Beam tracing in inhomogeneous anisotropic plasmas

Abstract

An asymptotic method for solving the wave equation in the short-wavelength limit is presented. This method, called beam tracing, takes into account the wave properties, i.e., diffraction and interference. It reduces the full wave equation to a set of ordinary differential equations. In this respect, it differs from all other asymptotic techniques describing diffraction which end up with much more complicated partial differential equations. The resulting system of beam tracing equations is expressed in terms of the same Hamiltonian function as in geometric optics (ray tracing) and, similar to the ray tracing, allows powerful numerical solving algorithms. Thus the beam tracing combines the simplicity of ray tracing with a description of the wave phenomena, which are not included in the ray tracing. The beam tracing technique provides an efficient tool for calculation of wave fields in all problems where the short-wave approximation is applicable such as rf heating, current drive and plasma diagnostics with microwave beams.

Electron-cyclotron-current-drive efficiency in DEMO plasmas

“…The ECCD calculations reported in this paper are performed with the beam tracing code TORBEAM [31,32], which employs the paraxial approximation to describe diffraction effects [33,34]. The modelling of absorption and current drive involves the fully-relativistic absorption routines written for the codes GRAY [35,36] and TORAY [37], whereas the CD efficiency is computed using Lin-Liu's routine [38], augmented with the procedure to ensure momentum conservation in electron-electron collisions [19,20,39] first developed for the TRAVIS code.…”

Paraxial WKB Method Applied to the Lower Hybrid Wave Propagation

“…The pWKB equations (9)- (11) constitute a system of ordinary differential equations 11,12,35 , for which an initial value problem is posed. In particular, the relevant quantities for the initial conditions are the launching position, the components of the refractive index (consistently with the dispersion relation) on the beam axis, the quadratic forms s ij and ϕ ij (consistently with the constraints) related to the phase front and the principal widths of the attenuation ellipse, respectively.…”

“…As mentioned in Section II, the wave energy transport equation has been evaluated on the reference ray, and that is rigorously justified only for a spatially non-dispersive medium 11,12 . The electron Landau damping is spatially dispersive, cf.…”

“…In particular, this approach allows one to derive a set of ordinary differential equations as in geometrical optics, taking into account diffraction effects [11][12][13] (see Section II). Techniques other than the pWKB approximation, such as the parabolic wave equation [14][15][16][17][18] and the quasi-optics approximation [19][20][21][22][23] , which address asymptotic solutions of Maxwell's equations in the same regime (3), have also been considered in literature.…”

Advanced launcher design options for electron cyclotron current drive on ITER based on remote steering

“…Beam tracing through the plasma has been carried out by means of the TORBEAM code [20], which includes general astigmatism and diffraction effects [21] and [22] neglected by the conventional ray tracing method. Results presented in Section 4.1 show that general astigmatic effects are of modest magnitude only, as comparison with previous results demonstrates [15].…”