Ion Trajectories Through the Wiffle-Field

TheRadicalModerate · Post by **TheRadicalModerate** » Mon Jun 16, 2008 4:21 am

Are ions injected from outside magnetic wiffle-field? While the B-field isn't huge, it's non-trivial. Has anybody done any analysis on how the ion trajectory gets affected as the ions pass through the diamagnetic limit?

I assume that the main trick is to inject through the cusps but they're awfully narrow. Won't you get some longitutidinal velocity on the way through?

The other thing I'm confused about is that, if you inject from outside the wiffle-field, then the ions will migrate back up through the field on each oscillation, won't they? In that case, they're clearly not going to hit the cusps. What happens then?

kcdodd · Post by **kcdodd** » Mon Jun 16, 2008 5:02 am

The idea is to have ions trapped in well created by the electrons which means injecting them inside coil structure. You are right, if you inject them outside then their KE is greater then the well and they'll just fly right through the machine out the other side.

edit: I'm sorry, I think I know what you're asking about now.

Yeah its a good question. The electric field is much larger then the magnetic field so the ExB drift will be large. Lets say youre looking at where the bfield is perpendicular to the efield and you have a 100kv/m efield at 1 tesla thats a 100km/s drift, and a proton at 10kev is like 1400km/s (0.1m from 0v) , which is a significant fraction. But as the ion drifts at 100km/s it will start to encounter the bfield which is near the cusp, which is more parallel the efield. When that happens you lose the drift and the ion should get sucked into the well at the full 1400km/s.

drmike · Post by **drmike** » Mon Jun 16, 2008 2:25 pm

Ideally you want the ions to oscillate radially, but a little curvature from the fields isn't going to change the impact zone size too much. If the ions can turn around near the grids, slam thru the center and end up on the other side, they just repeat the same thing going back. A long curve at the top of the trajectory in high B regions doesn't really change the electrostatic force drawing them towards the center.

What happens at high density is the hard question. You may well have currents that blow out the center no matter what, and that would destroy the virtual cathode that is so important for making the polywell concept work.

TheRadicalModerate · Post by **TheRadicalModerate** » Mon Jun 16, 2008 4:26 pm

drmike wrote:Ideally you want the ions to oscillate radially, but a little curvature from the fields isn't going to change the impact zone size too much. If the ions can turn around near the grids, slam thru the center and end up on the other side, they just repeat the same thing going back. A long curve at the top of the trajectory in high B regions doesn't really change the electrostatic force drawing them towards the center.

I think what you're saying is that any curvature induced dropping into the well is reversed climbing out of it, so, even though the transit point through the center is offset a bit, the offsets won't accumulate one successive transits.

I can buy that, but I don't buy that missing the center is fairly harmless. This starts smelling a bit like a beam brightness (or dimness, in this case) issue that you'd really like to avoid. (Yeah, it's not really a beam, but you still want a really bright spot in the center.) Maybe if the paths are conserved, you can prevent this from happening by imparting a little compensating longitudinal velocity at ion injection time?

I assume that coulomb scattering events, as long as they occur exactly in the center of the well, should retain the same curvature symmetry as they climb out, even though they're no longer climbing out 180 degrees away from their entry point.

BTW, I convinced myself that as long as the protons have 11x the energy of the B11 ions, any non-brem scattering, i.e., p-p, p-B, or B-B, should result in all ions maintaining the same radial momentum, as long as the scattering event occurs dead-center. This also seems to argue for getting the brightness up as much as possible at dead-center, as well as avoiding 1-D colliding beam configurations, since both of these conditions will increase the probability of scattering away from the center.

drmike wrote:What happens at high density is the hard question. You may well have currents that blow out the center no matter what, and that would destroy the virtual cathode that is so important for making the polywell concept work.

Not following you here. Are you saying that offset transits require that you have a higher ion density, which in turn gets you closer to the blow-out condition? Again, this would seem to argue that getting really high brightness at dead-center is absolutely essential.

tonybarry · Post by **tonybarry** » Tue Jun 17, 2008 3:19 am

If there were no other species in the polywell, then we might imagine a situation where the injected ions are able to pass right through the polywell, by aiming them just right, so they emerge on the other side of the MaGrid at the same velocity we sent them through from the ion gun.

My understanding is that collisions with other species wipes out the forward kinetic energy, and by aiming the gun correctly, the ion will spiral down to the polywell centre losing kinetic energy to electrons and other ions on the way.

Aiming two guns in the right way should cancel out the rotational impetus thus applied.

Regards,
Tony Barry

drmike · Post by **drmike** » Tue Jun 17, 2008 4:04 am

Here is a picture of the curved field lines and plasma inside the polywell, in a 2D sense. I don't see how electron motions can be radial. The electric force is much larger than the magnetic force, so ions will follow the electrons if their energy is low. As the approach the MaGrid though, they will be repelled and the center will be the "path of least resistance". If there is a radial current which is uniform, it bounces having a low density near the MaGrid and high density in the center. It also would have low velocity near the MaGrid and high velocity near the center.

