0.4A, Q ex =10 7 11.11.09
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Cavity modeling 2d Superfish model 3d HFSS model half cavity length quarter rotation boundary conditions 43 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
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Preliminar Cavity geometry Cavitiy shapes at 704.4MHz (symmetrical): 44 Medium βHigh β 5 Cellsmidendmidend β0.6581.0 R arc [mm]186.4190.8 R iris [mm]45 64.670 l cell [mm]70 106.47103.07 A [mm]45.145.0677.576.89 B [mm]45.149.5677.574.45 a [mm]12.1412.1122.118.5 b [mm]15.7915.7435.124.9 https://twiki.cern.ch/twiki/bin/view/SPL/Cavitydesign mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
![Preliminar Cavity geometry Cavitiy shapes at 704.4MHz (symmetrical): 44 Medium βHigh β 5 Cellsmidendmidend β R arc [mm] R iris [mm] l cell [mm] A [mm] B [mm] a [mm] b [mm] rd SPL Collaboration Meeting](http://images.slideplayer.com/32/10064703/slides/slide_44.jpg "Preliminar Cavity geometry Cavitiy shapes at 704.4MHz (symmetrical): 44 Medium βHigh β 5 Cellsmidendmidend β R arc [mm] R iris [mm] l cell [mm] A [mm] B [mm] a [mm] b [mm] rd SPL Collaboration Meeting")
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Monopole Modes 45 † linac definition βModef [MHz]HFSS (R/Q)† [Ω]Superfish (R/Q)† [Ω] 0.65TM 010 4/5π703.711 0.65TM 010 π704.4318330 0.65TM 011 3/5π176534 0.65TM 010 4/5π177443 0.65TM 01 cuttoff2550 1TM 010 π704.4525562 1TM 011 4/5π13283736 1TM 011 π1332137135 1TM 021 20902521 1TM 01 cuttoff1639 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
![Monopole Modes 45 † linac definition βModef [MHz]HFSS (R/Q)† [Ω]Superfish (R/Q)† [Ω] 0.65TM 010 4/5π TM 010 π TM 011 3/5π TM 010 4/5π TM 01 cuttoff2550 1TM 010 π TM 011 4/5π TM 011 π TM TM 01 cuttoff1639 rd SPL Collaboration Meeting](http://images.slideplayer.com/32/10064703/slides/slide_45.jpg "Monopole Modes 45 † linac definition βModef [MHz]HFSS (R/Q)† [Ω]Superfish (R/Q)† [Ω] 0.65TM 010 4/5π TM 010 π TM 011 3/5π TM 010 4/5π TM 01 cuttoff2550 1TM 010 π TM 011 4/5π TM 011 π TM TM 01 cuttoff1639 rd SPL Collaboration Meeting")
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Dipole Modes 46 † linac definition βModef [MHz]HFSS (R/Q)† [Ω] 0.65TM 110 2/5π102019 0.65TM 110 3/5π102728 0.65TM 110 4/5π10336 0.65TE 111 1/5π127013 0.65TE 11 cuttoff1952 1TE 111 3/5π915.118 1TE 111 4/5π939.833 1TE 111 π966.413 1TM 110 3/5π101419 1TE 11 cuttoff1255 mschuh@cern.ch3 rd SPL Collaboration Meeting 11.11.09
![Dipole Modes 46 † linac definition βModef [MHz]HFSS (R/Q)† [Ω] 0.65TM 110 2/5π TM 110 3/5π TM 110 4/5π TE 111 1/5π TE 11 cuttoff1952 1TE 111 3/5π TE 111 4/5π TE 111 π TM 110 3/5π TE 11 cuttoff1255 rd SPL Collaboration Meeting](http://images.slideplayer.com/32/10064703/slides/slide_46.jpg "Dipole Modes 46 † linac definition βModef [MHz]HFSS (R/Q)† [Ω] 0.65TM 110 2/5π TM 110 3/5π TM 110 4/5π TE 111 1/5π TE 11 cuttoff1952 1TE 111 3/5π TE 111 4/5π TE 111 π TM 110 3/5π TE 11 cuttoff1255 rd SPL Collaboration Meeting")
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