Beam-Tracing Codes
Beam-tracing codes extend ray tracing to finite-width Gaussian beams, capturing diffraction and focusing that a zero-width ray cannot represent.
Beyond the infinitely thin ray
A single ray has no width, so it cannot represent diffraction or the way a focused microwave beam spreads and converges. Beam-tracing codes carry additional information along the central ray, the complex curvature and width of a Gaussian beam envelope, so the finite transverse structure evolves correctly through the plasma.
This matters when the deposition is meant to be narrow and localized, for example driving current on a specific rational surface to suppress a tearing mode. A ray predicts a delta-function spot; a beam predicts the true finite width, which changes the effectiveness of the scheme.
The paraxial expansion
Beam tracing solves the wave equation in a paraxial (near-axis) expansion around the central ray. The central ray obeys the ordinary ray equations, while the beam width and phase-front curvature evolve according to auxiliary equations driven by the second derivatives of the dispersion relation.
Where it is preferred
Beam tracing is favored for electron-cyclotron systems with strong focusing and for any application where deposition width is a design quantity. It bridges the gap between simple ray tracing and expensive full-wave solvers, retaining most of the geometric-optics speed while restoring diffraction.
Design relevance
For the Hyperion breeder, beam tracing sharpens the predicted electron-cyclotron deposition width used in tearing-mode-suppression studies, giving a more honest estimate of how precisely power can be aimed. All such work is simulation before construction begins Q2 2027.
- Carries beam width and curvature along the ray
- Captures diffraction and focusing
- Paraxial expansion around the central ray
- Better deposition-width estimates than pure rays