Fig. 1. Dream fusion in an octahedral spherical hohlraum. An octahedral hohlraum has six LEHs of the same size, with one at each pole and four along the equator, injected with lasers in an ideal arrangement. For the sake of illustration, as shown in Fig. 2, we number the LEHs centered on the positive and negative z axes (denoted by +z and −z) as I and VI, respectively, those on +x and −x as II and IV, respectively, and those on +y and −y as III and V, respectively. The laser beams are clustered in quads, characterized by the incidence angle θ_L formed with the respective LEH axis and the azimuthal angle ϕ_L around that axis. In the ideal laser arrangement, all LEHs have the same quad number N_Q, all quads have the same θ_L ranging from 50° to 60°, and the quads of each LEH are aligned evenly in azimuth at ϕ_L = ϕ_L0 + k × 360°/N_Q (k = 1, …, N_Q) with 0° < ϕ_L0 < ϕ_LM and ϕ_LM = 360°/2N_Q. Here, ϕ_L0 is the initial azimuthal angle deviating from +x and −x in the xy plane for LEH I and VI, respectively, from +y and −y in the yz plane for II and IV, respectively, and from +z and −z in the zx plane for III and V, respectively. Cylindrical LEHs are used to improve the laser beam propagation inside the spherical hohlraum. Also, the use of LEH shields can be considered, with the aim of decreasing radiation loss via the six LEHs and increasing the radiation asymmetry.

Fig. 2. Elevation of octahedral spherical hohlraum with its characteristic regions of hot laser spots, cool re-emitting wall, and cooler closing LEHs (gray). The LEHs are numbered, and the laser spots are colored according to these numbers. In this model, there are 48 laser quads with θ_L = 55° and ϕ_L0 = 11.25°. The hohlraum radius is R_H = 5.5 mm, the LEH radius is R_LEH = 1 mm, and the radius of the focal laser waist at the LEH is R_Q = 0.6 mm. LEH VI and the other 24 laser spots are on the opposite side.

Fig. 3. A_H/A_C vs R_H/R_C for a cylindrical hohlraum (red line) and an octahedral hohlraum (blue line). Here, R_H,cyl/R_C (red numbers) and R_H,oct/R_C (blue numbers) are the hohlraum-to-capsule radius ratios of the cylindrical and octahedral hohlraums, respectively. The length-to-diameter ratio of the cylindrical hohlraum is taken as 1.75.

Fig. 4. Variations of C_lm (symbol) and η_Loss (dashed line, connected with the light green curve) with number of LEHs for spherical hohlraum of radius R_H = 4R_C (upper) and R_H = 5R_C (lower). Here, η_Loss is the energy loss efficiency via LEHs, defined as η_Loss = A_L/[(1 − α_W)A_W + (1 − α_C)A_C + A_L]. We take R_L/R_C = 1.732 for the 2-LEH spherical hohlraum, R_L/R_C = 1.22 for the 4-LEH hohlraum, and R_L/R_C = 1 for the 6-, 8-, 12-, and 20-LEH hohlraums. Thus, we take the same A_L for the spherical hohlraums with six and fewer LEHs, but the same R_L for the spherical hohlraums with six and more LEHs. Note that we take larger LEHs for the spherical hohlraums with two and four LEHs, because they both need lasers at multiple incident angles for symmetry tuning. A 4-LEH spherical hohlraum is usually called a tetrahedral hohlraum.^29,56,85,86 With the same A_L, η_Loss is the same for the 2-, 4-, and 6-LEH hohlraums. For the hohlraums with more than six LEHs, η_Loss increases with increasing number of LEHs. The dominant C_lm’s of the spherical hohlraums with different numbers of LEHs are indicated on the figure and connected by the magenta curve. C_2m appears only for the 2-LEH hohlraum, and C_3m appears only for the 4-LEH hohlraum. For R_H = 4R_C, both 6- and 8-LEH spherical hohlraums are dominated by C₄₀ ∼ 3.5 × 10⁻³, but the 8-LEH has a remarkable higher η_Loss. For R_H = 5R_C, the 6-LEH spherical hohlraum is at its golden hohlraum-to-capsule radius ratio, dominated by C₈₀ ∼ 1.1 × 10⁻⁴, and its asymmetry is the lowest among all these hohlraums.

Fig. 5. Design island (surrounded by gray and black regions) of an octahedral spherical hohlraum in the plane of R_H/R_C and R_L/R_C. In the blue region, C₄₀ ≤ 0.1%. The golden line corresponds to the golden radius ratio R_H/R_C ∼ 5 with C_4m = 0. Outside the design island, C₄₀ > 0.8% at t = 0 (dark gray region), C₄₀ > 0.8% at R_C*/R_C = 0.25 (black region), η_HC < 10% (light gray region), and R_L/R_C < 0.8 (transparent gray region).