Does a dodecahedron really meet Bussard's requirements?
Does a dodecahedron really meet Bussard's requirements?
One of the major loss mechanisms Bussard claimed was electrons exiting via line cusps. He further said that it was not possible to eliminate these in a cube geometry machine because each vertex has three faces around it, and you don't want two faces to have the same pole. Fair enough, but a dodecahedron has 12 faces, each a pentagon, and each vertex also has three faces on it! Taking out my collection of platonic solids (yes, I used to play D&D), I notice that the only such that meets his stated requirement is the octahedron, which does indeed have four faces off every vertex. What am I missing here?
Last edited by scareduck on Sun Jan 20, 2008 7:13 pm, edited 1 time in total.
How do you figure?MSimon wrote:The cube design that we are using now is a truncated octahedron.
Edit: I guess I see it... the coils end up on each vertex of the octohedron rather than on the faces. But an octohedron has six vertexes and eight faces. But I still don't see how a dodecahedron can escape having adjacent north-north pairs.
Last edited by scareduck on Sun Jan 20, 2008 7:49 pm, edited 1 time in total.
Isomorphism. The cube is an isomorph of the octa.scareduck wrote:How do you figure?MSimon wrote:The cube design that we are using now is a truncated octahedron.
The dodeca is an isomorph of the icosa.
Truncate the vertices of the octa and see what you get.
Engineering is the art of making what you want from what you can get at a profit.
Fundamental symmetry.
The problem with tokamaks, mirror machines, stellerators and all that is a lack of simple symmetry. They keep adding more and more twists to try to confine the plasma, but it always squirms out.
With the poles all pointing in, the field lines form loops around each coil, and are low density in the center with high density near the "corners" and edges. Where flux lines come together you get a mirror action - the electrons are bound to a set of flux lines, and as the flux lines squeeze in, the gyro-radius shrinks.
I tried to figure out how to place circles on a sphere such that they all have the same radius and they evenly cover the sphere, and they all touch each other somewhere. The result was 4, 6 or 12 circles.
If you look at the mag field from the electron's perspective going center to outside, you pick up a flux line of one coil that you are nearst the axis of. As you head towards any edge of the face, the gyro-radius has to shrink. If any of the coils were not uniformly placed, there would be a huge escape path compared to any other route.
As the electrons approach the grid, they gain energy. But not enough to escape, just enough to pick up more flux lines. They mirror, pass the center and follow the flux lines until they mirror again. But as they bounce, they pick up energy, and will eventually escape.
Without really good symmetry, the system of electrons would blow out rapidly.
The problem with tokamaks, mirror machines, stellerators and all that is a lack of simple symmetry. They keep adding more and more twists to try to confine the plasma, but it always squirms out.
With the poles all pointing in, the field lines form loops around each coil, and are low density in the center with high density near the "corners" and edges. Where flux lines come together you get a mirror action - the electrons are bound to a set of flux lines, and as the flux lines squeeze in, the gyro-radius shrinks.
I tried to figure out how to place circles on a sphere such that they all have the same radius and they evenly cover the sphere, and they all touch each other somewhere. The result was 4, 6 or 12 circles.
If you look at the mag field from the electron's perspective going center to outside, you pick up a flux line of one coil that you are nearst the axis of. As you head towards any edge of the face, the gyro-radius has to shrink. If any of the coils were not uniformly placed, there would be a huge escape path compared to any other route.
As the electrons approach the grid, they gain energy. But not enough to escape, just enough to pick up more flux lines. They mirror, pass the center and follow the flux lines until they mirror again. But as they bounce, they pick up energy, and will eventually escape.
Without really good symmetry, the system of electrons would blow out rapidly.
Interesting; Bussard himself patented the tetrahedron (4), cube (6), octahedron (8), and dodecahedron (12) (see claim 15 on patent 5160695).drmike wrote:I tried to figure out how to place circles on a sphere such that they all have the same radius and they evenly cover the sphere, and they all touch each other somewhere. The result was 4, 6 or 12 circles.
You've mentioned this before, drmike -- the question I would ask in reply is -- don't the electrons give up some energy as they slingshot away from the positively charged magrid?If you look at the mag field from the electron's perspective going center to outside, you pick up a flux line of one coil that you are nearst the axis of. As you head towards any edge of the face, the gyro-radius has to shrink. If any of the coils were not uniformly placed, there would be a huge escape path compared to any other route.
