The special shaped laser spot for driving indirect-drive hohlraum with multi-beam incidence
1 Introduction
The overall coupling efficiency of laser energy to the implosion capsule is an important parameter for inertial confinement fusion (ICF)[1, 2]. In indirect drive, the beam focal spot should be enlarged to reduce laser intensity when it propagates into hohlraum; continuous phase plate (CPP) is the key element to modify the shape and size of the focal spot. The shaped spot has been shown to reduce stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS) of gas-filled hohlraum and to increase the peak radiation temperature on SG-III prototype laser facility (TIL)[3]. However, the hohlraum is driven by multi-beams passing through two laser entrance holes (LEHs); the larger focal spot would bring more overlap of multi-beams in hohlraum, which is likely to degrade the hohlraum performance by some physical processes, such as cross beam energy transfer (CBET), filamentation and so on[4]. The design of focal spot size is a tradeoff of reducing single beam intensity and controlling multi-beam overlap. Traditionally the focal spot is shaped as an ellipse and becomes a circle on the LEH to maximize laser spot size[5]; nevertheless, the azimuthal symmetry is being worse in this case.
In this paper, the limiting condition of laser passing through LEH into hohlraum is analyzed integrally. With geometric structures of laser propagation, some special shaped laser spots are proposed to balance the opposite requirements. The corresponding CPP does not bring difficulties to the design and fabrication. The influence of phase aberrations to the special shaped spot is also analyzed. The conclusions obtained can give powerful guidance for the theoretical and experimental study of hohlraum energy in the future. At the same time, the technique of producing special shaped spots can be applied to a more general area, such as laser illumination for direct drive, laser processing, laser marking and so on.
2 Analysis on the overlap of multi-beams in hohlraum
2.1 The approximation and limitation of beam propagation in hohlraum
In indirect drive, a large focal spot is required to reduce the peak intensity of a single beam or quad (a quad is the superposition of several individual laser beams which act as a single beam). Subsequently, the ideal focal spot position is designed near the LEH to ensure the perfect laser shape, which can maximize beam filling and reduce peak intensity. Figure
Fig. 1. The approximation of beam propagation into hohlraum. (a) An actual beam (quad) passes through the LEH and reaches the hohlraum wall, the ideal focal spot position locates near the LEH and the incident beam is defocusing in hohlraum. (b) The relationship of beam projection in hohlraum with propagation approximation.
To prevent the beams from clipping the LEH wall, sufficient beam clearance is required[5] as shown in Figure
Fig. 2. Beam clearance is required for incident beams. The dashed circle represents the maximal boundary of focal spot at the LEH.
2.2 The overlap analysis of multi-beams in hohlraum
In the current laser facilities for driving indirect-drive hohlraum, such as National Ignition Facility (NIF) or SG-III laser facility, all quads (or beams, the same follow) are distributed at several different angles from the hohlraum axis: the smaller angle quads are defined as the ‘inner cone’, which contains 8 quads, while the larger angle beams are defined as ‘outer cone’ with 16 quads. All beams enter from each side, overlap on the LEH, and are distributed on the hohlraum wall uniformly over the azimuth. CBET can occur in plasma when two or more quads traveling in different directions overlap. The process becomes resonant when the ion acoustic wave (IAW) dispersion relation is satisfied. The plasma flow is along the radial direction and has maximal velocity at the LEH; these conditions can allow for induced Brillouin scattering between inner cone and outer cone beams even at the same wavelength. In addition, the quads in one cone have different azimuth angles; beam overlap in one cone would increase laser intensity to induce the higher electron density and distribution, which would bring more serious low-probability of intercept (LPI) effects and instability.
In order to control the energy deposition in hohlraum and tune the implosion symmetry, beam overlap between different cones is used as an important tool, named CBET with a wavelength shift, to regulate the relative power[6–8]. Nevertheless, beam overlap in one cone is also a threat to experiments, because it increases peak intensity and introduces beat waves, which would lead to some unexpected physical processes to degrade azimuthal symmetry. The relevant physical mechanism indicates that the primary impacting factor is the beam overlapping degree. Therefore, the overlapping volume is proposed to quantify beam overlapping degree, as shown in Figure
Fig. 3. Two nearest-neighbor beams (quads) pass through the LEH and reach the hohlraum wall. Beam overlapping volume is emphasized with dark color, which represents the integral of two quads propagating in hohlraum.
