Gauss's Law and hollow spheres

[D Tibbets]

Some enlightenment (for me) on the electric fields inside and outside a sphere. I had gained an understanding that there was no effective electric field inside a hollow container irregardless of it's shape or porosity. The link below is a video physics lecture about the three situations in which Gauss's law applies. This (hopefully) gave me a better understanding and that the lack of any field only occurs only under symmetrical conditions-ie. a sphere. A charged particle a given distance from the center would not see the cube as radially symmetrical and there would be some electric field influence on a charged particle, though I'm uncertain of the vectors involved or if the deviation from zero effect is significant. I'm not sure if considering cubes within cubes would be the same as spheres within spheres. I found these lectures thanks to a post by kunkmiester.

http://academicearth.org/lectures/elect ... -gauss-law

Dan Tibbets

[93143]

The 'any shape' thing only applies if the shell is a conductor. That way the charges distribute themselves in such a way as to null out the field inside the shell.

A charged nonconducting surface does not display this behaviour.

Porosity is actually rather important. Not critical, since Faraday cages obviously work, but technically Gauss' Law only deals with closed surfaces. A magrid breaks this condition rather egregiously, so the 'no field inside the magrid' assumption is only an approximation.

[D Tibbets]

The 'any shape' thing only applies if the shell is a conductor. That way the charges distribute themselves in such a way as to null out the field inside the shell.

A charged nonconducting surface does not display this behaviour.

Porosity is actually rather important. Not critical, since Faraday cages obviously work, but technically Gauss' Law only deals with closed surfaces. A magrid breaks this condition rather egregiously, so the 'no field inside the magrid' assumption is only an approximation.

In the video, the instructor uses two metal coated pingpong balls as a dipole, He dips them into a metal sphere that has been charged. There is a hole slightly bigger than the pingpong balls to gain access into the sphere. Despite this hole, the pingpong balls do not pick up a noticable charge detectable with his gross electrometer which demonstrates Gauss's law even with the hole in the sphere. so the breakdown of the isolation inside the incomplete sphere is not great. What I wonder about is if in the Magrid which has multiple larger holes, is the breakdown significant. In otherwords, will the ions and electrons see a significant portion of the (eg 10,000 plus volts) electric field of the magrid as they penitrate deep into a cusp, but are still within the magrid. This would seem to be a mechanism to seperate any ion- electron grouping that A. Carlson has championed.

A purely speculative example-
+10,000 volt magrid. Due to 'leakage' the charged particles would see a +1000 volt potential when a few cm inside of the magrid diameter. The electrons would see an accelerating voltage while the ions see a decelerating voltage. This would presumably seperate the ions and electrons. The ions would be less likely to escape, while the electrons would be more likely to escape (actually the electrons would already be guarenteed to escape once they found a cusp hole due to the excess electrons inside the Wiffleball). Once outside the magrid, the electron would have a recirculating potential of 9000 volts (10,000 volts on the magrid - 1000 volts potential that the electron sees when inside but close to the magrid). This would seem to be a mechanism to increase the ion containment at the cost of a proportionatly increassed potential on the magrid. Since the ions that reached heights near the magrid would be seeing a 1000 volt inward directed force, some if not most of this drive energy would be recovered(?).

I understand that WB4 and possibly WB5 was operated with the positive potential either on the magrid or the electron guns. I wonder if any measures of ion containment and/or electron containment changed with these conditions. I would expect the positive charge on the electron guns, while the magrid was at ground would benifit much less from the above effect (if it exsists at all).


Dan Tibbets

[D Tibbets]

As reemphasized by93143 and a subsequent lecture at the link the shape does not effect the lack of a field inside. The holes do. I may be greatly inflating the magnidude of the effect, but I don't think it is nessisarily completely irrelavent. Also, if there is some variation in the potential on the magrid the field is not completely static and the Faraday shielding will change based on the frequency. Higher frequencies will get through smaller holes.

Another issue brought up in a lecture may apply. Start with a hollow metel sphere/Faraday cage. Any static charge on the outside does not penitrate inside. If a charged particle is introduced inside (like an excess of electrons) then a positive charge will be induced on the inside surface of the sphere. If not spherical these charges will not be symetrical (I think). In anycase the inside of the magrid would have an induced positive charge (potential) from the excess electrons inside. I think this charge would have an effect on the ions (fortunatly the electron confinement is dominated by magnetic fields), adding some electrostatic effect independent of the leakage effect I supposed in the prevous post. I'm thinking that these two effects would provide some argument against ambipolar flow in the cusps. Varying the drive potential on the magrid at some appropiate frequency would increase the leakage effect restraining the ion flow into the cusps even more. Presumably this would effect the monoenergetic status of the electrons, so I suppose it is all a matter of compromises, and tuning to maximize the benificial effects over the detrimental effects may be in order. Who knows (certainly not me), this might even provide a knob to help slow the thermalization of the electrons and possible detrimental sheath effects (add vigorous hand waving here ).


