Another possible shape for the coils

[charliem]

If anyone have already suggested this I haven't seen it, if so my excuses in advance.

The shape I propose is a truncated cone, its projected apex in the geometrical center of the device. The section of one coil would be rectangular and also its shield, but this with the corners rounded to prevent shap edges. The shape would still be conformal to the B-field as required.

With this shape the solid angle that the coils occupy, as seen from the core, would be smaller, it could easily be reduced to 1/2 (or even less) of what a pure toroidal would take.

Some BOE calcs about the energy hitting the coil shields for BW100: If the shape is a toroid, its external diameter about 2 m, its thickness 0.2 m, and the distribution of the fusion reaction "exhaust" particles is isotropic in direction, about one third of them would end up colliding with those shields. So, more than 30 MW to dispose of. That's something...

Using a truncated cone would have some advantages.

A1-First the reduced solid angle, 1/2 or 1/3 is not difficult, so 15-10 MW instead of 30.

A2-Second. This shape makes possible to use a bitter-like design for the coils. Not a 100% bitter, because each layer of copper should have slightly different dimensions than the previous and next ones, but I think still doable, and with most of the good properties of a pure one about sturdines, fill factor, and cooling.

I also see some disadvantages:

D1-For the same amp-turns the B-field would be a bit smaller than with a toroid (although it looks easy to compensate).

D2-The B-field shape and gradients would also be a bit different (need more study, it could be neutral or even beneficial, but since I dont know I list it as a disadvantage).

D3-Others that I'm sure exist and I dont see...

What do you think, any worth studying?

[drmike]

Let's see if I understand this - I think my son's geometry book calls this a "frustrum". You'd have the coil wound so the tip of the cone would be the center of the fusor and each edge of the coil would be on a radial axis back to the center as well.

That would definitly reduce the cross section from impacts from the center. We'd definitly have to see how it would impact the magnetic properties, but sounds like a good idea to check out. Pretty easy to wind and excellent for cooling, so it has a lot of advantages from a pure engineering perspective.

[charliem]

Your are right drmike, it would be a conical frustum.

I think that without a graphic is a bit difficult to visualize. I'm going to try to describe it.

1.Lets start with a cube of side 2R (its center is where the fusion core would go).

2.Now, select one of the faces of the cube. Draw a cone, apex in the center of de cube, cone side just touching the center of the four square face's sides. Height a bit more than R (R+r, r>0).

3.Repeat 2. for the other 5 faces of the cube.

4.Delete every part of every cone inside the cube.

The 6 surfaces that rest are truncated cones or conical frustums.

5.Since they are only surfaces we need to give them some thickness so they have volume for the coils inside them.

The result would be something like deforming the shape of a cilindrical magnet coil making the radius of one of its bases bigger than the other.

[TallDave]

http://mathserver.sdu.edu.cn/mathency/math/c/c581.htm

[TallDave]

I imagine it would probably look more like this in practice:

http://en.wikipedia.org/wiki/Frustum

My guess is this would be non-optimal because the closer to a sphere you get with the Magrid, the sharper ion focus you should get at the core.

[tombo]

It could be made either as a tapered solenoid
or as a deformed Bitter coil.
My concern is making sure that all the field lines stay outside the material surfaces.
If the tapered solenoid were stretched lengthwise so there was room between the coils for electron recirculation it might work better.
The geometric problem there is how to make the connection to the inside end of the solenoid without catching alphas and electrons.

[charliem]

Here are some graphics I made to show the shapes I'm talking about.

The three alternatives delimit the same internal [truncated] cube of side=2 m.

Here is a front view:


And another slightly up and to one side:


Here is a ecuatorial 3D section of the above:


And last a 2D section (also at the ecuator):


All of them have the same internal area of aprox. 314 cm2.

The form factor W x L (width x length) of each is:

20x20 cm (circular), 10x34 cm (1er alternative), 6.7x55.3 cm (second)

The area of the sphere delimited for the internal cube (radius 1.41 m) is aprox. 25 m2. The area of the toriodal coils, seen from the machine center, is aprox. 6.8 m2 in total, the alternative shapes areas are half and one third of that figure (so the alphas intercepted should also be half and one third, diminishing the cooling problem).

I'm trying to calculate the strength and shape of the magnetic fields to determine if there are drawbacks.

