Beam Break-Up Effects in Dielectric Based Accelerators *

1. Advanced Accelerator Concepts AAC’08 Beam Break-Up Effects in Dielectric Based Accelerators* A.Kanareykin Euclid TechLabs LLC, Rockville, MD *This work is supported by the DOE, High Energy Physics

2. TEAM P.Schoessow, Euclid Techlabs LLC C.Jing, Euclid Techlabs LLC/ANL A. Kustov, Dynamic Software A.Altmark, Eltech University J.G.Power, Argonne National Lab W.Gai, Argonne National Lab A.Kanareykin, Euclid TechLabs LLC

3. Single Bunch BBU • Deflection of bunch tail by transverse wakefields from head • Amplification of injection errors as beam propagates • Especially significant for the high charge bunches used for wakefield acceleration • Not controlled using Chojnacki mode suppressor

4. BBU Effect Studies • Beam breakup (BBU) effects resulting from parasitic wakefields provide a potentially serious limitation to the performance of DLA accelerators. • The experimental program focuses on BBU measurements in a number of high gradient and high transformer ratio wakefield devices and based on a new pickup-based beam diagnostics. • The numerical part of this research is based on a particle- Green’s function beam breakup code we are developing that allows rapid, efficient simulation of beam breakup effects in advanced accelerators. • The goal of this work is to be able to compare the results of detailed experimental measurements with the numerical results to design an external FODO channel for the control of the beam.

5. Project Goals I • Implement transverse stage for controlling device transverse offset • Design heterodyne differential probe diagnostic operating in the range of 26 GHz for time evolution of the BBU instability for the high power extractor, transformer ratio enhancement and high gradient dielectric device experiments. • Design and model beam spot moment diagnostic for the 26 GHz high power extractor, transformer ratio enhancement and high gradient device experiments.

6. New Transverse Wake Diagnostics at AWA • Remotely controlled stage for transverse positioning of the test device with respect to the beam. • Phosphor screen moment analysis diagnostic. • Distortion of nonbend plane beam spot as test structure is moved parallel to beam • Modifications to the wakefield pickup system to permit measurement of 26 GHz HEM modes and their time evolution (and hence evolution of the instability)

7. Beam Envelope at AWA Test Section

8. 26 GHz DLA with Differential Field Probes Pair of coaxial probes mounted 180° apart monitor radial component of the electric field. Time evolution of the wake: Σ TM01, Δ  HEM11.

9. 26 GHz Heterodyne Signal/Data Path

10. Project Goals II • Code (DWA-BD-07) development for rapid, efficient simulation of beam breakup effects in advanced linear accelerators. • Simulations of the beam breakup experiments to be performed under Phase II: 26 GHz high power extractor, transformer ratio enhancement and high gradient device experiments.

11. Some History • DWA-BD-02 code in Pascal developed to study BBU in dielectric wakefield structures • Green’s function approach more efficient than PIC for this problem • Demonstration of control of single bunch BBU using an idealized FODO channel • W. Gai, A. Kanareykin, A. Kustov, J. Simpson, Phys. Rev. E, 55, 3481-3488 (1997)

12. Input the bunch parameters from the keyboard to create a new data set. Solve dispersion equation and create N simulated macroparticles. Input from file: coordinates, pulses, forces, FODO lattice, and energies for all N particles Calculate the wake forces affecting each particle via Green’s functions Output ‘snapshot’ to file Focusing (FODO) for all particles End of time range? Update coordinates Calculate energy losses of the particles Advance one time step Code Structure

13. ! The code does not self-consistently compute the wakefields; instead, the analytic expressions for the longitudinal and transverse mode fields are used to compute the wakefields at each time step using the macroparticle currents as sources

14. Code Upgrades • PascalC++ • 3D particle propagation algorithm • second order in time particle push (Runge-Kutta or leapfrog) • external magnetic fields from solenoids and other optical elements (quads, dipoles etc.) • optimization/parameter sweep • interface to standardized HDF5 data formatting and storage • intuitive GUI with problem setup, diagnostic, and plotting capabilities

15. New capabilities in DWA-BD-07 (I) • 3D particle algorithm. Field calculations are made via calls to an external process. In addition to being able to simulate the full 6D phase space, this framework greatly simplifies implementation of new algorithms. • Beam definition. The user can now specify either uniform or Gaussian particle distributions in the phase ellipse for a given emittance. • Arbitrary initial offsets of the distribution from the axis of the structure. • 3D beamline specifications with more realistic beamline model. Beamline elements can be individually specified as opposed to the simple tapered FODO channel model used previously.

