[redsnapper]

Brian H – sorry, missed the previous post! Yes, the very same redsnapper. Sorry it took me so long to check out FF – it was serendipity that I went back a couple of months ago and was rereading posts on the TM Forum from last September, and saw the link (which I’d totally missed the first time around – guess I’m becoming fairly predictable that way :-)). Fusion power has been another lifelong dream of mine. I’d wanted to get into that line of work when I graduated from Caltech, but there weren’t any good jobs in the field for an MSME. Thanks for the connection!

[redsnapper]

Personally, I favor the term “cooling tower,” because that’s what it is and does. (Chimney works for me, too – if a chimney is something that moves air from the ground to a higher altitude by virtue of the “chimney effect”, i.e., hot air rises.) I do recall studying (back in grad school) large-scale cooling towers that were entirely natural-convection driven – probably in the context of fission-based power generation. I don’t see why that existing technology wouldn’t be directly adaptable to any power plant, FF in particular.

[redsnapper]

What you mean, “we”, Kemosabe? I expect the Japanese engineers know quite well what the temperature and watts of the thermal input is. And because “we” know the first law of thermodynamics, we do to (that is, apparently we do, since you’ve said the electrical and thermal output have been published). I’m not sure what you’re trying to get at here. There’s no mystery about the efficiency, there was only a small disagreement as to whether it was being calculated correctly – not if it could be.

[redsnapper]

Yes, I intentionally said “waste” because the term “thermal” had been used previously without adequate specificity. From the primary power generation cycle’s perspective, it’s waste – but certainly if you can do something else useful with the relatively low-grade heat, it’s not entirely waste.

[redsnapper]

A diversion, I think.

So the electrical output leaves the power plant via the grid, and the thermal output via the cooling towers. One does not include the other, and they both came from the fission reaction. Neglecting any other significant losses, the total energy generated by the fission reaction is the sum of the two (1st law of thermodynamics). Efficiency is defined as useful energy output (electrical) divided by thermal input to the cycle, so you must do it the way Brian H has described: eff=w(elec)/(w(elec)+w(waste)).

[redsnapper]

I’m beginning to think zapkitty’s thermal number is (somehow) measured thermal output of the reactor core (i.e., thermal input to the high side of the conversion cycle), not thermal output of the low side of the conversion cycle. All along, I’ve been thinking (as is Brian H) the latter. In other words, zapkitty’s thermal number includes the electrical number. I suppose they’re well aware of the thermal output of the reactor core, and might choose to report that, just as they’re well aware of the total BTU’s of coal or oil or whatever that goes into a carbon-burning power plant. It’s simply a matter a making sure you read the footnotes in the report.

[redsnapper]

So BrianH was right, and it is only 25% efficient, not 33%. Leave it to me to make it complicated. Guess I was trying to give the nuclear industry the benefit of the doubt. 🙂

[redsnapper]

25% is actually pretty lousy conversion efficiency for any self-respecting power plant (not that I know typical values for nuclear plants). I noticed the error also, but was more inclined that the error was made going the other way – somebody read 33% efficiency somewhere, and made the common slip of converting that to “1 out of 3” in their head, and simply made the incorrect statement that meant 3x more was thrown away than produced. In other words, they should have said “reject 2 times as many megawatts …. 33%”.

[redsnapper]

Henning wrote:

electrodes themselves (for example: highly-conductive, Xray-transparent, ceramic electrodes that can handle 2000 degC; better yet, virtual electrodes that can handle 500MdegC)

Read: quite-conductive (36 nΩ·m, compared to 16.78 nΩ·m of copper at 20 °C), x-ray-transparent, beryllium electrodes that can handle 2400 °C

The electrodes never get into contact with the 500 M°C (actually 2 G°C) pinch.

I think you missed my point. I was hypothesizing an improved electrode. Beryllium melts at 1278degC, and what I’ve been reading about FF is that electrode temperature would be limited to 700degC – perhaps somewhat arbitrarily. Seems like I remember the words “electrode erosion” or something like that – I’m sure that the higher the electrode temperature, the quicker it sublimates into the plasma – however hot the plasma is that surrounds the electrodes. (Resistivity tends to go up with temperature, as well, though I don’t know the specifics of Be. That could be a design factor, too.) Still, a limit is a limit, which if raised, tends to open new opportunities. So I was hypothesizing that some future ceramic (ceramics typically handle much higher temperatures than metals) might be developed that had the resistivity and Xray transparency of Be, but because of the higher temperature allowed, would relax the cooling challenge. This is called science fiction, or literary license – take your pick. 🙂 You do remember Scotty’s amazing exposition of transparent aluminum in the “save the whales” Star Trek movie?

