I recently saw an interesting number, one I kind of knew, but it puts things in some perspective.
So excuse me for thinking out loud for a minute.
And it is: 1 amp is .629 e19 unit charges per second. So one microamp is .629 e13 charges per second.
OK, let's get to brown numbers here (you know, the ones you pull out of your a**). We just want to get close enough for rough order magnitude of the task at hand.
Call that .629 "one" for the moment, we're only interested in exponents right now. So, one microamp is now estimated as e13 e/s. If one microamp gets you a million fusions/second, that's a one in e7 rate, right? One ten millionth of the charges you accelerate make a fusion. Using DT and beam-target, the Phillips book shows about ten times that, or one in a million, for a decent borehole tube from the '50s (I don't have more recent numbers for newer ones that could be a little better).
I'll be duplicating that work with the nice quartz pieces MarkB made for me, but that's beside the point at the moment.
Lets look at gain per fusion. Assume 100kv in (close enough). We get perhaps 3.5 MeV out of DD, and maybe 20 MeV out of DT, for gains of 35 or 200, respectively. This means that to get to gain, we need to have an interaction/fusion rate of 1/35 or 1/200 to be "there" or close, not one in a million. For various reasons, we'd rather not need the tritium for this -- one being that the high energy neutrons are pretty hard on things, so lets go with needing 1/35 for the moment and be a little pessimistic. If you were doing p->Li into 2*He, you'd need about 1/64 or so, as that takes more like 250 KeV to make go decently, but puts out more energy (17 MeV or so). Still that gives us a nice brown number too - call it one in a hundred.
Again, being very brown, that implies we need to improve the rates e4-e5 or so to get to useful "gain", even remembering we can likely capture all the wasted input energy to help "boil that cup of tea" -- and that's for the already-better beam on target approach (so far it's better). What I'm saying here is that it takes about 2 units of heat to make one unit of net electricity, but assuming we put in 100 watts, and make 100 watts fusion on top -- we get 200 watts net heat, and that's enough to make our 100w of electricity to keep things going with more or less conventional heat engines. Lerner thinks he knows some tricks, but really, that's not where the attack needs to be made here -- even at 100% conversion efficiency, we only get a factor two more, and we need much larger factors, and even he's not claiming 100%, just better than a steam turbine at all.
For the fusor, we start off disadvantaged, even taking my super-good pulse mode into account -- we don't get a million fusions (or two million) per microamp, not hardly, and I do believe the Phillips numbers are for real. I'm only doing about 100th of that best-case so far.
In a normal fusor run, what I call static mode, we're putting in 50kv at about 10 milliamps. My superQ mode puts in 50kv at ~100ua (hard to read on my meter), a vast improvement in input for the same number of neutrons output. But still, not even close to beam on target, where 100 ua would result in e8 neutrons, where I'm doing e6-e7 neutrons in that mode (which could mean twice the actual fusions, but we're being brown here).
So we're only doing a millionth of the efficiency we need to get to gain, more or less. Kind of a sobering number -- I may have various small mistakes and fudge factors in here (please point out any you see), but that's the size of the problem in brown notation. And that's big, it's almost like the difference between zero and some actual number -- the difference between the mechanical energy out of a wood fire (hot air going up and logs falling down), vs the same kind of BTUs put into an internal combustion engine, which is pretty huge.
This implies that the required approach, and the subtlety needed is about similar to just burning fuel on the ground compared to burning it in an Otto cycle engine. An incremental difference, like say putting the fire in a woodstove and controlling the in-out flow is not the kind of thing needed, though it might be a step on the way, speaking in analogy.
Now, in Farnsworth's view, you get most of the acceleration energy back via induction -- things that pass through the grid are decelerated and by induction that provides energy back to accelerate them again, the old spring and mass deal. Tests here show that this doesn't actually happen with a plasma, though it's well known to work with pure charge in accelerators and ion traps, and is even responsible for input conductance at high frequencies in radio valves -- same effect of charge passing a conductor where energy is moved from one to the other.
Now, where can this observation possibly lead us? I've been pondering this awhile now (years). For the moment, let's assume we want to limit things to the e6 neuts/second range, so we don't have to bury our gear in a safe place to run it while we learn. Let's assume we can somehow get to that 1/100 fusion rate, so we only need to be putting in X deuterons/second -- 100 times that e6, for e8 charges per second. So we need to work that out in current. That would be on the order of e-19 * e8, or e-11 amps. Or e-5 microamps. Or e-2 nanoamps. Ten picoamps.