My first results look promising, the B of a truncated cone coil is almost the same than a toroidal one (less than 10% difference) in most of the volume of the machine, and it is even stronger at some interesting places, namely at a cusp between two coils.

I see a possible problem about cusps and electrons. With toroidal coils the shape of the field inside a corner cusp is something like two funnels welded by their thinnest extremes (or a sand clock). The alternatives I propose would be like separating them by welding some pipe in between. If a electron slows down to much inside that "pipe" it wont go back, but deviate sideways to impact on one of the coils.

Gradients are even harder to calc. Anyone with a mag-fields simulation program?

Carlos.

[MSimon]

The fields don't exactly have to stay inside the surface. They need to be conformal to the surface. i.e. flat surfaces require flat fields. Round is easier.

You also have the problem of no electric field concentrators (nothing in the least bit pointy) - due to charge concentration/particle streaming inducing arcing.

I think it is fairly strict (nothing smaller than a 1 cm radius).

[charliem]

Tombo, sorry but I dont understand what you mean.

Simon, I can have made some error integrating the B-field of course, but if I have not the field is very approximately conformal to the coils surface.

You could look them just like high radius/length cilindrical coils, a bit deformated.

And the smaller radius in figure 1 (toroid) is 10 cm, in figure 2 is 5 cm (the ends), and in figure 3 is 3.3 cm (ends also).

[MSimon]

charliem,

It sure looks interesting. It might also help with focusing the corner cusp beams which might be a help in reducing cusp losses.

It would be good to have enough computer horse power and some good code to model all this stuff.

If it can be done on the order you suggest it means 200 and 300 MW units are within easy reach and 500 MW units might be just the thing.

[tonybarry]

Hello Carlos,
I suspect that an ellipse might be the best cross-section, though as yet I don't know for sure; my "Vizimag" application does not let me easily model ellipses.

Regards,
Tony Barry

[Curtis Faith]

Funny, I was just thinking about this yesterday. It seems to me that the best shape would be one that is conformal to the shape of the field itself at any given point around the coil. I'm assuming that since round was much better than square and round is much closer to the shape of the fields, that elliptical would be even better and squashed elliptical better yet.

From all the diagrams I've seen this shape seems to look like a squashed ellipse not a perfect ellipse because the fields from the adjacent coils interact to squash the one side of the ellipse. This is the same shape that is listed in the dotted lines for Figure 6 of Tom Ligon's excellent article:
"The World’s Simplest Fusion Reactor Revisited" which shows the improvement made with WB-6 over the square coils of WB-5.

It also seems probable to me that the shape of the coil would need to vary around the circle as the proximity to the other coils changes so the shape at the cut-off corners would be different the shape where the two coils were closest. It seems to me that the ideal conforming shape would be more of a perfect ellipse where near the cut-off corners and more squashed farther from the corners where the coils were closest.

- Curtis

[charliem]

Funny, I was just thinking about this yesterday. It seems to me that the best shape would be one that is conformal to the shape of the field itself at any given point around the coil. I'm assuming that since round was much better than square and round is much closer to the shape of the fields, that elliptical would be even better and squashed elliptical better yet.

I came to think of this shape from the necessity of a way to lessen the thermic charge of the coils, and because I like the bitter design. In the process I contemplated some variants.

One interesting thing I've observed after calculating the field of a few cross-sections, is that its strength and form converge to the same value and shape as you get away from them, and that this phenomenon happens at relatively small distances from their surfaces.

Indrek showed us how a circular and a square section coil generate almost the same magnetic field at short distances. Barring mistakes in my numbers, that looks to be the case also with other shapes (and at very short distances the differences can even be beneficial).

Moreover, given that the key factor in that convergence seems to be the ratio (distance from coil section center) / (maximum dimension of that section), and not field strength, their shape tend to become irrelevant as you make them stronger (more powerful).

Carlos.

[MSimon]

Carlos,

An excellent point and one I have also made. Indrek's work has been of great importance to amateur understanding of the BFR. In fact I encouraged him obliquely to do round and square form factors to see the results.

I'd like to see more of him around here, but I gather he is spending his spare time studying microprocessors.

[hanelyp]

In terms of electron confinement, coils conformal to the magnetic field are prefered. In terms of alpha intersect, this frustum shape has the advantage.