## Polywell building difficulty compared to other power plants

### Polywell building difficulty compared to other power plants

here's a question-- presuming P+B11 works, with the direct conversion, how difficult it is to build compared to a fission plant or a conventional steam plant? It looks, to my admittedly unskilled eye, that polywell plants might actually be easier and less costly to construct, but I can't be certain.

It mostly depends how losses scale with B and R. Some (very optimistic) BOE estimates had it coming in at a tenth the cost of most current power sources. If that happens, it will be world-changing.

If it's comparable to fission, it will be a big deal.

If it's 10x fission, it was a nice science project that may have limited applications.

If it's 100x fission, it was a failed science project.

Costs scale as r^3, so we'll see.

If it's comparable to fission, it will be a big deal.

If it's 10x fission, it was a nice science project that may have limited applications.

If it's 100x fission, it was a failed science project.

Costs scale as r^3, so we'll see.

n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

Almost.TallDave wrote:Costs scale as r^3, so we'll see.

There are of course economies of scale. If r is scaled by 2, r^3 means the amount of stuff you need would be 8 times as much, but you don't usually pay 8 times the dollars for 8 times the stuff, except in one off situations. Economies of scale.

I hope this engenders HUGE economies of scale!

if costs scale as r^3 and power as r^7, then it's very, very easy to make money - just make the plant bigger.

But costs do not scale as r^3; there is a sweet valley, and costs go significantly higher outside it. That sweet valley is where liquid nitrogen can cool superconducting magnets, and boil off to drive turbines, then be re-liquified by a compressor. Use N2 as your working gas & fluid for the heat machine all around, save yourself a heat transfer step.

Below the 1m size (according to Dr. Bussard) we can't get the coolant (even though they've supercooled chips with N2) and above some size, the wiring will have interesting effects (wires work worse as they get bigger).

But costs do not scale as r^3; there is a sweet valley, and costs go significantly higher outside it. That sweet valley is where liquid nitrogen can cool superconducting magnets, and boil off to drive turbines, then be re-liquified by a compressor. Use N2 as your working gas & fluid for the heat machine all around, save yourself a heat transfer step.

Below the 1m size (according to Dr. Bussard) we can't get the coolant (even though they've supercooled chips with N2) and above some size, the wiring will have interesting effects (wires work worse as they get bigger).

Wandering Kernel of Happiness

Kite -- True, but there are also reverse economies of scale -- bigger projects run into additional challenges and complexities. R cubed is probably a reasonable rule of thumb.

As Art has pointed out, if the physics are marginal PW may end up stuck in the same trap as toks are in right now: at net power, too big to be economic. (We do have relatively high beta operation going for us, though.)

There are scenarios where in certain ranges we may only be able to increase power by r^2, while costs rise as r^3. That was brought up in relation to D-D first wall limits a while back.

WW-- Keep in mind, though, it isn't power that makes you money, it's gain. Power will likely be r^7, except where restricted by first wall or etc. If gain looks something like r^5, great. At r^3, not so great.

As Art has pointed out, if the physics are marginal PW may end up stuck in the same trap as toks are in right now: at net power, too big to be economic. (We do have relatively high beta operation going for us, though.)

There are scenarios where in certain ranges we may only be able to increase power by r^2, while costs rise as r^3. That was brought up in relation to D-D first wall limits a while back.

WW-- Keep in mind, though, it isn't power that makes you money, it's gain. Power will likely be r^7, except where restricted by first wall or etc. If gain looks something like r^5, great. At r^3, not so great.

n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

Speaking of gain, what is the anticipated gain of Tokamacs? If ITER is 5X breakeven (just above breakeven when steam electric power generation is included), how much bigger will DEMO or a production plant be? Does it scale as r ^1.5, r^2, r^3 ?.

Dan Tibbets

Dan Tibbets

Last edited by D Tibbets on Thu May 20, 2010 5:40 pm, edited 4 times in total.

http://en.wikipedia.org/wiki/DEMOWhereas ITER's goal is to produce 500 million watts of fusion power for at least 500 seconds, the goal of DEMO will be to produce at least four times that much fusion power on a continual basis. Moreover, while ITER's goal is to produce 10 times as much power as is required for breakeven, DEMO's goal is to produce 25 times as much power. DEMO's 2 gigawatts of thermal output will be on the scale of a modern electric power plant.[1]

...

To achieve its goals, DEMO must have linear dimensions about 15% larger than ITER and a plasma density about 30% greater than ITER

OK, so I get inputs of 500/10 = 50MW for ITER, 2000/25 = 80MW for DEMO.

So at ITER input (50MW) I get 1250MW power from DEMO, which is 2.5x the ITER output. Now we have to break that into the R and B components (plasma density varies with b^2, right?), or I guess we can pretend B and R scale together for convenience.

