ESS-Bilbao Initiative Workshop. Beam dynamics: Simulations of high power linacs

ESS Workshop

How Well Do Our Numerical
Simulations Predict the Beam
Performance in the Linacs We Build?
J. Stovall

April, 2009
Bilbao

ESS2009 Bilbao CERN/TERA

Are Accurate Simulations Important?
•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


Codes Do a Very Good Job Qualitatively
25
DTL-CCL Transition CCL-SCL Transition
1 0 L in a c s , a ll e r r o r s
Predicted beam loss in
20 + m is m a tc h

SNS warm linac with
Beam Loss (W)

P m in
errors
15 Pave
Pm ax

10

5

0
0 20 40 60 80 100 120 140 160 180 200
W (M e V )

Measured activation in
the SNS CCL
Measured Residual
activation @ 1ft after ~ 48h
1 W gives ~ 100 mRem/hr
at 1 ft after ~ 12 hrs

Galambos, SNS


Simulation Codes Agree at Few % Level
UNILAC RMS Beam Size
SNS DTL-1 99% Emittance
Profiles 4 Codes
Profiles 5 Codes
0.40
0.38
0.36
3% εt
0.34
εn,99% (πcm-mrad)

0.32
0.30
0.28
0.26
0.24
0.22
0.20
0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14
β

Groening, GSI


Codes Differ in the Details
Radial Distribution at Tank 1 Exit
6.0
10 8
5
4
3
1M particle
2
2
5.0
10 8
5
ParTrans
4
3
2
2
IMPACT
104.0
8
LINAC
5
4
3
2
2
PARMELA
I (nAmp)

103.0
8
PARMILA
5
4
3
2
2
102.0
8
5
4
3
2
2
101.0
8
5
4
3
2
2
100.0
7
11%
5
4
3
2
2
10-1.0
0 1 2 3 4 5 6 7 8
Normalized Beam Radius (σ)

Is This the Right Question?
•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

The Codes
•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
•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

Simulations Can Predict More than
the Diagnostics Can Appreciate
= 35 = 60 = 90
o o o

Experiment
Int / Int_max [%]
0–5
5 – 10
10 – 20

DYNAMION
20 – 40
40 -100

PARMILA
UNILAC, Final
Distributions (Horizontal)

• core: good agreement (ex. 35°)
TraceWin

• 90°: quot;wingsquot; seen in exp. & sims
• deviations at lowest densities
LORASR

Groening, GSI


One-to-One RFQ Simulation:~1 B Particles
• 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 10 10
8 1M 8 10M 8 100M
6 6 6
4 4 4
∆W/W (%)

∆W/W (%)

∆W/W (%)
2 2 2
0 0 0
-2 -2 -2
-4 -4 -4
-6 -6 -6
-8 -8 -8
-10 -10 -10
-100 0 100 -100 0 100 -100 0 100
∆φ (deg) ∆φ (deg) ∆φ (deg)

Phase space plots
for 865 M protons
after 30 cells in the
RFQ.
Mustapha, ANL


Even 1B Particles Yield a Poor Representation
of the Details

TRACK, 1B particle SNS measurement in
Simulation of an RFQ MEBT Jeon, SNS
Mustapha, ANL


SNS MEBT “Round Beam” Study

Jeon, SNS


The Roll of Codes in Machine Tuning
•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


Model-Based Tuning at SNS
•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'care what the core is
t
doing


SNS Warm-Linac Tuning
•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
•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 Codes
Beam optics codes Beam dynamics codes
(example: Trace-3D) (example: TRACK, IMPACT)
Matrix based, usually first order Particle tracking, all orders included
Hard-edge field approximation 3D fields including realistic fringe fields
Space charge forces approximated Solving Poisson equation at every step
Actual particles distribution: core, halo …
Beam envelopes and emittances
Slower, Good for detailed studies
Fast, Good for preliminary studies
including errors and beam loss
Simplex optimization: Limited number
Larger scale optimization possible
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 …
Mustapha, ANL


ESS-Bilbao Initiative Workshop. Beam dynamics: Simulations of high power linacs

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