L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
L. Groening, W. Barth, W. Bayer, G. Clemente, L. Dahl, P. Forck, P. Gerhard, I. Hofmann, G. Riehl, S. Yaramyshev,
GSI, Germany
D. Jeon, ORNL, U.S.A.
D. Uriot, CEA/Saclay, France
R. Tiede, University of Frankfurt, Germany
Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
• Introduction and set-up
• Data reduction
• Reconstruction of initial distribution
• Results of experiment and simulations
• Emittance growth reduction by rms-matching
• Summary & outlook
We acknowledge the support of the European Community – Research Infrastructure Activity under the FP6 "Structuring the European Research Area" program (CARE, contract number RII3-CT-2003-506395).
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
UNILAC at GSI: Overview
MEVVA
MUCIS
PIGRFQ IH1 IH2
Alvarez DTL
HLI: (ECR,RFQ,IH)
Transfer toSynchrotron
2.2 keV/uβ = 0.0022
120 keV/uβ = 0.016
11.4 MeV/uβ = 0.16
RFQ, IH1, IH2 Alvarez DTL
Gas Stripper
1.4 MeV/uβ = 0.054
1 ≤ A/q ≤ 9.5
1 ≤ A/q ≤ 65
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
The UNILAC Alvarez DTL
E [MeV/u]
:
Tank :
A1 A2a A3 A4A2b
1.4
3.6
4.8
5.9
8.6
11.4
• 5 independent rf-tanks
• 108 MHz, 192 rf-cells
• DTL based on F-D-D-F focusing
• DC-quads grouped to 13 families
• Inter-tank focusing : F-D-F
• Synchr. rf-phases -(30°,30°,30°,25°,25°)
54 m
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Section in Front of DTL
36 MHz 108 MHz
Gas Stripper
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Experimental Set-up & Procedure
• set beam current to 7.1 mA of 40Ar10+ (equiv. to FAIR design of 15 mA of 238U28+)
• measure hor., ver., emittance and long. rms-bunch length at DTL entrance
• set DTL transverse phase advance to values from 35° to 90°
• tune depression varied from 21% (90°) to 43% (35°)
• measure transmission, hor., and ver. rms-emittance at DTL exit
rms-bunch length measurement
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Data Reduction
Measurement
• projection of 6-dim to 2-dim plane
• matrix of pixels
• pixel size 0.8 mm / 0.5 mrad
• evaluation based on pixel contents
Simulations
• full 6-dim information available
to compare measurement and simulation adequately, the evaluation procedures must be identical
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Data Reduction
• particle coordinates from simulations are projected onto virtual meas. device
• projection is evaluated as a measurement
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Definition of Fractional rms-Emittance
rms-emittance from a fraction of p% of the total intensity
• calculate sum ∑100 of all pixel contents
• sort pixels from top by their contents
• sum them up until the fraction p from ∑100 is reached
• use the pixels included in this sum for rms-emittance evaluation
benchmarking used p = 95% of the intensity
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
horizontal
vertical
→ (α, β, ε)xy
rms-tracking backwards
meas. (α, β, ε)xy
guessed (α, β, ε)l
bunch length measurement
check (βε)l
Re-Construction of initial rms-Parameters for Simulations
1. Selfconsistent backtracking finding (α,β,ε)l that fit to measured bunch length
2. Varification wether applied machine settings would give full DTL transmission
DTLBuncher 108 MHz
Buncher 36 MHz
Start of Simulations
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
0.00
0.05
0.10
0.15
0.20
0.25
0 10 20 30 40 50 60 70 80 90 100
Number of Particles [%]
No
rm. F
ract
ion
al H
or.
rm
s-E
mit
tan
ce [
mm
mra
d]
hor., Exp.
hor., Gauss_2s
hor., Gauss_4s
hor., Input for Sim.
Re-construction of initial type of Distribution
0.00
0.05
0.10
0.15
0.20
0.25
0 10 20 30 40 50 60 70 80 90 100
Number of Particles [%]
No
rm. F
rac
tio
na
l Ve
r. r
ms
-Em
itta
nc
e [
mm
mra
d]
ver., Exp.
ver., Gauss_2s
ver., Gauss_4s
ver., Input for Sim.
measured in front of DTL
horizontal vertical
measured initial distribution inhabits different amount of halo horizontally and vertically
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Re-construction of initial type of Distribution
• Gauss, Lorentz, Waterbag distributions do not fit the measured amount of halo
• Several functions tried in order to fit halo in both planes
• function found as:
applying different powers for different planes the amount of halo can be reproduced
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Initial Distribution and Codes
initial distribution
Gaussian cut at 4σ assumed
Simulations with four different codes as used by the participating labs:
DYNAMION (GSI)
PARMILA (SNS)
PARTRAN (CEA/Saclay)
LORASR (Univ. of Frankfurt)
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Beam Transmission through DTL
All codes reproduce measured full transmission. LORASR is lower by few percent
91.0
92.0
93.0
94.0
95.0
96.0
97.0
98.0
99.0
100.0
101.0
30 40 50 60 70 80 90
Transverse Phase Advance (zero current) [deg]
DT
L T
ran
sm
iss
ion
[%
]
Exp.
