calculation of the beam dynamics of riken avf cyclotron e.e. perepelkin jinr, dubna 4 march 2008
TRANSCRIPT
![Page 1: Calculation of the beam dynamics of RIKEN AVF Cyclotron E.E. Perepelkin JINR, Dubna 4 March 2008](https://reader033.vdocuments.site/reader033/viewer/2022061612/56649f155503460f94c2ac66/html5/thumbnails/1.jpg)
Calculation of the beam dynamics of
RIKEN AVF CyclotronE.E. Perepelkin
JINR, Dubna
4 March 2008
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General view of the AVF cyclotron
Injection line
ESD
Dee
Magnet sectors
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Injection lineLEBT
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LEBT dimensions
Initial emittanceSuperbunch ~ 4000°RF. 10,000
ionsαx = αy = 0, βx = βy = 0.8
mm/mradεx = 115 π.mm.mrad, εy = 98
π.mm.mrad
Buncher
Glazer lens G2
Glazer lens G1
Inflector
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Buncher
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Buncher parameters
• Buncher voltage Vmax is 150 Volt, (beam energy 52 keV, ECRIS potential is 10.4 kV)
• Gap = 5 mm
0 0 0 0
1 1sin sin 2 sin 3 , 50
3 9V
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Buncher model
0.1 mm
0.1 mm 2 m
m
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Ez along OZ axis
Groundelectro
de
RFelectro
de
Calculation was performed for the RF potential 1 volt
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Z = -2.4 mm from buncher center
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Z = -2 mm from buncher center
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Z = 0 mm ( buncher center )
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Z = 2 mm from buncher center
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Z = 2.4 mm from buncher center
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Glazer lens G1
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G1 geometry
Maximum excitation 42.9 kA· t
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Model and mesh
Symmetry 1/12
More than 4 million finite elements
Maximum excitation 42.9 kA· t
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Bmod distribution at the XOZ plane
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Bmod on the OZ axis
Bc = 4.033 kGs
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Glazer lens G2
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G2 geometry
Maximum excitation 26 kA· t
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Bmod distribution at the XOZ plane
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Bmod on the OZ axis
Bc = 2.506 kGs
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Axial channel
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Remarks• Measured axial magnetic field, main coil
current = 650A• The current in the Glazer lens G1 and G2
was maximal• JW(G1) = 42.9 kA• t• JW(G2) = 26 kA• t
• Calculation of the magnetic field for the G1 and G2 was produced without taken into account the main coil field.
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Field in the axial channel
Glazer lens G1
Glazer lens G2
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Inflector
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Inflector parameters
• Particle 14N5+ with energy 52 keV• Gap 8 mm• Cutting 4 mm• No tilt• Electric radius A = 26 mm• Magnetic radius ρ = 16.396 mm• K = 0.8
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Opera 3D model and mesh
Cut 4 mm at the inflector entrance and
exitMesh step is about 1
mm
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Inflector entrance
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Inflector exit
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Magnetic and electricmaps area
LEBT
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Fields map area
G2 Magnetic
fieldG1
Magnetic field
Buncher Electric
field
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Fields map area
Inflector Electric
field
Axial channel Magnetic
field
G1 Magnetic
field
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Low beam intensity Test particle 14N5+
Space Charge effects are negligible
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Parameters LEBT
• G1 lens: Bc = 4.033 kG
• G2 lens: Bc = 3.007 kG ( 20% up from nominal )
• Injection energy = 45 keV ( 52 keV nominal )
• Buncher voltage = 80 Volt ( 150 V nominal )
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Buncher focusing animation
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Lenses effect animation
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Buncher losses
Ground
RF
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Buncher losses
Total buncher losses are 15 %
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Monitoring planes
Plane 1Buncher entrance
Plane 2Exit
buncher
Plane 3Begin G2
Plane 4Exit G2
Plane 5Begin G1
Plane 6Exit G1
Plane 726 mm from the median
plane
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Plane 1
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Plane 2
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Plane 3
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Plane 4
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Plane 5
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Plane 6
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Plane 7
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Nominal regime
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Cross - check
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Central trajectories
Calculated E-map
Analytical E-map
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Parameters
Radius, mm 21.6
Θ - azimuth, deg 53.34
ZC - axial position, mm
0
PrC, deg 38.634
PzC, deg 0
Energy, keV 50.9
Gaps
φRF , [deg]
Analytical E-map
φRF , [deg]
Calculated E-map
1 -29 -30
2 -29 -29
3 20 30
4 5 14
Starting parameters for
central trajectory
RF phase at the center of
acceleration gaps
1st turn
UDee = 46.7 kV, B-map – is measured, fRF = 16.3 MHz, Z=5, Mass = 14.
