DTL Beam Dynamics M Comunian Outline History of
DTL Beam Dynamics M. Comunian
Outline • • • History of DTL layout. Requirements on ESS DTL Beam Dynamics Design. Method used for Errors Study. Results on Errors Study.
History of DTL design • 2011: First study with J. Stovall and lattice comparison: 3 -50 Me. V, 70 m. A • 2012: Full optimization of DTL by using Gen. DTL • 2013: New DTL parameters: 3. 6 Me. V - 80 Me. V, 62. 5 m. A, 5 tanks. • 2014: ESS DTL Frozen Layout (V 84) and full errors study Design by Gen. DTL • 2015: ESS DTL CDR Design by Excel
FODO FFDD FDO 2011 LATTICE DESIGN FFODDO FFDDO FD Particles density plot for different focusing scheme along the DTL
DTL Main Figures of Merit Sync. Phase [deg] TTF 1. 00 0. 95 0. 90 0. 85 0. 80 0. 75 0. 70 1 51 101 151 -25 -30 -35 -40 51 101 Cell 151 -45 Emax [Kilp. ] ZTT/1. 25 [MΩ/m] Emax [Kilp. ] 65 55 45 35 25 15 0 50 100 Cell 150 1. 6 1. 5 1. 4 1. 3 1. 2 1. 1 1. 0 Rb 1. 3 1. 2 1. 1 E 0 = 3. 00 3. 16 3. 07 3. 04 3. 13 1. 0 0. 9 1 51 101 Cell 151 Bore Radius [cm] 1 Phase matching to SCL
DTL Layout Parameter / Tank 1 2 3 4 5 Cells per cavity 61 34 29 26 23 Accelerating field [MV/m] 3. 00 3. 16 3. 07 3. 04 3. 13 Maximum surface field [Kilp. ] 1. 55 -35 to -25. 5 Total power per cavity* [KW] 2192 2191 2196 2189 2195 Power on copper* [KW] 870 862 872 901 952 Quadrupole length [mm] 50 80 80 Bore Radius [mm] 10 11 11 12 12 Number of modules 4 4 4 Length [m] 7. 62 7. 09 7. 58 7. 85 7. 69 Beam output energy [Me. V] 21. 29 39. 11 56. 81 73. 83 89. 91 Synchronous phase [deg] * Total power = 1. 25 × Power on copper + Beam Power < 2. 2 MW. ** MDTfish calculation.
DTL Beam Dynamics parameters Parameter RMS Transverse norm. emittance [mmmrad] RMS Longitudinal emittance [mmmrad / Me. Vdeg] Value 0. 28 0. 39 / 0. 155 Input Current [m. A] 62. 5 Input energy [Me. V] 3. 62134 Duty Cycle [%] 4
Focusing Scheme FODO Max Gradient ~61. 6 T/m Intertank Space equal to 1 βλ. Intertank 1/2 2/3 3/4 4/5 Length [mm] 178. 30 238. 37 283. 48 319. 16
Transverse Acceptance
Ratio Bore/RMS beam size
Longitudinal Acceptance
Longitudinal Acceptance
RMS Emittance in the DTL (Uniform dist. As input) 0. 3798 (+6. 6%) 0. 3917 0. 2798 0. 2788 (+4. 9%) 0. 2936 (+5. 1%) 0. 2931
DTL Input distribution effects Gauss MEBT Uniform All distribution with MEBT (2014. V 0) Twiss parameters
DTL Sensitivity to input beam • • • Mismatch. Emittance change. Beam off-center. Current value. All the runs are made with a Gaussian input dist. cut at 3
Effects of Alfa. Z The limit of 10% emittance increase, respect the input emittance, is obtained with Alfa Z outside the range of 0 to 0. 9. All the runs are without losses. The matched value for Alfa Z is around 0. 4, all the other Twiss parameters are at the nominal values
Effects of Beta. Z The limit of 10% emittance increase, respect the input emittance, is obtained with Beta Z outside the range of 0. 3 to 0. 6 mm/Pi. mrad. All the runs are without losses. The matched value for Beta Z is around 0. 43 mm/Pi. mrad, all the other Twiss parameters are at the nominal values.
Mismatch X, Y, Z with gaussian beam input In the Figure the limit of 10% emittance increase, respect the input emittance, is obtained with around 10% of Trace. Win mismatch, i. e. with an equivalent value of (35, 50, 22)% Wangler mismatch, the runs with Trace. Win mismatch of more than 27% are with losses.
Emittance change X and Y The input emittance on both planes X, Y is increased. The 10% of output emittance increase, respect the input emittance, is reached for X, Y input emittance below of 0. 26 mmmrad. All the runs are without losses.
