Calibration simulation for 14N5+ ion acceleration regime 7 November 2008 Calibration simulation for 14N5+ ion acceleration regime E.E. Perepelkin and S.B. Vorozhtsov JINR, Dubna

Field in the axial channel GL I38 I = 252A, Nturn = 130 Bzmax =3.16 kGs GL I37 I = 115A, Nturn = 130 Bzmax = 1.442 kGs Distribution along OZ axis ( R = 0 m )

Beam before buncher Emittance εx = εy = 150 π.mm.mrad Case 1: β = 5 mm/mrad => Beam radius = 25 mm Case 2: β = 1 mm/mrad => Beam radius = 12 mm

Beam radius 25 mm

Emittance before buncher βx = βy = 5 mm/mrad 1000 particles in 3 period super-bunch

Transverse focusing GL I37 GL I38 One period selection 320 particles Focus point Z = 150 mm

Longitudinal focusing Buncher voltage U = 160 Volt (adjusted to get longitudinal focus at the 1st accelerating gap) At the inflector entrance Z = 26.5 mm At the middle of the 1st acceleration gap (cyclotron electric field is switched OFF)

Central region acceleration At the 1st gap φRF = - 30° UDEE1 = 41.2 kV Uinf = 3.6 kV fRF = 16.302 MHz UDEE2 = 49 kV Losses 61 % from the buncher to the 4th turn

Centering and RF phase Wk = 7 MeV/u “Spiral structure” is a result of the poor centering due to the asymmetry of the Dee voltages Wk = 7 MeV/u

For geometry courtesy of A. Vorozhtsov ESD For geometry courtesy of A. Vorozhtsov 8.2 mm Wk = 7 MeV/u Potential electrode Septum 1 mm Central trajectory 5.1 mm 4.9 mm 3.7 mm 2 mm

For geometry courtesy of A. Vorozhtsov ESD Potential electrode Septum Central trajectory For geometry courtesy of A. Vorozhtsov

Beam radius 12 mm

Emittance before buncher βx = βy = 1 mm/mrad 1000 particles in 3 period super-bunch

Transverse focusing GL I37 GL I38 One period selection 325 particles Focus point Z = 100 mm

Longitudinal focusing Buncher voltage U = 160 Volt (adjusted to get longitudinal focus at the 1st accelerating gap) At the inflector entrance Z = 26.5 mm At the middle of the 1st acceleration gap (cyclotron electric field is switched OFF)

Central region acceleration At the 1st gap φRF = - 30° UDEE1 = 41.2 kV Uinf = 3.6 kV fRF = 16.302 MHz UDEE2 = 49 kV Losses 54 % from the buncher to the 4th turn

Extraction

ESD central trajectory UESD = 37.6 kV 14N5+ Wk = 7.022 MeV/u Angle, Pr = 1° R = 727.84 mm Azimuth, φ = 0°

Conclusions Asymmetric dee voltages permit the beam to get through the channel at the 1st turn. =>Precession of the beam center as a side effect. There is clear visible the reserve for increasing the beam transmission by additional adjustment of the GLs setting. Extraction study will be upgraded by introduction of the effects of the harmonic coil and EMC field in the simulations

Discussion and question Inflector voltage 3.6 kV

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Goto-san central trajectory calibration Goto-san’s Central trajectory Theoretical inflector trajectory rotated at -3° Theoretical inflector trajectory used in CBDA Goto-san’s trajectory CBDA trajectory Strange

Reference particle initial parameters Case W MeV/u X mm Y Px MeV/c Py R Ɵ deg Pr degree Vesd kV Goto-san 12.03.08 7.02 728 −11 563 1603 −0.866 Word −11.63 −0.915 18.468 Excel 7.022 727 −0.51 − 727.84 −0.040 2.186 CBDA Analytical ESD field 1 47 3D ESD field 37.6

Goto-san’s parameters W = 7.02 MeV/u from Word file W = 7.022 MeV/u from Excel file X = 728 mm, Y = -11 mm from Word file X = 727 mm, Y = -0.51 mm from Excel file PX = 563 MeV/c, PY = 1603 MeV/c from Word file. Arctan(PY/PX) = 70.648 deg, ( Pr = 18.468 deg ) From Excel file Arctan(ΔY/ΔX) = 89.2 deg, where ΔX = X1-X0, ΔY = Y1-Y0, ( Pr = 2.186 deg )

CBDA parameters UESD = 47 kV ( obtained ) W = 98308 keV ( 7.022 MeV/u, Excel ) R = 727.84 mm ( Excel ) Θ = -0.04 deg ( Excel ) Pr = 1 deg ( obtained ) Mass A = 14 Integration step τ = 10-11 sec ( ~ 0.78 mm ) Angle between the analytical ESD field and the particle velocity is 90 deg.

ΔR(φ) = RCBDA(φ) – RGoto-san(φ) Comparison ΔR(φ) = RCBDA(φ) – RGoto-san(φ) ESD mouth ESD exit