Description
In Inertial Confinement Fusion (ICF), optical smoothing techniques produce wide laser spots with a relatively homogeneous intensity profile. However, the resulting laser field contains small-scale intensity modulations, the speckles, produced by interference effects. As the beams propagate in the plasma, they trigger parametric instabilities. To describe these phenomena precisely, an accurate description of the laser field propagation, which includes the speckles, is critical. While it is straightforward to do so with models based on a description of the field via envelopes (temporal, or spatio-temporal ones in paraxial codes), such a method remains computationally expensive.
We propose to model the laser field with thick rays [1]. The laser field is decomposed into a set of rays which propagate individually in vacuum or plasma, and then coherently projected onto a grid with wavelength-scale resolution to reconstruct the full laser field. Unlike ray tracing methods commonly used in rad-hydro-codes [2] (both with thin and thick rays), we sum the field carried by the rays instead of their intensity to retain the phase information.
Thick rays naturally overlap within the simulation domain, enabling to represent a field as a sum of overlapping contributions. Each thick ray is a solution of the electromagnetic wave propagation equation in the vicinity of a central ray. However, because the overlapping thick rays interfere, determining the appropriate set of ray parameters (wave vector, initial amplitude, curvature, and thickness, for each ray) constitutes a challenge.
We use a Gabor series decomposition [3]. In Gabor series, a signal results from a sum of kernels localized in space and modulated by a harmonic wave. Since the transverse profile of the field carried by thick rays is Gaussian, specifying that the Gabor kernels are also Gaussian creates a natural parallel between the two descriptions. Each Gabor element is then associated with a thick ray to determine the initial parameters that best represent the incident field. We compare the field modeled with thick rays with that obtained from an envelope code [4] for different laser fields, including a constant plane wave, a Gaussian field and a smoothed laser field.
References
[1] M. Popov, Ray theory and Gaussian beam method for geophysicists, Salvador-Bahia,
EDUFBA (2002)
[2] A. Colaïtis et al., Physical Review E 89, 033101 (2014)
[3] M.J. Bastiaans, Eindhoven University of technology Research Report, 95-E-295 (1995)
[4] G. Sary et al., Phys. Plasmas 26, 072118 (2019)