US Senators: What Will ITER Really Cost?

[KitemanSA]

I have to agree that the "no toroidal stars" argument against the tokomak and other toroidal devices is weak. Unfavorable field curvature is a much stronger argument.

Which is what you get with toroids.

Toroids are problematic because of the field curvature they produce, not because there are no toroidal stars.

True, the "no toroidal stars" is the symptom, not the cause. But when you can point at billions of symptoms, that suggests there is a cause, no?

Just telling folks what the cause is doesn't make them think!

[kcdodd]

What is a casp?

[MSimon]

What is a casp?

A hasp for caplocks.

[kcdodd]

Interesting.

Well, one thing is that curvature is not defined as dB/dr. Curvature is defined as (b dot grad)b, where b is the unit vector along magnetic field line. However, direction of curvature is intimately related to field gradient in a vacuum. However, if you want any pressure in the plasma, and assuming the plasma has a boundary, you have to have a field gradient to supply the forces necessary to support the pressure gradient at the edge. So, with a plasma, you can have gradient going in opposite the way you would expect in a vacuum. I would say in fact that all plasmas with non-zero pressure has to have field gradient pointing outward to even have a steady state no matter what the curvature is doing. So, I guess it would be true if only talking about a vacuum.

[Joseph Chikva]

So, I guess it would be true if only talking about a vacuum.

If you want to talk about plasma pressure that is always considered at the edge. Therefore in vacuum.
As plasma by its property is strongly diamagnetic. http://tfy.tkk.fi/aes/AES/courses/crspa ... _Jamsa.pdf
And talk about magnetic pressure inside does not make sense.

[kcdodd]

Plasma pressure is not just at the edge. It is everywhere the plasma is. And the edge is not vacuum. If it were vacuum then you would be outside the edge. Plasma pressure profile is rarely flat, so you get gradients all over the place besides the edge. The bare minimum is that there be one at the edge, not the only case. Of course plasma is diamagnetic that is single particle motion that is the whole point to magnetic confinement. And what are you talking about magnetic pressure does not make sense inside the plasma? It is well defined everywhere. So is plasma pressure. Define what you are talking about.

[Joseph Chikva]

Plasma pressure is not just at the edge. It is everywhere the plasma is. And the edge is not vacuum. If it were vacuum then you would be outside the edge. Plasma pressure profile is rarely flat, so you get gradients all over the place besides the edge. The bare minimum is that there be one at the edge, not the only case. Of course plasma is diamagnetic that is single particle motion that is the whole point to magnetic confinement. And what are you talking about magnetic pressure does not make sense inside the plasma? It is well defined everywhere. So is plasma pressure. Define what you are talking about.

We did not talk yet about plasma pressure p = n kBT here in this thread.
When you talk "Plasma pressure profile is rarely flat" you should take into consideration that there are two variables and plasma pressure is proportional to their product.
Profile will differ from machine to machine depending on profile of n and T.
And commonly "rarely flat profile" is wrong statement.

Yes, if to talk about magnetic pressure pmag = B²/2μ0, when due to plasma diamagnetic properties B diminishes inside in 50 times, pmag there will diminishes in 2500 times.

Your problems are:
• mixing of different terms
• usage of only one model and its application there where that is less applicable. As if you would like to consider profiles inside plasma you should for example solve Poisson equation and not to consider primitive mechanic model (ratio between plasma and mag pressures) that is good for first approach but does not provide detailed picture.

And for your reference, plasma behavior is much complex than single particle behavior.

Good luck.

[kcdodd]

Of course the profiles depend on the machine. I never said anything contrary to that. I was merely pointing out that your conclusions on field gradient and field curvature is only valid in a vacuum. We are not talking about vacuums here. We are talking about plasmas with pressures on order of atm's. I only mention that pressure profiles not being flat because of your assertion that pressure gradients don't exist inside the plasma. So, between your apparent claim that they are always flat, and my claim that they are rarely flat, which one do you think is less accurate? I am not mixing different terms. You're the one mixing up gradients and curvatures, in addition to several other things, which is why I posted to begin with.

[Joseph Chikva]

Of course the profiles depend on the machine. I was merely pointing out that your conclusions on field gradient and field curvature is only valid in a vacuum. We are not talking about vacuums here. We are talking about plasmas with pressures on order of atm's. I only mention that pressure profiles not being flat because of your assertion that pressure gradients don't exist inside the plasma. So, between your assertion that they are always flat, and my claim that they are rarely flat, which one do you think is less accurate? I am not mixing different terms. You're the one mixing up gradients and curvatures, in addition to several other things, which is why I posted to begin with.

