A higher order FDTD method for EM propagation in a collisionless cold plasma

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Abstract
A fourth-order in time and space, finite-difference time-domain (FDTD) scheme is presented for radio-wave propagation in a lossless cold plasma. As with previously reported fourth-order schemes, the methodology is founded on the principle that correction derivatives (i.e., three derivatives in time) can be converted into vector spatial derivatives. From the error analysis and phase-velocity data, it is argued that this approach will significantly minimize the dispersion errors while still maintaining minimal memory requirements. This claim is also supported by data obtained from FDTD simulations. Using a one-dimensional plasma slab problem as the test case, we show that the bandwidth and dynamic range associated with this fourth-order scheme are significantly improved with respect to its second-order counterpart. The impact of other error mechanisms, namely material boundary-related errors, is also discussed.