Final Emittance vs input emittance Very linear response of output emittance respect to the input emittance.
Single emittance change X The most sensible parameter is the change on a single emittance, due to the emittance exchange phenomena. The 10% emittance increase, respect the input emittance, is reached for X input emittance outside the range of 0. 27 – 0. 29 mmmrad. All the runs are without losses. The output <-> input emittance behavior is very linear.
Input Beam Displacement X; Y The limit of 10% emittance increase, respect the input emittance, is obtained with around 0. 3 mm of beam displacement on X and 0. 2 mm on Y, all the runs are without losses.
Input Beam Current The limit of 10% emittance increase, respect to the input emittance, is obtained with around 75 m. A of beam current, all the 1000 runs are without losses.
Errors study strategy DTL beam parameters Parameter Input Tran. Norm. RMS Emit. Input Long. Norm. RMS Emit. Input current - DTL definitions Value 0. 28 mmmrad 0. 39 mmmrad (=0. 15 Me. Vdeg) 62. 5 m. A Parameter Emit. Growth definition Maximum emittance growth Losses (above 30 Me. V) Value Δε=(εout-εin)/εin Δε <10% on top on the emittance evolution without errors < 1 W/m Gaussian input beam distribution cut at 3σ (overestimate the beam sensitivity to errors) Each error studied individually 50 000 macroparticles, 500 DTLs generated for each single error Final check with all errors applied and 500000 macroparticles DTL input is considered at 20 mm before the input flange 3 steeres/tank/plane (16 m. T*m). 3 BPM/tank/plane with a resolution of +/- 0. 1 mm. The errors examined, as single error and for all the planes, are: - Input beam: Emittance change, Current jitter, Position and divergence, Mismatch, Energy jitter, current range - PMQ: Position with and without Steeres, Rotation, Gradient, Ageing (PMQ gradient degradation), Multipoles and dipoles. - DTL RF: E 0 Field flatness cell by cell, Sync. Phase, i. e. DT relative position - DTL tanks: Klystron RF phase and amplitude, Relative position - Global: All the input beam errors, All PMQ, RF and tanks errors Observables: - final emittance: transverse/longitudinal RMS emittance is 0. 328/0. 441 mmmrad, i. e. +17%/+13%. The transverse acceptance of the DTL is 13. 4 mmmrad - presence of losses
Error study results: input beam RMS emittance growth as function of MEBT mismatch on the 3 planes. RMS emittance growth as function of Beam displacement X. RMS emittance growth as function of input energy The RMS emittance growth as function of the Input RMS longitudinal emittance. Lund - 2014_12_02 Audit
Error study results: PMQ RMS emittance growth as function of PMQ rotation along the beam axis roll angle. RMS emittance growth as function of PMQ position X, Y RMS emittance growth as function of the PMQ gradient RMS output emittance Ex, due to the multipoles components (dipoles included). Lund - 2014_12_02 Audit
Error study results: RF parameters RMS emittance increase as function of the phase change [deg]. RMS emittance increase as function of the E 0 change [%]. RMS emittance increase as function of the E 0 change Klystron by Klystron RMS emittance increase as function of the tank by tank position Lund - 2014_12_02 Audit
E 0 change cell by cell RMS emittance increase as function of the E 0 change [%]. CERN Linac 4 measured E 0 Fields
PMQ Positions effects RMS emittance growth as function of PMQ position X, Y, without steerers CERN Linac 4 measured Alignment
Emittance increase as published on Linac 2014
DTL tolerances Beam input Errors Values X, Y, Z RMS Emittance variation +15 % Current jitter Position and divergence X, Y, Z Mismatch Energy Jitter ± 10% ± 0. 2 mm; ± 1 mrad 10 %, ± 1% Effect of steerers - emittance growth reduced of 75% with an errors on the PMQ of +/-0. 1 mm - No losses without steeres ΔX-ΔY < +/-0. 08 mm on PMQ position - No losses with steeres ΔX-ΔY < +/-0. 18 mm on PMQ position. Lund - 2014_12_02 Audit DTL Errors PMQ position PMQ rotation Name δx, δy φx, φy, φz PMQ gradient ΔG/G PMQ ageing PMQ multipole contents ΔG/G E 0 field flatness ΔE 0/E 0 Synchronous phase Klystron RF phase and amplitude Tank to tank position BPM precision δφsynch Max Steeres strength Sx, Sy ΔEkly/Ekly; φkly Xtank, Ytank Xbpm, Ybpm Values ± 0. 1 mm, ± 1 deg, ± 0. 2 deg, ± 1 %, -5 %, ± 1 %, ± 2 %, ± 2 deg, ± 1 %, ± 2 deg, ± 0. 1 mm, ± 16 m. T*m
Conclusion • The beam dynamics is fully defined. • The error study performed permits to fully define the DTL tolerances. • These tolerances have been confirmed by end to end simulation done so far. • This set of tolerances for the DTL is less stringent respect to what is possible to get with real construction.
