Quasioptical modeling of wave beams with and without mode conversion. II. Numerical simulations of single-mode beams

Abstract

This work continues a series of papers where we propose an algorithm for quasioptical modeling of electromagnetic beams with and without mode conversion. The general theory was reported in the first paper of this series, where a parabolic partial differential equation was derived for the field envelope that may contain one or multiple modes with close group velocities. Here, we present a corresponding code PARADE (PAraxial RAy DEscription) and its test applications to singlemode beams in vacuum and also in inhomogeneous magnetized plasma. The numerical results are compared, respectively, with analytic formulas from Gaussian-beam optics and also with coldplasma ray tracing. Quasioptical simulations of mode-converting beams are reported in the next, third paper of this series.

Quasioptical modeling of wave beams with and without mode conversion. I. Basic theory

“…where the derivatives can be taken over the longitudinal or transverse coordinates. (Having g αβ,µ ∼ 1/L is indeed typical in typical applications [31].) Under these assumptions, Eq.…”

“…In Paper I, we introduce the basic theory of waves that diffract and mode-convert simultaneously. In Paper II [31] and Paper III [32], we apply this theory to perform quasioptical modeling of radiofrequency-wave beams in magnetized plasma as an example. In particular, we consider applications to mode conversion caused by magnetic shear in edge plasma [29], which, for example, is a known problem [33,34] in the Large Helical Device [35,36].…”

Quasioptical modeling of wave beams with and without mode conversion. III. Numerical simulations of mode-converting beams

“…We require H to be exactly zero initially, which is ensured by choosing an appropriate K; then, H remains zero at all ζ, as seen from Eqs. (21). The RR-based coordinates are introduced asx ≡ {ζ,˜ 1 ,˜ 2 }, where˜ σ are orthogonal coordinates transverse to the RR as specified in Paper II.…”

“…Let us split the matrix (17) into its scalar part H and its traceless part M; this gives Λ = H1 + M. We assume [21]. We can also rewrite this as…”

“…z 0 = 0.9 m, L n = 0.9 m, B 0 = 0.4 T, θ o = 80.0 • , θ s = 80.0 • , and L b = 0.9 m. The polarization angles are chosen to be α = 80.0 • and β = −27.0 • . We also adopt the initial beam profile as Gaussian[21,27] with the focal lengths Z 1 = Z 2 = 4.0 m and waist sizes w 0,1 = w 0,2 = 5.0 cm. The wave frequency is f = 77.0 GHz, which corresponds to the vacuum wavelength λ 0 ≈ 4 mm.The simulation results are presented inFig.…”