New FAQ - What are Cusps and what kind does a Polywell Have?

[Art Carlson]

I'm considering the simple case of the ideal mono-energetic, single-species electron plasma. I have a proposition that I think can help explain simply the much talked about "annealing" at the beta=1 plasma-field interface. Any spreading out of velocity distribution in this region has two effects;
i) the electrons that lose kinetic energy slow down and drop down back in towards the plasma core ... end of story, they will soon collide with higher energy electrons down in there and get pumped back up to the monoenergetic level

Are you sure about this? I haven't looked at the equations for a while, but I believe a test particle experiences an inward drift (slowing down) in velocity space when surrounded by a mono-energetic distribution. At the very least, energy conservation will require that other particles slow down if that one speeds up.

ii) the electrons that have gained enough extra energy are able to rise up across the interface (as unstable R-T eddies?) and get onto field lines that are headed to the cusps. Some calculable proportion of these higher energy electrons, that make it out of the plasma and onto field lines, will have velocity directions that lie in the loss cone of the magnetic mirror attributable to the point cusps.

In a beta=1 plasma, up the the cusp point there is no magnetic mirror. Since the field pressure exactly balances the plasma pressure, it is constant along the surface. The potential mirror effect I was talking about would occur if the field increases after the particles pass the cusp point. The question is, if you have a maximum field strength available, do you want to spend it on your cusp, or part of it on a mirror and the rest on the cusp. I strangly suspect it is best to go for the cusp and forget about the mirror, but I haven't worked through the math.

[Art Carlson]

I would posit that having the electric field orthogonal to the magnetic field at the plasma-field beta=1 surface is a crucial key to the enhanced electron confinement. The conformal cans for the MaGrid has done the trick, not only because of the reduced intersection of field lines out at the physical magnets, but critically down at the plasma surface it will keep the electron velocity vectors pointing away from the loss cones, resulting in an enhanced mirroring effect that is better than simple cusp confinement.

In addition to the problems I pointed out in my previous post, I'd like to know more exactly why you think an electric field will necessarily produce a prolate distribution, which, incidently, if it is supposed to enhance mirror confinement, must survive even when the electric field is removed. The usual lowest-order assumption is that the electron velocity distribution in an electric field is a shifted - not distorted - Maxwellian.

The run-away effect applies only to a small fraction of the electrons. I don't see any relevance here.

[rcain]

In a beta=1 plasma, up the the cusp point there is no magnetic mirror. Since the field pressure exactly balances the plasma pressure, it is constant along the surface. The potential mirror effect I was talking about would occur if the field increases after the particles pass the cusp point. The question is, if you have a maximum field strength available, do you want to spend it on your cusp, or part of it on a mirror and the rest on the cusp. I strangly suspect it is best to go for the cusp and forget about the mirror, but I haven't worked through the math.

arn't they sympathic? max -dt of line cusp length? more amps?

[chrismb]

I've never bothered to wade into debates which even mention beta before, because I think the notion with respect to Polywell is a bit absurd. But here we go;

Are we talking here about the beta *of the electrons* in the cusps or the beta *of the ions*? Unless they've thermalised into a 'regular' thermal plasma, with the ions cooler than the electrons, then the magnetic field will confine the electrons (by definition, beta=1) but will NOT confine edge ions. Surely, only if beta=1 *for the ions* will they be 'confined' by the magnetic surfaces, and if that were so then the electrons and ions would thermalise quickly?

(I don't even know that I know what that question means, such is my confusion over the notion of Polywell beta!)

[rcain]

I've never bothered to wade into debates which even mention beta before, because I think the notion with respect to Polywell is a bit absurd. But here we go;

Are we talking here about the beta *of the electrons* in the cusps or the beta *of the ions*? Unless they've thermalised into a 'regular' thermal plasma, with the ions cooler than the electrons, then the magnetic field will confine the electrons (by definition, beta=1) but will NOT confine edge ions. Surely, only if beta=1 *for the ions* will they be 'confined' by the magnetic surfaces, and if that were so then the electrons and ions would thermalise quickly?

