OPAL Introduction Lecture 1

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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

2 General Introduction Models in OPAL Architecture 3D Space Charge Examples Data Post Processing Output formats of OPAL H5root gnuplot Python scripts Building OPAL Use Cases Cyclotron and FFAG simulations URL of the lectures OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 2 / 46

3 Outline 1 History 2 Models in OPAL for Precise Accelerator Modelling 3 Open-Source Work: New FFAG modelling capabilities OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 3 / 46

4 History OPAL originated from MAD9p (2001) MAD9 (Cern) Pooma (LANL) split operator M(s) = M ext(s/2) M sc(s) M ext(s/2) + O(s 3 ) MAD9 & Pooma died: I refactored, improved and started OPAL Changed from s to t: OPAL-t With J.Y. Yang we wrote OPAL-cycl (2009) With R. Bakker & Y. Ineichen we integrated Bet (HOMDYN) OPAL-envelope (2008) Developer summit in Ticino 2012: lot of refactoring, C++11 D. Winklehner (MIT/PSI) generalised OPAL-cycl in 2014 Ch. Rogers added FFAG capabilities to OPAL-t in Version to be released soon OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 4 / 46

5 Outline 1 History 2 Models in OPAL for Precise Accelerator Modelling OPAL in a Nutshell Particle Matter Interaction Architecture A fast Direct FFT-Based PIC Poisson Solver Iterative Poisson Solver SAAMG-PCG 3D Geometry Handling Capability Interfacing to the Outside Selected Results 3 Open-Source Work: New FFAG modelling capabilities OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 5 / 46

6 Outline 1 History 2 Models in OPAL for Precise Accelerator Modelling OPAL in a Nutshell Particle Matter Interaction Architecture A fast Direct FFT-Based PIC Poisson Solver Iterative Poisson Solver SAAMG-PCG 3D Geometry Handling Capability Interfacing to the Outside Selected Results 3 Open-Source Work: New FFAG modelling capabilities Results from ERIT-FFAG (energy/emittance recovery internal target) Tracking Studies Results from 330 MeV to 1 GeV ns-ffag Design Studies OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 6 / 46

7 OPAL in a Nutshell I OPAL is an open-source tool for charged-particle optics in large accelerator structures and beam lines including 3D space charge, particle matter interaction and multi-objective optimisation. OPAL is built from the ground up as a parallel application exemplifying the fact that HPC (High Performance Computing) is the third leg of science, complementing theory and the experiment OPAL runs on your laptop as well as on the largest HPC clusters OPAL uses the mad language with extensions OPAL (and all other used frameworks) are written in C++ using OO-techniques, hence OPAL is easy to extend. Documentation is taken very seriously at both levels: source code and user manual Regression tests running evert day on the head of the repository OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 7 / 46

8 OPAL in a Nutshell II At the moment we have an international team of 14 developers A. Gsell (PSI), T. Kaman (PSI/ETH), Ch. Kraus (PSI), Y.Ineichen (IBM), S. Russell X. Pang (LANL), Y. Bi, Ch. Wang, J. Yang (CIAE), H. Zha (Thinghua University) C. Mayes (Cornell), D. Winklehner (MIT/PSI) Ch. Rogers, S. Sheehy (Rutherford) & AA (PSI) webpage: manual: problems, suggestion etc. mailing: opal AT lists.psi.ch the OPAL Discussion Forum: OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 8 / 46

9 OPAL and its Flavours I 4 OPAL flavours exist: OPAL-t OPAL-t tracks particles which 3D space charge using time as the independent variable, and can be used to model beamlines, guns, injectors and complete FEL s but without the undulator. Field emission (dark current studies) many more linac features like auto-phasing, wake fields (short range) OPAL-envelope OPAL-envelope is based on the 3D-envelope equation (à la HOMDYN) and can be used to design FEL s. OPAL-envelope could also be used for an on-line model (incl. space charge) same lattice than OPAL-t OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 9 / 46

10 OPAL and its Flavours II OPAL-map (not yet released) OPAL-map tracks particles with 3D space charge using split operator techniques. M(s) = M ext(s/2) M sc(s) M ext(s/2) + O(s 3 ) OPAL-cycl 3D space charge neighbouring turns time is the independent variable. from p to Uranium (q/m is a parameter) Solve Poisson equation with spectral methods Use 4th-order RK, Leap Frog or adaptive schemes [Toggweiler] Single particle tracking mode & tune calculation Particle Matter Interaction Multipacting capabilities OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 10 / 46