Mr. Carter, the history of this thread is following.
People saying "good curvature" or "bad curvature" mean that convex field is better for stability than concave.
I am stating that this is only assumption was being popular in the beginning of fusion research. And this assumption is the special case (for only flat models) of more common the so called "minimum-B principle" which consists in that plasma having diamagnetic properties always retracted in minimum-B space where that should be stable.
In fact plasma is really retracted. But for being stable many other conditions should be satisfied.
And commonly the statement: "Convex - therefore stable" is wrong.

Now about gradient and curvature.
In flat geometry "convex vs. concave" and commonly if to consider toroids which are not flat, namely gradient defines dependence of field strength on position. And not curvature.
As extremum of B-field is there, where gradient is equal to nil.
And "minimum-B principle" means that in all areas outside plasma gradient would be more than nil.
In flat or spherical geometry this case corresponds to so beloved here convex power lines.

Now you are saying:

I only mention that pressure profiles not being flat because of your assertion that pressure gradients don't exist inside the plasma.

Which pressure? Plasma or mag?
As mag field is diminished, so mag pressure is also diminished proportionally to B^2.
And I never told about flat pressure profiles. But for very simple spherically symmetric Polywell you can consider flat model.

Good luck.

[kcdodd]

In flat geometry "convex vs. concave" and commonly if to consider toroids which are not flat, namely gradient defines dependence of field strength on position. And not curvature.

Well at least you seem to have corrected yourself, even if you can't admit when you were wrong: gradient != curvature. That is correct.

[Joseph Chikva]

admit when you were wrong: gradient != curvature.

I never said that.
I only said that popular here reasonings about advantage of convex field for stability does not work.
And those reasoning is the special (flat) case of more common "minimum-B principle" that can be expressed by field gradient dB/dr>0
I am stating that Tokamaks providing dB/dr<0 (corresponds to concave fields) always were more stable than Stellarators providing the dB/dr>0 (corresponds to convex fields).
As that is an experimentally proven fact.

And from this follows for example that statement of Mr. hanylap (as well as many others here) that toroidal machines have worse field curvature is strongly wrong.
I understood that people here saying "good" or "bad" curvature talk about field configuration and have not purpose to really measure or calculate curvature (the current radius of curve in certain point).

[kcdodd]

I am pretty sure most of the heat loss in a tokamak goes outward (toward larger radius). This is why the outboard diverter strike plate requires more attention than the inboard one. It gets more of the heat load. It may be just a coincidence that the outboard plasma surface has bad curvature while the inboard surface has good curvature. And my simple thinking is of course guilty of concluding that all things being equal, it would be a better use of magnetic field to have good curvature everywhere, and not just on half the plasma. Am I saying that tokamak's can't work because of this? No, of course not. As long as you make them big enough it seems they have a pretty good shot of doing the job. The current research seems to be directed simply to find out just how big you have to make it. Although there is also some speculation that H-mode may actually stop working if the major radius gets too large as well, which could complicate that statement. Also financial constraints.

[Joseph Chikva]

It may be just a coincidence that the outboard plasma surface has bad curvature while the inboard surface has good curvature.

That is popular here myth. As toroidal machines Tokamak and Stellarator both have field's twist.

And my simple thinking is of course guilty of concluding that all things being equal, it would be a better use of magnetic field to have good curvature everywhere, and not just on half the plasma.

What is "good everywhere"? Convex but full of hole?
"In half bad" Tokamak's field provides plasma lifetime lasting minutes.
What lifetime can provide "good everywhere" field? E.g. Polywell?
What do you think what real number density was achieved in Polywell with 0.8 T field? And what number density earlier versions of TOKAMAKs provided at similar strength of field?
Answering on these simple questions you can better understand what really is good and what bad.

Good luck.

[kcdodd]

That is why I said all things being equal it would be better, because it would be a more efficient use of field, which is proportional to coil costs. Just because there is good evidence that tokamaks can exceed break-even by making them big enough doesn't mean anyone will ever be able to afford to build a tokamak fusion power plant, and it doesn't mean other avenues can't be developed as well that might turn out cheaper. You are stuck in a false dichotomy.

[Joseph Chikva]

That is why I said all things being equal it would be better, ........ You are stuck in a false dichotomy.

And why?
I asked two simple questions and by idea 8 generations of Polywell should prove something.
But those proved nothing.
Please answer on questions if you can.
Then let's talk where I stuck.