Backup Slides
Global Errors No steerers With steerers Half Errors Input beam: ± 0. 2 mm x, y; ± 1 mrad x, y; -0. 02 Me. V; -8% emittance x, y, z; +20% mismatch x, y, z; +4 m. A Quad errors: ± 0. 2 mm; ± 2°x, y; ± 0. 4°z; ± 2%Gradient Cav errors: ± 4% amplitude; ± 2° phase Tank to Tank: ± 0. 2 mm; Klystrons: ± 2% amplitude ± 2° phase 100 000 Macro Particles Gaussian (3 ) dist. 1000 statistical runs.
Global errors Longitudinal effects Input beam: ± 0. 2 mm x, y; ± 1 mrad x, y; -0. 02 Me. V; -8% emittance x, y, z; +20% mismatch x, y, z; +4 m. A Quad errors: ± 0. 2 mm; ± 2°x, y; ± 0. 4°z; ± 2%Gradient Cav errors: ± 4% amplitude; ± 2° phase Tank to Tank: ± 0. 2 mm; Klystrons: ± 2% amplitude ± 2° phase 100 000 Macro Particles Gaussian (3 ) dist. 1000 statistical runs.
Global errors Transverse effects Input beam: ± 0. 2 mm x, y; ± 1 mrad x, y; -0. 02 Me. V; -8% emittance x, y, z; +20% mismatch x, y, z; +4 m. A Quad errors: ± 0. 2 mm; ± 2°x, y; ± 0. 4°z; ± 2%Gradient Cav errors: ± 4% amplitude; ± 2° phase Tank to Tank: ± 0. 2 mm; Klystrons: ± 2% amplitude ± 2° phase 100 000 Macro Particles Gaussian (3 ) dist. 1000 statistical runs.
Global errors Losses Input beam: ± 0. 2 mm x, y; ± 1 mrad x, y; -0. 02 Me. V; -8% emittance x, y, z; +20% mismatch x, y, z; +4 m. A Quad errors: ± 0. 2 mm; ± 2°x, y; ± 0. 4°z; ± 2%Gradient Cav errors: ± 4% amplitude; ± 2° phase Tank to Tank: ± 0. 2 mm; Klystrons: ± 2% amplitude ± 2° phase 100 000 Macro Particles Gaussian (3 ) dist. 1000 statistical runs.
Half errors Transverse effects +20% +19% Input beam: ± 0. 1 mm x, y; ± 0. 5 mrad x, y; -0. 01 Me. V; -4% emittance x, y, z; +10% mismatch x, y, z; +2 m. A Quad errors: ± 0. 1 mm; ± 1°x, y; ± 0. 2°z; ± 1%Gradient Cav errors: ± 2% amplitude; ± 1° phase Tank to Tank: ± 0. 1 mm; Klystrons: ± 1% amplitude ± 1° phase 100 000 Macro Particles Gaussian (3 ) dist. 1000 statistical runs.
Half errors Losses Input beam: ± 0. 1 mm x, y; ± 0. 5 mrad x, y; -0. 01 Me. V; -4% emittance x, y, z; +10% mismatch x, y, z; +2 m. A Quad errors: ± 0. 1 mm; ± 1°x, y; ± 0. 2°z; ± 1%Gradient Cav errors: ± 2% amplitude; ± 1° phase Tank to Tank: ± 0. 1 mm; Klystrons: ± 1% amplitude ± 1° phase 100 000 Macro Particles Gaussian (3 ) dist. 1000 statistical runs.