11 Sketch of an inputfile ffag: Cyclotron, TYPE="FFAG", CYHARMON=1, PHIINIT=phi0, PRINIT=pr0, RINIT=r0, SYMMETRY=1.0, RFFREQ=200.0, BSCALE=10.0, FMAPFN="NSFFAGfieldPSI.dat"; rf0: RFCavity, VOLT=cavvol1, FMAPFN="Cav1.dat", TYPE="SINGLEGAP", FREQ=200.0, RMIN = , RMAX = , ANGLE=45.0, GAPWIDTH = 300.0, PHI0=ph; Di1:DISTRIBUTION, DISTRIBUTION = GAUSS, INPUTMOUNITS = EV, SIGMAX = , SIGMAPX = , SIGMAY = , SIGMAPY = , SIGMAT = 1e-8, OFFSETPZ = Edes*1e9, CORRX = -0.0, CORRY = 0.5; l1: Line = (ffag,rf0); OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 11 / 46

12 Sketch of an inputfile Fs1:FIELDSOLVER, FSTYPE=FFT, MX=64, MY=64, MT=64, PARFFTX=TRUE, PARFFTY=TRUE, PARFFTT=FALSE, BCFFTX=OPEN, BCFFTY=OPEN, BCFFTT=OPEN; beam1: BEAM, PARTICLE=PROTON, pc=p0, NPART=1E6, BCURRENT=1.0E-9, BFREQ=200.0; TRACK, LINE=l1, BEAM=beam1, MAXSTEPS=turns, STEPSPERTURN=180; RUN, METHOD = "CYCLOTRON-T", BEAM=beam1, FIELDSOLVER=Fs1, DISTRIBUTION=Di1; ENDTRACK; OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 12 / 46

13 OPAL Object Oriented Parallel Accelerator Library Field Maps & Analytic Models E sc = ρ/ε 0 = φ sc φ sc = ρ ε 0 & BC s Electro Magneto Optics H = H ext + H sc N-Body Dynamics Energy loss de/dx (Bethe-Bloch) Coulomb scattering is treated as two independent events: multiple Coulomb scattering large angle Rutherford scattering Field Emission Model (Fowler-Nordheim) Secondary Emission Model ([Furman & Pivi] & [Vaughan]) OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 13 / 46

14 Outline 1 History 2 Models in OPAL for Precise Accelerator Modelling OPAL in a Nutshell Particle Matter Interaction Architecture A fast Direct FFT-Based PIC Poisson Solver Iterative Poisson Solver SAAMG-PCG 3D Geometry Handling Capability Interfacing to the Outside Selected Results 3 Open-Source Work: New FFAG modelling capabilities Results from ERIT-FFAG (energy/emittance recovery internal target) Tracking Studies Results from 330 MeV to 1 GeV ns-ffag Design Studies OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 14 / 46

15 Particle Matter Interaction Energy loss de/dx (Bethe-Bloch) Coulomb scattering is treated as two independent events: multiple Coulomb scattering large angle Rutherford scattering Field Emission Model (Fowler-Nordheim) Secondary Emission Model ([Furman & Pivi] & [Vaughan]) Incident electron True secondaries Surface normal n Backscattered electron Rediffused electron θ Phenomenological- don t involve secondary physics but fit the data. Model 1 developed by M. Furmann and M. Pivi Model 2 (Vaughan) is easier to adapt to SEY curves OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 15 / 46

16 Particle Matter Interaction Energy loss de/dx (Bethe-Bloch) Coulomb scattering is treated as two independent events: the multiple Coulomb scattering and the large angle Rutherford scattering Space charge & halo generated by the obstacle A 72 MeV cold Gaussian beam with σ x = σ y = 5 mm passing a copper slit with the half aperture of 3 mm from 0.01 m to 0.1 m. OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 16 / 46

17 Particle Matter Interaction cont. 1/GeV/particle /solid angle/gev/particle FLUKA OPAL angle (deg) OPAL MCNPX FLUKA E (MeV) OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 17 / 46