Dan Tibbets

[Gary 7]

There is no potential difference from any point inside a charged sphere. That doesn't mean there is no electric field, just that all points inside would experience no potential voltage. With a charged core region, there IS a potential difference, as in Polywell.

[93143]

There is no potential difference from any point inside a charged sphere. That doesn't mean there is no electric field, just that all points inside would experience no potential voltage. With a charged core region, there IS a potential difference, as in Polywell.

Sorry, you're either confused or you're using the terminology wrong. Probably the latter.

Your first and third sentences are fine, if a little incomplete. It's the second sentence that's garbled:

1) Potential is a measure of the energy required to move a test charge to a certain point from a reference point. It is relative. You need to pick a reference point and define the potential as a difference from that. There's no such thing as an absolute value of the electric potential. (Don't bug me, chrismb, this is still basic electrostatics we're talking about here.)

In relation to the above:

2) Electric field is the gradient of the potential. It is NOT relative; it has to do with the force experienced locally by a test charge, and thus does not require a reference point. If the potential is uniform everywhere inside a volume (as in the interior of an empty closed conducting shell), there cannot be an electric field anywhere inside that volume. Basic calculus.

Nothing says the potential has to be zero. It depends on what you measure it with respect to. If you measure with respect to ground, the potential inside an empty, charged, conducting closed shell is almost certainly nonzero. But the electric field is always zero.

Note that I specified an "empty" shell. If there is nonzero space charge in any region inside the shell, it will of course induce electric fields, so there will be variations in the potential inside the shell. As you note, this is how a Polywell works. Of course, the shell (or magrid, in this case) still shields the interior from external electric fields...

Also, the term "potential voltage" is redundant, which is probably why no one uses it. "Voltage" means "potential difference", measured (naturally) in volts...



Gaah... my quasi-1D Boltzmann solver takes two-thirds of a second just to calculate the limiter values for a single time step... this isn't just a Matlab problem; I need a supercomputer...

[tomclarke]

As reemphasized by93143 and a subsequent lecture at the link the shape does not effect the lack of a field inside. The holes do. I may be greatly inflating the magnidude of the effect, but I don't think it is nessisarily completely irrelavent. Also, if there is some variation in the potential on the magrid the field is not completely static and the Faraday shielding will change based on the frequency. Higher frequencies will get through smaller holes.

Another issue brought up in a lecture may apply. Start with a hollow metel sphere/Faraday cage. Any static charge on the outside does not penitrate inside. If a charged particle is introduced inside (like an excess of electrons) then a positive charge will be induced on the inside surface of the sphere. If not spherical these charges will not be symetrical (I think). In anycase the inside of the magrid would have an induced positive charge (potential) from the excess electrons inside. I think this charge would have an effect on the ions (fortunatly the electron confinement is dominated by magnetic fields), adding some electrostatic effect independent of the leakage effect I supposed in the prevous post. I'm thinking that these two effects would provide some argument against ambipolar flow in the cusps. Varying the drive potential on the magrid at some appropiate frequency would increase the leakage effect restraining the ion flow into the cusps even more. Presumably this would effect the monoenergetic status of the electrons, so I suppose it is all a matter of compromises, and tuning to maximize the benificial effects over the detrimental effects may be in order. Who knows (certainly not me), this might even provide a knob to help slow the thermalization of the electrons and possible detrimental sheath effects (add vigorous hand waving here ).
Dan Tibbets

Re charge on inside on metal sphere (or any other shape). The way to understand this is in terms of potential. The conductor by definition is an equipotential volume. Surface charge will be present as necessary to cancel any electric field perperdicular to the conductor. Again by definition electric field parallel to conductor at its surface is impossible.

As far as the effect on particles inside. This is determined by the interior potential which is the solution of Laplace's equation subject to the boundary condition imposed by the equipotential of the conductor - note that surface charge does not enter into this - and the charges inside the sphere.

Best wishes, Tom

[93143]

Maybe the Bremsstrahlung radiation exiting the reactor would be reused or focused inward again to get pair production of electrons and positrons?

Not enough energy. You need over a MeV to do pair production of electrons and positrons; the only thing in the system with anywhere near that amount of energy is the ash.

What if electrons were created at the very near the center of the volume inside the magrid?

You'd get annihilation gammas, and that's probably about it. Charge is conserved, and the electrons are supposed to be slow near the centre anyway. Pair production electrons might possibly get trapped in the virtual anode, which could lower it if the positrons started annihilating faster electrons from the emitters.

But all this is moot because pair production can't happen the way you describe.

