• P. Lebrun
  Fermilab, Batavia
• P. Stoltz, S.A. Veitzer
  Tech-X, Boulder, Colorado

Simulation of the microwave transmission properties through the electron cloud at the Fermilab Main Injector have been implemented using the plasma simulation code ‘‘VORPAL". Phase shifts and attenuation curves have been calculated for the lowest frequency TE mode, slightly above the cutoff frequency, in field free regions, in the dipoles and quadrupoles. Preliminary comparisons with experimental results are discussed and will guide the next generation of experiments.

• D.T. Abell, I.V. Pogorelov, P. Stoltz
  Tech-X, Boulder, Colorado

Funding: Supported in part by the DOE Office of Science, Office of High-Energy Physics under grant No. DE-FG02-06ER84485.

We present realistic models, including fringes, for several standing-wave modes in rf cavities. These models include a simple accelerating mode and a TM-110 (crab) mode. They are useful for the accurate computation of transfer maps* as well as for constructing model fields that can be used for testing and comparing a variety of rf cavity codes.

*D.T. Abell, "Numerical computation of high-order transfer maps for rf cavities", Phys. Rev. ST Accel. Beams 9, 052001, (2006).

• M.C. Lin, C. Nieter, D.N. Smithe, P. Stoltz
  Tech-X, Boulder, Colorado

Funding: DoD FA9451-07-C-0025

This work introduces a conformal finite difference time domain (CFDTD) method as implemented in VORPAL to accurately and efficiently study RF cavities. For illustration, an A6 magnetron cavity has been employed and the corresponding dispersion relation has been carried out. The accuracy of the CFDTD method is measured by comparing with SUPERFISH calculations. To verify the accuracy of the CFDTD simulations, a geometric model has been constructed in VORPAL and simulated with different mesh numbers as 10,000, 40,000, 90,000, 160,000, and 250,000 for three DM_FRAC values equal to 0.75, 0.5 and 0.25, respectively. The results show an accuracy of 99.4% can be achieved by using only 10,000 meshes with Dey-Mittra algorithm. By comparison, a mesh number of 360,000 need be used to preserve an accuracy of 99% in the conventional FDTD method. One should be careful using conventional FDTD to study systems with complicated geometry as the staircased meshes fail to conform the boundary correctly. The simulation time of studying the interaction of particles with fields inside cavities can be dramatically reduced by using CFDTD particle-in-cell simulation without losing accuracy.

* C. Nieter, J. R. Cary, J. Comput. Phys. 196, 448-473 (2004).
** S. Dey, R. Mittra, and S. Chebolu, Microwave and Opt. Technol. Lett. 14, 213-215 (1997).

• C. Nieter, C. Roark, P. Stoltz
  Tech-X, Boulder, Colorado
• K. Tian
  JLAB, Newport News, Virginia

Funding: Department of Energy SBIR grant DE-FG02-05ER84172

We will present the results of benchmarking simulations run to test the ability of VORPAL to model multipacting processes in Superconducting Radio Frequency structures. VORPAL is an electromagnetic (FDTD) particle-in-cell simulation code originally developed for applications in plasma and beam physics. The addition of conformal boundaries and algorithms for secondary electron emission allow VORPAL to be applied to multipacting processes. We start with simulations of multipacting between parallel plates where there are well understood theoretical predictions for the frequency bands where multipacting is expected to occur. We reproduce the predicted multipacting bands and demonstrate departures from the theoretical predictions when a more sophisticated model of secondary emission is used. Simulations of existing cavity structures developed at Jefferson National Laboratories will also be presented where we compare results from VORPAL to experimental data.

• I.V. Pogorelov, D.T. Abell, P. Stoltz
  Tech-X, Boulder, Colorado

Funding: Supported in part by the DOE Office of Science, Office of High-Energy Physics under grant No. DE-FG02-06ER84485.

We present our recently developed capability for generating High-Order Mode (HOM) maps of rf cavity fields for use in particle tracking code-based simulations. We use VORPAL field data as a starting point, and follow the approach of* to produce the maps that are subsequently incorporated into the MaryLie/IMPACT and Synergia frameworks. We present and discuss the results of applying this new modeling tool to crab cavity simulations.

*D.T. Abell, "Numerical computation of high-order transfer maps for rf cavities", Phys. Rev. ST Accel. Beams 9, 052001, (2006).

• S.A. Veitzer, P. Stoltz
  Tech-X, Boulder, Colorado
• J.M. Byrd
  LBNL, Berkeley, California
• K.G. Sonnad
  FZK, Karlsruhe

Funding: This work funded by the Department of Energy under Small Business Innovation Research Contract No. DE-FG02-08ER85042.

Microwave transmission in accelerator beam pipes is providing a unique method for determining electron cloud characteristics, such as density, plasma temperature, and potentially the efficacy of electron cloud mitigation techniques. Physically-based numerical modeling is currently providing a way to interpret the experimental data, and understand the plasma-induced effects on rf signals. We report here recent applications of numerical simulation of microwave transmission in the presence of electron clouds. We examine the differences in phase shift induced by TE11 and TM01 modes in circular cross section beam pipes for uniform density electron clouds. We also detail numerical simulation of the cyclotron resonance and examine how the width of the resonance changes with applied dipole magnetic fields strength and cloud temperature.