TE/TM scheme for computation of electromagnetic fields in accelerators

We propose a new two-level economical conservative scheme for short-range wake field calculation in three dimensions. The scheme does not have dispersion in the longitudinal direction and is staircase free (second order convergent). Unlike the finite-difference time domain method (FDTD), it is based on a TE/TM like splitting of the field components in time. Additionally, it uses an enhanced alternating direction splitting of the transverse space operator that makes the scheme computationally as effective as the conventional FDTD method. Unlike the FDTD ADI and low-order Strang methods, the splitting error in our scheme is only of fourth order. As numerical examples show, the new scheme is much more accurate on the long-time scale than the conventional FDTD approach.

[1]  Fernando L. Teixeira,et al.  Dispersion-relation-preserving FDTD algorithms for large-scale three-dimensional problems , 2003 .

[2]  Alexander Novokhatski.  Transitions Dynamics of the Wakefields of Ultra Short Bunches , 1998 .

[3]  Bruno W Zotter,et al.  Impedances and Wakes in High-Energy Particle Accelerators , 1998 .

[4]  Bengt Fornberg,et al.  Some unconditionally stable time stepping methods for the 3D Maxwell's equations , 2004 .

[5]  Thomas Weiland,et al.  Transient Electromagnetic Fields Excited by Bunches of Charged Particles in Cavities of Arbitrary Shape , 1980 .

[6]  Rolf Schuhmann,et al.  A general stability analysis of FIT/FDTD applied to lossy dielectrics and lumped elements , 2004 .

[7]  Thomas Weiland,et al.  On the Unique Numerical Solution of Maxwellian Eigenvalue Problems in Three-dimensions , 1984 .

[8]  J. R. Cogdell.  Foundations of electrical engineering , 1990 .

[9]  Rolf Schuhmann,et al.  A uniformly stable conformal FDTD‐method in Cartesian grids , 2003 .

[10]  Petr N. Vabishchevich,et al.  Difference Schemes with Operator Factors , 2002 .

[11]  T. Weiland.  Time Domain Electromagnetic Field Computation with Finite Difference Methods , 1996 .

[12]  Rolf Schuhmann,et al.  Long-time numerical computation of electromagnetic fields in the vicinity of a relativistic source , 2003 .

[13]  Yuuki Sendo,et al.  Phase velocity errors of the nonstandard FDTD method and comparison with other high-accuracy FDTD methods , 2003 .

[14]  James B. Cole,et al.  High-accuracy Yee algorithm based on nonstandard finite differences: new developments and verifications , 2002 .

[15]  T. Namiki.  3-D ADI-FDTD method-unconditionally stable time-domain algorithm for solving full vector Maxwell's equations , 2000 .

[16]  Alexander W. Chao,et al.  Physics Of Collective Beam Instabilities In High Energy Accelerators , 1993 .

[17]  Rolf Schuhmann,et al.  Evaluation of the optimum tilt of a PV array using maximum global insolation technique: Research Articles , 2004 .

[18]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[19]  A. Samarskii.  The Theory of Difference Schemes , 2001 .

[20]  Rolf Schuhmann,et al.  Conservation of Discrete Energy and Related Laws in the Finite Integration Technique - Abstract , 2001 .

[21]  T. Weiland,et al.  TBCI and URMEL - New Computer Codes for Wake Field and Cavity Mode Calculations , 1983, IEEE Transactions on Nuclear Science.

[22]  N.V. Kantartzis,et al.  An unconditionally stable higher order ADI-FDTD technique for the dispersionless analysis of generalized 3-D EMC structures , 2004, IEEE Transactions on Magnetics.