ESS Workshop

How Well Do Our Numerical Simulations Predict the Beam

Performance in the Linacs We Build?

J. Stovall

CERN/TERA

April, 2009 Bilbao

ESS2009 Bilbao

Are Accurate Simulations Important?

CERN/TERA

•We rely on them initially to validate/certify the machine design

•Linac•Verify the design details•Bracket allowable errors•Identify expected sources of beam loss•Developing commissioning strategies

•Beam properties on target•Energy, emittance & halo at full current

•The codes themselves must be “certified” at some level

ESS2009 Bilbao

CERN/TERA

Codes Do a Very Good Job Qualitatively

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 1 8 0 2 0 0W ( M e V )

0

5

1 0

1 5

2 0

2 5B

eam

Los

s (W

)

P m inP a v eP m a x

1 0 L in a c s , a l l e r r o r s+ m is m a t c h

DTL-CCL Transition CCL-SCL Transition

Measured Residual activation @ 1ft after ~ 48h

1 W gives ~ 100 mRem/hr at 1 ft after ~ 12 hrs

Predicted beam loss in SNS warm linac with errors

Measured activation in the SNS CCL

ESS2009 Bilbao

Galambos, SNS

CERN/TERA

Simulation Codes Agree at Few % Level

0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14β

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

ε n,9

9% (π

cm-m

rad) 3% εt

ESS2009 Bilbao

UNILAC RMS Beam Size Profiles 4 CodesSNS DTL-1 99% Emittance

Profiles 5 Codes

Groening, GSI

Codes Differ in the Details

CERN/TERA

0 1 2 3 4 5 6 7 8Normalized Beam Radius (σ)

10-1.0

100.0

101.0

102.0

103.0

104.0

105.0

106.0

24

24

24

24

24

24

24

I (nA

mp)

2357

2358

2358

2358

2358

2358

2358

1M particleParTransIMPACTLINACPARMELAPARMILA

11%

ESS2009 Bilbao

Radial Distribution at Tank 1 Exit

CERN/TERA

•Some put far too much emphasis on how well our codes predict beam behave•Machines are never built exactly like our computer models say they should be

•There are always unknown errors introduced during fabrication & assembly

•We never know the exact initial conditions•Beam or linac parameters

•We can come close, and the codes will give a good indication of what the beam will look like•Equally important, however, is to to show how the beam will change with various machine parameters•Simulations can predict much more than the diagnostics can appreciate

Is This the Right Question?

ESS2009 Bilbao

The Codes

CERN/TERAESS2009 Bilbao

•Beam Optics codes like Trace3D•Transform envelope with analytical space charge•Do a very 1st order good job•Used as basis for most tuning algorithms

•PIC Dynamics codes•Parmila, Tracewin, Linac, Dynamion•106 particles with 3-D space charge•Matrix based•Do a good job on core simulations•Agree at few% level

•Integrating dynamics Codes•Impact, Track, Tstep (Parmela)•Can now integrate ~109 particles through field maps

Code Limitations

CERN/TERAESS2009 Bilbao

•The real problem is •An accurate 6-D description of the initial beam particle distribution•An accurate description of the fields

•Magnets and their alignment can be accurately mapped•The axial rf field distribution in RFQ’s is not measurable•The rf field distribution in DTLs & CCLs are probably reasonably well known from cavity calculations and bead pulls•The rf field distribution in SC cavities at operating temperature is anyone’s guess•Rf phase & amplitude errors are transient

• core: good agreement (ex. 35°)

• 90°: "wings" seen in exp. & sims

• deviations at lowest densities

Int / Int_max [%]

0 – 5

5 – 10

10 – 20

20 – 40

40 -100

Simulations Can Predict More thanthe Diagnostics Can Appreciate

�o = 35� �o = 60�

Experim

ent

�o = 90�

DY

NA

MIO

NPA

RM

ILATraceW

inLO

RA

SR

ESS2009 Bilbao CERN/TERA

Groening, GSI

UNILAC, Final Distributions (Horizontal)

One-to-One RFQ Simulation:~1 B Particles

CERN/TERAESS2009 Bilbao

• Benefits of simulating a large number of particles: actual number if possible- Suppress noise from the PIC method: enough particles/cell- More detailed simulation: better characterization of the beam halo

-10-8-6-4-202468

10

-100 0 100∆φ (deg)

∆W/W

(%)

1M

-10-8-6-4-202468

10

-100 0 100∆φ (deg)

∆W/W

(%)

10M

-10-8-6-4-202468

10

-100 0 100∆φ (deg)

∆W/W

(%)

100M

Phase space plotsfor 865 M protonsafter 30 cells in theRFQ.

Mustapha, ANL

Even 1B Particles Yield a Poor Representation of the Details

CERN/TERAESS2009 Bilbao

TRACK, 1B particle Simulation of an RFQ

SNS measurement in MEBTMustapha, ANL Jeon, SNS

SNS MEBT “Round Beam” Study

CERN/TERAESS2009 Bilbao

Jeon, SNS

The Roll of Codes in Machine Tuning

CERN/TERAESS2009 Bilbao

•Steering strategies, model-based vs. empirical• Matching strategies, model-based vs. empirical• Combined with beam measurements

•profiles & halo•emittance•beam loss•longitudinal measurements

•Code limitations•Diagnostics limitations•SNS has the most relevant experience

CERN/TERA

•The simulations do a good job on the core, but•The particles we are concerned with are in the halo; one part in 1E6•We are unable to measure beam properties at that level •We are lacking input distributions for simulations anywhere near that level

•We have pretty good results for model-based tuning, but of course that is exercising only the core•Particles destined to get lost don't care what the core is doing

Model-Based Tuning at SNS

ESS2009 Bilbao

SNS Warm-Linac Tuning

CERN/TERAESS2009 Bilbao

•In practice we set the warm linac quads up to the design values

•PMQs in the DTL•EMQs in the CCL•With these values, the measured Twiss parameters of the beam core are within ~ 10% of expected •This is about as good as any matching can do •Or as good as we believe the measurements

•Then at high beam intensity we adjust quad strengths manually to reduce beam loss down the linac.

•These adjustments are typically < 1% “tweaks”

SC Linac & HEBT Tuning

CERN/TERAESS2009 Bilbao

•In the superconducting linac we set up the quads to the design values

• The laser profile measurements show that the beam is poorly matched but• They are too slow to be used in iteratively with quad adjustments

•In the HEBT we typically see a large mismatch•It is easily corrected using a model based technique •But the resulting losses at ring injection are higher after matching•Since we inevitably run out of time we roll back to the unmatched setup

•Beam loss is minimized manually – monkey tuning.

Beam Tracking vs. Beam Dynamics CodesBeam optics codes

(example: Trace-3D)� Matrix based, usually first order � Hard-edge field approximation � Space charge forces approximated� Beam envelopes and emittances� Fast, Good for preliminary studies� Simplex optimization: Limited number

of fit parameters

� It is more appropriate to use beam dynamics codes for optimization:

– More realistic representation of the beam especially for high-intensity and multiple charge state beams (3D external fields and accurate SC calculation).

– Include quantities not available from beam optics codes: minimize beam halo formation and beam loss.

– Now possible with faster PC’s and parallel computer clusters …

Beam dynamics codes(example: TRACK, IMPACT)

� Particle tracking, all orders included� 3D fields including realistic fringe fields� Solving Poisson equation at every step� Actual particles distribution: core, halo …� Slower, Good for detailed studies

including errors and beam loss � Larger scale optimization possible

Mustapha, ANL

ESS2009 Bilbao CERN/TERA