Can the High beta fusion reactor work? Are the claims made about the  http://en.wikipedia.org/wiki/High_beta_fusion_reactor realistic? Can such a small fusion reactor really work?
 A: I personally doubt that the Compact Fusion Reactor as  presented by Lockheed Martin last week can work, but I haven't seen enough information to be certain. And to some extent, you never know until you try. (As I understand it, they only have a very early prototype, I mean try as in a full scale prototype.)
What I think I can say with certainty, is that it won't be as small as they claim - "can fit on the back of a truck". Trucks are about the same width as standard containers, so about 2.5m wide. I've had to make quite a few guesses, but I've tried to justify them and choose the smallest size possible.
In the second image here, you can see a grey blanket around the device which absorbs 14MeV neutrons to generate tritium and protect the rest of the plant. The internal coils will also need such a blanket to protect them (it's unclear if the orange skin is this blanket, or just the cryostat). It's also unclear if the outer coils are superconducting or not, but I'll assume they are otherwise the ohmic losses use too much of the power you're supposed to be generating. Superconducting coils need to be cooled with liquid helium and insulated inside a cryostat.
Blankets for a tokamak reactor are estimated at 1m thick. I'm not sure if this is dictated by the tritium breeding or the protection. If it's protection, you might be able to reduce their thickness if you're operating at 100MW instead of 1GW, so let's be optimistic and assume 0.2m thick. I'll assume the same width for the coils and the cryostat (probably optimistic again). I'll neglect any structural elements. So going from the outside of the machine to the centre we have

They don't give any figures for the size of the plasma, but I think it just looks silly if the plasma diameter is less than a third of the coil diameter, so I'll put 0.5m in both of those plasma columns. (Note that this is a very small distance between where the fusion happens at 10^8Kelvin and the wall at 10^3K, and would be extremely good magnetic confinement.)
Totalling up gives 2.6m from the outside to the centre, so the machine is about two trucks wide already. You might give them the benefit of the doubt at this stage, even though all those values were optimistic. But then you need to add peripherals:


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*heating system (the neutral beam injectors shown in the Lockheed diagram are usually about the size of a truck by themselves)

*cryogenic plant for liquid helium (at least half a truck)

*power supplies for the coils

*vacuum pumping system

*steam turbine

*bioshield. Even the 1m blanket on a tokamak doesn't block all of the 14MeV neutrons. Safety regulations will require a few metres of concrete shielding in all directions (multiple trucks)
So even if it would work, I don't think anyone will be putting it on a plane.
A: other people far smarter than I have since published more detailed reasons why the concept presented by Lockheed Martin can't work. One example is from two professors of plasma physics on the website of the Max Planck Institute for Plasma Physics. To summarise


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*coils inside the plasma need connections for a power supply and coolant. These connections will be in direct contact with the hot core of the plasma.

*size of shielding required for neutron protection is much larger than proposed

*fast particles are not well confined by the magnetic configuration which LM proposes. To understand this you need a good grasp of plasma physics, so I won't try to explain further. The effect has, however, been demonstrated and understood in other plasma physics experiments.

A: there are actually at least a dozen high-beta designs that have made it to the "small model" prototype stage, including a few different versions of polywells and field-reversed configurations, none have scaled to anything like a net power reactor though, all have unique issues
some of these designs have been ruled out in theory but then later re-examined (e.g. Rider seemed to have disproven all IEC devices at one point, but later simulations by Luis Chacon and others seemed to suggest the shape of the well was more important than thought)
will any of them ever pan out? maybe... the field seems to have advanced quite a bit in the last ten years
take any criticisms with the same big grain of salt as for proponents' claims... plasma physics is still very much in the learning phase, and people can spend decades on ideas like tokamaks without ever learning much applicable to quasi-neutral or high-beta concepts