And you’re right. Any physical surface representing the cooling boundaries (walls) never sees even the bulk fluid temperatures (using the word fluid here very fluidly – meaning plasma), because there must be a boundary layer gradient if there is indeed any heat transfer to the wall; further, I understand that the highest temperatures are within the plasmoids, which are microscopic and deep within the inner electrode. That’s why I was guessing that the plasma actually contacting the walls would be much cooler than the plasmoid temperatures. 500M vs. 1G or 2G seemed like an illustrative swag. But the bulk plasma is at such a low density that the heat transfer coefficient to the walls is such that the walls might indeed be as cool as 700degC, or 2400degC, or whatever – a few orders of magnitude lower than the “bulk” plasma temperature. Of course, my basic understanding of this system is feeble. Perhaps the “bulk” plasma temperature is only 700degC. After all, suppose a single shot (capacitor discharge) lasts only a microsecond – that’s plenty of time to take a few micrograms of localized plasmoid from 700degC up to 2GdegC – and if time-to-next-shot is a few milliseconds, there’s plenty of time for the residual plasma (not counting the hot ions that shot out the end of the core into the Rogowski coil) to begin to equilibrate and smooth out the temperature to a much-lower average. I assume also that only the teensiest fraction of the plasma actually fuses, so virtually all the plasma that’s heated during the pre-ignition phase remains at the required temperature until the plasmoid dissipates. I think if I saw quantitative simulation data of plasma temperature profiles in the DPF core I might quit making such terrible assumptions. Animated color CGI of the simulation is great, but it doesn’t show what I need to know to avoid gross error.

[redsnapper]

(My apologies if this is a sort-of duplicate – something weird happened when I tried to do the spell check!)

Well, yes, the total efficiency theoretically is very competitive, but let’s face it, until there’s a working core, and a working X-ray converter, and a working Rogowski coil, all playing together with a humongous capacitor bank and switches, that efficiency remains theoretical. Given that the efficiency numbers pan out, I agree that the problem is the (small) size of the FF rig. I’m not quite sure what you mean by the high electrode temperature being a problem (don’t confuse heat with temperature) – indeed, the theoretical Carnot efficiency of a heat engine will only improve as the high-side temperature goes up, so in that sense, the higher the electrode temperature, the better. (Part of the reason the theoretical efficiency of the FF device is so high is precisely because its energy originates at 1Billion degC – somewhat higher than the hottest fossil-fuel fired power plant. :-)) Further, the higher the permissible electrode temperature, the more feasible it becomes to remove that excess heat using real materials between the electrode and the outside environment. Remember, the waste heat isn’t generated because the electrodes are hot, the electrodes are hot because they’re adjacent to a billion-degree plasma, and because there’s a phenomenal amount of energy passing through them.

As for high efficiency thermocouples (or any other device depending on the thermoelectric effect), I wouldn’t hold my breath. Current state of the art is less than 10% efficiency. My guess is that once you’ve got a working reactor, you’ll get a far better bang-for-the-buck by incremental increases in X-ray conversion, or the Rogowski coil efficiency, or incremental improvements in the electrodes and FF device itself such that more energy comes out in the ion beam or Xrays. One day there will probably be a breakthrough design for the electrodes themselves (for example: highly-conductive, Xray-transparent, ceramic electrodes that can handle 2000 degC; better yet, virtual electrodes that can handle 500MdegC). Scavenging waste heat (excluding the obviously direct applications of waste heat, e.g. heating a hotel or a swimming pool) probably adds cost faster than saleable energy output. As you point out, FF already promises to be a very efficient process by fossil-fuel standards. (BTW – we have trouble building conventional photovoltaic devices with efficiencies higher than 25% – and we’ve been working at this, perhaps only semi-seriously, for the last 40 years. It does seem to me we might be ridiculously optmistic to think we can convert 80% of Xrays into electricity as early as three years from now. Is the argument that the entropy of Xrays is so much lower than that of visible light, that there’s reason for optimism?)