(I don't even know that I know what that question means, such is my confusion over the notion of Polywell beta!)

would you not expect (near-) isothermals/inversions also within sheath and other electro-inertail manifolds that form?

are we not assuming that edge ions will be compressable () against coloumb repulsion (+ thermo-acoustic) they will try and equalise pressure by blowing up wb, squirting out of loss cones & edges some del-t later?

can we not define it as a simpl comb filter (ang-mom - dx or dt) , possible additional well traps for ions thermalised out of our favoured reaction, and some far-off ones for our (eventual) output-capcha, might be helpful. we would need to agree a starting state and some specific/critical impulses (controls) state changes. eventualy we get to the Q>1 V Lawson scenario. (BEC anyone? POPS? FRC?). what critical must-have states do we need to see on on the spectrograph?

[TallDave]

Is there truly such a thing as "the standard Polywell view"?

I would describe that as what Bussard claimed and Nebel has agreed with. They have the experimental data, so...

But seeing as you seem to be the most prominent standard bearer of it ... I'll ask you directly ... is there any evidence we can point to that the ions never get far enough out of the potential well to see the electron sheath, i.e the beta=1 surface?

I'm basing that mostly on a vague recollection of something Rick said, which he probably gets from the PIC simulations and whatever other things they have going at EMC2. The Chacon paper might be relevant here too.

Surely some of them will become energetic enough to rise to this region?

Apparently not enough of them to matter much. We could probably set an upper limit if we did some math on WB-7 confinement.

This sounds like a cop out,

A cop out is exactly what it is. I'm more than happy to call the system too complex for this kind of thing, and there's very little chance I'm going to attempt to model it in software myself. Guilty as charged.

In the above statement, the inclusion of the word "dynamic" is a non-sequitur that may be more an attempt to bamboozle than add any useful information.

Innocent here, Your Honor. I mean this in the specific sense of "having a variable or constantly changing nature," i.e. something which requires a simulation rather than an equation.

you yourself have resorted many times to simplistic equations when it suits your cause

Well, some things are complex and dynamic and some aren't. Converting fusions to watts is relatively straightforward relative to modelling ion behavior. For instance, square wells give very different results than parabolic ones, but a watt is always a joule per second.

Actually, I'm surprised you would say that, Art has often been critical of me in the opposite direction.

[TallDave]

Are we talking here about the beta *of the electrons* in the cusps or the beta *of the ions*?

I think the standard Polywell view is that beta=1 is where electron pressure is not quite sufficient to blow out the cusps (i.e. electron pressure = magnetic field). The ions are confined by the electrons and the machine is run electron rich.

[rcain]

... is there any evidence we can point to that the ions never get far enough out of the potential well to see the electron sheath, i.e the beta=1 surface?

sorry to interject, i'm trying to sense this all out also...

...in possible answer - 'where/when would it get the energy from to do that?', - unsucessful proton impacts, inter-ion-displacements, (overall thermalisation & neutrals) - stored inertial-electro-magnetic moment and an impulse (step function). maybe blowing the wb out in a pulse mode is is useable (anealing?) to enhance productive collisions/effective crossection?

[TallDave]

Are we talking here about the beta *of the electrons* in the cusps or the beta *of the ions*?

I think the standard Polywell view is that beta=1 is where electron pressure is not quite sufficient to blow out the cusps (i.e. electron pressure = magnetic field). The ions are confined by the electrons and the machine is run electron rich.

I should add a couple things here: at reactor sizes, we know ions that do get this far out will be affected by the magnetic field; if the alphas are being funneled into the cusps a regular ion probably cant make it out at all. Also, the well gradient starts at the Magrid, so a large proportion of stray ions that do make it out to the edge probably head back in.

