Energy requirement?

[apouliot]

Hi questions from a newbie here. I look in the forum but I didn't see those question answered elsewhere

Supposing we have a designed 100MW PB11 reactor.

What would be the minimal amount of energy required to have a self sustaining reaction? And I don't mean for having a 100MW output but just enough to have a fusion that power itself(Q=1).

Also how long would an external power supply would require to sustain that power requirement for getting to a fusion rate necessary for Q=1 or little bit above? Are we talking µS/mS/Second/minutes?

From that question how much energy would it take to sustain the full reaction with 100MW(deliverable) output power?

I ask because I'm interested to see what would be the timing requirement for a reactor for going from 0 power(void installed) -> Q=1 -> Full Power. I suppose an external power source is needed to get the reactor to Q>=1 and after that the reactor can self power itself to full power, with some external control.

[TallDave]

I think Nebel has said their designs anticipate 5MW drive for a 100MW reactor.

IIRC the physics are so fast it would come up to power in milliseconds.

There would of course be a small delay between power production and the ability to power the drive with the fusion products. Not sure what that would be, and it probably depends to some extent on design. M Simon might have an idea. I would think it's pretty fast for a direct-conversion machine.

[Art Carlson]

Supposing we have a designed 100MW PB11 reactor.

What would be the minimal amount of energy required to have a self sustaining reaction? And I don't mean for having a 100MW output but just enough to have a fusion that power itself(Q=1).

The usual calculation goes like this: Under the conditions that produce a given amount of p-B11 fusion power, P_f, you can expect the Bremsstrahlung radiation emitted to have a power of at least P_b = 1.74*P_f. If you assume that both the charged particles from the fusion reactions and the x-ray radiation from bremsstrahlung can be made into electricity using direct conversion at an efficiency eta_dc, then you will be producing 2.74*eta_dc*P_f of electrical power. You have to put at least P_b back in to keep things going, so you have (2.74*eta_dc-1.74)*P_f left to sell. To have *anything* to sell, you need eta_dc of at least 64%. If you relax *any* of these wildly optimistic assumptions, your reactor is an energy sink, not a source.

If you want to make fusion power, use D-T.

Also how long would an external power supply would require to sustain that power requirement for getting to a fusion rate necessary for Q=1 or little bit above? Are we talking µS/mS/Second/minutes?

Rick Nebel seems to be thinking of ms timescales for energy confinement, which would be the timescale at which you could change reactor conditions, although there might also be some linger timescales involved, like that to ramp up the magnetic fields.

[93143]

I don't think it's quite honest to present the calculation like that without even mentioning the various ways in which EMC2 claims bremsstrahlung can be mitigated. You may assume, if you like, that the plasma is completely thermal, with equal electron and ion temperatures in the core and a 1:1 ratio of hydrogen and boron, but you should at least mention that you're assuming that, and that the experimenters who have actually run one of these reactors don't agree with you.

[Art Carlson]

I don't think it's quite honest to present the calculation like that without even mentioning the various ways in which EMC2 claims bremsstrahlung can be mitigated. You may assume, if you like, that the plasma is completely thermal, with equal electron and ion temperatures in the core and a 1:1 ratio of hydrogen and boron, but you should at least mention that you're assuming that, and that the experimenters who have actually run one of these reactors don't agree with you.

I'm not dishonest - I'm ignorant. Can you point me to the place they talk about this issue?

IIRC, the 1.74 figure comes from varying the H:B ratio and the electron and ion temperatures and taking the values that lead to the smallest factor. A brief summary can be found here. Todd Rider also discusses - and dismisses - a number of potential mitigation mechanisms.

The experimenters may have a different view of the issue, but they have never measured any mitigation mechanisms - on this question they are just doing theory like you and me.

[scareduck]

I don't think it's quite honest to present the calculation like that without even mentioning the various ways in which EMC2 claims bremsstrahlung can be mitigated. You may assume, if you like, that the plasma is completely thermal, with equal electron and ion temperatures in the core and a 1:1 ratio of hydrogen and boron, but you should at least mention that you're assuming that, and that the experimenters who have actually run one of these reactors don't agree with you.

But they haven't released any data backing these claims, either.

[Jboily]

I don't think it's quite honest to present the calculation like that without even mentioning the various ways in which EMC2 claims bremsstrahlung can be mitigated. You may assume, if you like, that the plasma is completely thermal, with equal electron and ion temperatures in the core and a 1:1 ratio of hydrogen and boron, but you should at least mention that you're assuming that, and that the experimenters who have actually run one of these reactors don't agree with you.

