Electron injection as an engineering issue

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D Tibbets
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Joined: Thu Jun 26, 2008 6:52 am

Re: Electron injection as an engineering issue

Post by D Tibbets »

hanelyp wrote:In an X-cusp the fields cancel.
In a face center point cusp or a line cusp the fields are aligned the wrong direction to contain a charged particle.
A "funny cusp", between the close approach of 2 coils, is something between a point and line cusp.

Of course a cusp of any type has a region between the magnets where the fields cancel. That is what I have been trying to say all along.That cancellation happens midway between the magnets assuming both are of equal strength. If different, then the cancellation will occur offset towards the weaker magnet. In practice one magnet could be so much stronger that the cancellation might occur within the can of the second magnet if the strength differential is to great. Of course that is a dismal result as the cusp then is running directly into metal and has no recirculation or injection purpose.

What seems to be the confusing point is how wide these weak field strength and corresponding geometry holes are. An x cusp, as represented, have close magnets that are up to 1/2 as strong as the regular magnet arrangements. The relative cusp hole size is the result of these two parameters. I think you imply that there is no magnetic shielding in the x-cusp location clear up to the borders of the magnet can surfaces. If so then it is a harmful structure. Even WB6 had one wire through the nubs.

An X- cusp while perhaps point like in loss area is still a combination of two short line cusps, an "X". A true point cusp, at least as I define it, has only acute angles from the central cusp to the borders of the magnetic field generating coils. In this case there are no line cusp extensions intercepting metal surfaces. With a line cusp, even with very strong fields surrounding it (very narrow width), at the end of the line matal is intersected. These corner cusps, x cusps might have the vast majority of their loss area in the region where the magnets are furthest apart. but the line extensions allow EyB (or is it properly called ExY?) drift to allow for the electrons to migrate toowards the ends of the line structures and hit the bridging metal directly or through concurrent ExB drift to hit the magnet cans in the narrowest separation region. These losses are a consequence of competing B field strength, distance to vunerable surfaces. It will always have greater losses than point cusps at equal magnetic strength considerations. The corner cusps losses in WB6 type machines is less because the average separation of the magnets is less and thus the B field strength fall off is smaller, or rather the gradient that makes up the effective walls of the cusp is steeper. It magnetically confines electrons better. This of course also means it rejects more of the electrons approaching from outside at any gien cone of electron vectors. In WB6 I think the face centered point cusps might have been better locations for the E-Guns because of this.

Note that better magnetic confinement need not be the dominate consideration once recirculation is considered. With point cusps nearly almost all of the electrons that escape will at least have the possibility of of recovery (ExB losses may be less and ExY losses are nonexistent). With line cusps the magnetic confinement lost electrons will more likely hit a surface and be lost. A smaller fraction will be available for recirculation. The best compromise needs to consider this. That this is evident comes from Nebel's comment about nub heating in WB7. I have pointed out that this heating loss at the nubs need not only be from electrons escaping internal confinement, but also failed electrons from the e-guns that never successfully penetrated the cusp to the inside of the machine.

The elimination of nubs by using wall standoffs, while not perfect, decreases the significance of ExY drift. The electron may move from the corner region to the closest approach of the magnet cans but without a bridging structure that traverses the line cusp (at least at radii close to the magrid radius where the recirculation action is occurring) direct impingement on the metal surface will be minimized. The electron would only migrate into the neighboring corner region. There is no significant unshielded or minimally shielded surfaces exposed. ExB losses would still need to be considered (why there needs to be at least several gyroradii separation of the magnet cans,) but the ExY (EyB) contributions would be less painful.

Dan Tibbets
To error is human... and I'm very human.

KitemanSA
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Joined: Sun Sep 28, 2008 3:05 pm
Location: OlyPen WA

Re: Electron injection as an engineering issue

Post by KitemanSA »

hanelyp wrote:In an X-cusp the fields cancel.
In a face center point cusp or a line cusp the fields are aligned the wrong direction to contain a charged particle.
A "funny cusp", between the close approach of 2 coils, is something between a point and line cusp.
The "funny cusp" is the result of an even number (≥4) of alternating opposed fields meeting at a point. The only distinction between my "X-Cusp" and Bussard's "funny cusp" is that his had metal in the way and mine doesn't.

Dan keeps mistakenly thinking that it has something to do with improper modeling but he has that wrong too.

The WB6's line-like cusp between the adjacent coils where the nubs were is where the funny cusps would have been if the magnets had a square plan-form like his patent had.

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