Doing it the easy way, I get 1.15 size to equate to 2.5 power at about R^7 (1.15^6.57 = 2.5). Hey, that sounds familiar! But r^7

*gain*is suspiciously friendly.

But I'm not sure "linear dimensions" equates to "radius." That sounds like it might be circumference. Plus it isn't a sphere, but a doughnut. Bleah, more math. I'm going back to paid work for the nonce.

n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

D Tibbets wrote:Speaking of gain, what is the anticipated gain of Tokamacs? If ITER is 5X breakeven (just above breakeven when steam electric power generation is included), how much bigger will DEMO or a production plant be? Does it scale as r ^1.5, r^2, r^3 ?.

Dan Tibbets

According to this site, on page 42 the gain is proportional to B^2 x a^2

http://iwrwww1.fzk.de/summerschool-fusi ... 8/T1-3.pdf

I assume 'a' is the area of the torus section (the donut crossection on one side of the center). So a = height X width (corrected for the squished shape of the plasma torus) of the torus section. Volume would be that times the circumference of the torus (circumference of the center of the torus section).

I'm uncertain of how this relates to radius for this irregular shape, but from this and what TallDave said, it seems that tokamac power gain rises rapidly, perhaps comparable to Polywell (which would dampen arguments that Polywell claimed power scaling is outrageous).

I'm guessing that the reason that the tokemacs are so big is because their starting point (plasma density and size to obtain minimally sufficient confinement(compared to time to fusion)) is inferior compared to the Polywell.

Then, in the link, there is mention that the diverter in ITER may have to handle thermal wall loads of ~ 50 MWper meter squared, so to have a survivable machine the engineering limits, not the physics, may drive machine size once a certain size is reached- similar to what is claimed for Polywell, but at thermal load conditions ~ 1 order of magnitude more challenging.

I'll suppose that the volume added by the lithium blanket in the Tokamac and the direct conversion system in a P-B11 Polywell add similar amounts of relative volume and difficulty to the machines. A D-D thermal Polywell conversion would be simpler (easier?) but less efficient at conversion.

[EDIT]- xcorrected- first attempt I edited my prevous post, when I intended to quote it.

Dan Tibbets

To error is human... and I'm very human.

Dan,

The Polywell power scaling is uncontroversial -- b^4*r^3 is just how the physics work for any system; it's the volume of reactions and how the fusion rate varies with density (and density with B). It's the gain scaling (i.e., the loss scaling, since gain is just power and loss combined) that's in question.

Ohhhhhhh, what I wouldn't give for a peek at WB-8 right now....

The Polywell power scaling is uncontroversial -- b^4*r^3 is just how the physics work for any system; it's the volume of reactions and how the fusion rate varies with density (and density with B). It's the gain scaling (i.e., the loss scaling, since gain is just power and loss combined) that's in question.

That's going to be interesting.Then, in the link, there is mention that the diverter in ITER may have to handle thermal wall loads of ~ 50 MWper meter squared,

My understanding is that it's because they are low beta, due to their magnetic curvature (in some places, field falls as you move away from the plasma). Polywells are convex to the plasma at all points, and so in theory should be able to operate at higher pressures relative to B. This means that for the same fusion power, a Polywell is much cheaper. If they're right.I'm guessing that the reason that the tokemacs are so big is because their starting point (plasma density and size to obtain minimally sufficient confinement(compared to time to fusion)) is inferior compared to the Polywell.

Ohhhhhhh, what I wouldn't give for a peek at WB-8 right now....

n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...

No, it's power. Net power, admittedly, but once the gain is comfortably over unity, net power is roughly proportional to power.TallDave wrote:...it isn't power that makes you money, it's gain.

Let's consider a test case. We have two reactors, one 1.5 times as large as the other. Assuming the R^5 and R^7 scaling laws apply strictly (ignoring the fraction of fusion power that comes from the potential well, among other things), we get:

gain ratio: 7.59375

gross power ratio: 17.0859375

Now let the smaller reactor have a gross power output of 100 MW and a gain of 10. Assuming 85% conversion efficiency, this gives you 75 MW to sell.

The larger reactor now has a power output of 1709 MW and a gain of 76, giving you 1433 MW to sell.

Revenue ratio at constant power price: 19.1090625

Notice that it's closer to the power ratio than to the gain ratio. Notice also that it's

*higher*than the power ratio. This is because there's a finite size and gross power output at which the power plant will have no revenue at all (the breakeven point), so smaller plants are penalized more. That's what gain is good for - minimizing the self-powering penalty. Once you're well past that, it doesn't matter very much how big the gain is so long as it's >>1, and revenue starts to scale directly with gross power (once the scaling losses (drive power lost to cusp leakage) are minimized, the non-scaling losses (bremsstrahlung, collector inefficiency, drive power leading to successful fusion) dominate, so gross power is roughly proportional to net power).