I think it’s going to come down to permissible “waste heat density” – so to speak. If a breadbox-sized 5MW-net-output DPF core simply can’t be maintained (or can’t simply be maintained) cool enough for the electrodes to survive, just divide that 5MW across however many cores you can keep cool. Or if the core is already far-and-away the most expensive fraction of the cost of the powerplant (it might not be, once you’ve factored in the cost of the “minimal” cooling system ), just scale down the power (cycles/second of operation). Yes that raises the cost/MW, but I assume that the afore-mentioned incremental improvements in efficiency will eventually allow you to run the power back up. You were already so far ahead of the conventional power cost that you can afford to miss the original target by a substantial margin. So what if FF1.0 can only generate enough power for 200 houses instead of 2000? Somewhere in the world, that’s just the right size. Or a yacht instead of a cruise ship? There’ll be plenty of market for fusion power, in whatever increment is available at any given time. It’ll only improve with FF2.0.

[redsnapper]

I don’t understand where you’d put a He cooling cycle, anyway? If the best picture of the reactor core (including X-ray converter and Rogowski coil) is what’s on the LPP page, then my initial concerns about cooling the core stand. It’s not that big! There’s no way to remove that kind of thermal energy from the inside (because that’s where the plasma is). But if you wait till the heat gets to the outside of the onion, you don’t need an X-ray transperent cooling fluid, because the X-ray’s are already gone; therefore you may as well use water impingement (something cheaper than He, I presume). In any event, either you can cool it adequately or you can’t, and the decision of whether to actually use that waste heat is an economic one. (Except if Henning’s fears are realized, the economics require it, because otherwise you can’t break even.) I’d certainly prefer to remain optimistic, however. 🙂

[redsnapper]

Henning,
Is there any info available on the size and composition of the X-ray converter? I saw that there was a patent issued, but my experience with patents is they’re unlikely to give you that kind of detail. (They’re supposed to be easily understood by someone “skilled in the art,” but that implies that they don’t tell you anything they absolutely don’t have to, presuming that you already know and/or are skilled enough to guess what they don’t say. That probably doesn’t cover me, in this context. :-)) I did actually take the link to the patent and I scanned the opening page – a couple of weeks ago – but really didn’t try to digest any of the content at the time.
Also, mjv1121 answered that the energy distribution between the two ion beams might only be determined after tests have gone to the next level – but I can hardy believe that there aren’t already some pretty concrete expectations – and there should be some fairly fundamental physics dictating the gross effects. (I took a plasma-physics course in grad school 33 years ago, and I hate to admit how much I’ve forgotten – though I’d feel worse if it was something I’d actually found a use for in the meantime!) In fact, I’d assume that if a Rogowski coil can be applied to the He nuclei, it could also be applied to the electron beam. If the electrons only emit 80% of their energy in X-rays, surely that remaining 20% is well-ordered kinetic energy worth going after with another Rogowski coil? The more energy you can get back directly as electricity, the better. Heck, because they’re moving electrons, they’re already electrcity (much more so than the He ions). Is there an even simpler and obvious way to funnel them into a conductor? Maybe that’s already part of the design – so self-evident that nobody’s mentioned it in one of these posts?

[redsnapper]

Let’s take a possible scenario – granted, this is again making some ballpark assumptions:
1) The 4MW of waste heat originates at 1000K (probably not this high – because probably the X-ray converter and the ion decelerator are made of material more delicate than solid Be or any other solid material – but for the sake of argument, let’s suppose they can handle 1000K)
2) Ambient is 300K
3) We “split the difference” between some sort of local conduction/convection/impingement whatever cooling at the heat source itself, so that 4MW emerges in the form of something like steam or another coolant capable of carrying that heat somewhere we can dispose of it safely. That means (for instance), we’ve got 4MW of power at 650K (375degC).
4) Based on the above, that means we need an “environmental” heat exchanger capable of unloading 4MW with a delta-T of 350degC. (Again, in thermal resistance terms, that’s on the order of 0.0009degC/W.)

