Front End Simulation, Recent Results

1. Front End Simulation, Recent Results Slava Aseev October 19, 2006

2. Content • TRACK: General Beam Dynamics Simulation Code • RFQ: design and simulations • Design of the input and output radial matchers • 8-term potential • 3D fields in the end regions • Transition cells • Recent updates of the TRACK code: • Improvement of space charge calculations • New elements supported by the TRACK • Matrix calculation • Quasi-periodical channels • Bending magnets

3. TRACK functions • Track multi-component heavy-ion beams • End-to-end simulation from ion source to target • Wide range of electromagnetic elements with 3D fields • Treat interaction of heavy-ion beams with matter • Error simulation for all elements • Beam loss analysis with exact location of particle loss • Fitting and optimization is partly supported

4. Equations The set of equations used for the step-by-step integration: where

5. Fields • Depending on the geometry and the type of the ion-optics device, • external fields can be defined as: • 3D tables of and in • 2D tables in for axial symmetric elements • 2D tables of in the median plane • for rectangular dipole magnets • 4) The fringe field fall-off for dipole and multipole elements is • described by a six-parameter Enge function: where D is the full element gap

6. Space Charge fields • Solving Poisson equation for multi-component heavy-ion beams. • The charge distribution is defined on a rectangular grid using the “cloud-in-cell” method. • The code calculates both 2D (for DC beams) and 3D (for bunched beams) space charge fields. • The 3D Poisson equation is solved with rectangular boundary conditions in the transverse direction and periodic conditions along the beam direction.

7. General Description: Supported elements • Any type of RF resonator (3D fields), DTL, CCL • Static ion-optics devices (3D fields) • Radio-Frequency Quadrupoles • Solenoids with fringe fields • Bending magnets with fringe fields • Electrostatic and magnetic multipoles • Multi-harmonic bunchers • Axial-symmetric electrostatic lenses • Entrance and exit of HV decks • Accelerating tubes with DC voltage • Transverse beam steering elements • Stripping foils or film • Horizontal and vertical jaw slits • Beam correctors • Combined static and electromagnetic fields

8. Radio Frequency Quadrupole Accelerator • 5 different sections: • Input radial matcher • Input transition cell • Regular cells • Output transition cell • Output radial matcher

9. REGULAR CELL EMS 3D geometry of the regular cell The regular cell shape The 8-term potential expansion of the regular cell

10. Multipole components of the regular cell field expansion. R0=0.34 cm, L=3.3768 cm, m=2 1. CST Electromagnetic Studio, User Manual Version 2.0, January 2004, CST GmbH, Darmstadt, Germany 2. K.R. Crandall. LANL report, LA-9695-MS, UC-28, April 19A.A. 3. A.A. Kolomiets. The code DESRFQ, ITEP/ANL, Technical note, 2005.

11. Entrance and exit transition cells: transition from zero modulation to finite modulation The entrance transition cell shape The exit transition cell shape Electric field distribution in the transition cell. The distance from the axis to electrodes of th exit transient cell.

12. Entrance and exit radial matcher sections Cut out view of the entrance RMS vanes Vane profiles of the entrance RMS Vane profiles of the exit RMS . Cut out view of the exit RMS vanes

13. Field distribution in the end regions (radial matchers) The distance from the axis to electrodes of the exit RMS. The potential expansion of the exit RMS Analytical and computer simulated falloff functions.

14. Final simulations

15. Phase space plots

16. In the beam rest frame a magnetic and electric field generated by beam space charge is where is the solution of the Poisson equation . This equation is solved in a box A boundary conditions are on a vacuum cambers walls and periodic along the beam axis Verification and improvement of space charge calculations: problem formulation

17. 2D Field of a Tilted Uniformly Charged Elliptical Cylinder in a Rectangular Pipe y x Electric field distribution along x-axis SFICH output 2D Space Charge Verification

18. Electric field Fluctuations of the electric field • Typical field as function of distance from the • bunch center • Recommendation a) Here hi is a mesh size and ri is a rms beam size, i=x,y,z

19. Mesh size variation Peculiarity of the electric field • Recommendations a) b) 0.25<hi /ri <0.5 TRACK checks conditions a) and b) and sends warning in SCwarning.dat file when this conditions are defaulted .