3 Laser spot shape design for reducing beam overlap
When multi-beams pass through LEH into cylinder hohlraum, they have maximum overlap at the LEH, followed by a rapid drop due to beams separating and being absorbed on the hohlraum wall. Figure
Circular spot is the applied focal shape in the current facility, as shown in Figure
Further analysis shows that at hohlraum section, there is a maximum laser-loaded area viewed as zonal shape which is determined by hohlraum and LEH size. The optimal objective is to fill the zone completely with beam overlap as little as possible. In this situation, we proposed a special laser shape that is a tailored circle as shown in Figure
Fig. 4. Circular spot, elliptical spot and special shaped spot, are designed to reduce the degree of beam overlap on hohlraum section. The dashed line is the maximal area limited from LEH as shown in Figure 2 .
Beam overlap patterns of the three shaped spots are shown in Figure
Fig. 5. Beam overlap characteristics of the proposed three shaped spots. (a) Circular spot; (b) elliptical spot; (c) special shaped spot.
Fig. 6. Peak intensity of single quad and beam overlapping volume as a function of the dimensionless numbers for (a) elliptical spot and (b) special shaped spot.
Considering the three laser spots for indirect drive with the same hohlraum and beam power, we calculated the times of overlapping volume varying with the times of peak intensity of a single quad to a circular spot for the relative comparisons. Simulated data is shown in Figure
Fig. 7. The times of overlapping volume varied with the times of peak intensity of single quad to circular spot for the two proposed shaped spots.
4 CPP design for special laser spot
With the projection relationship shown in Figure
Fig. 8. (a) The contour map of the designed CPP, which produces a special laser spot in the far field with super-Gaussian of order $sg=6$ . (b) Speckled far-field intensity patterns produced by the full aperture illumination (no additional phase aberrations applied) of the CPP.
Near-field phase aberration can have a profound effect on the performance of the special shaped spot. If the aberration is strong enough, it acts like a randomizer, and the resultant far-field shape tends toward circular Gaussian distributions. The influence on intensity statistics of a focal spot has the same laws to a symmetrical spot because of the autocorrelation theorem, and so the influence on shaped profile is the only consideration. Enclosed energy in the shaped contour was proposed to quantify the profile performance.
The phase aberration with the inverse power-law nature of power spectrum[10, 11] can be evaluated by the ratio
We have investigated the influence of beam aberration by numerical illustrations as follows. In the simulation, the area of spot objective is equal to the circle with a diameter of
Fig. 9. Energy in shaped contour is plotted as a function of the phase-aberration strength $\unicode[STIX]{x1D6FE}$ , the circular spot with equal area is also shown as a comparison.
Fig. 10. (a) Speckled far-field intensity patterns produced by phase aberrations, the profile of focal spot is a Gaussian distribution and the size is $30D_{DL}$ . (b) Speckled far-field intensity patterns produced by the full aperture illumination of the CPP and phase aberrations.
5 Conclusion
An improved laser spot design technique for indirect drive built upon the geometric structures of laser propagation into hohlraum has been introduced, which included shape approximation and limitation, CPP design, and beam aberration analysis. The proposed technique is able to generate appropriate CPP-producing special shaped spots that can balance the requirements for LPI of single quad and overlap of multi-beams. The calculation shows that the optimized shape of laser spot can reduce the overlapping degree of multi-beams by 30% with about 10% increment of single quad peak intensity. The corresponding CPP does not bring difficulties to the design and fabrication. Phase aberrations are more sensitive to the special shaped spot; however, it can be tolerable for the current beam control level. The obtained conclusions can give powerful guidance for the theoretical and experimental study of hohlraum energy in the future. And so in the future work, the performances of the special shaped spot in experiments would be studied, which include the laser plasma interaction uniformity, the time-dependent symmetry performance and finally the fuel target symmetry.
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
Article Outline
Ping Li, Sai Jin, Runchang Zhao, Wei Wang, Fuquan Li, Mingzhong Li, Jingqin Su, Xiaofeng Wei. The special shaped laser spot for driving indirect-drive hohlraum with multi-beam incidence[J]. High Power Laser Science and Engineering, 2017, 5(3): 03000e20.