Of Line Cusps

[seedload]

The Wiffle Ball affect is supposed to close all line cusps and result in only point cusps. Is that right?

If so, then what I don't get is why it is so important that WB6 and WB7 have spacing between coils so that the field lines do not intercect the next coil. Isn't this the gap where the line cusps are and where the line cusps should disappear if a true WB is acheived? If so, doesn't this indicate that a WB is not actually happening or at least that it's affect is less than expected.

It seems to me that the containment supposedly acheived by WB6 has a lot more to do with still having all the cusps but being very careful to not have field lines intersect anything that would impede recirculation than it does with the WB affect. The WB is imperfect which is probably why Bussard originally didn't even think to worry about the spacing between coils.

Do I have this right?

[kcdodd]

My understanding of the wiffleball effect is it does not "close" any cusp at all. The very center of the device without any electrons in it has zero magnetic components since all the faces cancel each other. However, it is just a point in the center where this happens. Any movement off the zero point and you will get at least some magnetic field, although very small. But when you introduce an electron cloud into the chamber the dia-magnetic effects of the electron paths will sort of "expand" this point of zero B-field into a small volume. That volume now is the so called wiffle ball because it in effect has a "surface" to which electrons will tend to reflect off of. To begin with the surface would have a certain thickness where the b-field increases from zero to it's non-zero magnitude

According to Bussard, it would be possible to expand the wiffle ball to the point where the "surface" has no thickness at all. It would then idealy be a perfect boundary between the center area where you have electrons, and everywhere else where you have a magnetic field (and no electrons). This is the beta = 1 condition, where nKT = B^2/(2*mu_0) at that boundary.

The cusps are still there though. Its just that ideally the electrons wont be able to travel outside of the boundary and hit the coils (where there is non-zero magnetic field). At the cusps the boundaries related to two magnetic field producing coils come very close to one another, but likely they will never actually touch, making a very small path for electrons to escape the center. The thing is the corner cusps will have effectively larger "holes" because they further away from the coils, so more will travel out of the corners then the space between the corners.

[TallDave]

Great explanation kcdodd.

As far as I can tell Bussard never mentions the line cusps and doesn't seem to consider them a loss mechanism. It may be that the need to not have the line cusp field lines going through coils has more to do with the recirculating electrons that have already escaped through the corner cusps than with any concern for electrons escaping through line cusps.

http://www.emc2fusion.org/2006-9%20IAC%20Paper.pdf

The highest value that can be reached by electron density is
when this ratio equals unity; further density increases simply
“blow out“ the escape hole in each cusp. And, low values of
this parameter prevent the attainment of cusp confinement,
leaving only Gmr, mirror trapping. When beta = unity is
achieved, it is possible to greatly increase trapped electron
density by modest increase in B field strength, for given
current drive. At this condition, the electrons inside the
quasi-sphere “see“ small exit holes on the B cusp axes,
whose size is 1.5-2 times their gyro radius at that energy and
field strength. Thus they will bounce back and forth within
the sphere, until such a —hole“ is encountered on some
bounce. This is like a ball bearing bouncing around within a
perforated spherical shell, similar to the toy called the
“Wiffle Ball“. Thus, this has been called Wiffle Ball (WB)
confinement, with a trapping factor Gwb (ratio of electron
lifetime with trapping to that with no trapping).
Analyses show that this factor can readily reach values of
many tens of thousands, thus provides the best means of
57th International Astronautical Congress (IAC) Valencia, Spain - October 2006
Bussard R.W. 10
achieving high electron densities inside the machine relative
to those outside the magnetic coils, with minimal injection
current drive.
In a recirculating MG machine, this factor is important since
it sets the minimum density that can be maintained outside
the machine, for any given interior edge density, as required
for sufficient fusion production. It is desired to keep this
outside density low, in order to avoid exterior Paschen curve
arcing, which can prevent machine operation. To have low
exterior density of electrons, and high interior density
requires large Gwb factors, thus, good Wiffle Ball
confinement is essential to system operation at net power.

If the corner cusps are only 2 times the gyroradius and the line cusps are smaller, it's going to be pretty hard for an electron to get through a line cusp.

[TallDave]

This also helps explain why the truncated dodec would be better than the truncated cube: the more like a sphere the shape is, the smaller those corner cusps get, and the better the ratio of trapped electrons to recirculating electrons you can achieve.

[kcdodd]

I am curious how he came to the 2x the gyro-radius figure, and I'm a bit confused about what he means exactly. Because if the electrons are on an escape trajectory they must be traveling at nearly parallel to the B-field, which means their gyro-radius is basically zero, no matter what the energy or B-field is. And if its at beta=1 then the b-field is basically zero anywhere else the electron might be.

