23P167-B
Optimization of illumination configuration for polar direct drive

レーザー核融合における円筒対称直接照射配位の最適化
Yuki Tsuda, Masakatsu Murakami
津田 祐輝, 村上 匡且
Institute of Laser Engineering, Osaka University
2-6 Yamadaoka, Suita, Osaka 565-0871, Japan
〒565-0871 大阪大学レーザーエネルギー学研究センター

We address laser illumination configuration for polar direct drive. The polar angles and deviations of thebeam axes from the target center are optimized such that the root-mean-square non-uniformity of laser
absorption is to be minimized. The present scheme provides practical and realistic illumination system forfuture laser fusion reactor.
1. Introduction
Beam configuration of such laser fusion
facilities as NIF in U.S. and LMJ in France are
originally designed for the irradiation system byindirect drive, where a number of laser beams (N B~ 200) are allocated on the chamber surface in acylindrically symmetric manner. Therefore, thebeam configuration is tuned such that a highest
illumination by the secondary x-ray radiation hits
the spherical pellet embedded in the cylindricalhigh-Z casing [1].
However, if these beams are directly irradiatedon a spherical pellet with the beam axes being
through the target center as is the case fororthodox direct drive illumination schemes, thelaser absorption uniformity is expected to be fatallydegraded compared with its best performance forindirect drive.

In the present work, we provide optimized
direct-drive illumination configuration in use ofsuch polar-arrayed beams for indirect drive as
NIF or LMJ that achieves high illumination
uniformity at a practically acceptable level. The
optimization is numerically done to minimize
the root-mean-square (rms) deviation ofabsorption efficiency distribution on thespherical pellet surface,[2,3], based on theidea of potential-gradient method, where focal
points and gaps of the beam axes from thetarget center of all the individual beams aretaken into account as free parameters. The
illumination configurations given by thepresent method are expected to apply to suchdirect drive schemes as shock ignition as wellas the orthodox central spark ignition, in use of
NIF and LMJ.

2. Geometrical factor
The fundamental assumption employed here isthat the energy influx onto the ablation surface
brought by the kth beam is also axially symmetricaround its beam axis ̂ , where the hat denotes aunit vector, and is expanded in Legendre
polynomials:∞𝐼 (𝒓̂) = 𝐼̅ [1 + ∑ 𝑎𝑛 𝑃𝑛 (𝑟̂ ∙ ̂ )]

(1)

𝑛＝１

Where 𝒓̂ is the unit vector for an arbitrary observing
point, and 𝐼̅ is the average intensity over the sphere.
The coefficients {𝑎𝑛 } are uniquely determined by theprofile, and are common for each beam. Suchprocesses as energy deposition and transport ofabsorbed beam energy, after all, are attributed to thecoefficients {𝑎𝑛 }. The total rms deviation, 𝜎=(∑𝑛 𝜎𝑛2 )1⁄2, is composed of factors of each mode[4]:𝜎𝑛 =𝑎𝑛√2𝑛 + 1𝐺𝑛(2)Where the first time accounts for the single beam
pattern, while the second term defined by [4, 5]
𝑁𝐵 𝑁𝐵

𝐺𝑛 = [∑ ∑ 𝑃𝑛 ( ̂ ∙ ̂ )𝐼̅𝑗 𝐼̅ ⁄𝐼𝑇2 ]1⁄2(3)

𝑗=1 =1Accounts for the irradiation configuration, and istermed the geometrical factor, where 𝐼𝑇 = ∑ 𝐼̅ .
The separability (Eq. 3), has been first shown by [4],and owing to this significant feature the irradiation
system can be optimized in terms of only thepointing ̂ and the energies{𝐼̅ } of the beams.

3. Cylinder Symmetrical SystemFig.1. shows the schematic picture of thecylindrically symmetric irradiation system with tworings per hemisphere. The beam axes do not point
to the target center, and arranged oncone
surfaces (= 2 in Fig. 1.); the ith cone ischaracterized by the polar angle , the gap ofbeam axes from a target center , and the totalenergy . For simplify, we start with the limitingcase where the number of beams is infinity large(= ) and are divided into
groupscharacterized by cone angles { 1},gaps
𝑁of the beam axes from the target center{ 1}, and energies { 1} [1].
𝑁𝑁
Moreover, energies were normalized, and 2 , andwere made into ratio to 1 as 1 = 1 (Fig.
𝑁2.).

Fig. 2. The calculation result of the cylindricallysymmetric irradiation system with three rings per
hemisphere
References[1] M. Murakami: Fusion Engineering and Design 44(1999) 111-115.
[2] M. Murakami, K. Nishihara, H. Azechi, J. Appl.
Phys. 74 (1993) 802.
[3] M. Murakami, Appl. Phys. Lett. 66 (1995) 1587.
[4] S. Skupsky, K. Lee, T. Appl. Phys. 54 (1983) 3662.
[5] M. Murakami, Nucl. Fusion 32 (1992) 1715.
[6] M. Murakami, N. Sarukura, H. Azechi, and A. J.
Schmitt, Phys. Plasma 17, 082702 (2010)

Fig. 1. Schematic view of the cylindrical irradiation
system for= case. The beam axes do not point
to the target center

4. Result and Conclusion
Fig. 2 shows the calculation result of thecylindrically symmetric irradiation system withthree rings per hemisphere.
By the cylindrical symmetrical irradiation system,
it turned out that more uniform irradiation can beenabled by making a target irradiate with laser
centering on a target in the shape of a ring. It is
expected that this calculation result will be adapted
also to laser irradiation systems, such as theNational Ignition Facility (NIF) in U.S. and Laser
Mega Joule (LMJ) in France, by the indirect drive.