Recirculation redux
Posted: Sun Nov 30, 2008 2:35 am
I was reading Art Carlson's all that can go wrong with recirculation thread and had a few questions / observations. The biggest one is:
is the current understanding of recirculation now that the electrons do not go out one cusp and back into a different one, ie, they go back in the same one they go out?
While the thread definitely went in that direction, there did not seem to be any definitive statement to that effect (say by Dr Nebel). Also, if this is the current thinking, is there still a need for circular cross section coils and coil casings? Wouldn't square ones be fine as long as the corners didn't protrude into the loss cones of the cusps?
I also had two observations that I did not see mentioned in the thread (possibly because they are either wrong or not significant effects).
For one, wouldn't the cusp loss cones be much bigger from the outside looking in than from the inside looking out when operating at high Beta. Under those conditions, you have diamagnetic effects of the plasma pushing the field out from the inside and closing up the cusps but there is no such effect on the outside. So wouldn't the holes an electron sees be smaller going out than those it sees going back in.
The second observation is that there is also an electron beam being injected into each cusp which will create a magnetic field perpendicular to the field created by the coils. The field would have the effect of pushing an electron going towards the core into the cusp where the beam is aimed (i.e. something like the pinch effect). Of course it would have exactly the opposite effect on electrons as they leave the cusps before they are turned around by the grid field. I still think, under certain conditions, it could have a net effect. My reasoning is as follows. At the exact center of the beam, its field would cancel itself out and there would be no effect on an electron traveling along this line. Since the beam has a finite width, this area of effectively zero field is also finite. An electron traveling straight out of a cusp would thus go a finite distance before E x B drift, space charge effects and other drift terms would sweep it out of the area of effective zero field and where the beam's field would cause it to diverge. If the electron goes a distance X before being turned around by the the coil's electric field then it would go some distance A before leaving the effective zero field region and being acted on by the force from the e beam. From there on, it would be acted on by beam's field for a distance of X -A. On it's return path when the electron reached a distance of X-A it would still be outside of the effective zero field area because of the various drift terms and thus would continue to be acted on by the by the e-beam's magnetic field, thus canceling out some of the drift. For this to be a significant effect, A would have to be a significant fraction of X. Also, the net current of the e-beam would need to be significant. If all of the electrons leave the cusps and then hit the chamber wall then the net current would be zero and the effect would be zero so the losses to the wall vs other loss channels would have to be below some level in order to have a significant effect. Can anyone tell me if this sounds reasonable or am I missing something?
Bill
is the current understanding of recirculation now that the electrons do not go out one cusp and back into a different one, ie, they go back in the same one they go out?
While the thread definitely went in that direction, there did not seem to be any definitive statement to that effect (say by Dr Nebel). Also, if this is the current thinking, is there still a need for circular cross section coils and coil casings? Wouldn't square ones be fine as long as the corners didn't protrude into the loss cones of the cusps?
I also had two observations that I did not see mentioned in the thread (possibly because they are either wrong or not significant effects).
For one, wouldn't the cusp loss cones be much bigger from the outside looking in than from the inside looking out when operating at high Beta. Under those conditions, you have diamagnetic effects of the plasma pushing the field out from the inside and closing up the cusps but there is no such effect on the outside. So wouldn't the holes an electron sees be smaller going out than those it sees going back in.
The second observation is that there is also an electron beam being injected into each cusp which will create a magnetic field perpendicular to the field created by the coils. The field would have the effect of pushing an electron going towards the core into the cusp where the beam is aimed (i.e. something like the pinch effect). Of course it would have exactly the opposite effect on electrons as they leave the cusps before they are turned around by the grid field. I still think, under certain conditions, it could have a net effect. My reasoning is as follows. At the exact center of the beam, its field would cancel itself out and there would be no effect on an electron traveling along this line. Since the beam has a finite width, this area of effectively zero field is also finite. An electron traveling straight out of a cusp would thus go a finite distance before E x B drift, space charge effects and other drift terms would sweep it out of the area of effective zero field and where the beam's field would cause it to diverge. If the electron goes a distance X before being turned around by the the coil's electric field then it would go some distance A before leaving the effective zero field region and being acted on by the force from the e beam. From there on, it would be acted on by beam's field for a distance of X -A. On it's return path when the electron reached a distance of X-A it would still be outside of the effective zero field area because of the various drift terms and thus would continue to be acted on by the by the e-beam's magnetic field, thus canceling out some of the drift. For this to be a significant effect, A would have to be a significant fraction of X. Also, the net current of the e-beam would need to be significant. If all of the electrons leave the cusps and then hit the chamber wall then the net current would be zero and the effect would be zero so the losses to the wall vs other loss channels would have to be below some level in order to have a significant effect. Can anyone tell me if this sounds reasonable or am I missing something?
Bill