[blaisepascal]

I am curious how he came to the 2x the gyro-radius figure, and I'm a bit confused about what he means exactly. Because if the electrons are on an escape trajectory they must be traveling at nearly parallel to the B-field, which means their gyro-radius is basically zero, no matter what the energy or B-field is. And if its at beta=1 then the b-field is basically zero anywhere else the electron might be.

I am not an expert, nor do I attempt to play on on TV. But my understanding is that the B-Field is (a) strong, and (b) tangent to the well except at the cusps. At the cusps it's perpendicular to the well.

Imagine a slice through the center of the cube parallel to a side. The B-Field lines in this plane, with well in the center, come in from the sides to the edge of the well, nearly perpendicular to the well, skirt around the well, tangent to it, and then exit towards the corners. The eight places where the fields are perpendicular to the well are the cusps. The stronger the field, given the same size of well, the more the area near the cusps will remain tangent to the well.

An electron which hits the B field not tangent to the B Field will experience a Lorentz force strong enough to make the electron follow a helical path around a field line with a characteristic gyro-radius. If the area of the cusps are smaller than twice this gyro-radius then when the electrons following the field-lines get near a cusp (where the B-Field changes direction rapidly) they will hop to different field-lines and be unable to follow the cusp out. So in order to escape an electron has to hit the polywell wall close to the cusp and nearly head-on. Otherwise it'll be caught by the B-Field, wander around on it, and be thrown back into the well.

[kcdodd]

My question is on the side of how he arrived at that number for the size of the hole. The b-field would be fairly uniform along the cusp axis, so what is to limit how large the hole would get.

[Solo]

Try askmar.com, in particular this report or maybe this one

[kcdodd]

Ah, thank you for the link what a treasure trove .

[Solo]

No problem! I imagine you can get more out of those docs than I can, alot of that was over my head. If you figure out what Dr. Bussard was getting at with the gyroradius stuff, maybe you can explain it more simply!

[Solo]

I've had a really hard time finding much discussion of cusp loss besides what Dr. Bussard said. (Now, I've found some abstracts for journal articles on IOP or other services, but I'm looking for freebies!) And in particular, I don't know of anyone who's talked about the polyhedral config. and the semi-line cusps it has. Also, I've not seen much on high-beta effects either. I know Art has said the cusp configuration is not new, so I was hoping we could find some info on it. I doubt Bussard's assertion that none of the prior research is applicable.

Here are some links to abstracts or titles of articles that might be applicable:

http://link.aip.org/link/?RSINAK/77/03A524/1

http://link.aip.org/link/?RSINAK/69/968/1

http://www.iop.org/EJ/abstract/0032-1028/23/4/011

http://ieeexplore.ieee.org/Xplore/login ... er=4316999

http://link.aps.org/abstract/PRL/v8/p305

http://www.epjap.org/index.php?option=a ... ap9064.pdf

The abstract from this last paper, emphasis mine:

The confinement properties of a low beta argon discharge plasma in a spindle cusp magnetic field was investigated. Plasma was produced by ionisation collisions by the electrons which were produced by thermionic emission of electrons. The central problem involved with plasma confinement by a cusped magnetic field is the loss of particles along the flux lines. Electron and ion leak widths were studied in the ring and point cusps and measured over a range of magnetic field strengths (B), neutral pressures (P) and discharge currents (). It was found that the leak width was reduced with increase in I_d and B. The ion leak widths were found to be larger than the electron leak widths. The normalised effect of magnetic field and pressure on ion and electron leak widths in cusps are reported, compared and discussed. The dependence of electron and ion leak widths on plasma densities were also studied. At very low pressures, high plasma densities and high magnetic field strengths, a quasineutrality condition was attained.

[choff]

My understanding is that electrons enter from the inside of the coils where they have lots of space and exit through the narrow corners.

I wonder if its possible for the corners to become so saturated with escaping electrons that at some point additional electrons arriving at the corners start getting repelled into the core.

With additional electrons corners could then start to act like emitters with as much energy as the faces.

[MSimon]

My understanding is that electrons enter from the inside of the coils where they have lots of space and exit through the narrow corners.

I wonder if its possible for the corners to become so saturated with escaping electrons that at some point additional electrons arriving at the corners start getting repelled into the core.

With additional electrons corners could then start to act like emitters with as much energy as the faces.

I don't know how this relates to your question, but the electron beams will be oscillating in and out of the cusps. If I was still in the Navy we would call it a f*****g machine. That kind of talk always impresses the sailors and fixes the concept in their minds.

[choff]

Then there's absolutely no debate the wiffle ball forms from the core and pushes out as opposed to from the cusps pushing inward, naval terminology notwithstanding.

[MSimon]

Then there's absolutely no debate the wiffle ball forms from the core and pushes out as opposed to from the cusps pushing inward, naval terminology notwithstanding.

I was only addressing the beams.