2988 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 56, NO. 9, SEPTEMBER 2008 Scattered-Field FDTD Algorithm for Hot Anisotropic Plasma With Application to EC Heating Christos Tsironis, Theodoros Samaras, Member, IEEE, and Loukas Vlahos Abstract—Nowadays, the finite-difference time-domain (FDTD) is accepted as a reliable tool in numerical electromagnetics. In the field of wave propagation in plasmas, the mainstream in theory and applications is oriented to frequency domain asymptotic methods, where the determination of the plasma response presents less dif- ficulty. However, in many cases of interest (like, e.g., mode conver- sion) this approach breaks down, the solution becomes question- able and therefore a full-wave analysis is necessary. In this work, we present a (novel) scattered-field FDTD algorithm for fully ki- netic, anisotropic plasma. As an application, we study the perpen- dicular electron-cyclotron propagation and absorption in simpli- fied tokamak geometry, under different physics models for the di- electric response of the plasma. In general, since FDTD is a time do- main technique, conversion from the frequency domain is needed in order to be able to exploit the existing knowhow on the dielectric response. However, in the case of a constant-frequency wave prop- agating in a stationary plasma, the FDTD method can be applied directly using the frequency domain dielectric tensor. Index Terms—Anisotropic plasma, electron-cyclotron (EC) heating, finite-difference time-domain (FDTD), hot plasma dis- persion, scattered-field. I. INTRODUCTION T HE injection of electron-cyclotron (EC) waves is a stan- dard method for coupling energy to plasma electrons in modern fusion devices (tokamaks, stellarators), with primary applications the plasma heating (ECRH) and the noninductive current drive (ECCD) (see [1] and references therein). In fusion experiments, the EC waves are launched in the plasma in the form of spatially narrow beams, and interact with the electrons when the EC resonance condition is fulfilled (1) where is the wave frequency, is the cyclotron frequency ( is the magnetic field), are the wavenumber and the electron velocity components parallel to the magnetic field, and the Lorentz factor. Since the cyclotron frequency is proportional to the magnetic field, which is nonuniform in fu- sion devices, this condition is satisfied in a narrow spatial region called “resonance layer.” Manuscript received July 23, 2007; revised January 1, 2008. Published September 4, 2008 (projected). This work was supported by the EURATOM Association-Hellenic Republic. The authors are with the Department of Physics, Aristotle University of Thes- saloniki, Thessaloniki 54006, Greece (e-mail: ctsironis@astro.auth.gr). Digital Object Identifier 10.1109/TAP.2008.928774 The propagation of EC waves in the plasma is described by Maxwell’s equations. In general, to obtain a full solution to the problem is burdensome because these equations are partial dif- ferential (PDE). In numerical applications, a PDE is equiva- lent to a spatial grid progressing on a time grid, which for the wave and plasma parameters occurring in fusion may be very re- source-demanding, in some cases prohibitively. When the wave- length is small compared to the scale length of inhomogeneity of the plasma, a simplification is reached by frequency-domain asymptotic methods: ray tracing [2], quasi-optics [3] or beam tracing [4]. The solution is obtained over Hamiltonian differen- tial equations, where the dispersion function plays the role of the Hamiltonian. The plasma response is derived in terms of the linear theory of plasma oscillations [5], based on that for typical experimental parameters the wave intensity is small and falls in the linear regime. In asymptotic methods, dispersion modelling follows the standard approach of calculating wave trajectories using the Appleton-Hartree (cold plasma) dispersion relation [5]. The motivation has been the fact that, to leading order, the trajec- tories near the cyclotron resonance are exactly those of cold plasma theory. However, in cases of particular interest like the perpendicular O-mode near fundamental resonance or the X-mode near the 2nd-harmonic, the contributions of the higher orders become very large. Recently, both experimental and theoretical evidence is pointing to the possible importance of hot plasma dispersion near resonance [6], [7]. Particularly in [7], the direction of ray propagation is shown to differ dramatically from the cold plasma trajectory. This implies effects on the evolution of the polarization vector, especially near resonance, and thus on the absorption of the wave. In such cases, a full-wave treatment is called for. The finite-difference time-domain (FDTD) method is nowa- days recognized as a reliable tool in numerical electromag- netism. However, for realistic ECRH simulations, the required spatial resolution makes the computational requirements very large, and that is why there has been little application of FDTD to those problems up to day. Among the existing FDTD litera- ture on hot plasma, worthy of mention are the 1D simulations of interferometry in [8] assuming cold plasma propagation but taking into account collisional and non-relativistic cyclotron damping, followed by 3D simulations where the plasma re- sponse is described in terms of the electric polarization [9]. Also of interest are the 2D simulations of reflectometry per- formed in cold plasma with elongated magnetic geometry [10], and the simulations of fundamental ECRH in [11] where the plasma response is described by an “artificial” conductivity tensor based on fluid theory. 0018-926X/$25.00 © 2008 IEEE