18 Outline 1 History 2 Models in OPAL for Precise Accelerator Modelling OPAL in a Nutshell Particle Matter Interaction Architecture A fast Direct FFT-Based PIC Poisson Solver Iterative Poisson Solver SAAMG-PCG 3D Geometry Handling Capability Interfacing to the Outside Selected Results 3 Open-Source Work: New FFAG modelling capabilities Results from ERIT-FFAG (energy/emittance recovery internal target) Tracking Studies Results from 330 MeV to 1 GeV ns-ffag Design Studies OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 18 / 46

19 OPAL Architecture classic Ext. MAD Lang. Parser Flavors: t,cycl,envelope Optimization OPAL Solvers: Direct, Iterative Integrators Distributions FFT D-Operators NGP, CIC, TSI H5hut Fields Mesh Particles IP 2 L Load Balancing Domain Decomp. Message Passing Particle Cash PETE Trilinos Interface Trilinos & GSL OPAL Object Oriented Parallel Accelerator Library IP 2 L Independent Parallel Particle Layer Class Library for Accelerator Simulation System and Control H5hut for parallel particle and field I/O (HDF5) Trilinos OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 19 / 46

20 Outline 1 History 2 Models in OPAL for Precise Accelerator Modelling OPAL in a Nutshell Particle Matter Interaction Architecture A fast Direct FFT-Based PIC Poisson Solver Iterative Poisson Solver SAAMG-PCG 3D Geometry Handling Capability Interfacing to the Outside Selected Results 3 Open-Source Work: New FFAG modelling capabilities Results from ERIT-FFAG (energy/emittance recovery internal target) Tracking Studies Results from 330 MeV to 1 GeV ns-ffag Design Studies OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 20 / 46

21 A fast Direct FFT-Based PIC Poisson Solver Assume you know G the Green s function Assign (scatter) all particles charges q i to nearby mesh points to obtain ρ Lorentz transform to obtain ρ in beam rest frame S beam. Use FFT on ρ and G to obtain ρ and Ĝ Determine φ on the grid using φ = ρ Ĝ Use inverse FFT on φ to obtain φ Compute E = φ Lorentz back transform to obtain E sc and B sc in laboratory frame S lab Interpolate (gather) E, B at particle positions x from E sc and B sc Charge assignment and electric field interpolation are related to the interpolation scheme. If e i is the charge of a particle, we can write the density at mesh point k m as N ρ(k m ) D = e i W (q i, k m ), m = 1... M (1) i=1 where W is a suitably chosen weighting function. OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 21 / 46

22 Parallel Performance OPAL Scaling on Cray XT3 Horizon at CSCS Production Run Setup Tracking 10 7 particles 3D FFT on a grid Gaussian distribution no parallel I/O Observations Solver scales still well Load balancing not optimal anymore Moving mesh has a problem Execution time (real time) [s] tot cpu integ solver bb-adapt repart Number of cores Parallel Efficency [%] tot cpu integ 20 solver 10 bb-adapt repart Number of cores OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 22 / 46

23 Outline 1 History 2 Models in OPAL for Precise Accelerator Modelling OPAL in a Nutshell Particle Matter Interaction Architecture A fast Direct FFT-Based PIC Poisson Solver Iterative Poisson Solver SAAMG-PCG 3D Geometry Handling Capability Interfacing to the Outside Selected Results 3 Open-Source Work: New FFAG modelling capabilities Results from ERIT-FFAG (energy/emittance recovery internal target) Tracking Studies Results from 330 MeV to 1 GeV ns-ffag Design Studies OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 23 / 46

24 Iterative Poisson Solver SAAMG-PCG Boundary Problem φ = ρ ε 0, in Ω IR 3, x 2 Γ 2 x 3 = z φ = 0, on Γ 1 φ n + 1 d φ = 0, on Γ 2 Γ 1 x 1 Ω IR 3 : simply connected computational domain ε 0 : the dielectric constant Γ = Γ 1 Γ 2 : boundary of Ω d: distance of bunch centroid to the boundary Γ 2 Γ 1 is the surface of an 1 elliptic beam-pipe 2 arbitrary beam-pipe element OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 24 / 46

25 Iterative Poisson Solver SAAMG-PCG cont. We apply a second order finite difference scheme which leads to a set of linear equations Ax = b, where b denotes the charge densities on the mesh. Ω : φ = 0 Ω R 3 h h E N h W h S solve anisotropic electrostatic Poisson PDE with an iterative solver reuse information available from previous time steps achieving good parallel efficiency irregular domain with exact boundary conditions easy to specify boundary surface OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 25 / 46