Would their rotation cause a a magnetic field and possibly a second well within the Polywell?

What rotation?

So hot Borons and Protons(or whichever fuel) would get a new drop in potential energy. They would go from an ion state back to one with electrons attached.

...you have no idea what you're on about, do you?

Would the neighboring ions also be drawn to the negative charge of the free electron(s)? More repulsive and get kicked to the shell and stir up the mess in a synchronized way? A blender?

Nope, you're definitely out of your depth. There's hand waving, and then there's this...


EDIT: Apparently the old rule about spelling flames applies to physics flames too. I meant virtual anode, not virtual cathode...

[chrismb]

Don't bug me, chrismb, this is still basic electrostatics we're talking about here.

Would I, ever?

[MSimon]

DW,

Feel free to start a thread with questions. There are always new guys who don't wish to mine the archives.

And as you may have noticed my moderation style is very loose.

Further - don't worry about appearing stupid. I have done it a couple of times myself. It is good for the soul.

[93143]

Sorry about that. I shouldn't have come down so hard on you. Perhaps I'm getting frustrated with my research...

But really, even if you could get pair production going in the core, I don't see what the advantage would be. The positrons can pretty much be ignored because they will annihilate almost instantly, usually with injected electrons, so all you're really doing is replacing injected electrons throughout the plasma with electrons having direction and energy distributions corresponding to those of the incoming gamma rays.

Naturally you have to subtract off 1.022 MeV from the gamma ray energy distribution (which is why bremsstrahlung from a sub-100 keV plasma isn't useful for this), but if there's any significant spread, the result will be replacement of injected electrons with very hot thermal electrons in a random pattern, at some rate corresponding to the intensity of the gamma irradiation. If the gammas aren't focused precisely, the direction of travel for the generated electrons will also be random. This would not be good.

If you could come up with a very tight energy distribution on the gammas (like a laser) and rely on very good ion focus (which we don't know happens) to produce cold electron-positron pairs almost exclusively at the centre, these might start replacing faster electrons transiting the virtual anode (NOT cathode, as I mistakenly said in my previous post), with the new electrons not having enough energy to get out of said virtual anode, and thus lowering it. This would be good.

Note, however, that this scenario relies on the implausible scenario of bombarding the core with a battery of concentrically-focused gamma-ray lasers, and even then it won't work well if ion focus isn't unrealistically tight.

Perhaps more importantly, I consider it a distinct possibility (any particle physicists here?) that the motion of the mediating ions will have a strong effect on the energy of the produced electron-positron pairs. Since the core is where the ions are fastest, this could produce a hot thermal distribution of electrons in the core even with monochromatic gamma bombardment, which would not be good. On the other hand, the ions are heavy and thus slow, so the effect might be small... It's late and I can't be bothered to try to work it out...

Okay, [edit]: A 50 keV boron travelling straight at a 1.022 MeV gamma source would see about 3200 eV of blue shift. A 10 keV proton would see about 4700 eV. So the effect might be medium-sized... [/edit]

Further, since most of the gamma radiation would probably shine right through, you now have to have a method of reflecting MeV-range gammas with nearly perfect efficiency. Does such a thing exist? And could you cover the entire reactor interior (including the graser emitters) with it?

In no case can I imagine this thing being power-positive... the whole point of a fusion reactor is to turn matter into energy, and now you want to go the other way? Seems counterproductive to me...

[D Tibbets]

Re David Willard's comments.

Your determination to generate antimatter as a suppliment to the Polywell's 'wasted' bremsstrulung radiation is doable I suppose, but the energy cost would be huge. I know that powerful lasers have been used to produce new matter, but the energy that has to be pumped in, even if you could reach 100 percent efficiency in the laser beam generation and then 100% efficiency of laser energy conversion into matter, the harvesting of the energy ( if matter- antimatter pair) could never be greater than the energy you put into the effort.
I know of two ways to recover some of the energy from the X-rays. One way is to allow them to contribute to the heating of a working fluid that then runs a steam plant or other thermal conversion system (like a Sterling engine) to recover ~ 25-40% of the energy. The other way would be to have a 'solar cell' that can absorb the x-rays and directly convert it to useful electricity- probably less efficient than the thermal approach. If you could convert the x-ray energy into electricity at 100% efficiency you could recycle it back into the system with theoretically net losses of zero percent, but never could you get a net gain, unless your recycled input somehow has a catalytic effect. The only thing that I know of that would do this is Muons, and they do not survive long enough to be practical.

You mention bismuth effecting P-P fusion rates. Do you mean Dr. Bussard when you mentioned Buzzard? He mentioned that someone had suggested a method to improve P-P fusion in his American Antigravity interview, when he was asked about the Bussard Ramscope interstellar drive, but I could not find any link.


Dan Tibbets