Marcel Schuh CERN-BE-RF-LR CH-1211 Genève 23, Switzerland 3rd SPL Collaboration Meeting at CERN on November 11-13, 2009 Higher Order Modes In The SPL, Transverse And Longitudinal Effects

Outline HOM Bunch Tracking Simulation Code Simulation input parameters Simulation results Chopping Conclusions & Outlook rd SPL Collaboration Meeting

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 rd SPL Collaboration Meeting

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 rd SPL Collaboration Meeting

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. position [mm]00.3trans Tr. momentum [mrad]00.3trans Basic beam settings used in all simulations: rd SPL Collaboration Meeting

HOM Parameter  Compare phase space (ε) of one pulse ( 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) * linac def. rd SPL Collaboration Meeting

Longitudinal - General Case 7 rd SPL Collaboration Meeting Longitudinal Bunch Center Emittance Growth Rate σ I = 3% σ f = 1MHz

Transversal - General Case 8 rd SPL Collaboration Meeting σ I = 3% σ f = 1MHz Transversal Bunch Center Emittance Growth Rate

Chopping Modes 9 rd SPL Collaboration Meeting New machine lines (created by chopping): N ci /N cb : x/8 : f mc1 = MHz y/80 : f mc1 = MHz z/800 :f mc1 = MHz 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

Effect Of Chopping Analytically (Longitudinal) 10 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

5/8 Chopping 11 rd SPL Collaboration Meeting 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]

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]

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]

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]

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]

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 ) rd SPL Collaboration Meeting

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 rd SPL Collaboration Meeting

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 rd SPL Collaboration Meeting

Thank You! 20 HOM Questions? rd SPL Collaboration Meeting

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]

Induced HOM Voltage – 5/8 chopping 22 rd SPL Collaboration Meeting β= 0.65 cavitiesβ= 1.0 cavities f HOM = 1321 ±1 MHz, I b =0.4A, Q ex =

Tr. Emittance growth – chopping 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

R/Q(β) maps rd SPL Collaboration Meeting Mono- pole Dipole

Statistic: 1000 linacs 25 Influence of input beam and cavity to cavity frequency distribution rd SPL Collaboration Meeting

Long. charge scatter 26 rd SPL Collaboration Meeting Bunch Center Emittance Growth Rate

Long. Machine Line 27 rd SPL Collaboration Meeting

Long. Klystron 28 rd SPL Collaboration Meeting

Long. Pulse length 29 rd SPL Collaboration Meeting

Long. Chopping 30 rd SPL Collaboration Meeting

TR. charge scatter 31 rd SPL Collaboration Meeting

Tr. Frequency scatter 32 rd SPL Collaboration Meeting

Tr. Machine line 33 rd SPL Collaboration Meeting

Tr. Max mode per cavity 34 rd SPL Collaboration Meeting

Tr. Pulse length 35 rd SPL Collaboration Meeting

TR. alignment 36 rd SPL Collaboration Meeting

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: rd SPL Collaboration Meeting

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: rd SPL Collaboration Meeting

Transverse Beam Dynamic Transfer Matrix between cavities Bunch induce an imaginary voltage: HOM kicks bunch/particle - momentum change: 39 rd SPL Collaboration Meeting

Observed Dipole Kick 40 rd SPL Collaboration Meeting

HOM voltage distribution (const R/Q) 41 Dipole: Mono- pole: rd SPL Collaboration Meeting

HOM voltage distribution (R/Q ┴ ( β )) 42 rd SPL Collaboration Meeting R1 R2 Dipole mode – 1000 simulations: I b =0.4A, Q ex =

Cavity modeling 2d Superfish model 3d HFSS model half cavity length quarter rotation boundary conditions 43 rd SPL Collaboration Meeting

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

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

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