Here's how combined fusion/fission plants would theoretically work:
A fusion reaction is used to create a large quantity of high-energy neutrons. These high-energy neutrons are then used to cause fission in an otherwise subcritical fission assembly with extremely low enrichment fuel. 'Natural' uranium (U-238) is fissionable, which means that it can undergo fission in the presence of /high energy/ neutrons.
The sun is a 100% fusion reactor.
If you mix a fusion and a fission reactor, probably you will have most of the disadvantages of the fusion reactors; in particular you will have a lot of long-living radioactive byproduct of the fission reactions.
Detonating a nuclear weapon inside of a power plant isn't really practical. :-) Existing nuclear power plants don't get anywhere near the temperature and pressure needed to start nuclear fusion.
So, now we have the engineers trying all sorts of ways to get to the needed temperature and pressure without turning the plant into a smoking crater. That's where all the fancy lasers and magnetic pulses described in the article come in: They're trying to aim the heat source so they can superheat the fuel without melting the containment vessel.
For instance, the test version of the Tsar bomb had its last fission stage removed, reportedly resulting in a 97% fusion detonation. Of course, those still cause a huge lethal neutron flux, but at least the amount of fission material released is pretty small in relation to the overall power of the device.