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Inflector
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Central trajectories
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Compare trajectories
Parameters TheoryCalculat
ed
Adjusted calculat
ed*
Radius, mm 21.6 20.8 22.1
Θ - azimuth, deg 14.7 16.5 13.7
ZC - axial position, mm
0 -0.04 0.54
PrC, deg 38.619 43.783 38.863
PzC, deg 0 -8.98 -0.93
Energy, keV 52 50.2 51.2* Shift 0.8 mm, slope 4.5
deg
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Emittance at the inflector entrance
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Beam parameters
ParametersCoordinates
α βmm/mrad
γmrad/mm
επ∙mm∙mrad
X 0 0.05 1 99.5
Y 0 0.05 1 99.5
Z 0 2.1 mm/keV
1 keV/mm 1 π mm ∙keV
ParametersCoordinates
Average-position
mm
2σ-deviation
mm
Average-anglemrad
2σ-anglemrad
X 0 2.2 0 43
Y 0 2.2 0 43
Z 27 1.5 52 keV 1 keV
Twiss
Statistics
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Emittance at the inflector exit
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Beam parameters
ParametersCoordinates
α βmm/mrad
γmrad/mm
επ∙mm∙mrad
R 0.8 0.01 195 161
Z -1.2 0.02 131 336
φRF-0.7 20 °RF/keV 0.07 keV/°RF 56 π °RF∙keV
ParametersCoordinates
Average-position
mm
2σ-deviation
mm
Average-anglemrad
2σ-anglemrad
R 23.1 1.2 617 177
Z 0.3 2.5 -7.5 210
φRF- 33.6 °RF 51.3 keV 2 keV
Twiss
Statistics
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Cyclotron
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Bunches
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Central region axial losses
Losses 57%
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Radial amplitude
Symmetric B-map
Real B-map
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B-map harmonics
R = 72 cm, Bm2 = 15 Gs
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Emittance for real B-map
Center Dee 1 – position, final radius
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Symmetric B-map
Center Dee 1 – position, final radius
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Flat - Top
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Model features
•B-map – measurements•E-map – analytical map•Flat-top system•Voltage radial dependencies
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Voltage radial dependencies
2cosC r R
3
1cos cos 3
9DeeU U C r C r
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Central trajectory parameters
φRF , deg -65
Radius, mm 23.3
Θ - azimuth, deg 64.1
ZC - axial position, mm
0
PrC, deg 38.74
PzC, deg 0
Energy, keV 55.1
• Operational frequency 16.222 MHz, harmonic = 2
• UDee= 50 kV
• m(14N5+) = 14.067
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Central trajectory
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Radial amplitude
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Phases and energy
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Emittance at the inflector exit
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Beam parameters
ParametersCoordinates
α βmm/mrad
γmrad/mm
επ∙mm∙mrad
R 2.2 0 274 104
Z -0.5 0 125 320
φRF-0.2 5.5
°RF/keV0.2 keV/°RF 273 π °RF
∙keV
ParametersCoordinates
Average-position
mm
2σ-deviation
mm
Average-anglemrad
2σ-anglemrad
R 23.4 1.5 38.75 205
Z 0 1.8 0 200.3
φRF-65 °RF 38.8 °RF 55.1 keV 7.2 keV
Twiss
Statistics
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Flat-Top off/on
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Axial motion (Flat-Top off/on)
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Emittances (Flat-Top off)
Dee 1 center – azimuth bunch position
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Emittances (Flat-Top on)
Dee 1 center – azimuth bunch position
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Beam parameters (Flat-Top off)
ParametersCoordinates
α βmm/mrad
γmrad/mm
επ∙mm∙mrad
R 0 0.5 1.9 268
Z -0.9 2 0.9 42
φRF-0.1 0 °RF/keV 96 keV/°RF 130 π °RF
∙MeV
ParametersCoordinates
Average-position
mm
2σ-deviation
mm
Average-anglemrad
