Diagmagnetic plasmas' resistivity Vrs Electrical resistivity

[mattman]

Hello All,


I was thinking today that diamagnetic plasma has an internal resistance to an outside field.

I thought that a good analogy for this would be electrical resistivity.


In high school we learned that different materials would resist externally applied electric fields differently. You put the same voltage across a block of wood or plastic or metal - you get a different current - like ohms law.


What if the same thing were true in plasmas? You put the same magnetic field across different plasmas and they behave differently. They have a diagmagnetic constant (like solids do). I drew this out:





Some questions:
What is the function predicting this diamagnetic constant?

diamagnetic constant = Function (plasma density, temperature, composition, ect...)

What conditions are needed for full rejection of the externally applied field? Were these conditions met in the WB8 Navy experiment?

Anyone have any good references or explanations on this topic?

[D Tibbets]

I'm not sure if this is related to what you are searching for, but tha plasma resistivity or the inverse, its coductivity depends on it's density and it's chariteristic- hydrogen , nitrogen, etc.
The Pashion arc breakdown is a process known since vacuum tube days and befote(?). An electric field is not very good at ionizing a gas to produce a conductive plasma. But, oncea few atoms/ molecules are ionized free electrons can ionize other gas atoms very quickly and this cascade leads to significant gas ionization. Generally the higher the applied voltage the faster, or at least more complete this process is. Also, the number of possible charge carriers/ density effects the conductivity. In a glow discharge fusor at about 5-20 Microns of pressuere the ionization increases rapidly. With a limited power supply, the voltage quickly droops ans the current increases. Because of this , unlerss you have a very robust power supply, the voltage maximum achievable is perhaps a few thousand volts at most when the density is ~ 20 Microns, the maintainable voltage goes up rapidly and eponentially below this pressuer, so that at ~ 0-5 Microns voltages of many thousands of volts can be maintained with reasonable current flow. This is manifest in the Polywell, when Bussard described the arcing that destroyed the potential well above a certain pressuere external to the magrid. Internal pressures could be higher due to careful control of geometry (no points), and the magnetic shielding of the magrid. This limits the achievable density that can be used in a Polywell. Basically the magrid pressure can be ~ 0.1 to 1 Micron (~ 1 millionth of an atmosphere) and the internal magrid pressure can be a multiple of this. This multiple is the Wiffleball trapping factor. If the external pressure is limited to ~ 1/ 10 millionth of an atmosphere, or ~ 10^18 charged particles/ M^3, then with a Wiffleball trapping factor of 10,000, the internal density can be ~ 10^22 charged particles/ M^3. That is where this often quoted Polywell density limit comes from.

Look up Pashin arch, Pashin discharge curve.

http://en.wikipedia.org/wiki/Paschen%27s_law

https://www.google.com/search?q=Paschen ... d=0CCYQsAQ

There are all sorts of modifications that might apply, such as neutral gas ionization, ion guns, external to the magrid structure exposures, geometries , insulation, electron injection efficiency, pumping capacity, etc.

In terms of the magnetic fields associated with the plasma current, I think it would be essentially zero on the large scale. In a plasma, both the negative electrons and positive ions are mobile and carry current. They move in opposite directions (perhaps thousands of times before finally escaping) so the magnetic fields should ~ cancel out. For further complications considerations like Debye length, plasma frequency, plasma waves , etc. can perhaps effect the final picture.

Dan Tibbets

[prestonbarrows]

I am not sure what you mean by 'magnetic resistivity'. But to expound a bit about magnetized plasma...

I am not very familiar with the mathematics of non-thermal plasmas so some of the following might not hold true is this case. But, for tokamak-like thermal plasmas, to first order (neglecting instabilities etc) you can simply apply a force balance to the system.

A magnetic field contains stored energy. This leads to a so called 'magnetic pressure'. Just like pressure in a gas due to thermal energy, a gradient in the magnetic field (and magnetic pressure) results in a force. In a typical device, you will have magnetic fields which are stronger towards the walls where the magnets are located; contrariwise, the plasma pressure will fall off towards zero as you approach the chamber walls.

It is easy to convince yourself that the two tend to oppose each other; this is the whole idea behind magnetic confinement after all. In a very basic limit, you can balance the force from the pressure gradient of the plasma with the pressure gradient of the confining magnetic field. Put simply, a stronger confining magnetic field will produce a higher density/temperature plasma in the core; no surprises there.

