The concept of a radiation temperature (Trad) and of the transport of radiation arises from a logical extension of the familiar concepts of heat emission from a thermally warm object. These concepts extend from infrared radiation from a hot metal bar at a few 100 K all the way to x-rays emitted from an extremely hot object (e.g., a blackbody radiator such as a fission primary) with an equivalent temperature in the million-degree range. Understanding radiation transport is important because it plays a prominent role in the evolution of stars and in the functioning of a nuclear weapon.
Like thermal temperature gradients that cause the diffusion of heat down a metal bar, Trad gradients cause the transport of radiation through systems. For example, radiation from a star is transported from the high Trad region deep within the star where it was created out into the cold surrounding interstellar region. On its way out, the radiation moves through regions where various radiation-transport models may be valid -- all driven by Trad gradients. Transport processes in a star are the subjects of intense study using astrophysical simulations.
In radiation thermodynamics, a hohlraum [in literal german "hollow area" or "cavity" a term of art synonymous with radiation case], is a cavity whose walls are in radiative equilibrium with the radiant energy within the cavity. This idealized cavity can be approximated in practice by making a small perforation in the walls of a hollow container of any opaque material. The radiation escaping through such a perforation will be a good approximation to blackbody radiation at the temperature of the interior of the container.
Key processes occur once the X-Rays from the fission primary have entered the hohlraum. Sequentially, those include the transport of those x-rays to other parts of the hohlraum wall and to the Lithium capsule in the center of the hohlraum. The evolution of the heated walls and the plasma directly heated by the x-rays are critical, along with the implications of those motions to the evolution of the region of x-ray production. All of these effects contribute to the net symmetry of x-ray drive incident upon the Lithium capsule, and must be understood and controlled in order to assure spherical implosions and good secondary fusion weapon performance.
Laboratory-scale Inertial confinement fusion research attempts to use certain directed power sources -- typically very large lasers, but also accelerator-produced particle beams -- to compress and heat a tiny target containing small quantities of fusion fuel (deuterium and tritium) to thermonuclear ignition conditions. The resulting "microexplosion" resembles a miniaturized thermonuclear weapon. These inertial confinement lasers that are used to replicate the coupling between the primary and secondary in a thermonuclear weapon.
The weapons laboratories studied all of these effects via the design and analysis of experiments on the Nova laser, and applies those lessons to the design of the hohlraum target that will achieve ignition and moderate gain on the National Ignition Facility.
In contrast to direct drive ICF, in indirect drive ICF the capsule is driven by soft x-rays generated in a hohlraum. Soft x-rays couple directly to capsule ablation front. Beams or power sources originating in a restricted solid angle can be converted into a symmetric x-ray flux onto the capsule. Symmetry can be tuned by variations in hohlraum to capsule radius ratio.
Deuterium and tritium can be loaded into a spherical capsule called a target and surrounded by a "hohlraum," and then heated by means of laser bombardment. The heat causes the compression of these elements, creating a nuclear fusion micro-explosion. This so-called "inertial confinement" technique permits nuclear weapons scientists to study nuclear explosions in miniature.
In the most popular indirect heating scheme, the spherical fuel capsule is mounted inside a cylinder that is about the size of a large paper clip. This cylinder is called a hohlraum, and it is usually made of some heavy element such as lead. Energy beams are shined through holes at the end of the hohlraum, vaporizing its inside surface and releasing a burst of x-rays. These x-rays bounce around inside the hohlraum, heating the fuel capsule much like heat from an oven bakes bread. Indirect heating achieves a highly uniform compression and heating of fusion fuel without the precise positioning of incoming energy beams required for direct heating.
Another key issue is investigation of hydrodynamic instabilities that limit capsule design. This includes mitigation of x-ray nonuniformity and imprinting by foam "buffering" (as in a dynamic hohlraum, in which the plasma sheath is moving). The foam quickly turns into a plasma with high thermal conductivity. The result is that the location of the x-ray absorption layer and the ablation surface can be separated by some distance. Hot spots in the absorption can be smoothed or "buffered" by thermal conduction before they get to and imprint on the ablation surface and seed Rayleigh-Taylor instabilities.
Analysis of lithium-ion-driven target experiments at Sandia National Laboratories in the mid 1990s revealed important features of ion-driven hohlraum performance. The truncated conical hohlraum (6 mm tall, 6 mm average diameter) contained low-density foam surrounded by a gold coating. The x-ray spectrum from the foam is nearly Planckian (i.e., the foam is "optically thin," with the entire volume participating in radiation cooling). Examination of the soft x-ray emission indicates that the gold shell acts as a radiation case and partially confines and redistributes the energy deposited in the foam. The foam is nearly transparent to x-rays, while the gold wall is optically thick. The gold radiation case and the low-density foam have a smoothing effect on an imploding fuel capsule. Moreover, the gold creates a static hohlraum for the duration of the power pulse, since its velocity is less than the instrument resolution of 3 cm/microsecond.
The X-ray intensity around the capsule must be very symmetrical to avoid hydrodynamic instabilities during compression. Earlier designs had radiators at the the ends of the Holhraum, but it proved difficult to maintain adequate X-ray symmetry with this geometry. By the end of the 1990s, target physicists developed a new family of designs in which the ion beams are absorbed in the Hohlraum walls, so that X rays are radiated from a large fraction of the solid angle surrounding the capsule. With a judicious choice of absorbing materials, this arrangement, referred to as a "distributed-radiator" target, gives better X-ray symmetry and target gain in simulations than earlier designs.
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