26 SAAMG-PCG Parallel Efficiency efficiency [%] solution time construction time application time total ML time number of cores [A. Adelmann, P. Arbenz, et al., JCP, (2010)] obtained for a tube embedded in a grid construction phase is performing the worst with an efficiency of 76% influence of problem size on the low performance of the aggregation in ML OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 26 / 46

27 Outline 1 History 2 Models in OPAL for Precise Accelerator Modelling OPAL in a Nutshell Particle Matter Interaction Architecture A fast Direct FFT-Based PIC Poisson Solver Iterative Poisson Solver SAAMG-PCG 3D Geometry Handling Capability Interfacing to the Outside Selected Results 3 Open-Source Work: New FFAG modelling capabilities Results from ERIT-FFAG (energy/emittance recovery internal target) Tracking Studies Results from 330 MeV to 1 GeV ns-ffag Design Studies OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 27 / 46

native VTK convert to h5 with vtk2h5grid OPAL

28 3D Geometry Handling Capability of OPAL obtain geometry in STEP format mesh geometry with GMSH and export to native VTK convert to h5 with vtk2h5grid OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 28 / 46

29 Triangle-line segment intersection Boundary bounding box to speedup the collision tests We can handle arbitrary structure as long as it is closed x 0 n n v t 2 r i n t i t I 0 w u t 1 s i x 1 [C. Wang, A. Adelmann, et al.] OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 29 / 46

30 Outline 1 History 2 Models in OPAL for Precise Accelerator Modelling OPAL in a Nutshell Particle Matter Interaction Architecture A fast Direct FFT-Based PIC Poisson Solver Iterative Poisson Solver SAAMG-PCG 3D Geometry Handling Capability Interfacing to the Outside Selected Results 3 Open-Source Work: New FFAG modelling capabilities Results from ERIT-FFAG (energy/emittance recovery internal target) Tracking Studies Results from 330 MeV to 1 GeV ns-ffag Design Studies OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 30 / 46

31 Architecture Connection with other Frameworks H5root H5root & Visit.h5 gnuplot.stat STEP file gmsh/netgen vtk OPAL.in,.stat..h5 n-way parallel Disk vtk2h5grid OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 31 / 46

32 Outline 1 History 2 Models in OPAL for Precise Accelerator Modelling OPAL in a Nutshell Particle Matter Interaction Architecture A fast Direct FFT-Based PIC Poisson Solver Iterative Poisson Solver SAAMG-PCG 3D Geometry Handling Capability Interfacing to the Outside Selected Results 3 Open-Source Work: New FFAG modelling capabilities Results from ERIT-FFAG (energy/emittance recovery internal target) Tracking Studies Results from 330 MeV to 1 GeV ns-ffag Design Studies OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 32 / 46

33 PSI 590 MeV Ring - last ma initial conditions from 72 MeV transfer line simulation (OPAL-t ) rf parameters from control room using measured mid-plane field and analytic trim-coil (tc15) single particle run to verify tun numbers and tunes FIXPO OPAL-cycl nur=2nuz OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 33 / 46

PSI 590 MeV Ring - last 8 turns @ 2.2 ma [Y. Bi, A. Adelmann, et al.

34 PSI 590 MeV Ring - last ma [Y. Bi, A. Adelmann, et al., PR-STAB 14(5) (2011)] OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 34 / 46

35 Neighboring Bunch Effects- Multi Bunch Model In the model, the injection-to-extraction simulation is divided into two stages: 1 First stage, big r single bunch tracking 2 Second stage, small r multiple bunches tracking Full 3D Energy bins & re-binning Large grids needed OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 35 / 46

36 Neighboring Bunch Effects- Multi Bunch Model Single bunch and multiple bunches at turn 80 and 130 PSI 590MeV Ring transverse (mm) transverse (mm) transverse (mm) bunch longitudinal (mm) bunches longitudinal (mm) bunches longitudinal (mm) transverse (mm) transverse (mm) transverse (mm) bunch longitudinal (mm) bunches longitudinal (mm) bunches longitudinal (mm) [J. Yang, A. Adelmann, et al., PR-STAB 13(6) (2010)] OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 36 / 46