Looks to me like we went big before we went smart, eh? Would it not be one heck of a lot easier to deal with things like space charge defocusing at 10 picoamps than it is at 10 milliamps? Are we lucky it didn't work? If we deem e6 n/s enough for research, and as much as we want to be in the same room with, getting to gain at the 10ma level implies how many neutrons per second again? Ratio of 10ma to 10pa times e6, or...e16 n/s, about the same flux as there is in a fission reactor per cc. We'd all be dead if it worked!
That's getting down there into a range where a lot of more precise techniques work well, and you can almost even ignore the repulsion between incoming projectiles as far as fine focus goes! You could begin to consider ion trap, pure positive charge types of things -- no electrons, and at that scale, no special issues with say a group of positive charge merely yanking electrons off the tank walls to put them back into play, wasting input energy, right? They do have problems like that at CERN, where the charge density of a bunch in the beam can yank electrons off the tank walls via field emission -- but they're working at milliamps, too.
This part of the parameter space seems almost completely unexplored. It's the kind of thing you do with an "infinite" mean free path, no neutrals, no electrons, just deuterons at +1, period.
And you do it with the amount of atoms that are more typical of a Bose-Einstein condensate, or what you can hold in an ion trap, no need for "big" before you get "accurate" it seems. And in fact, "big" comes with a bunch of issues we don't want or need -- space charge beam blowup, less accuracy aiming our little toys at one another, and energy loss via electron pathways.
So, forgetting scaling to gigawatts for the moment -- why not look for gain at *any* power level whatever and see what we can learn? If we don't have it, it seems a little premature to worry about scaling it up just yet.
This is what got me thinking of fusor-II and some other things -- how can we get to gain at all? Seems we start with these numbers, realize that at such low current densities different techniques are usable, and go from there. Chris' idea flows along similar lines, or something like it could do so pretty well. It's all about accuracy it seems, not brute force thermalized input power -- and a self ionizing fusor run in high pressure (by these standards) gas isn't even in the running for that. To get down to pa and without electrons, it's going to take a whole different class of technique than a simple grid in a volume with volts on it, no matter how well designed that is.
Let's suppose, as I do, that there's maybe another factor of 100 on top of my super pulse mode. That still leaves roughly e4 needed, and I just can't convince myself that's there to be had at this point -- my gut says there's 100, but not much more. Not much to go on, but my gut is pretty good.
I am also wondering what that other idea kicked around here might do for us, the one where we use the crystal lattice of silicon as a funnel to take two shotgun "beams" and push them down tiny paths where the interaction rate just has to be a lot higher -- Rutherford scattering should direct our projectiles into head on collisions if the silicon is thin enough that they don't lose too much energy traversing it from either side. In other words, I'm not thinking about implanting D into a target, then firing at it stationary, but having it coming in from both sides for energetic head-on collisions in there. Might not be super practical -- you'd tear up the target to the extent it worked, with the energy from the reaction products. But silicon is cheap, you could step and repeat, and perhaps it even anneals the xtal damage by the next time you step back to the same spot?
Or perhaps something like the Cone Trap, utilized as a recirculating beam collider with bunched beams counter rotating. I know when we discussed it that Curtis is a fan of the idea. Here's the cone trap as a ring. This idea is extensible to adding another beam going the other way, and adding bunching and focusing electrodes to get a collider that's pretty energy efficient, and which can re-gather scattered but non fusing nuclei back on path.
Or maybe some of the technique Crewe did with electron microscopes that could resolve atoms...we have shorter wavefunctions here, so if anything we should be able to do better than he did, and that should be good enough. And in fact, he was working in a similar range of current as I show we need...and he got results like what we need. I don't have his papers at hand just now, but here's a book on the topic.
I am further intrigued about that hint I got the other day that slight variations in conditions affect which DD reaction pathway is taken. Even when we weren't seeing neutrons, we were seeing gammas a factor of ~40 hotter than power supply voltage input, so something interesting was surely going on. Whether further development just lets us choose that pathway, or helps us with overall reaction rates is anyone's guess at the moment. For that matter, it needs to be re-verified at all, and it's on the list now that I'm back in action with no leaks and no EMI.
So, having tried to give something back to the fusor.net guys on fusor improvements (not my fault they didn't want to try it), I'm going to soon give up on the approach altogether, as it just doesn't look to me like it's going to get out of the toy range real soon. Very educational, and a quick way to fusion "at all" but not in the class of desired possible results. Maybe someone can show me how to do it with a fusor, and fusor-II is kind of a way to use almost the same hardware in the attempt, but it's really not a "fusor" in the classical sense at all anymore.
At any rate, radical as it is, these numbers show that the conventional wisdom is wishful thinking at best, and we're lucky it's wrong!