Re: 15th US-Japan Workshop on IECF
Posted: Sun Jan 12, 2014 6:07 pm
Torulf2, I'm not sure what you are saying, the line cusp in the picture is obvious. The two magnets shown are opposing. It is not a solenoid arrangement. The solenoid arrangements are generally accepted as hopeless, due to poor magnetic curvature surfaces leading to macro instabilities.
In the picture 1/2 of a ring magnet is seen on the right, and a full ring magnet on the left. The plasma shows a point cusp with plasma exiting to the left, and a line cusp between the magnets with the plasma exiting in a line or cone between the magnets. If the magnets were the same diameter, this would be a classic biconic opposed magnet mirror machine. In the picture the right magnet would also have a point cusp exiting to the right. What is not shown (in my opinion) is a third magnet located further right. This would result in a picture mirroring what is seen. Copy the picture, flip it horizontally, and paste it on the right side of the original picture. Now you can see the two line cusps along with the two end point cusps. If the central magnet is removed, it would have one equatorial line cusp- the classic mirror machine. By having the central magnet the single equatorial line cusp is split into two, but importantly the width of these two line cusps are now much narrower,and the net result is better containment. If you assume magnets of very narrow width(horizontal width in the picture) or mathematical lines representing the magnets much like Bussard used in his modeling until WB6) the gain would be modest, perhaps halving the net losses from the line cusp component relative to a two magnet mirror machine. But with real magnets with real significant width/ thickness, the relevant magnetic fields are measured from the can surface, not the center line of the magnet. As such the gains from splitting the equatorial line cusp results in significantly greater gains in the confinement efficiency of the line cusp. The fatter the central magnet the better, within some practical limit. For example an oval instead of a circular magnet cross section. For other reasons increasing the diameter of the central magnet may also have benefits. Primarily by increasing the internal volume and by changing the direction/ angle of the two line cusps. This may have benefits in direct conversion grid layout outside the magrid, along with external direction guiding of the escaping plasma- such as for a rocket engine or transformer like energy conversion if the machine is pulsed. Also, having smaller diameter end magnets help to push the B fields to a common focus between the central magnet.
In the Polywell there are at least 6 point face cusps, and these may dominate the losses. In this design there are only two point cusps, so there may be significant gains. The line cusps are very similar to the truncated cube polyhedral shape for the Polywell. There are two end magnets with a central magnet. The difference is that in the Polywell this central magnet is actually a complex assembly of four seperate magnets, but still the result is the splitting of a single wide equatorial line cusp into two much narrower line cusps. In the Polywell the resultant line cusps are spiky, but otherwise the same concept.
Consider a 2 dimensional representation of a 3 D object., much like a globe of the Earth. Lay out the two end magnets withe the central magnets laid out side by side- 4 long. Now assign line cusps to the end magnets- it is circular with spikes towards the intersections of the central magnets. Because the central magnets are close to the end magnets at the intercepts, the line cusps look almost like 4 separate point corner cusps, but they are still obviously line cusps. This picture may reveal the similarity of the two designs.
The end result is similar, the magnetic fields still converge to a central minimum/ focus. Any line drawn through the center is still symetrical. The line cusp (corner cusps in the Polywell) losses could be made similar . And the face point cusps are reduced from 6 to two. I'm not sure if full volume could be maintained with the three ring design compared to the Polyhedral design ,but it would be close, especially relative to the net cusp losses. The magnetic fields remain symetrical. A line drawn through the center will always be symetrical. I think Wiffleball inflation is still valid. The internal volume is similar, so plasma volume and trapping is similar.
That is the problem with the two magnet opposing magnet mirror machine. The magnets could be moved very close together to minimize the line cusp losses, but this results in the internal volume also shrinking proportionately. That is the whole point of the Polywell- avoiding the volume shrinkage that occurs with line cusp loss minimization in a mirror machine.
Your mention of the plasma recirculating through the center along field lines could occur, but as it has been hashed out on this forum, and stated clearly in the patent application, this is intolerable. Due to up scattering the electrons and boosting their energy with each cycle, the electron temperature would be out of control and criticisms by Dr A. Carlson would apply- that is- extremely high internal electron potentials would be required to keep losses in check. Once the electron escapes outside the space between the magnets, if it is to be recirculated, it must first stop (be decelerated), and re enter through the same cusp. That way the electron energy upon reentry remains constant. Failing to stop the electron (up scattered) requires that the electron needs to be removed from the system (hit a wall), before it can circle around along a field line and reenter through another cusp.
