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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