Introduction

Raytracing is one of the first theories of light propagation to ever

be developed. A ray, conceptually, represents the flow of power or

the path taken by “packet” of electromagnetic energy through a

system.

Introduction

Raytracing is one of the first theories of light propagation to ever

be developed. A ray, conceptually, represents the flow of power or

the path taken by “packet” of electromagnetic energy through a

system. Raytracing, more formally, is a reduction of Maxwell’s

equations to a much simpler and more computationally tractable form,

under fairly modest assumptions of smooth variation.

Raytracing has been used to study wave propagation and phenomena in

the ionosphere and magnetosphere for over 50 years

[Kimura(1966), Haselgrove(1955)].

Initially, the primary motivator was computational tractability. The

cost in computing a ray path in the magnetosphere is relatively small

compared to the cost of a global solution like that obtained using

finite difference or finite element methods. Initial investigations

were even carried out graphically

[Maeda and

Kimura(1956)].

In a modern context, however, raytracing is still a very important

computational tool for investigating magnetospheric phenomena. Due to

the enormous length scales (many megameters) and timescales (10s of

seconds), full simulations of wave propagation over the entire

magnetosphere are still difficult if not intractable on modern

computers.

Modeling efforts

The Stanford VLF group’s raytracing modeling efforts include:

**Flexible raytracing simulation**: The Stanford 3D ray tracer

can accommodate any arbitrary magnetic field or plasma density

function, opening up the possibility to study the role of

large-scale inhomogeneities, like plumes or notches, in the

propagation of VLF waves.

**Modeling of loss and growth processes**: Accurate modeling of

loss processes, like Landau and cyclotron damping, is essential to

accurate interpretation of raytracing results. The Stanford VLF ray

tracer can calculate the losses for any arbitrary distribution

function distributed over space, including observation-based models.

**Physically-based and observation-based models**: We have

integrated the IGRF, Tsyganenko, GCPM, and our own radial diffusion

model in our raytracer.

VLF Raytracing demonstrations

The VLF group at Stanford uses a 3D magnetospheric raytracer to study

many different wave propagation effects in the inner magnetosphere.

Ray paths in HF (as shown in Figure 1) show

characteristic total internal reflection off the ionosphere, an effect that is used for long-distance HF communication.

At VLF frequencies, however, the phenomena encountered are much richer

– rays can reflect off specular boundaries, magnetospherically

reflect, or even significantly drift in longitude, as shown in

Figures 2 and

3.

A short movie here illustrates how VLF

waves can propagate and reflect in the magnetosphere, in real time:

The panel on the left shows the refractive index surface, which is a

plot of the refractive index as a function of direction. The arrow in

blue on this plot shows the group velocity, or the direction of the

ray. On the right, we show the actual ray path superimposed on a

model-based electron density distribution with a very sharp

plasmasphere “knee”. The red arrow shows the direction of the

wavenormal, which in a plasma is not, in general, coincident with the

group velocity. A few interesting features can be seen clearly in

this visualization. Four of the reflections are termed MR

(magnetospheric reflections) and occur because the refractive index

surface’s topology changes from opened to closed, permitting an abrupt

change in the group velocity for a relatively small change in the

wavenormal at near-perpendicular propagation. The remaining two are

pseudo-specular reflections at the sharp plasmasphere boundary.

Bibliography

- Haselgrove(1955)

Haselgrove, J. (1955), Ray Theory and a New Method for Ray Tracing, in

Physics of the Ionosphere, pp. 355-+.- Kimura(1966)

Kimura, I. (1966), Effects of Ions on Whistler-Mode Ray Tracing,

Radio Science, pp. 269-283.- Maeda and Kimura(1956)

Maeda, K., and I. Kimura (1956), A Theoretical Investigation on the

Propagation Path of the Whistling Atmospherics, Rept. Ionosphere

Res., pp. 105-123.