16. New capabilities in DWA-BD-07 (II) • Replacement of particle push algorithm. The new version of the code uses a Runge-Kutta algorithm to advance the electrons in time. This provides improved accuracy and stability especially for extended computations compared to the first order (Euler) algorithm used in earlier versions. • Finite waveguide length effects, heuristic group velocity correction algorithm. The wakefield rf pulse is effectively shortened in duration because the tail of the pulse is moving with velocity vg.

17. INTERFACE (I) Twiss ellipse converted to new parameters in the cross-section (X-X’). Note that it is possible to select an individual bunch of a train Main screen of the user interface is used for experiment setup definition. Version 2.0 allows specifying 3D beams in Phase Space as upright Twiss ellipses.

18. INTERFACE (II) Focusing quads (in this case in the x-x’ plane) are plotted with a solid blue line. Defocusing quadrupoles are shown with a solid red line. Charge density pseudocolor plot for the Gaussian bunch. Brighter color corresponds to higher density.

19. INTERFACE (III) Cross-section view (x-y plane), Gaussian distribution Real time bunch train emittance

20. BBU EXPERIMENTS

21. POWER EXTRACTOR • Longitudinal wakefields are 15.3 MV/m (single 20 nC bunch and 56 MV/m for a bunch train. • Transverse wakefields generated by a single 1.5 mm, 20 nC, bunch at 1 mm offset will generate two major dipole modes (HEM11 at 23.5 GHz and HEM21 at 35.75 GHz). • Quadrupole channel around the decelerator could be used to control beam breakup • Except for the case of no offset, beam losses become noticeable around the half length of the structure. Relative intensity loss of a single bunch propagating through the 26 GHz power extractor.

22. Ramped Bunch Train Example of severe BBU in RBT experiment. Offset = .1 mm, linear taper. (x-z plane electron distributions at 100 ps intervals, top to bottom: bunches 1-4 respectively.)

23. High Gradient Experiment Maximum transmission case for high gradient structure experiment. Top: Transverse beam profile; Bottom: Bunch kinetic energy. The data is shown at 50os intervals; Z is the axial position along the structure. Optimum quad channel taper is 0.75.

24. GROUP VELOCITY The RF pulse generated in the decelerator by a single drive bunch. Snapshots of a single bunch and the excited RF pulse inside the decelerator region . (a) the bunch enters the decelerator (t=0); (b) the bunch and the RF pulse are fully inside the decelerator and the head and the tail of the RF pulse travel at different speeds (0<t<L/c); (c) the bunch reaches the exit of the decelerator (t=L/c); (d) the tail of the RF pulse exits the decelerator (t=vgL/c).

25. Future Prospects for DWA-BD-07 • Move beyond dielectric structures • Numerical Green’s functions • Use FDTD (Vorpal, Mafia…) computations of wake functions and RF cavity fields • Dielectric structure end effects • Photoinjectors, conventional linac RF structures • Future status of Parmela? DWA-BD-07 could evolve into a replacement...

26. SUMMARY • We have implemented software for rapid, efficient simulation of beam breakup effects in advanced linear accelerators, with a particular emphasis on modeling BBU in dielectric structures. • We have developed a flexible 2D and 3D Windows code, DWA-BD-07, based on analytic Green’s functions for the single particle fields in axisymmetric dielectric loaded structures. • A number of new features have been incorporated including a second order accurate particle push, finite group velocity correction, arbitrary focusing channels around wakefield structures, and new graphics. • We used the new code to model a number of planned BBU experiments. The results of the simulations show that these experiments are feasible at the Argonne Wakefield Accelerator linac. Furthermore, the usefulness of a linearly tapered quad channel in controlling beam breakup is confirmed.