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