Calculation of the beam dynamics of RIKEN AVF Cyclotron E.E. Perepelkin JINR, Dubna 4 March 2008

General view of the AVF cyclotron Injection line ESD Dee Magnet sectors

Injection line LEBT

LEBT dimensions Initial emittance Superbunch ~ 4000°RF. 10,000 ions α x = α y = 0, β x = β y = 0.8 mm/mrad ε x = 115 π.mm.mrad, ε y = 98 π.mm.mrad Buncher Glazer lens G2 Glazer lens G1 Inflector

Buncher

Buncher parameters Buncher voltage V max is 150 Volt, (beam energy 52 keV, ECRIS potential is 10.4 kV) Gap = 5 mm

Buncher model 0.1 mm 2 mm

E z along OZ axis Ground electrode RF electrode 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

B mod distribution at the XOZ plane

B mod on the OZ axis B c = kGs

Glazer lens G2

G2 geometry Maximum excitation 26 kA· t

B mod distribution at the XOZ plane

B mod on the OZ axis B c = 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 14 N 5+ with energy 52 keV Gap 8 mm Cutting 4 mm No tilt Electric radius A = 26 mm Magnetic radius ρ = mm K = 0.8

Opera 3D model and mesh Cut 4 mm at the inflector entrance and exit Mesh step is about 1 mm

Inflector entrance

Inflector exit

Magnetic and electric maps area LEBT

Fields map area G2 Magnetic field G1 Magnetic field Buncher Electric field

Fields map area Inflector Electric field Axial channel Magnetic field G1 Magnetic field

Low beam intensity Test particle 14 N 5+ Space Charge effects are negligible

Parameters LEBT G1 lens: B c = kG G2 lens: B c = 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 1 Buncher entrance Plane 2 Exit buncher Plane 3 Begin G2 Plane 4 Exit G2 Plane 5 Begin G1 Plane 6 Exit G1 Plane 7 26 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, mm21.6 Θ - azimuth, deg53.34 Z C - axial position, mm0 Pr C, deg Pz C, deg0 Energy, keV50.9 Gaps φ RF, [deg] Analytical E-map φ RF, [deg] Calculated E-map Starting parameters for central trajectory RF phase at the center of acceleration gaps 1 st turn U Dee = 46.7 kV, B-map – is measured, f RF = 16.3 MHz, Z=5, Mass = 14.

Inflector

Central trajectories

Compare trajectories ParametersTheoryCalculated Adjusted calculated * Radius, mm Θ - azimuth, deg Z C - axial position, mm Pr C, deg Pz C, deg Energy, keV * Shift 0.8 mm, slope 4.5 deg

Emittance at the inflector entrance

Beam parameters Parameters Coordinates αβ mm/mrad γ mrad/mm ε π∙mm∙mrad X Y Z 02.1 mm/keV1 keV/mm1 π mm ∙keV Parameters Coordinates Average- position mm 2σ- deviation mm Average- angle mrad 2σ-angle mrad X Y Z keV1 keV Twiss Statistics

Emittance at the inflector exit

Beam parameters Parameters Coordinates αβ mm/mrad γ mrad/mm ε π∙mm∙mrad R Z φ RF °RF/keV0.07 keV/°RF56 π °RF∙keV Parameters Coordinates Average- position mm 2σ- deviation mm Average- angle mrad 2σ-angle mrad R Z φ RF °RF51.3 keV2 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, Bm 2 = 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

Central trajectory parameters φ RF, deg-65 Radius, mm23.3 Θ - azimuth, deg64.1 Z C - axial position, mm0 Pr C, deg38.74 Pz C, deg0 Energy, keV55.1 Operational frequency MHz, harmonic = 2 U Dee = 50 kV m( 14 N 5+ ) =

Central trajectory

Radial amplitude

Phases and energy

Emittance at the inflector exit

Beam parameters Parameters Coordinates αβ mm/mrad γ mrad/mm ε π∙mm∙mrad R Z φ RF °RF/keV0.2 keV/°RF273 π °RF ∙keV Parameters Coordinates Average- position mm 2σ- deviation mm Average- angle mrad 2σ-angle mrad R Z φ RF -65 °RF38.8 °RF55.1 keV7.2 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) Parameters Coordinates αβ mm/mrad γ mrad/mm ε π∙mm∙mrad R Z φ RF °RF/keV96 keV/°RF130 π °RF ∙MeV Parameters Coordinates Average- position mm 2σ- deviation mm Average- angle mrad 2σ-angle mrad R Z φ RF °RF62.7 MeV3.5 MeV Twiss Statistics

Beam parameters (Flat-Top on) Parameters Coordinates αβ mm/mrad γ mrad/mm ε π∙mm∙mrad R Z φ RF 0.10 °RF/keV43 keV/°RF31.6 π °RF ∙MeV Parameters Coordinates Average- position mm 2σ- deviation mm Average- angle mrad 2σ-angle mrad R Z φ RF -27 °RF62.9 MeV1.17 MeV Twiss Statistics

Flat-Top effect

Extraction

Analytical ESD E=71 kV/cm

Comparison By Goto-san This calculation

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) V max = 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 ParametersTheoryCalculated Radius, mm Θ - azimuth, deg Z C - axial position, mm02.3 Pr C, deg Pz C, deg Energy, keV 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 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 Parameters Coordinates αβ mm/mrad γ mrad/mm ε π∙mm∙mrad X Y Z 02.1 mm/keV1 keV/mm1.5 π mm ∙keV Parameters Coordinates Average- position mm 2σ- deviation mm Average- angle mrad 2σ-angle mrad X Y Z keV1 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 Parameters Coordinates αβ mm/mrad γ mrad/mm ε π∙mm∙mrad R Z φ RF deg/MeV0.1 MeV/deg4.3 π mm ∙MeV Parameters Coordinates Average- position mm 2σ- deviation mm Average- angle mrad 2σ-angle mrad R Z φ RF MeV0.7 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.