Dynamical compensation of irradiation nonuniformities in a spherical hohlraum illuminated with tetrahedral symmetry by laser beams

Indirect‐drive inertial confinement fusion with laser beams requires focusing the beams through laser entrance holes (LEHs) onto the inside surface of the hi‐Z case comprising the hohlraum. The problem is how to illuminate the hohlraum so that the x‐ray flux upon the capsule is as highly symmetric as possible at all times. This approach involves putting four LEHs at the corners of an imaginary regular tetrahedron whose vertices lie on the spherical hohlraum and putting a multiple of three beams through each LEH. Strict tetrahedral symmetry is maintained, so that under any proper tetrahedral symmetry operation, beam cones map into beam cones and LEHs into LEHs. The radiation field can have no l=1, 2, or 5 spherical harmonic components. By using two sets of twelve beams with different pulse shapes, the single surviving l=3 and single surviving l=4 components of the radiation flux upon the capsule can be made to vanish at all times.