William & Mary

Gene Tracy: 'Ray Tracing and Beyond'


Ray tracing is simple to explain at one level: “We all do it all day long: That’s how you navigate the world visually,” Gene Tracy explains. “The fact that I know that you’re sitting there and not over there is because the light from you to my eye travels in a straight line.”

Tracy, the Chancellor Professor of Physics and current chair of the department at William & Mary, is one of the authors of a collection of techniques, methods and equations that can be used in more complex ray-tracing applications. Tracy and his co-authors have collaborated for almost twenty years on the work summarized in the book, and they felt it was important to bring the results together in one place, as well as to describe new ideas that haven’t yet appeared in print.

Ray Tracing and Beyond is directed especially at understanding the waves in plasma. Plasma, often called the fourth state of matter, is an electrically conductive fluid. Plasma is like a gas, but it’s not a gas.

Even in visible light, ray tracing can get complex pretty quickly. When you expand your thinking beyond a single set of rays reflecting from a single object, light enters your field of view from all different directions.

“If you want to characterize the light field, at each point in space, you have to know what the direction is and what the color is,” Tracy explained. The larger, more complex, set of information is known as the ray phase space. “That’s the space we work in.”

Even relatively small changes in temperature can warp visible light, complicating the ray behavior and creating the heat waves that you see above hot asphalt and other similar mirage phenomena. In comparison to the already considerable phase space of visible light, the phase space of plasma seems, to a layman, almost unimaginably more complex. Think of a mirage packed inside of an illusion living happily in a house of mirrors, none of which ever holds still.

Wait, there’s more. All of this goes on in four dimensions of spacetime and another four dimensions that characterize the direction of the ray and its color (actually, the wave frequency). So the natural phase space for a ray is eight dimensional, a state that Tracy acknowledges can be difficult to visualize.

“In plasma, the waves bend and do all sorts of funky stuff,” Tracy said. “In addition, they can split. There are these resonance phenomena that occur where you can have one ray come in and two come out.”

Ray Tracing and Beyond is a mathematical choreography of plasma’s funky dance. It’s important to understand—and predict—the behavior of plasmas. To understand plasma goes a long way toward understanding how we might produce fusion energy. Fusion is the nuclear energy that powers the sun and is different from fission—the nuclear process used in the nuclear power plants of today. Fusion offers great potential as an energy source, potential that is a long way from being realized.

“The long-term goals of the fusion program are to generate electricity,” Tracy said. “It’s been a very long-term research program. Fusion energy has always been 30 years away, because everything always turns out to be more difficult than you think.”

Ray Tracing and Beyond presents a methodology for solving equations that describe electromagnetic radiation in plasma—although Tracy notes that the mathematical tools  discussed in the book can be used in very general settings far removed from plasma physics. Plasma science has astronomical/cosmological applications (stars are essentially balls of plasma), but the subject of the book is primarily plasmas that are generated here on earth in devices called tokamaks.

In a sense, a tokamak is an artificial star. Hydrogen gas is heated to temperatures greater than the sun and contained in powerful magnetic fields to produce the electrically charged plasmas.

“The particular application of this research has to do with using electromagnetic waves to heat fusion plasmas to thermonuclear conditions,” Tracy said. “Our algorithm, our code—the whole theory is developed in the book—is the first algorithm that can deal with this ray-splitting phenomenon inside a tokomak. That’s the primary application we’ve worked on.”

Although along the way, Tracy and his co-authors have applied similar methods to study equatorial waves in the ocean, and others have used them to study what are called “magnetoacoustic” waves in the sun.

The book will draw an important readership of plasma/fusion scientists and engineers, although Tracy said that the audience is not likely to be large for a book that probably averages four equations per page.

“Right now, it’s around two-millionth on Amazon,” he deadpanned, “although it did rise to 160,000th.”