Russian Doll Teller Ulam? Can you trigger a thermonuclear explosion from a smaller thermonuclear explosion in a scaling way, so that starting from a small laser ignited fusion within a small fissile container, using the X-rays from the first explosion to implode a tiny adjacent Li-d wire, which is then used to implode a bigger wire, and so on to a big explosion after a few cycles? Or does the Teller-Ulam design not scale to miniature explosions?
If there is a russian-doll design, can you then trigger the first explosion using a free-electron x-ray laser available today? Any other laser trigger? I am asking because from the answer to this question: How much of the energy from 1 megaton H Bomb explosion could we capture to do useful work? , the PACER power-plant design presumably relies on a fission triggered bombs, and fission resources are limited and non-renewable. Further, the PACER folks suggested that future thermonuclear explosions can be laser-triggered, and this was the only way I could think of doing this. Is this really possible?
(I should add that it would also help with regards to proliferation and terrorism safety if the trigger was an expensive bulky free electron laser, as opposed to a standalone explosive nuclear bomb.)
 A: Inertial confinement using pellets with Deuterium and Tritium  exists

In the 1970's, scientists began experimenting with powerful laser beams to compress and heat the hydrogen isotopes to the point of fusion, a technique called inertial confinement fusion, or ICF. In the "direct drive" approach to ICF, powerful beams of laser light are focused on a small spherical pellet containing micrograms of deuterium and tritium. The rapid heating caused by the laser "driver" makes the outer layer of the target explode. In keeping with Isaac Newton's Third Law ("For every action there is an equal and opposite reaction"), the remaining portion of the target is driven inwards in a rocket-like implosion, causing compression of the fuel inside the capsule and the formation of a shock wave, which further heats the fuel in the very center and results in a self-sustaining burn known as ignition.

If you look at the image of the laser set up, it is a fairly large one, size of a football field. One needs new laser technology to start considering such bombs.
It may be possible that nested pellets with some engineering ingenuity could successively get a bigger and bigger implosion within a design like the Teller Ulam one  finally destroying the laser in the last explosion, if a small enough laser could be devised. This last seems to me improbable with current technology.
A: Starting in the fifties, there was a lot of work (see RDD-8, V.C.1.g) trying to build a pure fusion weapon for mainly two reasons: they promised to be cleaner than conventional thermonuclear devices (important for peaceful uses and some of the not-so-peaceful ones) and they wouldn't need relatively scarce fissionable materials. As you can use staging to scale to essentially unlimited yields, the problem was reduced to making the smallest possible fusion explosion (Early Steps Toward Inertial Fusion Energy, p. 1-2). Eventually this program transformed into inertial confinement fusion research.
The required energy to implode this "secondary" was originally estimated in approximately 1 MJ, but this result assumed an ideal driver/primary. After the failure of over-optimistic attempts to get ignition with smaller drivers, a test program called Halite/Centurion was carried out to induce ignition of ICF capsules using radiation from nuclear devices. This program was successful "putting to rest fundamental questions about the basic feasibility of achieving high gain" (Progress Toward Ignition and Burn Propagation in Inertial Confinement Fusion).
The exact results of this test program are still classified, but it seems that "some dozens MJ of driver energies" (Edward Teller Lectures, p. 6) were required to reach ignition with X-rays from fission primaries. It sounds reasonable to assume that a more controllable driver can reach ignition with a smaller amount of energy and NIF is trying to reach ignition using only 1.8 MJ of driver energy.
