24F02
Influences of Non-uniform Laser Irradiation on Implosion ofCone-Guided Targets
コーン付爆縮におけるレーザー不均一照射の影響
Takumi Yanagawa, Hitoshi Sakagami1, and Hideo Nagatomo2
柳川琢省, 坂上仁志，長友英夫
Department of Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
名古屋大学大学院理学研究科 〒464-8602 名古屋市千種区不老町
1
Fundamental Physics Simulation Research Division, National Institute for Fusion Science,
Oroshi-cho, Toki 509-5292, Japan
核融合科学研究所基礎物理シミュレーション研究系 〒509-5292 土岐市下石町2Institute of Laser Engineering, Osaka University, Yamadaoka, Suita 565-0871, Japan
大阪大学レーザーエネルギー学研究センター 〒565-0871 吹田市山田丘
The non-uniform laser irradiation is an inevitable problem for implosion of cone-guided targets. The
problem is investigated with simulations by use of a fluid code in which the Immersed Boundary (IB)method is installed to treat the boundary of the cone in Cartesian coordinates. This paper shows the IB
method and simulation results of non-uniform implosion for the cone-guided target based on laseralignment of GEKKO XII at the Institute of Laser Engineering, Osaka University.

1. Introduction
In laser fusion, a fuel target is compressed byimplosion using lasers, and both temperature anddensity of the fuel increase high enough tospontaneously initiate fusion reactions. Since thebeginning of laser fusion researches, many schemes
have been proposed and developed. Fast ignition(FI) is one of these schemes [1]. There are someapproaches in the FI, and especially, in the case of
fast ignition with cone-guided targets (FICG), thetarget is compressed by implosion lasers, and at themaximum compression time, the imploded core isignited by fast electrons generated by an ultrahighintense laser.
The implosion laser, GEKKO XII at Osaka
University, has twelve laser beams. The
conventional spherical target is irradiated by lasers
arranged with dodecahedron orientation. The
non-uniform implosion is inevitable because thenumber of beams is limited. Furthermore, thesymmetry degrades in the case of FICG because
lasers are injected except the cone area. In these
implosions, the fluid motion of the target is very
complicated and may cross the origin. Cartesian
coordinates are preferred to other coordinates forsimulating these flows because the Cartesian issuited to calculate such turbulent flows and has no
singular points even at the origin. However, theboundary of the cone is not treated adequately inthe Cartesian. Therefore, we installed Immersed
Boundary (IB) method [2,3] to a three-dimensional
Cartesian fluid code IMPACT-3D [4]. The IB
method was developed by Peskin (1972) to simulate

flows with embedded boundaries on the Cartesiangrid, which does not conform to the boundary.
2. Immersed Boundary method
In the IB method, each grid point is categorized
to solid, fluid or ghost points shown in Fig. 1. Thesolid point is defined as a point inside the boundary,while the fluid point is defined as a point outside
the boundary. The ghost point is determined as thefollowing procedure. If at least one of the four
adjacent points of the solid point is outside theboundary, such a solid point is redefined as theghost point. After determining ghost points, animage point is defined as mirror projection
corresponding to the ghost point shown in Fig. 1,
which is used for calculating values of flow
variables of the ghost point. The values at the image
point are interpolated from the adjacent fluid points.
Once the values of the image point are calculated,the values at the ghost point are obtained from theimage point to satisfy the boundary condition. Timestep can be advanced using ghost and fluid points.

Fig.1. Schematic illustration of the IB method: G is theghost point. I is the image point.

3. Simulation
3.1 Initial condition
The fuel target is assumed to be a shell capsulefilled with fuel and the cone is inserted to it. The
cone is treated by the IB method. To drive the target
inward, a high-pressure region is introduced to apart of the shell as a driven layer. The initial
profiles with the spherical implosion are shown inFig. 2. Pd is the pressure of the driven layer. ρs isthe density of the shell. Pf and ρf are the pressureand density of the fuel, respectively.
To investigate the effect of non-uniform
irradiation, a pressure perturbation (δP) isemployed to the driven layer following as,
 ϕ 1 Ai ⋅ 1+ cos π 2δP =  ϕ w 0(ϕ ≤ ϕ w ) ,(ϕ > ϕ w )−1

ϕ = cos (e r ⋅ e i ) ,€€3.2 Results
Figure 4 shows an isosurface of the density at themaximum compression of the cone-guided target
with non-uniform laser irradiation. The surface
shows the contact surface between the shell andfuel. Figure 5 shows the time evolution of thedensity averaged over the fuel region. The solid anddot lines indicate the case of the sphericalimplosion without the cone and of the non-uniform
implosion of the cone-guided target, respectively.
The density in the case of the non-uniform
implosion decreases by 8 percent compared withthe spherical implosion.

(1)and Fig. 3 shows the schematic illustration. Ai, ϕw,ei, and er represent the perturbation amplitude, theperturbation width in angle, a unit vector withdirection pointing from the origin to the center of
each side of the dodecahedron, and a unit vector in
the direction of the perturbation point, respectively.
i is an index of each vertex of the dodecahedron.

Fig.4. The density isosurface corresponding to thecontact surface between the shell and fuel.

Fig.2. Initial values with the spherical implosion
Fig.5. The time evolution of the density

References[1] M. Tabak, J. Hammer, M.E. Glinsky, W.L. Kruer,S.C. Wilks, E.M. Gampbell et al.: Phys. Plasmas 1(1994) 1626.

[2] C.S. Peskin: J. Comp. Phys. 10 (1972) 252-271.
[3] Y.-h. Tseng and J.H. Ferziger: J. Comp. Phys.
192 (2003) 593-623.
[4] H. Sakagami and K. Nishihara: Phys. Rev. Lett.
65 (1990) 432-435.
Fig.3. Schematic illustration of pressure perturbation