Beam dynamics of RAON accelerator system 20th May 2013 Eun-San Kim KNU (Kyungpook National Univ.)

Contents  Beam dynamics in - FRONT-END ( LEBT, RFQ, MEBT ) - LINAC ( Linac-1, Charge stripper, Linac-2, HEBT)  Beam dynamics in - Post accelerator ( Linac-2, Charge stripper) - P2DT - Linac-2

LEBT EQ BM PS Length :15.872m HV 1 DG D G 2 3 4 2.69 m ρ=0.65m 3.42 m Slit D G 3 deflector VE RFQ PS ECRIS EQ Sol 1 DG Col 2 2.69 m 3.42 m 7.42 m 4 Length :15.872m BM ρ=0.65m Chop : Chopper DG1 : Slit,View,WS,FC DG2 : EM,FC DG3 : Slit,View,WS,FC DG4 : WS PS : pair solenoid EQ : Electrostatic Quadrupole (Triplet) Col : collimation system MHB : Multi Harmonic Buncher VE : Velocity Equalizer

LEBT 1m 16m PS BM1 SLIT Chop DG2 BUN SOL VE RFQ BM2 DG1 COL D G 3 EQ Verti 6cm 4cm 2cm 1m Hori 2cm 16m 4cm 6cm PS BM1 SLIT Chop DG2 BUN SOL VE RFQ BM2 DG1 COL D G 3 EQ DG4 E C R

LEBT (1 M particle tracking) ■ Energy : 10 keV/u 238Uranium Q : 33+,34+ ■ Emittance(n,r) : 0.08 π mm mrad ■ ΔE/E ~1.5% Exit ECR Between two bends

LEBT (1 M particle tracking) Downstream MHB Upstream VE Entrance of RFQ

LEBT components Element Amount Strength Length [cm] Bending Magnet 2 Θ = 90 ˚ Pair Solenoid 4 5.0 kG 30, 30 Solenoid 1 6.0 kG 50 ESQ 3 10.0 kV 15 ,15 ,15 10.0kV 15,15 MHB 40.625 MHz . 81.250 MHz . 121.875 MHz . 24 Velocity Equalizer 40.625 MHz 10 Chopper 3 kV 15

238U+33 238U+34 RFQ (using 1 M particles from LEBT) 10 keV/u 500keV/u 81.25 MHz, 70kV124kV 238U+33 238U+34

(using 1 M particles from LEBT) RFQ (using 1 M particles from LEBT) Exit of RFQ ■238U+33 ■238U+34 Phamteq TRACK TRACK

                                                                                                                                                                                                                                                                                                                                  MEBT Exit of MEBT Exit of RFQ

Charge stripper section ORBIT

Charge stripper section Magnet parameter in CS line 　Charge state Population [%] Charge state 74+ 0.43 80+ 20.80 75+ 1.53 81+ 12.77 76+ 4.41 82+ 5.17 77+ 11.24 83+ 1.32 78+ 18.78 84+ 0.203 79+ 23.33 Slit Slit Magnet parameter in CS line Rc, Gap [mm] Leff [mm] Btip, Bgap [T] Max B' [T/m] # of element Remark* Q1 25 250 0.53 21.2 4 Q2 60 300 0.6 10 8 Bend 50 1257 1.3　 1 Q3 100 0.65 6.5 Q4A Q4 0.35 14 Q4B

Linac Layout

Linac1+CS+Linac2 (U beam from LEBT)

Linac1+CS+Linac2 (1 M particles from LEBT)

Linac1+CS+Linac2 (1 M particles from LEBT) εnx: 0.149 mm-mrad εny: 0.202 mm-mrad εnx: 0.112 mm-mrad εny: 0.135 mm-mrad εnz: 5.51 keV/u-ns εnz: 0.265 keV/u-ns

Linac1+CS+Linac2 (1 M particles from LEBT)

Linac1+CS+Linac2 (1 M particles from LEBT)

HEBT (Optics) J. Yoon

HEBT (1 M particles from LEBT)

HEBT (1 M particles from LEBT)

Proton beam (Initial Beam condition) ■ Energy : ■ Qdesign : 1 Adesign : 1 ■ Emittance(n,r) : 0.15 π mm mrad Emittance(n,full) : 0.9 π mm mrad ■ ECR extraction hall size : 5 mm ■ ΔE/E ~0.05%

