Anyone have a better explaination for Magnetic Mirrors?

[mattman]

Hello all,

I went to a party Saturday night and I was trying to explain The Polywell to a physicist I met there.

I could get through most of the material well enough - explaining my current understanding of this machine – and being careful to say: “I don’t know” as much as I need to.

I did not have a good analogy for the magnetic mirror effect. I had walked through the mathematical explanation – but this does not work for a party. As I understand it, the magnetic field gets very dense at the corners and this causes the particle to make a U-turn. The analogy I used was that the potential energy rises at the corners so high that the particle cannot occupy the space because it does not have enough kinetic energy to be there.

Does anyone have a better way to describe the magnetic mirror effect?

[kcdodd]

The magnetic field does not change the total kinetic energy of the particle.

[asdfuogh]

Magnetic mirrors hold charged particles by the non-uniformity of the fields. I'd say it's easier to think of.. balls in liquid that stay in the less dense liquid in the center because it is harder to move past the denser liquid. It's not a perfect analogy (no analogy ever is), and more complicated things happen from the charged nature of the particles and the way the B-field acts on them.

[hanelyp]

A magnetic mirror is something like a funnel. A particle headed towards the opening escapes. But a particle on a trajectory sufficiently away from the opening is reflected.

[happyjack27]

it's like the way gravity makes massive objects attract each other. or how an aero-foil provides lift. near the stronger mag field, the path of the charged particle will curve more than it does on the side of the weaker field. the net effective of this is that the the electron will drift in the direction of the weaker field.

[D Tibbets]

Magnetic fields do not generally change the KE of a charged particle. It only turns it, or changes its vector. Ideally, with magnetic confinement the effect can be compared to a hard wall. The charged particle adiabatically (no loss of energy) bounces off of it. It does this through gryoradii orbits around a fieldline. In a non varying magnetic field the particle is stuck on this field line and orbits with a circular orbit- actually a spiraling orbit. It is stuck until something else acts on it- like a collision with another particle..
When the magnetic field strength is non constant with distance, the gyro orbits become ovals or parabolic. When the long axis of this parabolic orbit reaches distances greater than the radius of the machine the particle no longer can be said to be confined by an orbit dictated by the magnetic field and the plasma can be considered as non magnetic. This occurs in a Polywell at least in part because of the rapid change in magnetic field strength at the Wiffleball border , which is mediated in part by the non dominate vectors of the charged particles ( just as many traveling outward, inward, up, down, left or right ), unlike in a Tokamak where the charged particles dominate motion creates it's own magnetic field. So not only is the plasma contributing to a magnetic field, it effectively excludes the Magrid magnetic fields.

Magnetic Mirroring or sometimes called bouncing is more complex. The charged particle travels along a field line (spirals), slows with an increased gyro orbit frequency till its motion along the field line is stopped and reversed. I don't know the mechanism, but it is seen mostly where the field lines are coming closer together- the field strength in changing faster, like at the pole of a magnet or a cusp. This reflection, mirroring or bouncing applies to a charged particle traveling along a field line. A particle that is traveling more perpendicular to the field line might become entrapped and follow this pattern and in this instance it behaves as a magnatized plasma. This is shown in some Sims of a Polywell, but I believe that this is a small part of the story. In a collisional plasma like the Polywell and with magnetic field gradients over short distances, many approaching particles from the non magnetized region of the plasma (inside the Wiffleball) only complete ~ 1/2 of a spiraling gyro orbit before traveling back into the core region. This behavior is best described as as a bounce back into the interior off of a hard surface, more like billiard balls, or balls inside a Wiffle Ball toy.

Cusps are regions where the B field (magnetic field) is changing rapidly, though perhaps not more than the Wiffleball border throughout the machine. Also in the cusp regions the geometry of the B field lines are changing from perpendicular to the center to parellel to the center. and thus the shallow angle impacts of charged particles from near the center may glance off the cusp walls at shallow angles and proceed further down the cusp. The cusp throat (to differentiate it from the mid line narrowest portion of the cusp) thus acts as a funnel that collects particles and feeds them through the cusp. Magnetic mirroring/ bouncing plays a role, but more simplistically and perhaps more accurately The Wiffleball border can be considered as a reflective surface- like a billiard table. A ball may enter the pocket directly and pass through , or more likely it may bounce several times off of the beveled bumpers on the sides of the pocket, and after several bounces or ricochets it finally falls in the pocket. Snooker is another Pool game except the table may be larger and the beveled bumpers surrounding the pockets are smaller. Thus the target that the ball must hit to get into the pocket is smaller, otherwise it bounces back towards the center of the table. The Wiffleball effect carries the Snooker analogy to extremes. The pockets and feed in beveled bumpers may cover the same area, but the table itself becomes much larger, so the contribution of these loss 'pockets' become much less as a percentage of the total table wall surface area. 'There are pockets that occupy a certain small area of the table boundaries. All sorts of angles are possible and this effects the final outcome, just as with magnetic cusps.

