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Code parameters optimization&
DTL Tank 1 error studies
Maud Baylac, Emmanuel Froidefond
Presented by JM De Conto
LPSC-Grenoble
HIPPI yearly meeting, Oxford, September, 2005
Overview
• Goal, recall TW inputs • Optimization of code parameters
• Nb runs• Nb calculations per βλ• Nb particles• Space charge routine:
• 2d vs 3d• Mesh size
• Error study• Individual sensitivity: longitudinal & transverse• Effect of input distribution• Global errors, loss• Set of tolerances
Goal
• For us: learn how to use TraceWin• Study sensitivity of DTL to quadrupole and field errors • Determine set of tolerances for tank 1 for
quadrupole alignmentquadrupole gradientklystron field amplitude and phasegap field amplitude
TraceWin inputs• Several inputs: evolutive DTL design • Input distribution: mainly type -32 (Gaussian) file
Worse case scenario &
Same for all studies• 2 types of simulations:
Sensitivity: one type of error at a time (e.g.: δx )
Global error effect: all types of errors at once
• Each error generated randomly & uniformly in [–max; +max] • For all cases, transport to the end of the DTL
Number of runs
• Study convergence with nb of runs
1000 runs
DTL 2004
Nb space charge calculations per βλ
Inactive on DTL cells
Default for DTL cells:
• was 1 space charge calc. per cell (ie: 20 calc. per betatron oscil.)
• modified to up to 3 calc. per cell (depending on cell length)
Number of particles• Most simulations use 50 kparticles (1000 runs)
– Fast calculation– Minimal loss: 20 ppm
• A few global error runs use 106 particles (5000 runs)– 250 to 400 CPU hours– Minimal loss: 1 ppm
Space charge routines
Space charge routines comparison
2d vs 3d disagreement can be very large
Not understood
Example: 1 run with 1.5 mm x displacement of the 1st quad with PICNIR & PICNIC
PICNIR (2d)
PICNIR (2d)
PICNIC (3d)
PICNIC (3d)
DTL 2004
• large for large emittance growth
• if X ≠ Y (our case)
• increases with beam current
• much more pronounced for FFDD vs FODO
• for transverse phenomenonAgreement for longitudinal errors (unexplained)
Space charge routines disagreement
Use 3d PICNICwith optimized mesh size
Optimization of mesh sizeGausup
3d (PICNIC)
2d (PICNIR)
Mismatch beam (40% in x/y/z)at DTL input to generate large emittance growth
7x7 mesh size through DTLGausup
3d (PICNIC)
2d (PICNIR)
Matched beam through DTL:validation of mesh size
DTL with all errors
7x7 mesh statistically compatible with high resolution mesh& keeps calculation time reasonable
Sensitivities to longitudinal errors
Gaussian distribution, 50 kpart, 1000 runs
Error type
Max error amplitude(mm or deg)
<εx / εx > ± rms (%)
< εy / εy > ± rms (%)
< εz / εz > ± rms (%)
Longitudinal errors
Eklys/Eklys = ± 1%
φklys = ±1degEgap/Egap = ± 1%
0.0 ± 0.5 0.0 ± 0.6 0.5 ± 0.7
Very little effect for all 3 longitudinal errors combined
DTL 2005
Sensitivities to transverse errors
Gaussian distribution, 50 kpart, 1000 runs
Error type
Max error amplitude
(mm or deg)
<εx / εx > ± rms (%)proba (%)
< εy / εy > ± rms (%)proba (%)
< εz / εz > ± rms (%)proba (%)
Displ x ±0.1 mm 1.0 ± 0.8
<1% : 60<5% : 100
0.1 ± 0.1
<1% : 100<5% : 100
0.7 ± 0.5
<1% : 76<5% : 100
Rota x(pitch)
±0.5 deg 0.01 ± 0.01
<1% : 100<5% : 100
1E-3±3E-3
<1% : 100<5% : 100
0.01 ± 0.01
<1% : 100<5% : 100
Rota z(roll)
±0.2 deg 0.8 ± 0.6
