Transcript The 4 linac D. Jeon (SNS) I. Hofmann, L. Groening, G. Franchetti (GSI)

The 4n=1 resonance of a high intensity
linac
D. Jeon (SNS)
I. Hofmann, L. Groening, G. Franchetti (GSI)
HB 2008 August 25-29, 2008
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 This work is the result of the collaboration
between GSI and SNS.
 Thanks to J. Galambos, S. Henderson for the
support.
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History of halo formation mechanisms
 Until 1998, mismatch was the only known mechanism of
halo formation.
 Late 1998, halo formation by the 2nx - 2ny =0 resonance
in the ring was discovered by D. Jeon (presented by J.
Holmes at PAC99)  leading to other resonance
induced halo studies in the ring.
 Since then coupling resonance in the linac has been
studied extensively by many.
 Other halo formation mechanisms have been
discovered such as non-round beam (D. Jeon, APAC07),
rf cavity (M. Eshraqi) etc.
 Widely believed that there is no other resonance in the
linac…
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Review
Non-Round Beam induced Halo Formation
Optics modification improves beam quality
z
Nominal SNS MEBT Optics
Round Beam MEBT Optics
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Round Beam Optics improves X beam quality
(Emittance Measurement)
Nominal Optics
eX= 0.349 mm-mrad (1% threshold)
0.454 mm-mrad (0% threshold)
Round Beam Optics
eX= 0.231 mm-mrad (1% threshold)
0.289 mm-mrad (0% threshold)
 Round Beam Optics reduces halo and rms emittance
in X significantly
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Tail is significantly reduced for Round Beam Optics
Nominal Optics
Measured
Round Beam Optics
Measured
No Tail!!
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
Round Beam Optics reduces beam tail visibly

This tail is the source of beam loss in downstream linac
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Round Beam Optics improves Y beam quality
(Emittance Measurement)
Nominal Optics
eY= 0.353 mm-mrad (1% threshold)
0.472 mm-mrad (0% threshold)
Round Beam Optics
eY= 0.264 mm-mrad (1% threshold)
0.306 mm-mrad (0% threshold)
 Round Beam Optics reduces halo and rms emittance
in Y significantly
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Envelope instability
 Envelope equation predicts envelope instability
at 90° phase advance.
 Linac design including the SNS linac has
avoided the 90° phase advance because of the
envelope instability!
 GSI UNILAC has the capability to scan well
beyond 90° phase advance + emittance scanner.
 D. Jeon made a proposal to GSI to do an
experiment to measure the stop-band of the
envelope instability.
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SNS Linac design
Phase & Quad Laws Avoid the Envelope
Instability and the Coupling Resonance
90
0t
0 (°/period)
80
9
70
60
0l
50
40
DTL
30
0.0
0.2
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CCL
0.4

