kcdodd wrote: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.