37 Outline 1 History 2 Models in OPAL for Precise Accelerator Modelling 3 Open-Source Work: New FFAG modelling capabilities Results from ERIT-FFAG (energy/emittance recovery internal target) Tracking Studies Results from 330 MeV to 1 GeV ns-ffag Design Studies OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 37 / 46

38 New OPAL Element Ring mostly contributed by C. Rogers OPAL requires modification to adequately track FFAG field maps OPAL-t allows tracking through a set of beam elements in linac-type geometry OPAL-cycl previously hard coded to use 2D mid plane field map + single RF cavity Aim to introduce the capability to track through a set of arbitrary beam elements in ring-type geometry Additionally introduce specific capability to track through a 3D field map in a sector-type geometry Use ERIT ring as test-bed for this development OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 38 / 46

39 Implementation in OPAL Software Work OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 39 / 46

40 Outline 1 History 2 Models in OPAL for Precise Accelerator Modelling OPAL in a Nutshell Particle Matter Interaction Architecture A fast Direct FFT-Based PIC Poisson Solver Iterative Poisson Solver SAAMG-PCG 3D Geometry Handling Capability Interfacing to the Outside Selected Results 3 Open-Source Work: New FFAG modelling capabilities Results from ERIT-FFAG (energy/emittance recovery internal target) Tracking Studies Results from 330 MeV to 1 GeV ns-ffag Design Studies OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 40 / 46

41 Getting closed orbit through OPAL All ERIT simulations are curtesy of C. Rogers OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 41 / 46

42 Getting closed orbit through OPAL All ERIT simulations are curtesy of C. Rogers OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 41 / 46

43 Dynamic Apperture t = s After 100 turns aperture looks okay in OPAL Is this dynamic aperture or field map aperture? Field map extent is ± 250 mm in x Particles outside aperture are lost after < 1 turn OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 42 / 46

44 Outline 1 History 2 Models in OPAL for Precise Accelerator Modelling OPAL in a Nutshell Particle Matter Interaction Architecture A fast Direct FFT-Based PIC Poisson Solver Iterative Poisson Solver SAAMG-PCG 3D Geometry Handling Capability Interfacing to the Outside Selected Results 3 Open-Source Work: New FFAG modelling capabilities Results from ERIT-FFAG (energy/emittance recovery internal target) Tracking Studies Results from 330 MeV to 1 GeV ns-ffag Design Studies OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 43 / 46

45 Lattice design & tracking with OPAL S. L. Sheehy, C. Johnstone, A 1 GeV CW FFAG High Intensity Proton Driver, IPAC MeV to 1 GeV ring 4-cell quasi-isochronous non-scaling FFAG design short (1cm long) 1 π mm mrad proton bunch acceleration is achieved with 3 cavities with an energy gain of 22 MV per turn, which is sufficient to open the serpentine channel the beam exhibits expected phase space distortion and filamentation even in the 0 ma OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 44 / 46

46 Lattice design & tracking with OPAL cont. S. L. Sheehy, C. Johnstone, A 1 GeV CW FFAG High Intensity Proton Driver, IPAC2012 OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 45 / 46

47 Lattice design & tracking with OPAL cont. S. L. Sheehy, C. Johnstone, A 1 GeV CW FFAG High Intensity Proton Driver, IPAC2012 OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 45 / 46

48 Lattice design & tracking with OPAL cont. S. L. Sheehy, C. Johnstone, A 1 GeV CW FFAG High Intensity Proton Driver, IPAC2012 OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 45 / 46

49 References A. Adelmann, P. Arbenz, et al., J. Comp. Phys, 229 (12): 4554 (2010) M. A. Furman and M. Pivi, Phys. Rev. STAB 5, (2002) Y. Bi, A. Adelmann et al., Phys. Rev. STAB 14(5) (2011) J. Yang, Adelmann et al., Phys. Rev. STAB 13(6) (2010) J. Yang, Adelmann et al., NIM-A 704(11) (2013) J. R. M. Vaughan, IEEE Transactions on Electron Devices 40, 830 (1993) M. Toggweiler, A. Adelmann, P. Arbenz, J.J. Yang, arxiv: (2012) C. Wang, A. Adelmann, et al., arxiv: OPAL Introduction Lecture 1 PSI OPAL lectures FFAG Workshop 2014 Page 46 / 46

Challenges in Simulating MW Beams in Cyclotrons

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