Lowest tech, cheapest solution:

Free convection from large fins. A bit of circular/iterative computation is in order, but textbook values for free convection film coefficients at this scale (TBD) turn out to be anywhere between 3 (laminar) and 10 (turbulent) W/m^2/degC. Again, at this scale and temperature difference, we’re well into the turbulent regime. Indeed, textbook correlations yield a film coefficient (vertical, heated flat plate) of 9.2 W/m^2/degC, so at the 350degC delta-T, this implies a heat exchanger surface area of 1200m^2! Now, coming from the semiconductor business, I hardly qualify as a power-plant cooling expert, but at first, I thought cramming 1200m^2 of fin area into a two-car-garage model seemed a bit of a stretch. But maybe not: for instance, if you had 20 fins, 3m tall and 10m long, spaced at 1m, you’d have 1200m^2 of total fin area (counting both sides of each fin) – in a space 3x10x20 m^3. Sounds like a two-car garage to me. So I guess we’re not outside the realm of feasibility. Obviously there are other logistics involved, like the volume of fluid you have to pump from the compact heat source (DPF reactor core, Rogoski coils, X-ray converter), and so forth – but it’s probably doable. Remember, too, a heat exchanger using air as the external working fluid it going to suck a lot of air, and that air is going to come out hot. The same calculations above show that the minimum volume flow rate of air is going to be 15m^3/s (STP), and that’s if it comes out at the maximum fin temperature (i.e. 375degC, in this case). If you don’t want to dump air that hot into the environment, you’ll have to move a lot more air. (Actually, for free convection, the amount of air that moves isn’t an independent variable. That 15m^3/s figure isn’t based on free convection principles, it’s simply based on the heat capacity of air. So the actual value is likely to be a much higher figure, but it won’t be a back-of-the-envelope calculation with stuff I carry around in my head.) You can also lower the fin temperature, but at the expense of needing more fin area. But I think my original impression that the physical size of the final-stage heat exchanger was ridiculously large was unnecessarily pessimistic for low tech cooling methods. (I don’t think it will “fit on a truck.”)

I do remember studying the design of large cooling towers (passive, free convection cooling) in one of my grad-school classes. It can certainly be done, and should be considered in more detail. If you do have a source of water and can otherwise justify it environmentally, you can also vastly reduce the size of the cooling system. I mentioned in my first post that it only takes 2kg/s of water to absorb 5MW, if you take it through the liquid-vapor phase change. That’s 40,000 gal/day. For many reasons, that wouldn’t be my first choice for the final-stage cooling, but it’s also something to consider. (In the context of my first post, that was a possibility for cooling the core – and that water would be in a closed loop, not a continuous external supply.)

Also trying to put the waste-heat figures into perspective – sanity check on the above rough figures: a 5MW power plant is large enough to supply the needs of approximately 2000 homes. Each of those homes ultimately dumps all that energy as waste heat into the environment. So we’re taking 80% of that figure (i.e. 4MW ), which would be the equivalent of 1600 homes, and injecting it into the environment “locally” to the reactor. That’s a pretty dense compression of power into a small space. It should be no surprise that this takes some fairly large fins. (A relatively small “neighborhood” power plant – mainly oil-fired – near my home is a 110MW output plant. The whole facility covers hundreds of acres and has some very large cooling towers. It most certainly does not make optimal use of its real estate, but there’s a reason they gave it so much room!)

Actually, AaronB made a comment about using the waste heat from a 5MW reactor for something as mundane as heating at a hotel. That’s actually a great idea, and in my mind, the sort of thinking that should be pursued. Any operation for which a few MW is the expected low-entropy power requirement, if you can think of other high-entropy needs that could simultaneously be met, a 5MW-sized fusion reactor would be amazing. Come to think of it, any open-ocean applications – like cruise ships (AaronB) – would be excellent candidates, because you’ve got all that water to use for cooling. Cruise ships dump their waste heat into the environment anyway, and the fusion source of energy is so much cleaner in every other respect!

Don’t get me wrong – I still think there are issues at the core end, and knowing sizes and materials of the Rogowski coils and X-ray converter would help better establish the parameters there.

[redsnapper]

wait a sec – was that unclear or nuclear?

