Abstract
The Yee finite-difference time domain method (FDTD) is commonly used in wake field and particle-in-cell simulations. However, in accelerator modeling the high energy particles can travel in vacuum faster than their own radiation. This effect is commonly referred to as numerical Cherenkov radiation and is a consequence of numerical grid dispersion. Several numerical approaches are proposed to reduce the dispersion for all angles and for a given frequency range, that justifies itself for domains big in all three directions. On the contrary, in accelerator modeling the transverse dimensions and transverse beam velocity are small, but it is extremely important to eliminate the dispersion error in the well-defined direction of the beam motion for all frequencies. In this paper we propose a new two-level economical conservative scheme for electromagnetic field calculations in three dimensions. The scheme does not have dispersion in the longitudinal direction and is staircase-free (second order convergent). Unlike the FDTD method, it is based on a ``transversal-electric/transversal-magnetic'' (TE/TM)-like splitting of the field components in time. The scheme assures energy and charge conservation. Additionally, the usage of damping terms allows suppressing high frequency noise generated due to the transverse dispersion and the current fluctuations. The dispersion relation of the damping scheme is analyzed. As numerical examples show, the new scheme is much more accurate on the long-time scale than the conventional FDTD approach.
Highlights
The particle-in-cell (PIC) method [1] is an effective approach for simulation of beam dynamics in accelerators.The electromagnetic fields in many PIC codes are computed using the finite-difference time domain (FDTD)method [2,3]
In accelerator modeling the high energy particles can travel in vacuum faster than their own radiation
This effect is commonly referred to as numerical Cherenkov radiation and is a consequence of numerical grid dispersion
Summary
The particle-in-cell (PIC) method [1] is an effective approach for simulation of beam dynamics in accelerators. Several approaches [4 –8] have been proposed to reduce the accumulated dispersion error of large-scale threedimensional simulations for all angles and for a given frequency range These methods require the usage of larger spatial stencils and a special treatment of the material interfaces. It is extremely important to eliminate the dispersion error in the longitudinal direction for all frequencies As it is well known, the FDTD method at the Courant limit is dispersion free along the grid diagonals and this property can be used effectively in numerical simulations [9]. (TE/TM)-like splitting of the field components in time It uses an enhanced alternating direction splitting of the transverse space operator that renders the scheme computationally as effective as the conventional. The problem reads: for a bunch moving with the velocity of light c and characterized by a charge distribution , find
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