Ray Tracing and Beyond

Abstract

This complete introduction to the use of modern ray-tracing techniques in plasma physics describes the powerful mathematical methods generally applicable to vector wave equations in nonuniform media, and clearly demonstrates the application of these methods to simplify and solve important problems in plasma wave theory. Key analytical concepts are carefully introduced as needed, encouraging the development of a visual intuition for the underlying methodology, with more advanced mathematical concepts succinctly explained in the appendices, and supporting MATLAB code available online. Covering variational principles, covariant formulations, caustics, tunneling, mode conversion, weak dissipation, wave emission from coherent sources, incoherent wave fields, and collective wave absorption and emission, all within an accessible framework using standard plasma physics notation, this is an invaluable resource for graduate students and researchers in plasma physics.

Pseudo-differential representation of the metaplectic transform and its application to fast algorithms

“…Eikonal solutions to physical systems are frequently sought as a means to develop approximate, reduced models; an example is the JWKB approximation for quantum particles [38]. In reduced models, phase and envelope dynamics are typically governed by separate equations, which often makes it convenient to consider the phase and envelope as separate entities [17]. Let us therefore explore how the PMT partitions eikonal functions.…”

“…In particular, consider the modeling of electromagnetic waves in media with slowly-varying parameters. Such waves are usually described by the equations of geometrical optics [17], but this approach fails near reflection points, where the local wavenumber goes to zero. The MT provides a means to reinstate geometrical optics near reflection points, because a simple rotation of the phase space can make the wavenumber nonzero again [18].…”

Quantum versus classical effects in the chirped-drive discrete nonlinear Schrödinger equation

“…inserts this expansion into Eq. (3) and defines the continuous space-like variable x ≡ n to get [43], where S is viewed as a rapidly oscillating phase variable, whereas b is a slow amplitude. In addition, it is assumed that the derivatives of the fast phase k ≡ ∂S ∂x ,…”

“…are both slow. The slowness in our problem means |∂(ln G)/∂x| ≪ k, where G is any of the slow variables above [43]. The eikonal ansatz models our basis modes Ψ m n in discrete formalism.…”

Optical mechanical analogy and nonlinear nonholonomic constraints

“…We remark that the optical analogy may also be rephrased as follows (see e.g. [16] and [17]). We simply replace the classical mechanical action with…”