2σ-anglemrad
R 552 11.8 -14.6 22.7
Z 0 9.4 0 6
φRF- 36.8 °RF 62.7 MeV 3.5 MeV
Twiss
Statistics
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Beam parameters (Flat-Top on)
ParametersCoordinates
α βmm/mrad
γmrad/mm
επ∙mm∙mrad
R -1.3 0.9 2.7 63
Z 0.3 1.5 0.7 33.5
φRF0.1 0 °RF/keV 43 keV/°RF 31.6 π °RF
∙MeV
ParametersCoordinates
Average-position
mm
2σ-deviation
mm
Average-anglemrad
2σ-anglemrad
R 552 7.8 -23.3 13
Z 0 7 0 4.9
φRF- 27 °RF 62.9 MeV 1.17 MeV
Twiss
Statistics
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Flat-Top effect
1.5Flat Top
r
r
3Flat Top
E
E
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Extraction
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Extraction
Analytical ESDE=71 kV/cm
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Comparison
By Goto-san
This calculatio
n
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Optimization
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Main result
Losses from the inflector ground to the
ESD mouth is 35% instead of 60%.
And this result can be improved.
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Modification of buncher parameters
• Initial beam energy 45 keV (ECRIS potential 9 kV, instead of 10.4 kV)
• Vmax = 80 Volt (instead of 150 kV)
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Modification inflector parameters
• Electrode potential ±3.14 kV or ±3.2 kV
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Central trajectories
Starting position (x,y,z) = (0,0,36) mm
Injection - strongly axial direction
Energy 45 keV
Parameters TheoryCalculat
ed
Radius, mm 21.067 21.52
Θ - azimuth, deg 53.1 52.4
ZC - axial position, mm
0 2.3
PrC, deg 39.074 42.3
PzC, deg 0 -0.45
Energy, keV 52 46.1
At the inflector exit
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Cyclotron
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B map modification• First trim coil• We added the magnetic field to the measurement B-map
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Electric field parameters
• Dee voltage 40 kV instead of operational 46.7 kV• RF frequency 16.219 MHz instead of operational 16.3
MHz• No flat-top
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RF phase at the Dee’s centre
For the central trajectory
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Emittance at the inflector entrance
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Beam parameters
ParametersCoordinates
α βmm/mrad
γmrad/mm
επ∙mm∙mrad
X 0 0.05 1 99.5
Y 0 0.05 1 99.5
Z 0 2.1 mm/keV
1 keV/mm 1.5 π mm ∙keV
ParametersCoordinates
Average-position
mm
2σ-deviation
mm
Average-anglemrad
2σ-anglemrad
X 0 2.2 0 43
Y 0 2.2 0 43
Z 27 1.5 45 keV 1 keV
Twiss
Statistics
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Cyclotron animation
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Central region losses
2.7%
4.4% 1.8
%
7.6%
Total axial
15.8%
Total losses 34.7%
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Axial motion
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3D view
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Emittance at the radius ~66 cm
Center Dee 1 – position, not final radius
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Beam parameters
ParametersCoordinates
α βmm/mrad
γmrad/mm
επ∙mm∙mrad
R 0.8 1.2 1.4 33
Z 0.3 1.9 0.6 14
φRF0.6 13.1
deg/MeV0.1 MeV/deg 4.3 π mm
∙MeV
ParametersCoordinates
Average-position
mm
2σ-deviation
mm
Average-anglemrad
2σ-anglemrad
R 659 5.6 34.6 6.3
Z 0.2 5.2 1.2 2.9
φRF- 7.5 88.12 MeV 0.7 MeV
Twiss
Statistics
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Future activities
• Decrease axial losses by the inflector axial shift on 2.3 mm
• Optimization of the inflector cutting• Implementation of the beam centering procedure• Assessment of the modified central electrode
structure• Extraction study for the completed deflector
model
Last but not the least:It would be advisable to performer an experimental
checking of simulation results obtained so far.