The paper is a one pager of introductory plasma physics. It isn't a serious calculation and it wasn't meant to be. Anyway ...
Their model is as follows. A plasma will reflect all electromagnetic radiation below a certain frequency, determined by its density. The plasma exerts a pressure like a gas and they then assume confinement of the plasma with a magnetic field, balancing the plasma pressure with the 'pressure' that a magnetic field exerts on charged particles. They then say that we can make magnetic fields in the range up to 100 T and working back, estimate the plasma frequency, which turns out to be in the UV. So great, you can deflect lasers into the UV with a modest confining field.
You need to look at some of the other numbers though.
First, what sort of plasma density do you need to reflect UV ? The answer is something like 10^28 per cubic m. This is enormous - fusion plasmas are about a million times less dense). It's getting close to solid state density eg if a solid has atoms 0.2 nm apart this is 10^29 atoms per cubic m. That is not going to be easy .... The other problem is that at such a high density, the collision frequency is very high so that a magnetic field is not very effective at producing confinement. Probably useless in fact.
The other thing to look at is the required plasma temperature. They assume a temperature of 1000 K, Unfortunately, the density of a plasma at 1000 K at thermal equilibrium is extremely low unless the background pressure is huge. So it has to be a lot hotter, in particular, comparable with the ionization energy which is roughly 100 000 K. And really, we need a fully ionized plasma because the magnetic field is not going to confine the neutral gas that we are using to make the plasma so that means we need a 100 000 K plasma. This means that the required magnetic field goes up by a factor of 10.
Would somebody else like to estimate how much power you need to dump into the plasma ?