Challenges in Simulating MW Beams in Cyclotrons

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1 Challenges in Simulating MW Beams in Cyclotrons Y. J. Bi (CIAE & PSI & Tsinghua Univ.), A. Adelmann, R. Dölling, M. Humbel, W. Joho, M. Seidel (PSI), T. Zhang (CIAE) HB2010 Morschach, September 28, 2010 Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 1 / 22

2 Outline 1 Motivation & Background 2 Physics Model 3 Initial Conditions for the Ring Cyclotron 4 Towards Realistic Ring Simulations 5 Conclusion Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 2 / 22

Motivation: Upgrade Project of the PSI Cyclotron Facility The most powerful machine of this kind worldwide Better quantitative understanding of this

3 Motivation: Upgrade Project of the PSI Cyclotron Facility The most powerful machine of this kind worldwide Better quantitative understanding of this machine Cover: 72 MeV and Ring Cyclotron simulations Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 3 / 22

4 Background The Simulation Tool OPAL OPAL (Object Oriented Parallel Accelerator Library) is a tool for charged-particle optics in large accelerator structures and beam lines including 3D space charge OPAL-t tracks particles which 3D space charge uses time as the independent variable. OPAL-cycl tracks particles which 3D space charge including neighboring turns in cyclotrons with time as the independent variable At PSI lots of Measurements are available 18 profile monitors are available in the 72 MeV transfer line 3 time structure probes between Injector 2 and Ring Radial probes in the Ring cyclotron Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 4 / 22

5 Particle Matter Interaction Model Why implement a particle matter interaction model? General-purpose Monte Carlo codes can t track particles in both complex external field and space charge fields The particle matter interaction model Energy loss Multiple Coulomb scattering Large angle Rutherford scattering Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 5 / 22

6 Particle Matter Interaction Model cont. Ω R 3 absorbed particle Ω m t n t n+1 t deflected particle Ω v Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 6 / 22

7 Particle Matter Interaction Mode cont. Energy loss: Bethe-Bloch equation de dx = Kz2 Z Aβ 2 (1 2 ln 2m ec 2 β 2 γ 2 Tmax I 2 β 2 ) Energy straggling: Gaussian in form σ 2 0 = 4πN Ar 2 e(m e c 2 ) 2 ρ Z A s Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 7 / 22

8 Particle Matter Interaction Model cont. Multiple- and single-scattering distributions (Classical Electrodynamics, by J. D. Jackson) P M (α)dα = 1 e α2 dα, π 1 dα P S (α)dα = 8ln(204 Z 1/3 ) α 3 α = θ < Θ 2 > 1/2 = θ 2θ0 θ 0 = 13.6MeV z s/x 0 [1+ βcp 0.038ln( s/x 0 )] Relative probability P/P(0) Statistics with OPAL Jackson s formula Normalized scattering angle α Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 8 / 22

9 Particle Matter Interaction Model cont. Code Benchmark 0.02 y (m) screen z (m) Trajectories of Particles through a Slit A 72 MeV cold Gaussian proton beam with σx = σy = 5 mm is send through a copper slit with the half aperture of 3 mm. Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 9 / 22

10 Particle Matter Interaction Model cont. Comparison against two General-Purpose Monte Carlo Codes 1/GeV/particle /solid angle/gev/particle FLUKA OPAL angle (deg) OPAL MCNPX FLUKA E (MeV) Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 10 / 22

11 Initial Conditions for Ring Cyclotron 72 MeV Transfer line Add Dispersion to the initial particle distribution, including the correlation coefficient between x,px and t,pt. Specify off-center beams for the initial distribution. sigmax= 2.935e-03, sigmapx= , corrx=-0.139, offsetx= , sigmay= 0.471e-03, sigmapy=62.867, corry=0.068, offsety= , t=0.0062, sigmat= , pt= e6, sigmapt=74.8, corrt=0.0, r61=-0.920, r62=0.0, r51=0.0, r52=0.0; Fitting the profile monitor data using transport Ring cyclotron The transverse emittance obtained at the end of the transfer line The bunch length measured with the time-structure measurement Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 11 / 22

12 Initial Conditions for Ring Cyclotron cont. Simulation of the Transfer Line (2 ma) 2 σ envelope y (mm) 2 σ envelope x (mm) *SM4 *AXC *QXA11 *AXD *ZS3 *MIC OPAL-T Measurement pos (m) OPAL-T Measurement 0 *SM4 *AXC *QXA11 *AXD *ZS3 *MIC pos (m) Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 12 / 22

13 Towards Realistic Ring Simulations Flattop the energy difference from the main cavity the linear part of the space charge force voltage main cavity ideal flattop harmonic phase deg voltage main cavity tilted flattop harmonic phase deg Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 13 / 22

14 Towards Realistic Ring Simulations cont. Using Trim Coil TC15 to move away from the coupling resonance MeV without TC15 ν r =2ν z with TC15 ν z MeV 532 MeV 514 MeV 582 MeV 579 MeV 546 MeV 564 MeV ν r Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 14 / 22

15 Towards Realistic Ring Simulations cont. Δ B (kgs) Trim Coil TC x r (mm) db/dr (kgs/mm) νr 2 = 1 n νz 2 = n + ν r R 2ν r N2 N 2 1 F(1 + 2tan2 δ) } {{ } const n = db R dr B db BdR ν z ν r ν z ν r Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 15 / 22

16 Towards Realistic Ring Simulations cont. Injection Position and Angle x Centroid beam: dr dn = γ γ + 1 RdE/dn 1 E 1 + n R Turn pattern: R ν r Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 16 / 22

17 Towards Realistic Ring Simulations cont. Compare Radial Beam Profile Simulations with Measurements Effect of TC Septum 188 Intensity (a.u) Measurement OPAL with TC15 OPAL without TC r (mm) Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 17 / 22

18 Towards Realistic Ring Simulations cont. For fixed energy, the change on radius eg. p = qbr R R = B B τ τ max= 2.7e 4 B B = γ2 τ τ R max = 3mm Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 18 / 22

19 Towards Realistic Ring Simulations cont. Compare Radial Beam Profile Simulations with Measurements Impact of the initial distribution Septum 188 Intensity (a.u) Measurement Gaussian distribution Parabolic distribution r (mm) Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 19 / 22

20 Conclusion New features in OPAL The particle matter interaction model: enables the prediction of lost particles including space charge Energy loss Multiple Coulomb scattering Large angle Rutherford scattering Transfer Line and Ring simulation: Beam profiles: quantitative agreement with experiments Losses at extraction septum: quantitative agreement with experiments Large scale simulations with 4 orders of magnitude dynamic range Work in progress The experimental verification of the particle matter interaction model in the PSI 72 MeV line A better characterization of the initial conditions at the entrance of the Ring Cyclotron - correlation measurements Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 20 / 22

21 Acknowledgments C. Kraus, Y. Ineichen, J. J. Yang, H. Zhang and AMAS group member for many discussions regarding programming and experiments. D. Kiselev for the MCNPX simulations and fruitful discussions about the particle matter interaction models. *** Thanks for your attention! Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 21 / 22

22 Particle Matter Interaction Model cont. Ω R 3 absorbed particle Ω m t n t m t m+1 deflected particle t m+2 Ω v t Challenges in Simulating MW Beams in Cyclotrons HB2010 Morschach, September 28, 2010 Page 22 / 22

OPAL Introduction Lecture 1

OPAL Introduction Lecture 1 Andreas Adelmann PSI OPAL lectures FFAG Workshop 2014 OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 1 / 46 General Introduction Models in OPAL Architecture