Two-Dimensional Steady Boussinesq Convection: Existence, Computation and Scaling

This research investigates laser-induced convection through a stream function-vorticity formulation. Specifically, this paper considers a solution to the steady Boussinesq Navier–Stokes equations in two dimensions with a slip boundary condition on a finite box. A fixed-point algorithm is introduced in stream function-vorticity variables, followed by a proof of the existence of steady solutions for small laser amplitudes. From this analysis, an asymptotic relationship is demonstrated between the nondimensional fluid parameters and least upper bounds for laser amplitudes that guarantee existence, which accords with numerical results implementing the algorithm in a finite difference scheme. The findings indicate that the upper bound for laser amplitude scales by O(Re−2Pe−1Ri−1) when Re≫Pe, and by O(Re−1Pe−2Ri−1) when Pe≫Re. These results suggest that the existence of steady solutions is heavily dependent on the size of the Reynolds (Re) and Peclet (Pe) numbers, as noted in previous studies. The simulations of steady solutions indicate the presence of symmetric vortex rings, which agrees with experimental results described in the literature. From these results, relevant implications to thermal blooming in laser propagation simulations are discussed.

Continuous wave high-power laser propagation in water is affected by strong thermal lensing and thermal blooming already at short distances

When laser beams propagate through media with non-vanishing absorption, the media is heated resulting in a change of the refractive index, which can lead to thermal lensing and thermal blooming. However, experimental details about both phenomena for propagations in water are lacking, especially for high-power lasers in the kilowatt range. We show that significant thermal lensing occurs only for high input powers before the onset of convective flow, while for low input powers, no strong thermal lens arises. After the onset of water flow, thermal blooming occurs at low input powers comparable to that known for propagations over kilometres in the air. However, for high input powers a thermal blooming on a qualitatively higher level is shown. By wavefront sensing, the change of refractive index distribution in water is investigated. This clearly shows the fast development of a strong thermal lens for high input powers and the onset of convection. Furthermore, a qualitatively good agreement of the accompanying simulations is observed. It is found that the absorption coefficient is linear with a value of $$\mu ={13.7}\,{\mathrm{m}^{-1}}$$ μ = 13.7 m - 1 at least up to 7.5 kW, i.e. 8 $$\mathrm{kW/cm}^2$$ kW / cm 2 . However, the directed transmission into an aperture is only constant before any thermal lensing of blooming occurs.

A Fast Calculation Method of Far-Field Intensity Distribution with Point Spread Function Convolution for High Energy Laser Propagation

The turbulence effect, thermal blooming effect, laser beam aberration, platform jitter, and other effects in the process of high energy laser propagation in the atmosphere will cause serious degradation of laser beam quality, which will have a negative impact on the actual application of laser propagation engineering. It is important in the engineering application of high-energy laser propagation to evaluate the far-field intensity distribution quickly. Based on the optical transfer function (OTF) theory of imaging system, the propagation process of high-energy lasers is modeled as the imaging process of point source. By using the convolution of point spread function (PSF) of jitter, turbulence, thermal blooming, and aberration of emission system, fast calculation of the far-field intensity distribution of high energy laser is realized. The calculation results are compared with those obtained by the 4D wave optics simulation program in different propagation scenarios. The results show that the calculated facula distribution and encircled energy of this method are in good agreement with the simulation results of wave optics, which can realize the fast and accurate evaluation of the far-field intensity distribution of high-energy laser propagation and provide a reference for practical engineering application.