Time-domain formulation of cold plasma based on mass-lumped finite elements

Recent advances in FDTD simulations of simple dielectrics have opened the possibility of various forms of local refinement [1]. These possibilities are based on writing FDTD as a special case of a finite element technique. We have shown [3] that these techniques can be extended to Body-Of-Revolution (BOR) FDTD which is well-suited for modelling toroidal cavities. Further extending this technique to the time-domain modelling of plasmas presents difficulties: The classical "Whitney" basis-functions (and their analogues in toroidal geometries) are insufficiently smooth to be used as "testing" functions the time-domain constitutive equations of cold plasma [2]. In this paper, we present a set of basis-functions that can be used to write time-domain cold plasma as a mass lumped finite element scheme

Implicit local refinement for evanescent layers combined with classical FDTD

In this letter we hybridize the well-known FDTD method with the fully implicit method of [1]. In effect, this enables local space refinement without necessitating a smaller time step. In particular, this is very useful for thin layers of highly conducting material or to treat complex media, such as plasma, allowing evanescent waves

A time-domain discretisation of Maxwell's equations in nontrivial media using collocated fields

In this paper we present an unconditionally stable time-domain discretisation of Maxwell's equations where the discretized fields are collocated. This allows us to combine Maxwell's equations, which are usually discretized on a staggered grid, with constitutive differential equations which may not be well-suited for staggered grids. This approach guarantees that the numerical dispersion relation always closely mimics the exact one

A new approach to BOR-FDTD subgridding

In this paper the approach followed by Chilton et all. to develop a provably passive and stable 3D FDTD subgridding technique, is adapted to Body-Of-Revolution (BOR) FDTD. To this end a new set of basis functions is presented together with the mechanism to assemble them into an overall mesh consisting of coarse and fine mesh cells. To preserve the explicit nature of the leapfrog time stepping algorithm, appropriate mass-lumping concepts, again specifically adapted to the BOR-FDTD situation, are invoked. Numerical examples for toroidal cavities demonstrate the stability and accuracy of the method

3-D discrete dispersion relation, numerical stability, and accuracy of the hybrid FDTD model for cold magnetized toroidal plasma

The Finite-Difference Time-Domain (FDTD) method in cylindrical coordinates is used to describe electromagnetic wave propagation in a cold magnetized plasma. This enables us to study curvature effects in toroidal plasma. We derive the discrete dispersion relation of this FDTD scheme and compare it with the exact solution. The accuracy analysis of the proposed method is presented. We also provide a stability proof for nonmagnetized uniform plasma, in which case the stability condition is the vacuum Courant condition. For magnetized cold plasma we investigate the stability condition numerically using the von Neumann method. We present some numerical examples which reproduce the dispersion relation, wave field structure and steady state condition for typical plasma modes