Once again KitmanSA primary means of debating, or rather argueing its to belittle the opposition. Some points . He conceeds that there is a nullo (zero) B field in the center of the Polywell, yet he ignores that the B field isobars extend into and through the cusps. The above illistration earlier shows this though the regons are compacted so it is not well appreciated The illistration in this link shows it better.
http://www.aero.umd.edu/sedwick/present ... tation.pdf\
First illistration shows the "null" field extending from the center and through each cusp
Note that the field lines/ isobars do not nessisarily designate the zero level, but the arbitary fall off that heads towards zero. There may be some magnetic field remaining, but is EFFECTIVELY zero. The true zero field would only exist at an infinatly small region between the magnets. I pointed this out, though it was apparently ignored. In the center of the machine this "null " B field region is wide- and even wider with Wiffleball inflation, so an electron can travel significant distances with no/ or rather negligable spiralling (gyroradius effects). In the cusps the situation is different. The space betwoeen B field isobars is much less. Unless the electron is traveling almost exactly perpendicular to the cusp and on the midline, it will at some point within a smmall distance enter a region where the B field becomes significant and the resultant gyroradius becomes important. So, for most of the electrons entering the cusp (99% to 99.99999999% ?) there will be gyroradi consecuences.
It also evident from the illustrations that the B field continually falls off towards the center of the cusp. Initially mostly due to the inverse square law, then the opposing fields becomes the primary driver. I don't know how this scales, but I suspect it may be an inverse cubed law, or perhaps the inverse square law *2. At any rate the field strength will fall off at an increasingly rapid rate (the isobars become closer together) till the minimum is reached. It seems to me that this would be zero, before the field begins building again on the other side. KitemanSA seems to deny this, despite his contradicting statements.
And how KitemanSA concieves as the X cusp obaying some other set of rules is beyond me.
All cusps reach zero strength at the mid line between the magnets (whether they are on opposite sides of the Polywell or on opposite sides of the faces.
The pratical size of this "null" zone is based on the electron energy and starting magnet strength and some limit on the resultant gyroradii that can be ignored. This feeds into confinement considerations , and more importantly for this discussion the result and ExB diffusion (or transport). The importance of this drift or transport in the cusp is reflected by Bussard's claim of 10 gyroradii seperation of the magnets are ideal, but that 2-3 gyroradii separation is the best compromize between cusp losses and ExB losses. And, Nebel's comment that there was significant heating of the nubs in WB7 leading to a redesign . Here there was no way to provide for spacing. If the machine was larger perhaps multiple wire windings through the nub could help ( similar idea to the X cusp except the cusp is buried inside the metal, perhaps providing a smaller target (or not). I suspect for various reasons they (I presume) went to the wall standoffs instead.
If most electrons that are reaching the midplane of the cusp are traveling very near the midline of the cusp, the gyroradii will be large, and the resultant ExB per collision will be large. At some point the collision deflections will be effected by the extreamly weak B field, that it's contribution can be ignorred and only the collision effects considered. Obously the electron density in the cusp also matters as this affects the frequency of collisions. If the electron is traveling further from the center on the mid line of the cusp, the gyroradii will be smaller, and thus the ExB will be smaller. This is an iterative process that has two possible outcomes. Either the electron passes through the cusp (or is reflected back) or it hits the wall of the magnet. Note that a large gyroradius does not dictate hitting the wall. You also need to consider the gyroradial orbital frequency (wavelength). If the gyroradius frequency is low a particle may complete only a tiny portion of its gyroradius orbit befor exiting the cusp. Taken to extreams the particle path approaches a straight line. Again , as I have repeatedly stressed this is a special situation. The vast majority of electrons are in between the extreams. Note that most of this discussion is about single events at a defined point in the cusp. The dynamics though is a very complex dance with cascading effects on any single particle. This is why computer models have to make very general approximations in order to solve the problems in less than a few centuries.
Magnetic shielding context enters here . This view point often expressed by Bussard, is that a charged particle that is traveling towards a wall, will hit it. It cannot be avoided. It can be delayed by having strong B fields oriented so that turning the particle impedes progress , but in a collisional plasma, eventually the sequential scattering will allow the particle to reach the wall. How fast this occurs for the electron instead of the ion is of tremendous importance. In WB6, making some assumptions, the electron current was ~45 Amps. Of this ~ 40 to 44.5 amps was lost through the cusps, while ~ 0.5% to 5%were lost through cross field transport (mostly ExB drift). How this cross field transport losses stacked up in the cusp areas verses the other parts of the magnets . I suspect the near cusp- and especially the corner going into the funny cusp/ interconnects region ExB losses dominated based on the gains made with WB6, and possible further gains with WB7.1
The corners of X cusps, or the nubs between magnets a have B Fields oriented differently, the drift here does not turn the particle away from the metal, so leakage is greater. These areas are small so they may not be to painfull. Bussard believed that these unavoidable weakly shielded areas were tolerable if they were less than ~ 1/10,000th of the total netal surface. Moving the nubs back- untill they become standoff from the vacuum vessel wall or something like the X cusps might or might not improve this magnetic shielding consideration, but it does not eliminate it.
Another source that mentions zero B field strength in the center of a cusp-
http://accelconf.web.cern.ch/accelconf/ ... opo-23.pdf
Note first page.
The magnetic field increases along and
across the magnetic lines of force starting from zero at the
center and maximum value at the periphery
\
And-
http://ieeexplore.ieee.org/xpl/login.js ... r%3D605204
Just because I had not seen this paper (abstract) before.
Dan Tibbets
To error is human... and I'm very human.