[Art Carlson]

Are we talking here about the beta *of the electrons* in the cusps or the beta *of the ions*? Unless they've thermalised into a 'regular' thermal plasma, with the ions cooler than the electrons, then the magnetic field will confine the electrons (by definition, beta=1) but will NOT confine edge ions. Surely, only if beta=1 *for the ions* will they be 'confined' by the magnetic surfaces, and if that were so then the electrons and ions would thermalise quickly?

We are talking about a configuration of plasma and field such that

• an interior region, where the total plasma pressure is large compared to (local) magnetic pressure, and
• an exterior region, where the magnetic pressure is large compared to the total (local) plasma pressure, are separated by
• a relatively thin sheath, with thickness at least as big as the larger of the electron gyro-radius and the Debye length.

The total plasma pressure is the sum of the electron and ion pressures. For a thermal plasma that is ( n_e*kT_e + n_i*kT_i ). For a non-thermal distribution, kT must be replaced by an appropriate "average" energy.

Since the fields generally decrease moving toward the center of the device, for a given current in the coils, this definition can be met by a small and relatively low pressure plasma, or by a larger plasma with higher pressure. There is a limit to the possible increase in size/pressure, given roughly by the condition where one or more cusp points reach the position of maximum field. We sometimes might be thinking of this maximum pressure/size/energy plasma when we say (sloppily) beta = 1.

[chrismb]

I can anticipate the answer *you* will give, Art, as I think we've mostly got the same view on this.

For a non-thermal distribution, kT must be replaced by an appropriate "average" energy.

Ah..therein lies the dilemma. Whereas *we* are happy to take a 'partial pressure' function of the ions AND electrons as the total plasma pressure, this would imply that the ions and the electrons react (i.e. bounce off and therefore would share energy) against each other.

As far as I understand the 'classic view' of Polywell, electrons do their thing, ions to theirs, and ne'er the twain shall meet. This is clearly contrary to the notion of a function of partial e- and ion+ pressures. (If there *were* to be interactions, the electrons would suck on the ions' energy, whether or not they are at the edge/cusps. The flow of ions through the device would eventually draw the energy out of the reaction volume ions also.)

So, when talking about 'beta' in a Polywell, is it, or is it not, the 'total resultant' interactions of the electrons WITH the ions, or some view of each as two separate calculations.

[Art Carlson]

I can anticipate the answer *you* will give, Art, as I think we've mostly got the same view on this.

For a non-thermal distribution, kT must be replaced by an appropriate "average" energy.

Ah..therein lies the dilemma. Whereas *we* are happy to take a 'partial pressure' function of the ions AND electrons as the total plasma pressure, this would imply that the ions and the electrons react (i.e. bounce off and therefore would share energy) against each other.

As far as I understand the 'classic view' of Polywell, electrons do their thing, ions to theirs, and ne'er the twain shall meet. This is clearly contrary to the notion of a function of partial e- and ion+ pressures. (If there *were* to be interactions, the electrons would suck on the ions' energy, whether or not they are at the edge/cusps. The flow of ions through the device would eventually draw the energy out of the reaction volume ions also.)

So, when talking about 'beta' in a Polywell, is it, or is it not, the 'total resultant' interactions of the electrons WITH the ions, or some view of each as two separate calculations.

The electrons react to the electric field and the magnetic field. The ions also react to the electric field and the magnetic field. For a quasi-neutral plasma (although it is not hard to generalize), the charge density of electrons and ions are equal, so the electric force per unit volume is equal and opposite for the two species. If we add the two species together, the electric forces cancel. That is why it is correct to just consider the interaction of the total plasma with the magnetic field. It doesn't matter whether one species or the other or both directly interact with the magnetic field.

Those are macroscopic fields, and the typical timescale is the inverse of the plasma frequency. Energy transport between the species is the result of binary collisions between them (although each particle experiences thousands of binary collisions at the same time). The time scale is calculated from the Coulomb cross section and is generally much slower, although still plenty fast that we need to take it into account in polywells.

I wasn't aware that any poly-apologists take umbridge with this view.

[chrismb]

I would say the same, but that I felt there was objection to the notion that the ions don't get to do their own thing, and end up having plenty of electron collisions.