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 alignment quadrupole gradient klystron field amplitude and phase gap 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.

: δ x ) 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 DTL 2004

1000 runs

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 10 6 runs) particles (5000 – 250 to 400 CPU hours – Minimal loss: 1 ppm

Space charge routines

Space charge routines comparison

Example: 1 run with 1.5 mm x displacement of the 1 st quad with PICNIR & PICNIC DTL 2004 PICNIR (2d) PICNIC (3d) 2d vs 3d disagreement can be very large Not understood PICNIR (2d) PICNIC (3d)

Space charge routines disagreement

• large for large emittance growth • if X ≠ Y (our case) • increases with beam current • much more pronounced for FFDD vs FODO • for transverse phenomenon Agreement for longitudinal errors (unexplained)  Use 3d PICNIC with optimized mesh size

Optimization of mesh size

Gausup Mismatch beam (40% in x/y/z) at DTL input to generate large emittance growth 3d (PICNIC) 2d (PICNIR)

7x7 mesh size through DTL

Gausup 3d (PICNIC) Matched beam through DTL: validation of mesh size 2d (PICNIR)

DTL with all errors

7x7 mesh statistically compatible with high resolution mesh & keeps calculation time reasonable

Sensitivities to longitudinal errors

Error type Max error amplitude (mm or deg)

Longitudinal errors  E klys /E klys = ± 1%  φ klys = ±1deg  E gap /E gap = ± 1% DTL 2005

<



ε x / ε x > ± rms (%)

0.0 ± 0.5

<



ε y / ε y > ± rms (%)

0.0 ± 0.6

Gaussian distribution, 50 kpart, 1000 runs

<



ε z / ε z > ± rms (%)

0.5 ± 0.7

Very little effect for all 3 longitudinal errors combined

Sensitivities to transverse errors

Error type Max error amplitude (mm or deg) ±0.1 mm

DTL 2005

<



ε x / ε x > ± rms (%) proba (%) 1.0 ± 0.8 <



ε y / ε y > ± rms (%) proba (%) 0.1 ± 0.1 <



ε z / ε z > ± rms (%) proba (%) 0.7 ± 0.5 Displ x

Rota x (pitch) ±0.5 deg

<1% : 60 <5% : 100

0.01 ± 0.01

<1% : 100 <5% : 100

1E-3±3E-3

<1% : 76 <5% : 100

0.01 ± 0.01 <1% : 100 <5% : 100

0.8 ± 0.6

<1% : 100 <5% : 100

0.7 ± 0.6

<1% : 100 <5% : 100

0.02 ± 0.02 Rota z (roll) ±0.2 deg



G/G ±0.5% <1% : 76 <5% : 100 0.1 ± 0.2 <1% : 77 <5% : 100 0.1 ± 0.3

<1% : 100 <5% : 100 0.02 ± 0.07 <1% : 100 <5% : 100 <1% : 100 <5% : 100

Gaussian distribution, 50 kpart, 1000 runs

<1% : 100 <5% : 100 Some emittance growth No loss Energy jitter: a few 10-4 Phase jitter: a few 10 -4

Longitudinal rotation (roll)

DTL 2005 • Emittance growth similar in x & y (coupling) • Emittance growth quadratic with roll angle

Confirmed by theoretical calculations

• No longitudinal emittance growth

Effect of input distribution

Design & Distribution <



ε x / ε x > ± rms (%) proba (%) 2.0 ± 1.0 2005 Gaussian <1% : 13 <5% : 99 2005 KV 1.5 ± 1.0

<1% : 35 <5% : 100 <



ε y / ε y > ± rms (%) proba (%)

DTL 2005

<



ε z / ε z > ± rms (%) proba (%) RMS x (mm) & RMS x’ (mrad) RMS y (mm) & RMS y’ (mrad) 1.9 ± 1.0

<1% : 15 <5% : 99 1.5 ± 0.8

<1% : 28 <5% : 100 0.9

& 1.0

1.5 ± 1.0

1.1 ± 0.7

<1% : 37 <5% : 100 <1% : 57 <5% : 100 0.9

& 1.1

Gaussian distribution, 50 kpart, 1000 runs

1.1

& 0.8

1.1

& 0.9

Losses Loss < 2E-5 Loss < 2E-5 Simple shift (30-50%), no broadening

Effect of input distribution: transverse errors

DTL 2005 DTL 2005

Global effect with high statistics: transverse & longitudinal errors

10 6 particles, 4291 runs, Gaussian input, 250 to 400 CPU hours for each run Design & errors <



ε x / ε x > ± rms (%) proba (%) 2.0 ± 1.0 2005

Trans.

<1% : 13.8

<5% : 98.7

2.0 ± 1.2 2005

Trans.+ longi.

<1% : 20.4

<5% : 98.5

<



ε y / ε y > ± rms (%) proba (%) 2.0 ± 1.0 <1% : 14.2

<5% : 98.6

2.0 ± 1.2 <1% : 20.3

<5% : 98.1

<



ε z / ε z > ± rms (%) proba (%) 1.5 ± 0.8 <1% : 26.5

<5% : 99.9

1.9 ± 1.1 <1% : 20.1

<5% : 99.1



E ± rms (keV) 56.6 ± 0.4



φ ± rms (deg) Losses 3.11 ± 0.01 Loss < 1E-6 56.5 ± 2.6 3.13 ± 0.15

Loss < 1E-6

δ x/y = ±0.1 mm Φ x/y = ± 0.5 deg Φ z = ± 0.2 deg  G/G = ±0.5% and  φ/φ=±1 deg  E/E klystron = ±1%  E/E gap = ±1%

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: δ x,y = ±0.1 mm longitudinal rotations: Φ x,y = ±0.5 deg transverse rotations: Φ z = ±0.2 deg gradient:  G/G = ±0.5% • accelerating field: klystron field amplitude:  E klys /E klys klystron field phase:  φ klys = ±1deg gap field amplitude:  E gap /E gap = = ±1% ±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