The Wiffleball analogy,or Pool table analogy or funnel analogy are all useful when considering the charged particles as bouncing balls, and this is actually similar to the physics as the gyro orbits on the week side of the confining field line is so wide that the particle has traveled to the other side of the machine before it reaches the most distant portion of its orbit. Meanwhile the particle has had Coulomb collisions or fusion collisions and any 'memory' of it's magnetically induced orbit is lost.

Why I say that the collisional behavior of a pool table is more important than magnetic gyroradius spiraling behavior is because the charged particles do not spiral along the field line. Most, especially away from the cusps turn about a field line , and fly back towards the center. Note that this turning or bounce is not straight back the way it came from, the parabolic orbit and the spiraling movement tends to decrease central focus. Also , the convex field lines relative to the center may also add to the angular momentum. Bussard noted this for ions that are mildly up scattered and enter the magnetic domain before being turned, as opposed to the ideal fully elecrostatic confinement of the ions. When you add very many passes/ bounces among very many charged particles, the dance becomes very complex.


The short answer -

When discussing the Polywell use the Wiffle Ball analogy where you shrink the holes or alternately keep the holes the same size but increase the size of the ball, both are equivalent and I believe, both processes are actually occurring*.
Reassure the listener that actual charged particle,behavior in magnetic fields and magnetic field boundaries has been considered in deriving the simple descriptive model, and refer the listener to Askmar for sources if they wish to pursue it..


* The actual mid portion of the cusp is not changing, that would be a pinch and the Polywell definitely does not do this. The cusp throat or feed in portions that funnel the particles into the cusp does get flattened out as the overall surface of the Wiffleball expands. You are not changing the size of the Pool table pockets, but you are making the beveled bumpers that feed into the pocket smaller, until effectively there are no beveled bumpers at all- at Beta=1.

Dan Tibbets

[KitemanSA]

Wow, here is a near first, I almost agree with Dan's short answer.

I don't know about his long answer cuz I didn't bother to read it.

[MSimon]

A magnetic mirror is something like a funnel. A particle headed towards the opening escapes. But a particle on a trajectory sufficiently away from the opening is reflected.

This is the best short answer if you throw in non uniform fields/fields at right angles to particle motion.

[mattman]

See Below....

[KitemanSA]

I would almost call them “Triconic” cusps. Bussard called them Funny Cusps.

If this statement applies to this picture, than you have a misunderstanding of what the "funny cusp" is. What you are showing is the point cusp in the center of a virtual magnet. The funny cusp would be where the cross bars are but in the round planform WB6 type machine, they get replaced by line like cusps.

[D Tibbets]

In the biconic cusp mirror machine there are two point or polar cusps, and one line or equatorial cusp. The same applies to the Pollywell (sort of, actually there are two modified line cusps). The line cusp geometry is highly modified but it is still a line cusp. . By invoking so called vertual magnets in the corner regions of the Polywell you can treat most of the line cusps that separate the magnets as point cusp like regions but that doesn't change the physics, just provides a close approximation of point like cusp behavior.

The funny cusps were a term Bussard used to describe cusp behavior in his mathematical model. Since line (no width) representations of the magnets allowed them to come infinitely close together it was possible to describe losses here as almost nonexistent because the width of the cusps were infinitly small. As the magnets diverge the cusp widens till the corner is reached. I'm unsure how far from this midpoint Bussard extended the "funny cusp". What remained was the corner cusp which in this model was infinitely close to a point cusp and describing a corner cusp as a point cusp is very accurate. But WB6 changes illustrate the change in perspective. The magnets are real and have real widths. You could still bring the cans together, but now there is a real surface for ExB drifted electrons to hit. This led to the realization that there had to be some several gyroradii separation of the magnets., so the funny cusps are now real extensions of the line cusps between the magnets. The corner point like cusp description, while still useful, is now not so absolute.

Dan Tibbets

[KitemanSA]

The term "funny cusp" was used to describe the location where four or greater even number of magnetic fields met at a point yielding a location of null field. The simplified line description merely yielded a point of zero radius rather than a more realistic small area.

[mattman]

See Below...

[hanelyp]

The magnetic mirror reflection comes from magnetic field lines converging, not from just curving.

[mattman]

hanelyp,

Yes - over the weekend I talked with a physicist and he corrected me on a few points. I plan to get the correct motions explained out.

As I understand it, (1) the mirror is due to denser fields, NOT curved fields and (2) curved fields do create a “drift force” which pushes the particle away from the center.

I had these muddled together.