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1
0.6
2
0.8
1.0
Discovery of the 4n=1 resonance of a
linac driven by space charge
 Linac simulation study finds the 4n=1 resonance
when the depressed phase advance is about 90°,
rather than the envelope instability.
 This 4n=1 resonance is dominating over the
better known envelope instability and practically
replacing it.
 It should be stated that linac design should avoid
90° phase advance because of the 4n=1
resonance rather than the envelope instability!!
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4n=1 resonance crossing from below
0.018
100
0.017
rms emittance [cm mrad]
105
phase advance
95
90
85
80
sigx
75
sigy
sigz
70
0.016
0.015
0.014
0.013
EpsXn
0.012
EpsYn
EpsZn
0.011
65
0.010
60
0
50
100
150
200
250
50
100
150
200
gap number
gap number
 rms emittance
 phase advance
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0
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Beam distribution when crossing the 4n=1
resonance from below
Initial beam distribution
X’
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Y’
X
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Y
4n=1 resonance crossing from above
110
0.024
sigx
105
phase advance
rms emittance [cm mrad]
sigy
100
sigz
95
90
85
80
75
70
0.022
0.020
0.018
0.016
EpsXn
0.014
EpsYn
EpsZn
0.012
65
0.010
60
0
50
100
150
200
250
50
100
150
200
gap number
gap number
 rms emittance
 phase advance
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0
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250
Beam distribution when crossing the 4n=1
resonance from above
X’
Y’
Y
X
 Stable fixed points move from the origin afar.
 This traps beam particles.
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No resonance effect  > 90º
When  ~ 95°
100
0.020
0.018
rms emittance [cm mrad]
phase advance
95
90
85
80
sigx
sigy
75
#REF!
0.016
0.014
0.012
EpsXn
0.010
EpsYn
0.008
EpsZn
0.006
0.004
0.002
0.000
70
0
50
100
150
200
250
50
100
150
200
gap number
gap number
 rms emittance
 phase advance
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0
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250
It seems that no resonance effect  > 90º
When  ~ 95°
X
Y
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It seems that no resonance effect  > 90º
When  ~ 95°
X’
Y’
X
Y
There is no sign of resonance effect
on the beam distribution
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Resonance takes effect for  <= 90º
When  ~ 85°
105
0.060
sigy
#REF!
phase advance
95
90
85
80
75
rms emittance [cm mrad]
sigx
100
0.050
0.040
EpsXn
0.030
EpsYn
EpsZn
0.020
0.010
0.000
70
0
50
100
150
200
250
300
350
400
0
50
100
200
250
300
gap number
gap number
 rms emittance
 phase advance
 Emittance growth when  <= 90°
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350
400
resonance effect  <= 90º
When  ~ 85°
X
Y
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resonance effect  <= 90º
When  ~ 85°
X’
Y’
X
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Y
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Effects of input beam mismatch
effects of resonance and mismatch manifest
well matched
X’
Y’
X
Y
mismatched
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Scaling law when crossing the 4n=1 resonance
 Emittance growth is a function of S≡ DnDn = (Dn)2/(dn/dn).
(I. Hofmann et al)
 e  (1 + aDnDn) eo
 De/eo  aDnDn
 For the linac 4n=1 resonance, the emittance growth is a
linear function of DnDn.
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Scaling law when crossing the resonance
a=0.37
S
a=0.31
 De/eo  aDnDn = aS.
 For downward 4n=1 resonance crossing, a  0.31
 For upward 4n=1 resonance crossing, a  0.37
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(Dn ) 2

n
Emittance growth for fixed phase advance
X
 roughly proportional to X3.5
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Efforts to measure the 4n=1 resonance
stop-band using the GSI UNILAC
rms emittance [cm mrad]
0.060
0.055
0.050
0.045
0.040
0.035
0.030
90
95
100
105
110
115
120
125
130
phase advance [deg]
 Simulated erms vs 0 at the end of Tank A1 of UNILAC.
 About 45% of rms emittance increase is anticipated.
 New emittance scanner to be installed between Tank
A1 and A2.
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Summary
 Discovery of a new halo formation mechanism,
4n=1 resonance for a linac was made.
 This is one step forward to Grand Unification of
Linac and Ring beam dynamics.
 Linac design should avoid 90° phase advance
because of the 4n=1 resonance rather than the
better known envelope instability!!
 Efforts are undertaken to measure the 4n=1
resonance stop-band at GSI, Germany.
 Is envelope instability a theoretical artifact??
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 Thanks for the attention.
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Fraction of core in x plane sees nonlinear space
charge force, resulting in halo formation in x plane
Beam at the chopper target
potential halo
Space charge force and real space distributions
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Sources of Front End halo generation
• MEBT is the largest contributor to FE halo generation
• Nonlinear space charge force stemming from a large transverse
beam eccentricity generates halo in MEBT
(D. Jeon et al, PRST-AB 5, 094201 (2002))
• As minor contributors, several FE components and physical effects
may contribute to the generation of beam halo
MEBT optics
Chopper target
Z
X
RFQ
DTL
Beam
~1.6 m
Y
Region with a large transverse beam eccentricity ~2:1
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Optics modification alone reduces halo significantly in
simulations (Simulation)
Half optics
modified
Round Beam Optics
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Nominal Optics
CCL bore
Tail is significantly reduced for Round Beam Optics
Round Beam Optics
Measured
No Tail!!
Nominal Optics
Measured

