How do protons make it into the centre?

chrismb · Post by **chrismb** » Sun Dec 14, 2008 6:24 pm

Maybe I am completely missing something, but as I understand it, the argument is that the 1T field confines the central core electrons, but the protons aren't affected because they are too massive.

But surely the gyroradius (=mv/qb) of a proton at, say, 550keV (= 10Mm/s) in a 1T field is 0.01m (1 cm).

At slower energies/velocities, this gyroradius is even smaller than this - the gyroradius is a linear function of velocity. Slower than 550keV = smaller gyroradius than 1cm.

So how does a proton manage to reach the centre of the Polywell?

The Polywell conditions are well below the limiting magnetron conditions that any protons have a chance of getting further than 1cm. Protons will be 'frozen' at some radius in ExB drifts and will not be able to propagate down into the potential well.

best regards,

Chris MB.

Art Carlson · Post by **Art Carlson** » Sun Dec 14, 2008 7:14 pm

The central volume is presumed to be field-free, so the ions (and electrons) have no trouble crossing it in straight-line paths. All the action is near the edge.

chrismb · Post by **chrismb** » Sun Dec 14, 2008 7:59 pm

If we take the 'parallel plate magnetron' condition, Vcrit = [q.B^2.s^2]/2m, and presume our Vcrit is the 110kV well between 'anode' and 'cathode' surface potentials of 1m separation (s), then we get B = 0.05T as the minimum field required to arrest the motion of a proton.

So the presumption is that we have this 1T field pushing into the centre, yet outside this central electron cup region there are NO fields stronger than 0.05T?

Let's take the result for WB-6: deuterium at 10kV, s (radius)=0.15m. So deuterons would be arrested in a field of anything more than SQRT(2.m.10000/q(0.15)^2)=0.01T.

I have to say that I am unconvinced that magnetic fields in such small spaces can be so accurately targetted into a central region that there is a cut-off of 90% within a couple of centimetres from the dead centre of that structure with such cumbersome inelegant coils. It just doesn't seem to fit right.

If it is possible to project a magnetic field with <5% seepage into the surrounding space over a distance of 1m, then that is quite a new technology and has many many other applications. But as it is 'just' electromagnetic coils, I can't see where the novel step in Polywell magnets is that leads to this previously unknown level of sophisticated magnetic field control.

Is this arrangement of coils really that good?

best regards,

Chris MB.

TallDave · Post by **TallDave** » Mon Dec 15, 2008 1:03 am

The electrons push the field back; this is the wiffleball effect.

This came up before, back in June. I'll let Dr. Nebel answer:

As for the ion confinement, operating in the “wiffleball” mode (electron beta ~ 1) will push the magnetic field into the boundary. This mode was achieved experimentally a long time ago, so we know this works. Only the highest energy ions will enter this edge region. What this effect should do is to just slightly lower the effective potential well depth for the ions.

If this is an issue, then we can operate the WB-7 in the same dimensionless parameter regime as the large device where the magnetic and electrostatic forces have the same ratio. Since all real physics depends on dimensionless parameters, this should give some useful insight. Plasma simulation is also a possibility.
...
The 8 mm gyroradius isn't a big deal since few of the ions will ever access that region of the device.In the middle the gyroradius is infinite which is where the ions spend their time.

He also mentions reactor designs are looking at 5-10T.

Art Carlson · Post by **Art Carlson** » Mon Dec 15, 2008 8:31 am

I'm not sure what you're getting at, chrismb. Are you worried about the actual level of magnetic fields within the central, presumably field-free region? In the language of plasma physics, that beta < 1? If you are, that is probably a good question. It helps that even the vacuum fields will approach zero in the center with a large exponent since they are high-order multipoles, but you are suggesting that beta > 99.99% is required, which is a very tall order. I have been generous and simply gave the poly-wogs the benefit of the doubt up to now.

chrismb · Post by **chrismb** » Mon Dec 15, 2008 8:35 am

The words are fine words, but do they make sense. What is meant by 'pushing the magnetic field' out?

Are we saying that there are 1T magnetic surfaces surrounding the electrons in the centre, then, just a few mm out, suddenly 'puff' - nothing, no more magnetic field at all??

You can't do that if you stick a magnet on top of a lump of unmagnetised ferrite - the magnetic flux would dominantly flow through the ferrite, but there is always some leakage. So how can this be done successfully in a vacuum, in 3 dimensions, with a whisper thin density of electrons?

Art Carlson · Post by **Art Carlson** » Mon Dec 15, 2008 9:14 am

If you throw a copper ball into a magnetic field, surface currents will flow to exclude the field from the interior - for a while. A plasma with T_e = 100 keV has a *much* higher conductivity than copper, which buys you some time. If you manage to refuel your plasma from the inside (or operate from the beginning in a pulsed mode), then the rate at which you replenish the surface can be equal to the rate at which the field penetrates. You wind up with a transition region with a thickness on the order of a Larmor radius (probably the geometric mean of the electron and the ion Larmor radii).

chrismb · Post by **chrismb** » Mon Dec 15, 2008 12:39 pm

But surely that field neutralisation would happen almost instantly, quicker even than the transit time of an ion across the device (by definition - the former only requires the transit of an electron across the core).

So when you say 'pulse mode' are you suggesting a pulse shorter than the cross-device transit time of an ion?

On your other point, are you also suggesting this may only work if you can feed the device from the centre?

TallDave · Post by **TallDave** » Mon Dec 15, 2008 3:10 pm

What is meant by 'pushing the magnetic field' out?

As I understand it, this is the effect of electrons moving along the field lines, trying to get to the positively-charged Magrid.

Are we saying that there are 1T magnetic surfaces surrounding the electrons in the centre, then, just a few mm out, suddenly 'puff' - nothing, no more magnetic field at all??

I think your view of the geometry is inverted. My understanding is there is a magnetic field outside, which tends to vanish as you move inward.

chrismb · Post by **chrismb** » Mon Dec 15, 2008 3:30 pm

Maybe this is so; a difference between how I think the device 'will' operate compared with its design intent. I will follow this through in the other threads...

best regards,

Chris MB.

MSimon · Post by **MSimon** » Mon Dec 15, 2008 10:08 pm

chrismb wrote:Maybe this is so; a difference between how I think the device 'will' operate compared with its design intent. I will follow this through in the other threads...

best regards,

Chris MB.

The design is all like poles facing in to the center canceling the field in the center. This has the interesting effect of compressing the field outside the reaction space as well. According to field simulations.

hanelyp · Post by **hanelyp** » Tue Dec 16, 2008 5:20 am

Regarding the electrons pushing the magnetic field away from the center:

Consider an electron flying out from the center. The magnetic field will turn the electron to fly sideways, in a direction so the electrons magnetic field will add to the external magnetic field on the outside, and subtract closer to the center. Given a multitude of electrons the effect is current loops around the outside of the plasma mirroring and opposing the current loops in the magrid.