Intensity of focused waves near turning points

Area of Science:

• Plasma physics
• Wave propagation
• Catastrophe theory

Background:

• Standard wave models near turning points use Airy functions.
• This approximation is insufficient for complex wave fields like focused beams.

Purpose of the Study:

• To present a more complete description of wave behavior near turning points.
• To introduce the hyperbolic umbilic function as a key element in realistic wave field descriptions.

Main Methods:

• Asymptotic matching of incoming wave fields.
• Analysis of hyperbolic umbilic functions in wave propagation.
• Modeling focused Gaussian beams in varying density profiles.

Main Results:

• Wave behavior transitions from Airy to hyperbolic umbilic functions due to phase front curvature.
• Detailed morphology of caustic lines is presented, influenced by plasma density, beam focal length, and injection angle.
• Goos-Hänchen and focal shifts at oblique incidence are observed, absent in simpler ray models.

Conclusions:

• Hyperbolic umbilic functions provide a more accurate description of waves near turning points.
• The findings enhance understanding of wave phenomena relevant to nuclear fusion experiments.
• Improved reduced wave models can be developed based on these insights.