TE/TM field solver for particle beam simulations without numerical Cherenkov radiation

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 a...

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Bibliographic Details
Published in:Physical review special topics. PRST-AB. Accelerators and beams 2005-04, Vol.8 (4), p.042001, Article 042001
Main Authors: Zagorodnov, Igor, Weiland, Thomas
Format: Article
Language:English
Subjects:
Cerenkov radiation
Damping
Electromagnetic fields
Finite difference method
Finite difference time domain method
Frequency ranges
Mathematical models
Particle beams
Particle in cell technique
Radiation
Time domain analysis
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Summary: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.
ISSN:1098-4402
1098-4402
2469-9888
DOI:10.1103/PhysRevSTAB.8.042001