[redsnapper]

mjv,

Thanks for the helpful post! It helps me tremendously – and even after my post Friday I realized there were huge holes in my grasp of where the heat actually appears. For this post, then, for the sake of argument I’ll accept that there isn’t a significant thermal load on the outer electrode, and I’ll temporarily set aside the questions of cooling the inner electrode, which won’t be a trivial problem, but perhaps is still not the biggest concern. With your correction, I think this is where it leaves me:
4MW thermal instead of 5MW (same ballpark)
of that, 2MW appears in the onion skin X-ray converter (somewhat bigger than a breadbox, I presume, since a breadbox sits inside it)
and 2MW appears as heat in the walls/wires/whatever of the nucleon decelerator (also bigger than a breadbox, I presume, but this structure remains totally vague in my mind)

Basically, we’ve spread the heat over two ballparks instead of just one. So instead of being 20x over the thermal budget following my original misguided assumption that the sizes of things were immediately related to the DPF core itself, we’re what – 5x over? 2x over? The Be core might actually have handled higher temperatures than these peripherals, too, so maybe the heat is being generated in somewhat larger volumes, but can the X-ray converter handle 1000K? Can the nucleon decelerator? The other crucial questions, of course, are exactly how large are these peripherals? Because we’ve still got a tremendous heat load in a relatively confined space. Until someone can give me some hints as to these size scales, there’s not a whole lot else to do at this stage for the local cooling challenge, other that recognize it’s still not a slam dunk.

Actually, there are a couple of other “sanity check” calculations I’d appreciate somebody following for me and commenting, because I’d like to be sure that I’m not missing something else. Following mjv’s description of the overall energy balance, then for a 5MW machine operating at 300Hz, each capacitor pulse must deliver 38kJ of energy. If the pB reaction adds 80% of that (30kJ), we then have (38+30)/2, or 34kJ exiting the core in two equal ion beams. (BTW, off the top of my head I don’t remember my basic plasma physics well enough, but would we expect equal energy between the two beams, or equal momentum? Or something in between? I guess the ion and electron temperatures are different, but surely they don’t scale in inverse proportion to the ion mass, do they? The He nuclei outweigh the electrons by 3600:1 – 1 He nucleus at 4*1800 for 2 electrons – surely the electron temperature isn’t 3600 that of the He? Regardless, the total’s all that matters for the present calculation.) If we extract 80% from the two beams (X-ray capture for the electrons, electric-field decelerator for the nucleons – again it doesn’t matter for this calculation whether it’s equally divided), that’s 55kJ back in electricity, of which 38kJ goes back to the caps for the next pulse, net 17kJ useful electricity. The 20% waste heat, if equally divided between the X-ray capture and the beam decelerator, is 6.8kJ each peripheral. If you do this 300 times every second, we have net output of 17kJ*300=5MJ/s (i.e., 5MW electric), and 6.8kJ*300=2MJ/s waste heat in each peripheral, with 11.4MW recirculating in and out of the caps.

I understand that the prototype device (i.e. the capacitor bank) will be delivering something on the order of 2MA of current, and the voltage is 45kV. If we assumed square pulses and a full capacitor discharge each cycle, that would suggest pulse power of 90GW (shades of Doc Emmett Brown in Back to the Future!) – and the pulse length would be 420ns. (I suppose the return pulse is spread out somewhat, but it’s got 3ms available at 300Hz.) If the caps don’t discharge fully each cycle, you’ve still got to get 38kJ, so the pulse gets wider accordingly. There are also bound to be some conduction losses in getting 2MA through the wiring, but I’m not sure where to start – I’ll assume they’re small compared to the overall energy balance. But for example, suppose you lost only 100V of the 45kV in conduction – that gives you 50kW RMS power loss in the wiring (between the ignition and return pulses). That’s a minor cooling problem in its own right.

So if somebody (mjv? AaronB?) would comment on the foregoing, I’d appreciate it. In the mean time, I’m going to work on a separate post regarding the macro-cooling problem at the “environment” end of the reactor. Because although the details of the DPF core itself may be somewhat vague at this point, you’ve still got to dissipate that 4MW to the environment, and that’s my other major concern. (Ironically, I actually spent an hour writing a second post on this subject Friday night, then went to preview the post, made a booboo of opening another tab in IE, went back to the original tab, thinking I was still on the new tab, and lost everything! The “back” button took me to an *empty* reply window, and I couldn’t find any way to get back to my original text! Argh! If I’m smart, I’ll do all my creative writing in another text editor first, and then paste it in here. Webmaster, is there any hope of avoiding this problem otherwise?!)

[Author]

Posts