Round Beam Optics reduces beam tail visibly

This tail is the source of beam loss in downstream linac
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Gesellschaft für SchwerIonenforschung GSI
Synchrotron, Br = 18 Tm
p: 4 GeV
Ne: 2 GeV
U: 1 GeV
3 sources
Fragment Separator
Stor. Ring, Br = 10 Tm
UNILAC, p – U : 3 – 12 MeV/u
High Energy Physics
ion species vary from pulse to pulse:
simultaneous experiments using different ions
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FAIR: Facility for Antiproton and Ion Research
The FAIR Accelerator Complex
GSI Today
SIS 100
SIS18
p-linac
SIS 300
UNILAC
SIS100
p-linac
SIS300
Unila
c
HESR
Antiproton
Prod. Target
HESR
Super- FRS
p-bar targetFAIR
CR
71010 cooled pbar / hour
RESR
RESR
NESR
CR
100 m
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UNILAC at GSI: Overview
RFQ, IH1, IH2
Alvarez DTL
Single Gap
Resonators
Transfer to
Synchrotron
From HLI
36 MHz
MEVVA
PIG
Pepper Pot
Gas Stripper
Slit-Grid
RFQ
2.2 keV/u
β = 0.0022
IH1
IH2
120 keV/u
β = 0.016
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Buncher
Quads
HLI: (ECR,RFQ,IH)
From HSI
MUCIS
Alvarez
108 MHz
Beam Current
U4+
Long. Emitt.
Alvarez DTL
U28+
Gas Stripper
1.4 MeV/u
β = 0.054
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11.4 MeV/u
β = 0.16
Set-up for Measurements
• Beam Current Measurement
• Beam Emittance Measurement (transv.)
Matching to DTL
• Beam Profile Measurement
from
HSI
Alvarez DTL Section
Gas Stripper
40Ar1+
 40Ar10+
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SGR
UNILAC at GSI
: (ECR,RFQ,IH)
Requirements (Uranium)
HLI:
SIS 18
Injection
238U73+
4.6
4.2·1010
11.4
±2·10-3
0.8
Design: 4.6 mA, Status 2001: 0.37 mA, Status today: 2.0 mA
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Benchmarking efforts at GSI
 It needs to better understand the UNILAC for
higher beam current requirement of FAIR
project.
 GSI waged a campaign of measuring the
output beam emittance, varying the zero
current phase advance from 35° to 90°.
 Efforts to compare the experiment with
simulation of codes.
 Three different codes have been used:
DYNAMION (GSI), PARMILA, PARTRAN
(France).
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Code benchmarking effort
comparing exp (100%) and simulation (100%)
Norm. transv. rms-Emittance (100%) [mm*mrad]
0,9
Exp
0,8
DYNAMION
PARMILA
0,7
PARTRAN
initial
0,6
0,5
0,4
0,3
0,2
0,1
0,0
30
40
50
60
70
80
90
Transverse Phase Advance (zero current) [deg]
 Comparison of 100% rms emittance suffers from
noise in measurement data
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Code benchmarking effort
comparing exp (90%) and simulation (95%)
0,7
Norm. transv. rms-Emittance [mm*mrad]
Exp, 90%
0,6
DYNAMION, 95%
PARMILA, 95%
PARTRAN, 95
0,5
initial, 90%
0,4
0,3
0,2
0,1
0,0
30
40
50
60
70
80
90
Transverse Phase Advance (zero current) [deg]
 Gap between experiment and simulation narrows.
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Code benchmarking effort
comparing exp (95%) and simulation (95%)
 Coming soon!!
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