If the radial currents are uniform, it is an electrostatic confinement system. But the electrons won't be radial, they will drift when they hit the MaGrid field. It is those currents which I don't fully understand, nor do I have a feel for what they will do to the ion motions.

The concept of "center" may need some definition. It might be "the B field is 1% of the coil center" or something. That 1% surface then defines "center", which may be star shaped.
So long as 90% of the ions are in the "center" 90% of the time, you can generate profitable power. (These are all made up numbers!!! - I'm just trying to make the idea concrete).

It will be really interesting to see what it does take to make it work!

TallDave · Post by **TallDave** » Tue Jun 17, 2008 4:00 pm

It's been shown that a double well does form in IEC devices.

http://wwwsoc.nii.ac.jp/aesj/division/f ... hikawa.pdf

Also, the most comprehensive study of ion scattering is the Chacon paper, which concludes it is not a problem.

http://scitation.aip.org/getabs/servlet ... s&gifs=yes

and that would destroy the virtual cathode that is so important for making the polywell concept work.
...
Again, this would seem to argue that getting really high brightness at dead-center is absolutely essential.

Nebel has pointed out that for Polywells ion focussing isn't that critical anyway. Even without ion focussing, ion density is three orders of magnitude greater than in a tokamak.

Mike Holmes · Post by **Mike Holmes** » Tue Jun 17, 2008 7:05 pm

"Critical"... "essential"...

How about "beneficial?" Is it worth shooting for at all? Or are there problems with creating focus that are greater than the benefits?

Mike

TallDave · Post by **TallDave** » Tue Jun 17, 2008 8:38 pm

Don't get me wrong, ion focus very helpful and according to Chacon it's not likely to not pose a major problem. But if for some reason we can't get it, this may still be vastly superior to a tokamak, if the wiffleball concept is sound. That's the really really critical piece.

In most IEC fusors, focus is very important because they operate at much lower densities than a Polywell.

MSimon · Post by **MSimon** » Tue Jun 17, 2008 8:47 pm

Focusing can be done with focusing grids and a focus control.

They still have them on analog O-Scopes.

drmike · Post by **drmike** » Wed Jun 18, 2008 1:56 pm

Focusing can be accomplished with wakefield acceleration and POPS. It's an afterburner boost, not needed for proof of principle but really useful for increasing efficiency.

TheRadicalModerate · Post by **TheRadicalModerate** » Wed Jun 18, 2008 7:08 pm

drmike wrote:Focusing can be accomplished with wakefield acceleration and POPS. It's an afterburner boost, not needed for proof of principle but really useful for increasing efficiency.

When you and Simon talk about focusing, are you talking about focusing ions into beams, or about concentrating ions in a spherical shell and then ensuring that they all arrive in the center simultaneously?

Seems to me that the latter is more doable, although it's an enormous pain with dual-population ions.

BTW, if anybody has a formula for the amount of time it takes a charged particle to reach the center of a point-charge E-field, in terms of its mass, charge, and starting radial distance, I'd love to see it. I've been trying to figure out whether you can get B11 and p ions to arrive at the center of the well simultaneously if you constrain the p ions to have the same momentum as the B11 ions (and hence 11x the energy). I've been trying to derive this but I've fallen and can't get up. Seems like you'll do much better if the ions don't transfer momentum between themselves, but then you've got to make them arrive at the proper times if you want to reduce collisionality outside the center.

MSimon · Post by **MSimon** » Wed Jun 18, 2008 7:31 pm

Focus grids would have to be outside the reaction space so that only electrons would be focused.

==

Assume a linear field (for convenience). You know the energy at every point in the field. Which means you know the velocity at every point. Now add up all the ds/dt bits and you have time of flight. I'm sure it has been worked out. If not, a pretty simple computer program should give you close enough answers by iterating a FOR/NEXT loop 1,000 or 10,000 times.

Simon

tombo · Post by **tombo** » Wed Jun 18, 2008 10:41 pm

When you talk of "convergence" what do you mean?
Do you mean physically aimed at the device center?
Do you mean in the time domain ie. they arrive at the same time?
Do you mean in the velocity domain ie. keeping the ions mono-energetic?
Or
Do you mean something more esoteric?

drmike · Post by **drmike** » Thu Jun 19, 2008 1:13 am

I think there are lots of ways to make it work. You could have "shells" of ions, some moving radially out, some moving radially in, and when they hit center you get maximum fusion.

You could have smooth currents flowing mostly radially - some particles flowing out, some flowing in, and most of them having peak velocity as they whip through the center.

Some of these currents could be on faces or cusp lines so that the B field does not affect their motion too much. These currents could be "beams" in the classical sense.

The main trick is radial motion, not rotational motion. If the electron density is high enough in the center, and MaGrid is high enough at the coils, radial motion should be the normal steady state.

I don't think "beams" or "convergence" are critical - but having most of the ions with peak radial velocity getting close to the center will help make the reactor more efficient.

Good things to think about, and I better get some models running.....