You could refer to these old documents;
http://www.askmar.com/Fusion_files/EMC2 ... Losses.pdf

You can get better performances with a 8.2% B11 to H fuel ratio.
http://www.askmar.com/Fusion_files/EMC2 ... Losses.pdf

from table 1;

FUSION-TO-BRE4MMSTRAHLUNG FACTORS FOR P-11B FUEL
Optimum Fuel Mixtures
Fuel p-11B
Ef (MeV) 8.7
Mi 0.92
f 2 0.082
Fb 2.28

These are old documents, and do not consider the reactivity peak at 140KeV, an some other refinements. I would not be surprised that much better performances can be archived.

The Fb factor would mean a Fusion power of 2.28 would lead to a brem losses of 1, or basically 44% losses.

[93143]

I'm not dishonest - I'm ignorant. Can you point me to the place they talk about this issue?

Sorry about the broadside...

The theory says that you can beat Bremstrahlung, but it's a challenge. The key is to keep the Boron concentration low compared the proton concentration so Z isn’t too bad. You pay for it in power density, but there is an optimum which works. You also gain because the electron energies are low in the high density regions.

This is from the MSNBC article comments section, if I'm not mistaken. This, plus a lot of other comments from when this issue has come up in the past, is what I was thinking about.

There have also been comments about controlling the virtual anode height carefully so as to maintain a relatively cold electron distribution in the core.

IIRC, the 1.74 figure comes from varying the H:B ratio and the electron and ion temperatures and taking the values that lead to the smallest factor. A brief summary can be found here. Todd Rider also discusses - and dismisses - a number of potential mitigation mechanisms.

I believe that calculation assumes a thermal plasma with hot electrons - the text actually mentions that the electrons are at least as hot as the ions, which shouldn't be the case in a Polywell core. Also, whether or not Polywell actually works, the consensus around here (endorsed by Dr. Nebel) appears to be that Rider was a bit pessimistic in some of his assumptions - it's been a while since I read any of his stuff myself, though, and I have no time now...

The experimenters may have a different view of the issue, but they have never measured any mitigation mechanisms - on this question they are just doing theory like you and me.

True, but their mechanisms for mitigation are reasonable if they're right about how the reactor works in the first place. And if they're wrong about that, the reactor could very well not work at all. I still think bremsstrahlung mitigation deserves a mention at least.

[Art Carlson]

You could refer to these old documents;
...
http://www.askmar.com/Fusion_files/EMC2 ... Losses.pdf

Quoting from this report:

If the electron energy is so low that the electron speed is comparable to the ion speed, ... This latter condition can obtain only ... if the electron/ion collision rates are sufficiently small that no significant collisional heating of electrons can take place during the electron lifetime in the machine.

Since bremsstrahlung power is proportional to sqrt(T_e), obviously it can be reduced by reducing the electron temperature. There can be many terms in the electron power balance. Two which are unavoidable are the loss of energy due to the bremsstrahlung itself, and the heat transfer from the ions due to Coulomb collisions. The factor 1.74 I gave above assumes these are the only terms, i.e., that the electron temperature takes on the value such that the energy the electrons pick up from collisions with the hot ions is balanced by the energy lost through bremsstrahlung. Bussard here assumes that the electron lifetime in the polywell is short, so that there is an additional energy loss term that keeps the electrons cold and therefore the bremsstrahlung power low. That is his good right. However, I do then insist that he reconsider the ion power balance. If we let the electron temperature "float", then the ion energy loss power is exactly equal to the bremsstrahlung power. If, in contrast, we push the electron temperature down by any means, then the power transferred from the ions to the electrons by collisions will go up. The ratio of bremsstrahlung power to fusion power will become smaller than 1.74, but what we really care about, the ratio of ion energy losses to fusion power, will become even larger than 1.74. Bussard skips over this fact in the report cited.

These are old documents, and do not consider the reactivity peak at 140KeV, an some other refinements. I would not be surprised that much better performances can be archived.

There are some games you can play that will give you a small improvement in the power ratio. One is assuming a mono-energetic (non-thermal) ion energy distribution that exploits the resonance in the cross-section at 140 keV. Maintaining such a distribution also costs energy, ... but that's another thread.

P.S. These comments serve as a reply to 93143 as well. Optimizing the fuel mixture is so obvious that I didn't think it necessary to mention in my brief summary of the power balance calculation. Rick Nebel as quoted is placing his money on keeping the electron temperature low, but he doesn't mention the effect that has on the collisional power loss from the ions.