As the electrons approach the grid, they gain energy. But not enough to escape, just enough to pick up more flux lines. They mirror, pass the center and follow the flux lines until they mirror again. But as they bounce, they pick up energy, and will eventually escape.
Yes, they do have to give back some of the energy gained falling into the grid, but they have a new flux group they don't want to give up. The new
gyro radius prevents all the kinetic energy from going back to potential.
It's not like a ball rolling in a valley. Try cutting the current flowing thru a coil - the magnetic field keeps the current going. The electron is part of a transformer - it is a current which is part of a magnetic field.
I don't think the octahedron will work. At least not as well as the others.
gyro radius prevents all the kinetic energy from going back to potential.
It's not like a ball rolling in a valley. Try cutting the current flowing thru a coil - the magnetic field keeps the current going. The electron is part of a transformer - it is a current which is part of a magnetic field.
I don't think the octahedron will work. At least not as well as the others.
drmike,
That is true only if you keep supplying energy to the coil. If the energy is fixed (as in a superconductor) the magnetic field must decay.
If the case is as you state then superconductors can never contain the electrons since the electrons will keep extracting energy from the field. Or else the energy must be supplied by a current to the e-field producers.
If what you state is true the device can not possibly generate net energy and we might as well give up now and save the money.
Dr. B. did some simulations and did not come up with the results you claim - or else he was lying to us. Something I doubt.
Some where there is a fundamental flaw in your equations.
If not, time to work on something else.
That is true only if you keep supplying energy to the coil. If the energy is fixed (as in a superconductor) the magnetic field must decay.
If the case is as you state then superconductors can never contain the electrons since the electrons will keep extracting energy from the field. Or else the energy must be supplied by a current to the e-field producers.
If what you state is true the device can not possibly generate net energy and we might as well give up now and save the money.
Dr. B. did some simulations and did not come up with the results you claim - or else he was lying to us. Something I doubt.
Some where there is a fundamental flaw in your equations.
If not, time to work on something else.
Engineering is the art of making what you want from what you can get at a profit.
Or, given that he knew there was a maximum number of electron transits necessary for fusion anyway, he figured as long as the electrons didn't pick up too much energy in that number of transits, the system would be okay overall. Or maybe there are other electron energy loss mechanisms that drmike isn't taking into account.MSimon wrote:Dr. B. did some simulations and did not come up with the results you claim - or else he was lying to us.
I'm usually pretty good at divining what is wrong with theory without being able to do the math.drmike wrote:Yes, they do have to give back some of the energy gained falling into the grid, but they have a new flux group they don't want to give up. The new
gyro radius prevents all the kinetic energy from going back to potential.
It's not like a ball rolling in a valley. Try cutting the current flowing thru a coil - the magnetic field keeps the current going. The electron is part of a transformer - it is a current which is part of a magnetic field.
I don't think the octahedron will work. At least not as well as the others.
Fingerspitzengefühl
I think you got a sign wrong somewhere.
I think Indrek was right. Field energy that goes into gyrorotation is field energy that can't go into speed.
Engineering is the art of making what you want from what you can get at a profit.
I think doing this serves as a good cross check. Wrestling is good. What else do we have to do for the next 60 to 120 days?scareduck wrote:I wish we had access to Bussard's code. We could stop wrestling with this stuff.
Engineering is the art of making what you want from what you can get at a profit.
A very weak argument without apparent foundation. The polywell differs in a few primary aspects I see:drmike wrote:Fundamental symmetry.
The problem with tokamaks, mirror machines, stellerators and all that is a lack of simple symmetry.
- The polywell confines electrons with the magnetic field but not ions. Electrons can be confined to a much smaller radius with a smaller magnetic field. This I see as the major factor in a polywell machine being projected to hit Q>1 at such small size and magnetic field as compared to the above machines. A machine on the same shape that attempted to confine ions directly by magnetic field would have the same symmetry, but must be much larger or have much stronger magnetic field,
- The polywell externally imposed magnetic field has a well before the plasma pushes out on it. This appears to help on some drift modes.
- The polywell employs a structured plasma where the more conventional designs attempt to impose a uniform plasma.