ABCI Features and Applications

1. ABCIFeatures and Applications Yong Ho Chin KEK ICFA mini-Workshop on “Electromagnetic wake fields and impedances in particle accelerators” Erice, Sicily, on 24-28 April, 2014 ICFA Mini-Workshop, Chin

2. Outline • ABCI Package • Special Features • Parallel processing in OpenMP for shared-memory computers • Scaling in the number of cores/threads • High accuracy, often used for benchmarking of other codes. • Two Examples of Demanding Benchmark Tests • Impedance of a ceramic insert in a chamber gap • Directional symmetry of wake potential • Moving window and mesh • Shobuda-Napoly Integral • Example of Unique Application • Wake potential for a counter rotating beam ICFA Mini-Workshop, Chin

3. ABCI • ABCI is a computer program which solves the Maxwell equations directly in the time domain when a bunched beam goes through an axi-symmetric structure on or off axis. • Development started at CERN in 1992. • The comprehensive package of the Window version (both in 32-bit and 64-bit) is now available with • Windows stand-alone executable module (no installation) • Parallel processing in OpenMP for shared-memory computer • Dynamic memory allocation • Allowing any number of meshes as far as the total allocated memory is within a physical memory of your PC. • Windows version of Topdrawer for graphical outputs ICFA Mini-Workshop, Chin

4. Movie; KEK ARES Cavity ICFA Mini-Workshop, Chin

5. Download and Run ABCI • Download the Window package from the ABCI home page • http://abci.kek.jp/abci.htm • Linux version is also available from • http://abci.kek.jp/linux.htm ICFA Mini-Workshop, Chin

6. Special Features • Parallel processing in OpenMP for shared-memory computers (PC with several CPUs or a CPU with multiple cores/threads which share the same memory (e.g., Corei7 – 4 cores/8 threads). • Handy for users who run ABCI on their own PCs, rather than a large cluster system of a central computer lab. • Easier control of CPU power and more flexible job management. ICFA Mini-Workshop, Chin

7. Scalability of Parallel ABCI Good Linearity of Run Speed to No. of Threads ICFA Mini-Workshop, Chin

8. Benchmark Tests Demonstrating High Accuracy • Two examples of demanding benchmark tests • A ceramic insert in a chamber gap (Shobuda’s talk) • The exact theoretical solution exists • Open boundary (no reflection) surrounding the insert • Beam pipes as waveguides for propagation of wakefields • Co-exsitence of two (three) different kinds of materials: • Ceramic insert (dielectric material) • Trapped modes inside the ceramic • Perfectly conductive metal pipes in both ends g t e Metal pipes Ceramic insert a ICFA Mini-Workshop, Chin

9. Trapping Mechanism of Wavesinside Ceramic • With e=11, a wave will be ~50% reflected at the boundary between the ceramic and the vacuum. • This reflection can loosely trap waves and then creates trapped modes inside the ceramic. Metal Metal Ceramic ICFA Mini-Workshop, Chin

10. Comparison between Theory, ABCI and CST Studio • a=65mm, t=5mm, g=10mm, e=11 Red: Theory Black: ABCI Blue: CST Studio Red: Theory Black: ABCI Blue: CST Studio Red: Theory Black: ABCI Blue: CST Studio g ICFA Mini-Workshop, Chin

11. Transverse Impedances of the Ceramic Insert for the Same Geometry • Perfect agreement between the theory and ABCI, including the precise structures of trapped modes inside the ceramic insert, while CST Studio always tends to give larger impedances, though the resonant frequencies look all right. Red: Theory Black: ABCI Blue: CST Studio ICFA Mini-Workshop, Chin

12. For Other Combinations of Parameters • Perfect agreements between the theory and ABCI for any combination of the parameters. Red: Theory Black: ABCI Blue: CST Studio Red: Theory Black: ABCI Blue: CST Studio a=65mm, t=5mm, g=20mm, e=11 a=35mm, t=5mm, g=10mm, e=11 ICFA Mini-Workshop, Chin

13. A Simpler Test • Directional symmetry of wake potential • Wake potentials should be identical when the direction of a structure is reversed: Difference ~0.1% ICFA Mini-Workshop, Chin

14. Moving Mesh • Moving window and mesh. • The mesh is dynamically generated only for the window frame where wake fields are computed, as the windows moves together with the beam. • Only the mesh for this segment of the structure, or the window frame, exists in the computer memory. • It drastically reduces the number of mesh points, and thus allows calculation of wake potentials in very long structures and/or for very short bunches. Window ICFA Mini-Workshop, Chin

15. Integration Path for Wake Potential Computation • The total momentum change of test particle due to wake fields has no dependence on its radial position for longitudinal wake potentials in monopole fields (m=0), and the transverse wake potentials in dipole fields (m=1). • Therefore, the most efficient choice of the integration path should be along the straight line at the beam pipe radius, because along the beam pipes for perfectly conductive walls ICFA Mini-Workshop, Chin

16. Iris and Step-in/out • The conventional integration method along a straight line at the beam pipe radius breaks down for the geometries: • Iris - parts of the structure extend to smaller radii • Step-in and step-out structures with beam pipes of unequal radii at the two ends. Iris Step-in ICFA Mini-Workshop, Chin

17. Napoly Integral • Napoly showed that the integration path can be detoured along the structure surface. • It eliminates the contribution from the outgoing beam pipe and puts the integration contour back to the finite length over the structure gap. • This feature was implemented to ABCI and demonstrated to be valid in 1992. (Napoly, Chin, Zotter, NIM A 344, p. 255) C Ez Ez Er+Z0H Er+Z0H Ez Ez   ICFA Mini-Workshop, Chin

18. Step-in/out Structure C Ez Er+Z0H Ez ain Ez aout   The difference between the potential energies of the electromagnetic fields surrounding the beam in the two beam pipes ICFA Mini-Workshop, Chin

19. A Problem of Napoly Integral • The original Napoly method cannot be applied to the transverse wake potentials in a structure where the two beam tubes on both sides have unequal radii. ICFA Mini-Workshop, Chin

20. Shobuda-Napoly Integral • Shobuda et al. (Phys. Rev. ST Accel. Beams 11, 011003) extended the Napoly integration method to general cases and now the Shobuda-Napoly method allows the integration contour to be confined to the finite length for any cases(the formula is exact). aout z1 z2 ain a0 ICFA Mini-Workshop, Chin

21. New Formula for Wake Potentials for Dipole Mode ICFA Mini-Workshop, Chin

22. Convergence of the Brute-Force Calculation as a Function of L L ICFA Mini-Workshop, Chin

23. Comparison between Shobuda-Napoly Integral and Brute-Force Result ICFA Mini-Workshop, Chin

24. Unique Application: Wake Potentials for a Counter-Rotating Beam • Particles in the counter-rotating beam in a circular collider can receive some effects from wakefields created by the driving beam (such as in LEP). z=0 ICFA Mini-Workshop, Chin

25. Special Case • The shunt impedance of each eigenmode seen by the counter-rotating particle is in general complex. • However, if the cavity is symmetrical in the longitudinal direction about z=0, the shunt impedance becomes real, and changes its sign according to the symmetry of the eigenmode about z=0: z=0 z=0 for symmetric mode for antisymmetric mode Ez Ez symmetric mode antisymmetric mode ICFA Mini-Workshop, Chin

26. Example for the LEP Cavity(Possibly, Another Benchmark Test) Real part of impedance for particles counter-rotating against the driving beam Real part of impedance for particles trailing behind the driving beam. ICFA Mini-Workshop, Chin