Proton beam (LEBT) -60 ˚ < 84.5% < 60˚ 1D dE/E (%) 4*ezn : 1.29560 keV/u ns 1D dE/E (%) event 1D phase (degree) -60 ˚ < 84.5% < 60˚ event

Proton beam (RFQ)

Proton beam (MEBT) Exit of RFQ Exit of MEBT envelope

Proton beam (Charge stripper section)

Proton beam (Linac+CS+Linac2) Beam parameters E0 = 630.07 MeV/u for 1p σx = 1.31 mm, εnx = 0.236 mm-mrad σy = 1.43 mm, εny = 0.259 mm-mrad σz = 0.565 deg (@ 81.25 MHz) εnz = 1.10 keV/u-ns

Proton beam (Linac1+CS+Linac2)

Start-to-End Simulation (U-beam) Number of Particle Transm. Efficiency (%) Current[puA] 33+, 34+ 77 78 79 80 81 Nor.rms εx [mm-mrad] Nor. rms εy Nor. rms εz [MeV-deg] Initial 1000002 100 6/6 0.075 - LEBT 998000 99.8 0.082 3.56 RFQ 976562 97.6 5.92/5.7 0.11 0.13 1.81 MEBT 0.112 0.135 1.84 SCL1 972430 97.2 0.124 0.146 3.92 CS 822143 82.2 0.148 0.193 25.69 SCL2 813787 81.3 1.12/1.97/2.56 2.42/1.57 (9.8) 0.15 0.2 39.05 HEBT 8137887 1.12/1.97/2.56/2.42/1.57 (9.6) 0.195 0.229 165 FRIB

Start-to-End Simulation (proton) Number of Particle Transm. Efficiency (%) Current[mA] Nor.rms εx [mm-mrad] Nor. rms εy Nor. rms εz [MeV-deg] Initial 10000 100 1 0.15 - LEBT 0.005 RFQ 8784 87.8 0.87 0.175 0.174 0.019 MEBT 0.197 0.207 0.021 SCL1 8783 0.218 0.241 0.024 CS 0.233 0.250 SCL2 0.236 0.259 0.032

SCL3+P2DT+SCL2 (132Sn beam)

Linac 3 [132Sn20 , TRACE_WIN]

Linac 3 [132Sn20 , TRACE_WIN]

P2DT (132Sn beam)

SCL3+P2DT+SCL2 (132Sn beam)

SCL3+P2DT+SCL2 (132Sn beam)

SCL3+P2DT+SCL2 (132Sn beam) Beam parameters E0 = 183.60 MeV/u for 132Sn45+ σx = 2.44 mm, εnx = 0.490 mm-mrad σy = 2.46 mm, εny = 0.407 mm-mrad σz = 0.453 deg (@ 81.25 MHz) εnz = 1.62 keV/u-ns

Used simulation codes LEBT : TRACK, IMAPCT, TRANSPORT RFQ : TRACK, PARMTEQ MEBT : TRACK, IMAPCT, TRACE3D LINAC : TRACK, IMPACT, TRACE_WIN P2DT : TRACK, TRACE3D HEBT : TRACK, IMPACT, GCOSY

Errors in Linac Initial energy : 500 keV/u Beam current : 0.2 mA for each charge state Macro-particle : 1k particles for each charge state # of seed : 116 Misalignment error QMs : 150 um [Uniform] BMs : 150 um [Uniform] Cavities : 500 um [Uniform] Tilt error All elements : 5 mrad Cavities Voltage & Phase error : 1 % [Gaussian]

Orbits in Linac-1 Before correction Before correction After correction

Scheme for orbit correction [QWR] Two cell was merged to one for correction. 1cell Corrector BPMs Beam ~75.5 cm 15cm 16cm 74cm QWR Beam-line specification Strength of QMs : 0.315 ~ 0.410 T (effective length : 16 cm) Effective length of QWRs : 22 cm , Peak E field : 15 ~ 30 MV/m Initial energy : 0.5 MeV/u, Final energy : 2.57 MeV/u, # of cell : 22 BPMs and Correctors are installed in each QMs.