93143's arguments seem reasonable with a couple of points added. Where is the cutoff between gain and net power dominance. In a Polywell burning P-B11 with a Q of ~ 3-5 , or perhaps a maximum of 20? A D-D Polywell with a Q of 100 would presumably fit in the power category (except see below). How about a RFC or Focus fusion with Q of perhaps <2?

Also, consider cost, if capital costs scale as r^3, high gain devices have a considerable advantage so a multiple platform approach has greater advantage when redundancy, and grid power distribution is considered. I understand that this is one of the economic disadvantages of the Tokamac. It can hopefully be scaled to produce a lot of power, but only at huge sizes and with only a few machines. Electricity costs is only 50% power plant, the rest is in distribution infrastructure and transmission losses, etc. The final determination of gain vs power is complicated, with a lot of variables.

Dan Tibbets

Also, consider cost, if capital costs scale as r^3, high gain devices have a considerable advantage so a multiple platform approach has greater advantage when redundancy, and grid power distribution is considered. I understand that this is one of the economic disadvantages of the Tokamac. It can hopefully be scaled to produce a lot of power, but only at huge sizes and with only a few machines. Electricity costs is only 50% power plant, the rest is in distribution infrastructure and transmission losses, etc. The final determination of gain vs power is complicated, with a lot of variables.

Dan Tibbets

To error is human... and I'm very human.

Q is sort of unimportant (as long as its above 1), a low Q just means more heat rejection equipment and a larger electrical generation system.D Tibbets wrote:93143's arguments seem reasonable with a couple of points added. Where is the cutoff between gain and net power dominance. In a Polywell burning P-B11 with a Q of ~ 3-5 , or perhaps a maximum of 20?

There are perhaps 100 markets for a 25GW plant (metropolitan areas > 3.0 million).

There would be tens of thousands of markets for a 1 GW plant.

Fission easily produces for the 1GW range.

One of the reason for polywell is that the focus, mirror, tokamak and other fusion systems couple the plasma density with the plasma containability, which is an unstable feedback system.D Tibbets wrote:A D-D Polywell with a Q of 100 would presumably fit in the power category (except see below). How about a RFC or Focus fusion with Q of perhaps <2?

In the words of my physics professor "it goes where you don't want it. and if you design for it to go there, it goes somewhere else."

http://www.jcmiras.net/surge/p130.htm seems to indicate costs are more linear for other technologies.D Tibbets wrote:Also, consider cost, if capital costs scale as r^3, high gain devices have a considerable advantage so a multiple platform approach has greater advantage when redundancy, and grid power distribution is considered. I understand that this is one of the economic disadvantages of the Tokamac. It can hopefully be scaled to produce a lot of power, but only at huge sizes and with only a few machines. Electricity costs is only 50% power plant, the rest is in distribution infrastructure and transmission losses, etc. The final determination of gain vs power is complicated, with a lot of variables.

Wandering Kernel of Happiness

Well, sort of. The Piratical Q more accurately. A machine burning D-T or D-D with a thermal conversion steam plant requires a Q sufficiently high to compensate for conversion efficiency. If steam conversion efficiency is 25% overall, then a fusion Q of 4 is necessary to breakeven. With a P-B11 direct conversion of 80% you only need a fusion Q of ~ 1.3 to breakeven( energy in = useful energy out). That is why it is so important for the DPF approach. This is one reason I think P-B11 fusion with direct conversion (if it works) has significant advantages. Even with 1/3rd the fusion output, it will deliver the same amount of electricity as a thermal cycle reactor. In a since this is a power over gain advantage. The P-B11 reactor might only have a fusion Q of 20, but an otherwise equal D-D fusion/ thermal cycle reactor would need a fusion Q of ~ 60 to match it.WizWom wrote:Q is sort of unimportant (as long as its above 1), a low Q just means more heat rejection equipment and a larger electrical generation system.D Tibbets wrote:93143's arguments seem reasonable with a couple of points added. Where is the cutoff between gain and net power dominance. In a Polywell burning P-B11 with a Q of ~ 3-5 , or perhaps a maximum of 20?

...

Also, in a thermal cycle machine size where gain is the dominate factor, addiding a direct conversion system to capture the portion of energy of the charged fusion products may make economic sense. While more difficult because of the greater energy spread, capturing the high energy protons, He3 and tritium ions from D-D fusion might result in an overall energy conversion efficiency of perhaps 50%. While this would be impossible(?) with a Tokamac machine, it would be possibble with a cusp machine like the Polywell, where ignition is not an issue.

Dan Tibbets

To error is human... and I'm very human.