DYNAMION
PARMILA
PARTRAN
LORASR
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Shapes of Final Horizontal Distributions
σo = 35° σo = 60°
Exp
erim
en
t
σo = 90°
DY
NA
MIO
NP
AR
MIL
AP
AR
TR
AN
LO
RA
SR
• agreement for intermediate σo
• disagreement for low/high σo
• high σo: attached wings (islands)
Int / Int_max [%]
0 – 5
5 – 10
10 – 20
20 – 40
40 -100
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
σo = 35° σo = 60°
Exp
erim
en
t
σo = 90°
DY
NA
MIO
NP
AR
MIL
AP
AR
TR
AN
LO
RA
SR
Shapes of Final Vertical Distributions
• differences even at intermediate σo
• high σo: no attached wings
Int / Int_max [%]
0 – 5
5 – 10
10 – 20
20 – 40
40 -100
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Evolution of Simulated rms-Emittances (100%)
• growth occurs mainly along first two tanks (agrees to previous measurements*)
• LORASR predicts strongest growth
• lowest growth at intermediate phase advances
*www-dapnia.cea.fr/Phocea/file.php?class=std&&file=Doc/Care/care-report-07-030.pdf
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
30 40 50 60 70 80 90
Transverse Phase Advance (zero current) [deg]
No
rm. H
or.
95
%-r
ms
-Em
itta
nc
e [
mm
mra
d]
hor., initial
hor., Exp.
hor., DYNAMIONhor., PARMILA
hor., PARTRAN
hor., LORASR
Final 95%-rms Emittances as Function of Phase Advance
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
30 40 50 60 70 80 90
Transverse Phase Advance (zero current) [deg]
No
rm. V
er.
95
%-r
ms
-Em
itta
nc
e [
mm
mra
d]
ver., initial
ver., Exp.
ver., DYNAMION
ver., PARMILA
ver., PARTRAN
ver., LORASR
horizontal vertical
• three codes underestimate growth
• LORASR predicts more growth
• codes predict peak at σo=70°
• three codes fit to meas. (except σo≤ 45°)
• LORASR predicts more growth
• codes predict peak at σo=70° (but LORASR)
results do not depend on initial long. emittance within 0.1∙εl,o and 2∙εl,o
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Final 95%-rms Emittances as Function of Phase Advance
(horizontal + vertical) / 2
• codes and measurements reveal minimum growth at σo≈ 60°
• LORASR predicts strongest growth
• DYNAMION, PARMILA, PARTRAN fit well at σo≥ 60°, LORASR fits well at σo≤ 60°
• codes predict peak at σo=70° (but LORASR)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
30 40 50 60 70 80 90
Transverse Phase Advance (zero current) [deg]
No
rm. T
ran
sv
. 95
%-r
ms
-Em
itta
nc
e [
mm
mra
d]
initial
Exp.
