Rayleigh-Ritz based expansion method for wakefields in dielectrically lined rectangular waveguides

Abstract In this work, a semi-analytical method for determining wakefields in dielectrically lined rectangular waveguides is presented. This approach is based on a Rayleigh–Ritz method to analytically identify the eigenmodes of the structure, which is currently studied for the application as a so-called ‘wakefield dechirper’. The electric field is subsequently determined through an eigenmode expansion, and the wakefield is calculated from the electric field. By virtue of using an analytic ansatz throughout the wakefield determination, an expression for the Green's function wakefield is found. The semi-analytical method is then benchmarked against simulations using purely numerical approaches. Compared to numerical approaches, the advantages of the presented method are the independence from any need of discretisation, the computational efficiency of the method's presented Python-based implementation and finally the opportunity to calculate a true Green's function wakefield. From this Green's function, the wake potentials of different bunch shapes can be obtained via convolution.

[1]  A. Mosnier,et al.  Wakefields of short bunches in the canal covered with thin dielectric layer , 1997, Proceedings of the 1997 Particle Accelerator Conference (Cat. No.97CH36167).

[2]  Carlsten,et al.  Subpicosecond compression of 0.1-1 nC electron bunches with a magnetic chicane at 8 MeV. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  V Yakimenko,et al.  Experimental observation of energy modulation in electron beams passing through terahertz dielectric wakefield structures. , 2012, Physical review letters.

[4]  Paul Schoessow,et al.  Electromagnetic Wake-fields and Beam Stability in Dielectric Slab Structures , 1997 .

[5]  Thomas Weiland,et al.  Wake Fields and Wake Field Acceleration , 1984 .

[6]  Paul Schoessow,et al.  ELECTROMAGNETIC WAKE FIELDS AND BEAM STABILITY IN SLAB-SYMMETRIC DIELECTRIC STRUCTURES , 1997 .

[7]  Gennady Stupakov,et al.  Corrugated Pipe as a Beam Dechirper , 2012 .

[8]  Guido Vanden Berghe,et al.  Efficient computation of high index Sturm-Liouville eigenvalues for problems in physics , 2008, Comput. Phys. Commun..

[9]  Alexei Kanareykin,et al.  Transverse operator method for wakefields in a rectangular dielectric loaded accelerating structure , 2013 .

[10]  C. Swinson,et al.  Experimental demonstration of energy-chirp compensation by a tunable dielectric-based structure. , 2013, Physical review letters.

[11]  Alexei Kanareykin,et al.  PASSIVE MOMENTUM SPREAD COMPENSATION BY A "WAKEFIELD SILENCER " , 2016 .

[12]  Heung-Sik Kang,et al.  Femtosecond Electron Beam Bunch Compression by Using an Alpha Magnet and a Chicane Magnet at the PAL Test Linac , 2004 .

[13]  Guido Van Rossum,et al.  Python Tutorial , 1999 .

[14]  D. Mihalcea,et al.  Three-dimensional analysis of wakefields generated by flat electron beams in planar dielectric-loaded structures , 2012, 1204.6724.

[15]  T. Weiland,et al.  Wake fields and impedances , 1992 .

[16]  C. D. Park,et al.  Experimental demonstration of energy-chirp control in relativistic electron bunches using a corrugated pipe. , 2014, Physical review letters.

[17]  R. Collin.  Field theory of guided waves , 1960 .

[18]  Ursula van Rienen,et al.  Numerical methods in computational electrodynamics , 2000 .

[19]  Perry B. Wilson,et al.  Introduction to wakefields and wake potentials , 1989 .