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

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

3. Injection line LEBT

4. 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

5. Buncher

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

7. Buncher model 0.1 mm 2 mm

8. E z along OZ axis Ground electrode RF electrode Calculation was performed for the RF potential 1 volt

9. Z = -2.4 mm from buncher center

10. Z = -2 mm from buncher center

11. Z = 0 mm ( buncher center )

12. Z = 2 mm from buncher center

13. Z = 2.4 mm from buncher center

14. Glazer lens G1

15. G1 geometry Maximum excitation 42.9 kA· t

16. Model and mesh Symmetry 1/12 More than 4 million finite elements Maximum excitation 42.9 kA· t

17. B mod distribution at the XOZ plane

18. B mod on the OZ axis B c = 4.033 kGs

19. Glazer lens G2

20. G2 geometry Maximum excitation 26 kA· t

21. B mod distribution at the XOZ plane

22. B mod on the OZ axis B c = 2.506 kGs

23. Axial channel

24. 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.

25. Field in the axial channel Glazer lens G1 Glazer lens G2

26. Inflector

27. 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 = 16.396 mm K = 0.8

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

29. Inflector entrance

30. Inflector exit

31. Magnetic and electric maps area LEBT

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

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

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

35. Parameters LEBT G1 lens: B c = 4.033 kG G2 lens: B c = 3.007 kG ( 20% up from nominal ) Injection energy = 45 keV ( 52 keV nominal ) Buncher voltage = 80 Volt ( 150 V nominal )

36. Buncher focusing animation

37. Lenses effect animation

38. Buncher losses Ground RF

39. Buncher losses Total buncher losses are 15 %

40. 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

41. Plane 1

42. Plane 2

43. Plane 3

44. Plane 4

45. Plane 5

46. Plane 6

47. Plane 7

48. Nominal regime

49. Cross - check

50. Central trajectories Calculated E-map Analytical E-map

51. Parameters Radius, mm21.6 Θ - azimuth, deg53.34 Z C - axial position, mm0 Pr C, deg38.634 Pz C, deg0 Energy, keV50.9 Gaps φ RF, [deg] Analytical E-map φ RF, [deg] Calculated E-map 1-29-30 2-29 32030 4514 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.

52. Inflector

53. Central trajectories

54. Compare trajectories ParametersTheoryCalculated Adjusted calculated * Radius, mm21.620.822.1 Θ - azimuth, deg14.716.513.7 Z C - axial position, mm0-0.040.54 Pr C, deg38.61943.78338.863 Pz C, deg0-8.98-0.93 Energy, keV5250.251.2 * Shift 0.8 mm, slope 4.5 deg

55. Emittance at the inflector entrance

56. Beam parameters Parameters Coordinates αβ mm/mrad γ mrad/mm ε π∙mm∙mrad X 00.05199.5 Y 00.05199.5 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 02.2043 Y 02.2043 Z 271.552 keV1 keV Twiss Statistics

57. Emittance at the inflector exit

58. Beam parameters Parameters Coordinates αβ mm/mrad γ mrad/mm ε π∙mm∙mrad R 0.80.01195161 Z -1.20.02131336 φ RF -0.720 °RF/keV0.07 keV/°RF56 π °RF∙keV Parameters Coordinates Average- position mm 2σ- deviation mm Average- angle mrad 2σ-angle mrad R 23.11.2617177 Z 0.32.5-7.5210 φ RF -33.6 °RF51.3 keV2 keV Twiss Statistics

59. Cyclotron

60. Bunches

61. Central region axial losses Losses 57%

62. Radial amplitude Symmetric B-map Real B-map

63. B-map harmonics R = 72 cm, Bm 2 = 15 Gs

64. Emittance for real B-map Center Dee 1 – position, final radius

65. Symmetric B-map Center Dee 1 – position, final radius

66. Flat - Top

67. Model features B-map – measurements E-map – analytical map Flat-top system Voltage radial dependencies

69. 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 16.222 MHz, harmonic = 2 U Dee = 50 kV m( 14 N 5+ ) = 14.067