DYNAMION
PARMILA
PARTRAN
LORASR
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Mismatch to Periodic DTL Envelopes
rms-tracking algorithm for re-construction of initial distribution was used to estimate mismatch to DTL
0.0
0.2
0.4
0.6
0.8
1.0
30 40 50 60 70 80 90
Transverse Phase Advance (zero current) [deg]
Mis
ma
tch
at
DT
L E
ntr
an
ce
horizontal
vertical
longitudinal
T.P. Wangler, Rf Linear Accelerators, p. 217
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Reduction of Mismatch
• algorithm used to rms-match (incl. space charge) the initial distribution to periodic DTL
• test of matching by re-measuring emittance growth (one year later)
0.0
0.2
0.4
0.6
0.8
1.0
30 40 50 60 70 80 90
Transverse Phase Advance (zero current) [deg]
Mis
mat
ch a
t D
TL
En
tran
ce
horizontal
vertical
longitudinal
0
100
200
300
30 40 50 60 70 80 90
Transverse Phase Advance (zero current) [deg]N
orm
. Tra
ns
v. 9
5%
-rm
s-E
mit
tan
ce
Gro
wth
[%
]
mismatched
re-matched
• significant reduction of emittance growth by rms-matching including space charge
• reduction demonstrates that algorithm to re-construct initial rms-values is valid
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Summary
• rms-emittance growth along a 5-tank DTL measured for 12 phase advances from ..35° to 90°
• Measurements simulated using four codes (DYNAMION, PARMILA, PARTRAN, LORASR)
• Special emphasis put on re-construction of amount of halo within initial distribution
• Very good agreement found among DYNAMION, PARMILA, and PARTRAN
• LORASR predicts higher growth rates with respect to other three codes
• Codes describe well the behavior of measured sum of hor. and ver. emittances
• Considerable differences between meas. & sim. growth within single planes
• For low and high phase advances orientations and shapes of final distributions ..depend on the code
• Systematic reduction of rms-mismatch to DTL under space charge conditions
• rms-mismatch reduction resulted in considerable emittance growth reduction
(experimental reduction from 90% to 20% for space charge conditions equivalent to FAIR requirements)
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Outlook
• Using improved rms-matching measurements to be extended towards σo≈ 130°
• Emittances to be measured after first DTL tank to avoid inter-tank-mismatch
• Simulations predict a space charge driven 4th order resonance (talk by D. Jeon)
• Attempt for experimental verfication at UNILAC scheduled for Dec. 2008
0.0
0.1
0.2
0.3
0.4
85 95 105 115 125
Transverse Phase Advance (zero current) [deg]
No
rm. 9
5%
-rm
s-E
mit
tan
ce
[m
m*m
rad
]
hor., initialver., initialhor., DYNAMIONver., DYNAMIONhor.,LORASRver., LORASR
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Gesellschaft für SchwerIonenforschung GSI
UNILAC, p – U : 3 – 12 MeV/u
Synchrotron, Bδ = 18 Tm
p: 4 GeV
Ne: 2 GeV
U: 1 GeV
3 sources
ion species vary from pulse to pulse:
simultaneous experiments using different ions
Stor. Ring, Bδ = 10 Tm
Fragment Separator
High Energy Physics
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Alvarez 1st
Tanktransv. emitt. meas.
"t"
Buncher 36 MHz Buncher 108 MHzQuadrupoles
bunch length meas. "l"
15° 15°
30°
starting point of simulations
"s"
Construction of initial rms-Parameters for Simulations
• DTL transmission is very sensitive to buncher settings, i.e. long. mismatch
• applied buncher settings resulted in full DTL transmission and minimized low energy tails
-> useful in re-constructing the long. input distribution for simulations
• transv. and long. emittance were measured at different locations, i.e. at "t" & "l"
• distances from "l" and "s" to point "A" differ by 0.4 m
• to merge transv. & long. measurements together some approximations were used
"A"
initial bunch length & transv. emittances measured at different locations !!
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
transv. emitt. meas. "t"
Buncher 36 MHz Buncher 108 MHzQuadrupoles
bunch length meas. "l"
15°15°
30°
Starting point of simulations "s"
Re-construction of initial rms-Parameters for Simulations
• to merge measurements together some approximations were used :
• "transport" from "l" to "s" approximated by drift of 0.4 m (with space charge)
• at "t": combine measured x&y-rms-Twiss parameters with guessed long. rms-Twiss ..parameters
• rms-tracking with space charge from "t" to "s-0.4m", using applied machine settings
• if bunch length at "s-0.4m" agrees reasonably with measured one at "l": -> ok
• if not: -> do different guess on long. Twiss parameters at "t"
• put "s"-rms-Twiss parameters (x,y,l) into rms-matching routine
• compare suggested buncher settings with those used during experiment
• agreement: -> ok, rms-parameters of distribution re-constructed
• no agreement: -> do different guess on long. Twiss parameters at "t"
"A"
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Re-construction of initial type of Distribution
• emittance growth is sensitive to type of initial distribution (i.e. amount of halo)
• amount of halo can be visualized by plotting the fractional emittance vs. fraction
fract
ional rm
s-em
itta
nce
fraction of particles [%]0 100
no halo (KV)
some halo
strong halo
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
Phase Advances
L. Groening, Simulation of Experiments on Transverse rms-Emittance Growth Along an Alvarez DTL
0.0
0.1
0.2
0.3
0.4
0.5
0 20 40 60 80 100 120
Init. Long. Emittance [100%, rms, deg mrad]
No
rm. r
ms
-Em
itta
nc
e [
mm
*mra
d]
hor., DYN ver., DYN
hor, exp ver, exp
hor., PARMILA ver., PARMILA
Dependence on Initial Long. rms-Emittance Value
(using Gaussians cut at 2σ in each plane)