Dan Tibbets
In the picture 1/2 of a ring magnet is seen on the right, and a full ring magnet on the left. The plasma shows a point cusp with plasma exiting to the left, and a line cusp between the magnets with the plasma exiting in a line or cone between the magnets. If the magnets were the same diameter, this would be a classic biconic opposed magnet mirror machine. In the picture the right magnet would also have a point cusp exiting to the right. What is not shown (in my opinion) is a third magnet located further right. This would result in a picture mirroring what is seen. Copy the picture, flip it horizontally, and paste it on the right side of the original picture. Now you can see the two line cusps along with the two end point cusps. If the central magnet is removed, it would have one equatorial line cusp- the classic mirror machine. By having the central magnet the single equatorial line cusp is split into two, but importantly the width of these two line cusps are now much narrower,and the net result is better containment. If you assume magnets of very narrow width(horizontal width in the picture) or mathematical lines representing the magnets much like Bussard used in his modeling until WB6) the gain would be modest, perhaps halving the net losses from the line cusp component relative to a two magnet mirror machine. But with real magnets with real significant width/ thickness, the relevant magnetic fields are measured from the can surface, not the center line of the magnet. As such the gains from splitting the equatorial line cusp results in significantly greater gains in the confinement efficiency of the line cusp. The fatter the central magnet the better, within some practical limit. For example an oval instead of a circular magnet cross section. For other reasons increasing the diameter of the central magnet may also have benefits. Primarily by increasing the internal volume and by changing the direction/ angle of the two line cusps. This may have benefits in direct conversion grid layout outside the magrid, along with external direction guiding of the escaping plasma- such as for a rocket engine or transformer like energy conversion if the machine is pulsed. Also, having smaller diameter end magnets help to push the B fields to a common focus between the central magnet.
In the Polywell there are at least 6 point face cusps, and these may dominate the losses. In this design there are only two point cusps, so there may be significant gains. The line cusps are very similar to the truncated cube polyhedral shape for the Polywell. There are two end magnets with a central magnet. The difference is that in the Polywell this central magnet is actually a complex assembly of four seperate magnets, but still the result is the splitting of a single wide equatorial line cusp into two much narrower line cusps. In the Polywell the resultant line cusps are spiky, but otherwise the same concept.
Consider a 2 dimensional representation of a 3 D object., much like a globe of the Earth. Lay out the two end magnets withe the central magnets laid out side by side- 4 long. Now assign line cusps to the end magnets- it is circular with spikes towards the intersections of the central magnets. Because the central magnets are close to the end magnets at the intercepts, the line cusps look almost like 4 separate point corner cusps, but they are still obviously line cusps. This picture may reveal the similarity of the two designs.
The end result is similar, the magnetic fields still converge to a central minimum/ focus. Any line drawn through the center is still symetrical. The line cusp (corner cusps in the Polywell) losses could be made similar . And the face point cusps are reduced from 6 to two. I'm not sure if full volume could be maintained with the three ring design compared to the Polyhedral design ,but it would be close, especially relative to the net cusp losses. The magnetic fields remain symetrical. A line drawn through the center will always be symetrical. I think Wiffleball inflation is still valid. The internal volume is similar, so plasma volume and trapping is similar.
That is the problem with the two magnet opposing magnet mirror machine. The magnets could be moved very close together to minimize the line cusp losses, but this results in the internal volume also shrinking proportionately. That is the whole point of the Polywell- avoiding the volume shrinkage that occurs with line cusp loss minimization in a mirror machine.
Your mention of the plasma recirculating through the center along field lines could occur, but as it has been hashed out on this forum, and stated clearly in the patent application, this is intolerable. Due to up scattering the electrons and boosting their energy with each cycle, the electron temperature would be out of control and criticisms by Dr A. Carlson would apply- that is- extremely high internal electron potentials would be required to keep losses in check. Once the electron escapes outside the space between the magnets, if it is to be recirculated, it must first stop (be decelerated), and re enter through the same cusp. That way the electron energy upon reentry remains constant. Failing to stop the electron (up scattered) requires that the electron needs to be removed from the system (hit a wall), before it can circle around along a field line and reenter through another cusp.
Dan Tibbets