[TallDave]

Rick Nebel as quoted is placing his money on keeping the electron temperature low, but he doesn't mention the effect that has on the collisional power loss from the ions.

Shouldn't that be relatively small? How much extra collisional energy can a giant ion lose to a little tiny electron? Luis Chacon seemed to think he could reach useful conclusions while ignoring ion-electron collisions entirely. Maybe Rick can share his own calculations on this.

Guess I should get to work reading the previously-referenced chapter 4 of Glasstone and Lovberg's Controlled Thermonuclear Reactions (got it in the mail yesterday).

[93143]

If we let the electron temperature "float", then the ion energy loss power is exactly equal to the bremsstrahlung power. If, in contrast, we push the electron temperature down by any means, then the power transferred from the ions to the electrons by collisions will go up. The ratio of bremsstrahlung power to fusion power will become smaller than 1.74, but what we really care about, the ratio of ion energy losses to fusion power, will become even larger than 1.74.

I don't recall this being mentioned before. New information? I consider my ill-considered flame a success.

Hmm... I haven't looked at it that way before... I'll have to think about this one...

Doesn't a lot of the bremsstrahlung come from the high-energy tail? If the distribution isn't fully relaxed, shouldn't that reduce the loss significantly all on its own?

Optimizing the fuel mixture is so obvious that I didn't think it necessary to mention in my brief summary of the power balance calculation.

I had a feeling I was going to regret including that...


Anyway, I doubt that 60% efficient power conversion of x-rays was part of the plan for p-11B, so clearly you and EMC2 see things a bit differently on this issue. We'll eventually find out whether they had something up their sleeves.

[Art Carlson]

Doesn't a lot of the bremsstrahlung come from the high-energy tail? If the distribution isn't fully relaxed, shouldn't that reduce the loss significantly all on its own?

Actually, it's the other way around. Since the Coulomb cross section drops rapidly with velocity (~v^-4), most of the bremsstrahlung comes from the low energy bulk. If you want to tailor an electron energy distribution to emit less bremsstrahlung (for a given average energy), you need to make a hole at low energy. This has been considered (see Rider again), but it costs a lot of energy to shovel out the electrons that fall into the hole.

[Art Carlson]

Rick Nebel as quoted is placing his money on keeping the electron temperature low, but he doesn't mention the effect that has on the collisional power loss from the ions.

Shouldn't that be relatively small? How much extra collisional energy can a giant ion lose to a little tiny electron?

How easy is it for an itty bitty electron to lose energy to a big fat ion? It bounces off and changes direction, but it doesn't lose much energy. In fact, the isotropization of the electron energy distribution occurs much faster than the slowing down. Anyway, the factor of 1.74 comes from a quantitative calculation, and lowering the electron temperature will have to make it worse.

[Jboily]

Rick Nebel as quoted is placing his money on keeping the electron temperature low, but he doesn't mention the effect that has on the collisional power loss from the ions.

Shouldn't that be relatively small? How much extra collisional energy can a giant ion lose to a little tiny electron?

How easy is it for an itty bitty electron to lose energy to a big fat ion? It bounces off and changes direction, but it doesn't lose much energy. In fact, the isotropization of the electron energy distribution occurs much faster than the slowing down. Anyway, the factor of 1.74 comes from a quantitative calculation, and lowering the electron temperature will have to make it worse.

Art,
The documents says the other way. It seem you are in disagreement with what is said in EMC2-0891-04 1991 Bremmstrahlung Radiation Losses, or maybe I am reading in wrong. They also calculated the optimum Pf/Pb to be about 12.16 at the 560Kv well dept, because of the low electron temperature (see Table 2). The synchrotron losses would be about 10:1 also. It would appear only 20% losses, with Brem&Synch losses combined is possible.

[Art Carlson]

Anyway, the factor of 1.74 comes from a quantitative calculation, and lowering the electron temperature will have to make it worse.

Art,
The documents says the other way. It seem you are in disagreement with what is said in EMC2-0891-04 1991 Bremmstrahlung Radiation Losses, or maybe I am reading in wrong.

I think we're getting confuddled over the various terms in the various power balances. There is a particular (optimum) value of T_e for which P_coll (the collisional energy transfer from ions to electrons) is equal to P_brem (the bremsstrahlung radiation from the electrons). At this value of T_e, P_brem = P_coll = 1.74*P_fusion. If T_e goes down, then P_brem goes down, but P_coll goes up. If you do the power balance on the ions, then you have to use this larger value of P_coll. If you do the power balance on the electrons, then you have to add another term to cover the mechanism that is keeping the electrons cold.