Oooh! Can I play, too?
Don't know how accurate your component estimates are (I'd rather hear Rick Nebel's figures.), but we can take them as a jumping off point.
First let me check the power figure. I suppose we are talking about magnets with maybe 1 m diameter and 0.5 m bore. That should translate to R_plasma ~ 0.5 m. I would expect losses from 12 line cusps, each somewhat less than a quarter circumference long, and an equivalent loss from the point cusps. That makes an effective length of about 2*12*(2pi*R/4), call it 15 m. Let's guess B = 1 T, so rho_e at 100 keV is around 1 mm. Multiply that times 8 (the fourth root of the deuteron/electron mass ratio) for the hybrid gyroradius, assuming standard theory holds. Makes 8 mm cusp width.
Ouch. That's a gaping wound. Good thing we're only building an experiment, not a power reactor. What's the power loss through the cusp, again assuming standard theory (or worst case, depending on your point of view)? An area of 0,1 m^2. An energy density of (1 T)^2/(2mu_0) ~ 4e5 J/m^3. A sound speed of about 2e6 m/s. Adds up to 100 GW. We're gonna need a bigger boat!
Did I make a big mistake somewhere? Possible. (Excuse: I'm sick, remember?) If not, then you need 10,000 of your power supplies (You could build ITER for that money!), to be sure you can definitively test the theory.
Or you can just spend 10 million in the hope that the thing will work 10,000 times better than the theory says.
Actually, I had all kinds of clever things to say about your cost estimate, but considering the above result, it seems kind of pointless.
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Since I never know when to shut up, let me ask how we could make those numbers look better.
- Reduce R. Maybe, but P only scales with R in this model, and if you make the thing too small you start getting confounding effects like atomic physics. At most one order of magnitude, if you are willing to reduce the plasma to R = 5 cm.
- Reduce the voltages. There is again a linear dependence, partly through the cusp width and partly through the sound speed. Reducing the energy makes the atomic physics effects worse, and, of course, you lose any chance of using fusion reactions as a diagnostic. Still to save the program, we could reduce the voltage from 100 kV to, say, 1 kV, giving us two orders of magnitude.
- Reduce the magnetic field. Yet again a linear dependence, the width of the cusp partially offsetting the energy density. We've already got an 8 mm cusp width and a 5 cm plasma radius. I don't think we want to go any farther here. More generally we can choose a minimum value for R/rho and then trade off field for volume without affecting the power requirement.
- Go to argon. This is the only other dependence I can find. Argon is 20 times heavier than deuterium, so the sound speed is 4.5 times less, reducing the flow of particles and energy out the cusps. Nearly an order of magnitude.
Well, looky there! We're back to an experiment that we could build for a double-digit-million sum. Of course, it's tiny and has a puny voltage, and runs on argon, and has a few other quirks, but it at least has a decent chance of giving us some unambiguous answers.
) the cusps aren't being asked to confine anything.