Scheme for orbit correction [HWR] Two cell was merged to one for correction. 20cm ~14.5 cm 1.40 m HWR1 cell 19 cm ~25cm 20cm ~14.5 cm 1.40 m 19 cm ~25cm Corrector BPMs 20cm 16.5 cm 2.72 m HWR2 cell 19 cm 25 cm 20cm 16.5 cm 2.72 m 19 cm 25 cm Corrector BPMs HWR Beam-line specification Strength of QMs : 0.364 ~ 0.540 T (effective length : 20 cm) Effective length of HWRs : 25 cm , Peak E field : 21 ~ 30 MV/m Initial energy : 2.57 MeV/u, Final energy : 18.6 MeV/u , # of cell : 13 (HWR1), 14 (HWR2) BPMs and Correctors are installed in each QMs.

Summary Start-to-end beam simulations were performed to optimize the beam and accelerator parameters for multi-charge state beams. - The simulation results show that our design is within scope of our goals. More things to do - Longitudinal emittance needs to be reduced more. - Error effects

LEBT Initial Beam condition ■ Energy : 10keV/u Uranium ■ Q_design : 33,34 A_design : 238 ■ Emittance(n,r) : 0.07/0.08 π mm mrad (U33,34) ■ ECR extraction hall size : 5 mm ■ ΔE/E ~1.5% (Q : 33.5)

LEBT (Longitudinal distribution @ RFQ entrance)

U33.5+ IMPACT-Z result U33.5+ TRACK result

LEBT Electrostatic deflectors - - - - - - - - E + + + + + + + + + d l Extraction voltage L d = 5.25 cm → beam size should become smaller than 2.5cm @ collimator

Multi harmonic buncher rf Voltage ratio for a three freq. 40.625 MHz = 1 81.25 MHz = 0.351 121.875MHz= 0.115 diameter of electrode : 4 cm CST code simulation

LEBT Velocity Equalizer system ■ Reduce the effective energy spread of two-charge state beams Shape of VE E-field e : elementary charge V0 : accelerating voltage A : mass number m0 : nucleon rest mass q0 : highest charge state of ions c : speed of light 10keV/u in 238U34+, 238U33+ Δp/p = 0.75% RFQ_Frequency : 81.25 MHz V0 : 71.04kV A : 238 m0 : 938.5 q0 : 34 MHB to RFQ → L = 1.12 m

LEBT (Proton) Element Amount Strength Length [cm] Bending Magnet 2 Θ = 90 ˚ Pair Solenoid 4 1.0 kG 30, 30 Solenoid 1 50 ESQ(Triplet) 3 2.0 kV 15 ,15 ,15 ESQ(doublet) 1.0kV 15,15 MHB 40.625 MHz . 81.250 MHz . 121.875 MHz . 24 Velocity Equalizer 40.625 MHz 10 Chopper 1 kV 15 □ Magnet strength for proton beam transport is weaker (~ 1/7) than Uranium’s

LEBT Pair solenoid FEMM code simulation

LEBT Solenoid FEMM code simulation

Charge stripper section (collimator) Collimators to prevent the damage on cryomodule Liquid Li Carbon stripper SCL1 Charge stripping section with matching section Horizontal and vertical width of collimator X [cm] Y [cm] 1st slit 0.6 2nd slit 0.8 3rd slit 0.5 1.0 4th slit 0.7 5th slit Collimation rate in each collimator in CS line Loss particle 77 78 79 80 81 % kW 2nd slit 0.145 0.084761 0.005 0.01 0.06 0.05 0.02 3rd slit 0.195 0.113989 0.025 0.04 0.065 4th slit 0.105 0.061378 0.03 0.015 5th slit 0.13 0.075992 0.035

Charge stripper section Energy straggling : 0.011 % rms (solid carbon) 2. SRIM calculation (straggling) Stripper Solid carbon ΔE (MeV/u) 0.14 E FWHM (MeV/u) 0.00209 Angle (mrad) 0.19 Angle FWHM (mrad) 0.45 SRIM 0.3 mg/cm2 (carbon foil) Energy loss : 0.14 MeV/u Energy straggling : 0.011 % rms Angular straggling : 0.19 mrad

Charge stripper section (solid carbon) The simulation of the stripping efficiency and straggling are required to estimate the effect of the solid carbon stripper. Charge stripping rate estimation → LISE ++ 0.3 mg/cm2 (carbon foil)