20. Matrix calculation • Necessary for beam optimization and matching • To compare with other beam optics codes • Use realistic fields (no “hard” edges) • Higher-order matrices are necessary for various tasks (large momentum spread, magnet spectrometers, mass-separation,…) • Method: • Use probe particles to track through the 3D external and space charge fields. Define matrices in COSY or TRANSPORT notation

21. Transport matrix calculations Probe particles coordinates at the entrance of a beam channel Probe particles coordinates at the exit of a beam channel Matrix element calculations

22. Transport matrix calculations TRACK coordinates First order matrix transformation TRACE3D and TRANSPORT coordinates CANONICAL coordinates COSY, GIOS and more…

23. TRACK calculates a rotation matrix and transforms the matrix to block diagonal form TRACK tests a sypmlecticity condition where J is the Jacobian matrix A phase advance and matched beam parameters are calculated Matrix calculation TRACK calculates 1st order matrix wrt canonical coordinates.

24. Matrix calculation: Bending magnet 2nd order transformation 1st order transformation COSY TRACK TRANSPORT 1 11 -0.305E+00 -0.287E+00 -0.308E+00 1 12 0.672E+00 0.670E+00 0.675E+00 1 22 0.155E+00 0.157E+00 0.159E+00 1 33 0.253E+00 0.110E+00 0.309E-02 1 34 -0.419E+00 -0.422E+00 -0.510E-01 1 44 -0.636E+00 -0.634E+00 -0.683E+00 1 16 0.414E+00 0.416E+00 0.422E+00 1 26 -0.221E+00 0.187E+00 0.181E+00 1 66 -0.183E+00 -0.182E+00 -0.123E+00 2 11 -0.686E-01 -0.356E-01-0.692E-01 2 12 -0.662E-01 -0.333E-01 -0.653E-01 2 22 -0.493E+00 -0.477E+00 -0.498E+00 2 33 -0.933E+00 -0.108E+01 -0.103E-01 2 34 0.571E-01 -0.382E-01 -0.556E-02 2 44 -0.348E+00 -0.448E+00 -0.347E+00 2 16 0.129E+00 0.428E+00 0.416E+00 2 26 -0.990E-01 -0.888E-01 -0.985E-01 2 66 -0.194E+00 0.462E+00 -0.332E+00 3 13 -0.762E+00 -0.797E+00-0.784E+00 3 23 -0.159E+01 -0.158E+01 -0.174E+01 3 14 0.294E+00 0.299E+00 0.207E+01 3 24 0.141E+00 0.140E+00 0.978E+00 3 36 0.349E+00 0.345E+00 0.482E+00 3 46 -0.104E+00 0.280E+00 0.354E+01 COSY TRACK TRANSPORT 1 1 0.73243 0.73013 0.73056 1 2 0.81346 0.81030 0.81657 1 6 0.25293 0.25178 0.25440 2 1 -0.57041 -0.57597 -0.57103 2 2 0.73181 0.73042 0.73056 2 6 0.53638 0.53746 0.53913 3 3 0.36111 0.36636 0.35854 3 4 0.77199 0.77010 7.61600 4 3 -1.12330 -1.12416 -0.11442 4 4 0.36784 0.36665 0.35854

25. New elements: Electrostatic chopper Side view Top view An inter electrode voltage is defined as V=U(x,y,z)*f(t), where U(x,y,z) is 3D electrostatic field between plates and f(t) is user defined function

26. eh_EM#02 eh_EM#03 eh_EM#04 eh_EM#01 eh_EM#05 New elements: Accelerating column Cut out view of the accelerating column

27. New elements: Accelerating column Input structure file for the TRACK code 1 deck Vf d R1 nstep 2 deck Vf L R nstep 3 deck Vf L R nstep 4 deck Vf L R nstep 5 deck Vf d R1 nstep Electric field along the accelerating column axis

28. V r z New elements: Grid-less four harmonic buncher Cat out view of the buncher Electric field along the buncher axis Longitudinal phase space transformation

29. Summary • The code will be available in the web-site in 1-3 months • Parallel version is ready and will be available soon (Physics Division BD group) • The Poisson solver is working now in round beamline too. • Problem: Manuals and Documentation does not describe all available features of the code. There is no “Getting Started” Manual; there are no systematic examples.