70. Central trajectory

71. Radial amplitude

72. Phases and energy

73. Emittance at the inflector exit

74. Beam parameters Parameters Coordinates αβ mm/mrad γ mrad/mm ε π∙mm∙mrad R 2.20274104 Z -0.50125320 φ RF -0.25.5 °RF/keV0.2 keV/°RF273 π °RF ∙keV Parameters Coordinates Average- position mm 2σ- deviation mm Average- angle mrad 2σ-angle mrad R 23.41.538.75205 Z 01.80200.3 φ RF -65 °RF38.8 °RF55.1 keV7.2 keV Twiss Statistics

75. Flat-Top off/on

76. Axial motion (Flat-Top off/on)

77. Emittances (Flat-Top off) Dee 1 center – azimuth bunch position

78. Emittances (Flat-Top on) Dee 1 center – azimuth bunch position

79. Beam parameters (Flat-Top off) Parameters Coordinates αβ mm/mrad γ mrad/mm ε π∙mm∙mrad R 00.51.9268 Z -0.920.942 φ RF -0.10 °RF/keV96 keV/°RF130 π °RF ∙MeV Parameters Coordinates Average- position mm 2σ- deviation mm Average- angle mrad 2σ-angle mrad R 55211.8-14.622.7 Z 09.406 φ RF -36.8 °RF62.7 MeV3.5 MeV Twiss Statistics

80. Beam parameters (Flat-Top on) Parameters Coordinates αβ mm/mrad γ mrad/mm ε π∙mm∙mrad R -1.30.92.763 Z 0.31.50.733.5 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 5527.8-23.313 Z 0704.9 φ RF -27 °RF62.9 MeV1.17 MeV Twiss Statistics

81. Flat-Top effect

82. Extraction

83. Analytical ESD E=71 kV/cm

84. Comparison By Goto-san This calculation

85. Optimization

86. Main result Losses from the inflector ground to the ESD mouth is 35% instead of 60%. And this result can be improved.

87. 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)

88. Modification inflector parameters Electrode potential ±3.14 kV or ±3.2 kV

89. Central trajectories Starting position (x,y,z) = (0,0,36) mm Injection - strongly axial direction Energy 45 keV ParametersTheoryCalculated Radius, mm21.06721.52 Θ - azimuth, deg53.152.4 Z C - axial position, mm02.3 Pr C, deg39.07442.3 Pz C, deg0 -0.45 Energy, keV5246.1 At the inflector exit

90. Cyclotron

91. B map modification First trim coil We added the magnetic field to the measurement B-map

92. 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

93. RF phase at the Dee’s centre For the central trajectory

94. Emittance at the inflector entrance

95. Beam parameters Parameters Coordinates αβ mm/mrad γ mrad/mm ε π∙mm∙mrad X 00.05199.5 Y 00.05199.5 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 02.2043 Y 02.2043 Z 271.545 keV1 keV Twiss Statistics

96. Cyclotron animation

97. Central region losses 2.7% 4.4% 1.8% 7.6% Total axial 15.8% Total losses 34.7%

98. Axial motion

99. 3D view

100. Emittance at the radius ~66 cm Center Dee 1 – position, not final radius

101. Beam parameters Parameters Coordinates αβ mm/mrad γ mrad/mm ε π∙mm∙mrad R 0.81.21.433 Z 0.31.90.614 φ RF 0.613.1 deg/MeV0.1 MeV/deg4.3 π mm ∙MeV Parameters Coordinates Average- position mm 2σ- deviation mm Average- angle mrad 2σ-angle mrad R 6595.634.66.3 Z 0.25.21.22.9 φ RF -7.588.12 MeV0.7 MeV Twiss Statistics

102. 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.