In one sense that's pretty cool. In another it's hard to see where they're going to get the energy to run the fusion generator from.

First some background. One of the main ways that you could get to Mars or elsewhere fast is by burning more fuel than you need to to get where you're going. If you're going to do that you don't want to have a humongous ship with lots of stages so you want something with a higher exhaust velocity than a normal chemical reaction.

But not too much higher. The energy required to power your engine is half the product of the exhaust velocity and the thrust it produces. So if you're constrained by energy because you're using electricity or the sunlight from a concentrating mirror or something then you've got a tradeoff between thrust and how much fuel you have to use. Too high an exhaust velocity and it takes you forever to get up to speed. Too low and your ship gets too big and expensive. The further you're going the less it matters that you take a long time getting up to speed and the higher the power to weight ratio of your power system the more you want to lean towards high exhaust velocity too.

For mars an engine with an exhaust velocity of 40 km/s like NASA's NEXT ion drive will let you do a Holman transfer there and back for just 1/3 of your mass as fuel. With a combination of drives and the most efficient modern solar cells that'll take weeks to get up to speed but if you're going to carry a bit more fuel or use aerocapture when you arrive you can you can make the trip pretty fast.

Since this fusion drive isn't producing much more energy than it takes in, I don't see why it would be better than an Ion drive. And you'd have to deal with the heavy depleted uranium nozzle and all the shielding to protect the crew from the radiation the drive gives off.

The fusion-fission thing is really clever though. D-T fusion gives off most of it's energy in the form of a high energy neutron and it's hard to turn those into useful thrust since their velocity is way too high. Using them to trigger U238 fission gives you some decay products which are easier to use to heat the greater mass of your propellant to a temperature that'll give you an exhaust velocity in the sweet spot.

EDIT:

Oh, someone found an ungated version of the paper and it's cleverer than I assumed:

Our phase 1 proposal discussed a pulsed fission-fusion propulsion system
that injected gaseous deuterium (D) and tritium (T) as a mixture in a column, surrounded concentrically
by gaseous uranium fluoride (UF6) and then an outer shell of liquid lithium. A high power current would
flow down the liquid lithium and the resulting Lorentz force would compress the column by roughly a
factor of 10. The compressed column would reach criticality and a combination of fission and fusion
reactions would occur. The fission reactions would further energize the fusion center, and the fusion
reactions would generate neutrons that promote more complete burnup of the fission fuel. The lithium
liner provides some help as a neutron reflector but also acts as a propulsive medium, being converted to
plasma which is then expanded against a magnetic nozzle for thrust. The expansion of the (primarily)
lithium plasma against the nozzle’s magnetic field inducts a current that is used to charge the system for
the next pulse

So they've got a story for how they're getting the electricity they need. This could actually be really cool