Calculation of the beam dynamics of RIKEN AVF Cyclotron E.E. Perepelkin JINR, Dubna 4 March 2008.
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Transcript of Calculation of the beam dynamics of RIKEN AVF Cyclotron E.E. Perepelkin JINR, Dubna 4 March 2008.
Calculation of the beam dynamics of
RIKEN AVF CyclotronE.E. Perepelkin
JINR, Dubna
4 March 2008
General view of the AVF cyclotron
Injection line
ESD
Dee
Magnet sectors
Injection lineLEBT
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
Buncher
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
Buncher model
0.1 mm
0.1 mm 2 m
m
Ez along OZ axis
Groundelectro
de
RFelectro
de
Calculation was performed for the RF potential 1 volt
Z = -2.4 mm from buncher center
Z = -2 mm from buncher center
Z = 0 mm ( buncher center )
Z = 2 mm from buncher center
Z = 2.4 mm from buncher center
Glazer lens G1
G1 geometry
Maximum excitation 42.9 kA· t
Model and mesh
Symmetry 1/12
More than 4 million finite elements
Maximum excitation 42.9 kA· t
Bmod distribution at the XOZ plane
Bmod on the OZ axis
Bc = 4.033 kGs
Glazer lens G2
G2 geometry
Maximum excitation 26 kA· t
Bmod distribution at the XOZ plane
Bmod on the OZ axis
Bc = 2.506 kGs
Axial channel
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.
Field in the axial channel
Glazer lens G1
Glazer lens G2
Inflector
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
Opera 3D model and mesh
Cut 4 mm at the inflector entrance and
exitMesh step is about 1
mm
Inflector entrance
Inflector exit
Magnetic and electricmaps area
LEBT
Fields map area
G2 Magnetic
fieldG1
Magnetic field
Buncher Electric
field
Fields map area
Inflector Electric
field
Axial channel Magnetic
field
G1 Magnetic
field
Low beam intensity Test particle 14N5+
Space Charge effects are negligible
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 )
Buncher focusing animation
Lenses effect animation
Buncher losses
Ground
RF
Buncher losses
Total buncher losses are 15 %
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
Plane 1
Plane 2
Plane 3
Plane 4
Plane 5
Plane 6
Plane 7
Nominal regime
Cross - check
Central trajectories
Calculated E-map
Analytical E-map
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.
Inflector
Central trajectories
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
Emittance at the inflector entrance
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
Emittance at the inflector exit
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
Cyclotron
Bunches
Central region axial losses
Losses 57%
Radial amplitude
Symmetric B-map
Real B-map
B-map harmonics
R = 72 cm, Bm2 = 15 Gs
Emittance for real B-map
Center Dee 1 – position, final radius
Symmetric B-map
Center Dee 1 – position, final radius
Flat - Top
Model features
•B-map – measurements•E-map – analytical map•Flat-top system•Voltage radial dependencies
Voltage radial dependencies
2cosC r R
3
1cos cos 3
9DeeU U C r C r
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
Central trajectory
Radial amplitude
Phases and energy
Emittance at the inflector exit
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
Flat-Top off/on
Axial motion (Flat-Top off/on)
Emittances (Flat-Top off)
Dee 1 center – azimuth bunch position
Emittances (Flat-Top on)
Dee 1 center – azimuth bunch position
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
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
Flat-Top effect
1.5Flat Top
r
r
3Flat Top
E
E
Extraction
Extraction
Analytical ESDE=71 kV/cm
Comparison
By Goto-san
This calculatio
n
Optimization
Main result
Losses from the inflector ground to the
ESD mouth is 35% instead of 60%.
And this result can be improved.
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)
Modification inflector parameters
• Electrode potential ±3.14 kV or ±3.2 kV
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
Cyclotron
B map modification• First trim coil• We added the magnetic field to the measurement B-map
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
RF phase at the Dee’s centre
For the central trajectory
Emittance at the inflector entrance
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
Cyclotron animation
Central region losses
2.7%
4.4% 1.8
%
7.6%
Total axial
15.8%
Total losses 34.7%
Axial motion
3D view
Emittance at the radius ~66 cm
Center Dee 1 – position, not final radius
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
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.