<1% : 76<5% : 100
0.7 ± 0.6
<1% : 77<5% : 100
0.02 ± 0.02
<1% : 100<5% : 100
G/G ±0.5% 0.1 ± 0.2
<1% : 100<5% : 100
0.1 ± 0.3
<1% : 100<5% : 100
0.02 ± 0.07
<1% : 100<5% : 100
Some emittance growth No lossEnergy jitter: a few 10-4 Phase jitter: a few 10-4
DTL 2005
Longitudinal rotation (roll)
• Emittance growth similar in x & y (coupling)• Emittance growth quadratic with roll angle
Confirmed by theoretical calculations
• No longitudinal emittance growth
DTL 2005
Effect of input distribution
Design &
Distribution
<εx / εx > ± rms (%)
proba (%)
< εy / εy > ± rms (%)proba (%)
< εz / εz > ± rms (%)proba (%)
RMS x (mm)&
RMS x’ (mrad)
RMS y (mm)&
RMS y’ (mrad)Losses
2005Gaussian
2.0 ± 1.0
<1% : 13<5% : 99
1.9 ± 1.0
<1% : 15<5% : 99
1.5 ± 0.8
<1% : 28<5% : 100
0.9&1.0
1.1&0.8
Loss < 2E-5
2005 KV
1.5 ± 1.0
<1% : 35<5% : 100
1.5 ± 1.0
<1% : 37<5% : 100
1.1 ± 0.7
<1% : 57<5% : 100
0.9&1.1
1.1&0.9
Loss < 2E-5
Gaussian distribution, 50 kpart, 1000 runs
Simple shift (30-50%), no broadening
DTL 2005
Effect of input distribution:transverse errors
DTL 2005 DTL 2005
Global effect with high statistics: transverse & longitudinal errors
and φ/φ=±1 deg E/Eklystron=±1%E/Egap=±1%
Design &errors
<εx / εx > ± rms (%)
proba (%)
< εy / εy > ± rms (%)proba (%)
< εz / εz > ± rms (%)proba (%)
E ± rms(keV)
φ± rms (deg)
Losses
2005Trans.
2.0 ± 1.0
<1% : 13.8<5% : 98.7
2.0 ± 1.0
<1% : 14.2<5% : 98.6
1.5 ± 0.8
<1% : 26.5<5% : 99.9
56.6 ± 0.4
3.11 ± 0.01 Loss < 1E-6
2005Trans.+longi.
2.0 ± 1.2
<1% : 20.4<5% : 98.5
2.0 ± 1.2
<1% : 20.3<5% : 98.1
1.9 ± 1.1
<1% : 20.1<5% : 99.1
56.5 ± 2.6
3.13 ± 0.15 Loss < 1E-6
106 particles, 4291 runs, Gaussian input, 250 to 400 CPU hours for each run
δx/y= ±0.1 mm
Φx/y = ± 0.5 deg
Φz = ± 0.2 deg
G/G = ±0.5%
Some broadening in longitudinal direction
Main trends of quadrupole alignment
• Transverse displacement (symmetric x/y ) transverse & longitudinal emit. growth 2005 design: ~ 1% for ±0.1 mm
• Transverse rotation (pitch & yaw):no effect
• Longitudinal rotation (roll): transverse emit. growth
2005 design: ~ 0.8% for ±0.2 deg• Emittance growth with 2005 design vs 2004 design:
slightly worse with errors on all tanks • Individual sensitivities roughly add up
DTL tank 1 tolerances
Tolerances agreed upon by DTL task force:• quadrupoles:
longitudinal displacements: δx,y = ±0.1 mmlongitudinal rotations: Φ x,y = ±0.5 deg transverse rotations: Φ z = ±0.2 deg
gradient: G/G = ±0.5%• accelerating field:
klystron field amplitude: Eklys/Eklys = ±1%
klystron field phase: φklys = ±1deg
gap field amplitude: Egap/Egap = ±1%
Conclusions• Sensitive parameters: transverse displacement & roll• Little effect due to longitudinal errors (longitudinal shift
cannot be tested with TW)• With present tolerance budget, beam quality sees little
degradation through DTL: Emittance growth x, y and z < 5% in 98% of runs Loss < 10-6 RMS width in x and y < 1.2 mm RMS width in x’ and y’ < 1.1 mrad
• Multipolar component contribution: waiting for TW debug
• Code benchmarking to validate results
Acknowledgements
• Didier URIOT (CEA/DSM) for discussions and multiple debugs
• Nicolas PICHOFF (CEA/DAM) for discussions regarding space charge calculations
• Edgar Sargsyan, Alessandra Lombardi and Frank Gerigk (CERN) for inputs and discussions
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