Now the topic of diamagnetism. If you dig a bit deeper into charged particle motions in magnetic fields, you will see that electron and ion drifts are sometimes polarized in opposite ways . This can give rise to spontaneous currents. This plasma current is dependent in part on the plasma density and temperature. Like any currents, these produce a magnetic field. The plasma currents and plasma-induced-fields are always oriented such that they oppose the original externally applied field; otherwise you would get a positive feedback loop and infinite spontaneous energy.

So, the magnetic fields from these two sources, the external magnets and the plasma itself, tend to cancel out; this leads to a negative feedback like effect in the bulk of the plasma. Magnetic fields create plasma currents which reduce magnetic fields which reduce plasma currents. If you have a hot and dense enough plasma, it will 'shield out' an external magnetic field, creating a core with no magnetic field. From Gauss's law for magnetism, we know that magnetic fields are divergence-free, so this shielding effect tends to expel the magnetic field lines from the bulk of the plasma towards its edge and create a high magnetic gradient driven by plasma currents on this surface.

A quick search came up with the attached relevant chapter from an intro to plasmas text.

What conditions are needed for full rejection of the externally applied field? Were these conditions met in the WB8 Navy experiment?

Again, to first order, you can get a rough number by equating the plasma pressure to the magnetic pressure. You would need to know the relevant data such as plasma density, plasma temperature, magnetic field profile etc. to work this out. Park et al. recent preprint shows pretty convincing evidence for field repulsion in their small scale device.

[D Tibbets]

From the previous post, I will nit pick and clarify that the increased confining B field does not produce a hotter more dense plasma. It does allow for such a denser/ hotter plasma to be contained within a given volume. There is an extension of this that I am scratching my head about but I will avoid confusing the issue, or myself further...

Instantaneous currents as the electrons and positively charged ions gyro rotate- spiral in opposite directions in a magnetized plasma is straight forward. . In a quasi spherical geometry, with cusps and thus mirroring points the charged particles reverse many times, so given a sufficient amount of time- more than several mirroring reversals, and much less than confinement time, the current polarity would be all but averaged out. For very short burst/ instantaneous time scales it would polarize, but given a little time the polarization is damped out/. I wonder how this would effect transient start up conditions

In a high beta situation where the charged particles do not spiral (to first order) but complete only ~ 1/2 gyro orbit, there would be a slight polarity , the electrons would deflect one way and the ions the other. I suspect these angles are small, but real. Bussard mentioned the up scattered ion deflection by the B field as decreasing central ion focus. But, with convex B fields, and many multiple deflections , I suspect that this small polarity would dampen out, especially when internal collisions dominate motions. And, at least in the ideal situation the ions may only infrequently turn around at the Wiffleball border. Most of the time they may turn at the top of the electrostatic potential well without confining B field interaction. The electrons on a vectored path from near the center would deflect at an angle greater from the center on one side of the convex B field (decrease central focus), but on the other side the deflection would decrease the deflection angle relative to the center. The two would cancel each other out I think. Closer to the cusps where there would be multiple deflections from either side of the cusp before the electron was finally deflected back into the interior would be more complex.


As for Mattman's question about WB8, I do not think the confining B field was pushed out or excluded much, some, but not much. From Dr Park's comments, Beta approaching one was not achieved, or at least it was difficult and uncertain. He is somewhat vague. In the small 'Mini-B' machine, he did have measurements/ calculations(?) that a Beta of 0.7 was achieved, and at the radius of the B field sensors (coaxial wire loops) the B field was excluded/ weakened to ~ 40% of the low Beta startup conditions. I take this to mean that a nice hard Wiffleball surface was approached only moderatly. This was still enough to show remarkable improvements in confinement. I wonder if subsequent predictions about a break even machine is based on this performance, or from extrapolation to a full Beta=1 (or rather Beta= 0.9999) condition.

My gross guestimation of the Beta condition is that it is equal to temperature * density / B^2.
In the 'Mini-B' example , if the average temperature was constant and the B field was constant, then a doubling of density would push Beta to ~ 1. The square of 0.7 is 0.49, so the density would need to double to reach Beta= 1 conditions. Dr Parks set up the expirement to show the desired effects based on his predictions. I don't know how closely the actual expirement matched his plans, but it was good enough to show the desired clear signal. Dr Park's did mention that he planned to have results in three months, while it actually took ~ a year for the experimental setup to be implemented with the bugs worked out. I wonder if this delay played a role in the Navy contract termination. I can imagine a Navy administrator condition- 'Show proof of Wiffleball confinement by such and such date or else. Oh, and do it with the money you have left over...'.

Dan Tibbets