happyjack27 wrote:D T: part of the problem, at least as it appeared in my sims, is precisely THAT the electron going from outside toward the WB are accellerating, and precisely THAT they're not so thermalized like they are on the inside of the WB. This leads to a stronger and more focused lorentz force effect, causing them to spiral out faster and faster and farther and farther as they approach the wiffleball.
in other words, the magnetic fields are pulling them off of the center cusp line, and the faster they go and the further of the cusp center they are, the faster they're pulled off.
i would presume things would be in general different once the area outside the wb is sufficiently populated and thermalized. then the effect is different in nature; it becomes gestalt and statistical. the math is different. i.e. you might need recirculation to get an excess electron charge in the wb as much as you need it to increase electron lifetimes. but that's too much sim time for my sim, and i didn't have a grounded chamber in any of the runs so the recirculation orbits were unbounded.
A complex problem. I don't think the electrons inside the Wiffleball are fully globally thermalized, that would pretty much exclude the possibility of usefull P-B11 fusion due to bremsstrulung. As I see it the major difference between inside and outside is the much greater B field gradient at the Wiffleball border. This results in very elongated elliptical gryro (or Lorentz) orbit so that essentially on the inside of the Wiffleball border the magnetic characteristics are lost, so that cumulative effects are aborted. It is a different story for electrons that embed furtherinto the magnetic domain due to scattering, but this must make up a small fraction of the total internal electrons or describing it as a non magnetic plasma would be inappropriate. Out side the magnetic field lines are certainly less compressed except for very near the midpoint of the cusp where the field line compression is almost as much as the Wiffleball border regions. Of course the maximum B field compression occurs atthe cusp (mid plane of the magrid radius). The Wiffleball border can approach this compression but not exceed it (Beta slightly less or equal to one )
A question I have is if the opposing B fields decrease to zero between the magnets (I think so). This region is very narrow (~ equal to the electron gyro radius?). The question is if this space is wide enough for magnetic characteristics to be lost. And, would this would cancel any progressive magnetic spiraling?
I admit that I am also uncertain what you mean by increasing spirals, except that as the electrons pick up speed they have wider gyro radii.. My understanding is that a fixed energy charged particle will spiral around a field line at the same gyro radius provided the B field is constant, and that the orbits are more elliptical if there is a significant gradient to the B field. Inside the Wiffleball this more extended portion of the orbit is disrupted because the MFP is shorted than the major radius of the orbit- the electron plasma is not magnatized. With ions, the story is somewhat different because the MFP for them may be greater than the machine radius so the magnetic gyro orbit would dominate over the scattering effects(and ignoring the magnetic anceleing effects of the electron motions). Except the ions are mostly confined electrolytically within the B field free region. Also low energy , high collisionality conditions at the Wiffleball edge results in a local Coulomb collision dominate regon (annealing) that scrambles any lingering magnetic effects on the ions, except those that are knocked deeper into the magnetic domain.
Back to the electrons. Because of the above reasoning, if reasonable
, The distance over which the electrons accelerate may be very important. The relationship of the electron distance from the cusp at birth (or turn around point for a recirculating electron) is important. If the electron is introduced 1 mm from the cusp and the gyroradius and spiral length is also ~ 1 mm average, then only ~ 1 gyro orbit would be completed before the electron penetrated past the cusp.* Due to the reduced magnetic field on one side (towards the line through the center of the cusp, and local collision effects (that might dominate, or at least contribute) the magnetic spiral progression may be minimized sufficiently. On the other side of the problem is cusp plugging issues which harm ion confinement. Thus a compromise: the electron guns are placed far enough away from the cusp to minimize cusp plugging effects, but close enough that the gradual acceleration associated gryro radius expansion does not compromise injection to much.
The potential well cannot ever reach the potential of the accelerating voltage. Bussard stated that this was due to magnetic interactions. I was (and remain) uncertain of the dynamics of this, but this could be due to this, at least in part. Given a hole in a magnetic field , there is a voltage that will pull the electron in despite any diverting/ turning force that a magnetic force might apply, so long as the hole is large enough to prevent the loss of the electron to a surface. This is why there is spacing between the magnets in WB6 of several electron gyroradii. I'm guessing that this 'resistance' to penitration (the energy nessisary to prevent or delay mirroring) may make upa small to large part of the difference between the potential well depth and the accelerating potential.
The experimental evidence of WB6 (if you accept it)and earlier machines is that electrons are injected into the machine in sufficient quantities and at reasonable efficiency (~ 85%?) to inflate a Wiffleball to near Beta = 1 conditions. Thus the theory or simulation must accommodate this through the above mechanisms or by other means.
* The acceleration rate of the electron is dependent on the starting distance. Due to an aspect of Gauss Law the terminal velocity is independant of the starting distance from the cusp.
Dan Tibbets
To error is human... and I'm very human.