Emittance increase with half errors Input beam: ± 0. 1 mm x, y; ± 0. 5 mrad x, y; -0. 01 Me. V; -4% emittance x, y, z; +10% mismatch x, y, z; +2 m. A Quad errors: ± 0. 1 mm; ± 1°x, y; ± 0. 2°z; ± 1%Gradient Cav errors: ± 2% amplitude; ± 1° phase Tank to Tank: ± 0. 1 mm; Klystrons: ± 1% amplitude ± 1° phase 100 000 Macro Particles Gaussian (3 ) dist. 1000 statistical runs. Around 60% of the cases are below 20% of emittance growth
Steerers Tank 2 Tank 1 Tank 3 Tank 4 Tank 5 Fine tuning on the steerers position in order to maximize the average efficiency in both the planes (x, y), in figure is reported the position of steerers, BPM and of the empty tubes as function of the integral transverse phase advance, without current, along the DTL. The BPM resolution considered is +/- 0. 1 mm. The maximum strength of the steeres is 16 m. T*m. Element / Tank Steerer X [DT] Steerer Y [DT] BPM [DT] T 1 3 5 17 T 1 21 23 37 T 1 41 43 59 T 2 1 3 9 T 2 11 13 21 T 2 23 25 33 T 3 2 5 10 T 3 12 14 20 T 3 22 24 28 T 4 2 4 8 T 4 10 12 16 T 4 18 20 24 T 5 1 3 5 T 5 7 9 13 T 5 15 17 21
Half errors Losses with Steeres Lower losses of one ORDER of Magnitude Input beam: ± 0. 1 mm x, y; ± 0. 5 mrad x, y; -0. 01 Me. V; -4% emittance x, y, z; +10% mismatch x, y, z; +2 m. A Quad errors: ± 0. 1 mm; ± 1°x, y; ± 0. 2°z; ± 1%Gradient Cav errors: ± 2% amplitude; ± 1° phase Tank to Tank: ± 0. 1 mm; Klystrons: ± 1% amplitude ± 1° phase 100 000 Macro Particles Gaussian (3 ) dist. 1000 statistical runs. Using Steerers and BPM.
Emittance increase with Steerers Input beam: ± 0. 1 mm x, y; ± 0. 5 mrad x, y; -0. 01 Me. V; -4% emittance x, y, z; +10% mismatch x, y, z; +2 m. A Quad errors: ± 0. 1 mm; ± 1°x, y; ± 0. 2°z; ± 1%Gradient Cav errors: ± 2% amplitude; ± 1° phase Tank to Tank: ± 0. 1 mm; Klystrons: ± 1% amplitude ± 1° phase 100 000 Macro Particles Gaussian (3 ) dist. 1000 statistical runs. Using Steerers and BPM. About 70% of the cases are below 20% of emittance growth
90% cases with emittance growth below 20% Half errors case 0. 4 errors case Input beam: ± 0. 1 mm x, y; ± 0. 5 mrad x, y; -0. 01 Me. V; -4% emittance x, y, z; +10% mismatch x, y, z; +2 m. A Quad errors: ± 0. 1 mm; ± 1°x, y; ± 0. 2°z; ± 1%Gradient Cav errors: ± 2% amplitude; ± 1° phase Tank to Tank: ± 0. 1 mm; Klystrons: ± 1% amplitude ± 1° phase 100 000 Macro Particles Gaussian (3 ) dist. 1000 statistical runs. Using Steerers and BPM. Max power lost=10. 2 Watts; average=0. 02 Watts Input beam: ± 0. 08 mm x, y; ± 0. 4 mrad x, y; -0. 008 Me. V; -3. 2% emittance x, y, z; +8% mismatch x, y, z; +1. 6 m. A Quad errors: ± 0. 08 mm; ± 0. 8°x, y; ± 0. 16°z; ± 0. 8%Gradient Cav errors: ± 1. 6% amplitude; ± 0. 8° phase Tank to Tank: ± 0. 08 mm; Klystrons: ± 0. 8% amplitude ± 0. 8° phase 100 000 Macro Particles Gaussian (3 ) dist. 1000 statistical runs. Using Steerers and BPM. Max power lost=0 Watts
99% cases with emittance growth below 20% Half errors case 0. 3 errors case Input beam: ± 0. 1 mm x, y; ± 0. 5 mrad x, y; -0. 01 Me. V; -4% emittance x, y, z; +10% mismatch x, y, z; +2 m. A Quad errors: ± 0. 1 mm; ± 1°x, y; ± 0. 2°z; ± 1%Gradient Cav errors: ± 2% amplitude; ± 1° phase Tank to Tank: ± 0. 1 mm; Klystrons: ± 1% amplitude ± 1° phase 100 000 Macro Particles Gaussian (3 ) dist. 1000 statistical runs. Using Steerers and BPM. Max power lost=10. 2 Watts; average=0. 02 Watts Input beam: ± 0. 06 mm x, y; ± 0. 3 mrad x, y; -0. 006 Me. V; -2. 4% emittance x, y, z; +6% mismatch x, y, z; +1. 2 m. A Quad errors: ± 0. 06 mm; ± 0. 6°x, y; ± 0. 12°z; ± 0. 6%Gradient Cav errors: ± 1. 2% amplitude; ± 0. 6° phase Tank to Tank: ± 0. 06 mm; Klystrons: ± 0. 6% amplitude ± 0. 6° phase 100 000 Macro Particles Gaussian (3 ) dist. 1000 statistical runs. Using Steerers and BPM. Max power lost=0 Watts
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