What is a convex magnetic field?
Posted: Sat Nov 05, 2016 1:20 am
It has been repeatedly stated that the convex magnetic fields in the Polywell eliminates concerns about edge instabilities/ macro instabilities. While this may be true or mostly true, the question I am asking here is how does a bundle of wires not have concave fields between them? To rephrase the question- How do you get a smooth convex B field when there ae concavities in the field between individual windings? If you have 100 wires in a magnet bundle, there is some separation between them, even if it is only a small fraction of a mm due to the varnish insulation. The overall wire bundle magnetic field would be rippled on the surface-concave and convex as it bridged between wires. I do not know the answer but I speculate that several considerations may apply. Any corrections or enlightenment would be appreciated.
If the separation between each wire in the bundle is much less than the gyroradius of the moving charged particles of interest. The average shape of the magnetic field would be dominated by the overall convex field generated by the wire bundle in total. Would the gyroradius variation of the particles (electrons primarily since they have the much smaller gyroradii) in a thermalized plasma be more challenging than a mono energetic plasma?
Also, as the wires/ superconducting tape and possibly other materials in the immediate vicinity of the enclosed magnet would have a permitivity much higher than that in a vacuum or rarefied gas. The internal B fields would thus be much stronger. Would this contrast of the B field inside and outside of the can play a role in presenting a smooth contour B field outside of the can?
In a solenoid with a cylindrical magnetic wire winding, how close do the windings have to be to prevent the concave- convex wobbling in the B field relative to the plasma? I presume a solenoid/ cylinder with parallel walls could be vulnerable to macro instabilities due to local variations in the plasma pressure (due to various plasma characteristics). As such, a small local bulge could occur and then grow due to the favorable energy balance. How much convexity is required to prevent most of these local excursions from occurring? I think cylindrical B fields of this nature are vulnerable to macro instabilities. Would this slightly- to mildly diverging near cylinder help? Combined with separate end opposing ring magnets it starts to look like thee three ring magnet magrid that I have describe before . And, except for the central curvature, like old and discarded cylindrical with end cap designs.If the 'cylinder, or big ring if you prefer, might still allow for central focus (it does as demonstrated by some magnetic modeling I have done before and presented here) provided the length of this curving cylinder is not to long and appropriate B field strengths are applied to this central curving 'cylinder' or fat or oval minor radius magnet and the opposing end magnets. I like a central donut or torus magnet that has a length of ~ 1.5 to 2 times the length/ radius of the opposing end magnets. Also having a greater radius from the midline of the 'cylinder' for the central magnet helps with central focus into the previously mentioned torus, near sphere or dumbell core. I don't know if this central magnet to end magnet length along the cylindrical axis could be pushed past this ratio.
Note that the Lockheed design has elements of this and I originally thought that it was essentially the same. But emphasis on circulating FRC type flows/ recirculation between cusps and lack of a potential well are a major divergence from my concept.
Dan Tibbets
If the separation between each wire in the bundle is much less than the gyroradius of the moving charged particles of interest. The average shape of the magnetic field would be dominated by the overall convex field generated by the wire bundle in total. Would the gyroradius variation of the particles (electrons primarily since they have the much smaller gyroradii) in a thermalized plasma be more challenging than a mono energetic plasma?
Also, as the wires/ superconducting tape and possibly other materials in the immediate vicinity of the enclosed magnet would have a permitivity much higher than that in a vacuum or rarefied gas. The internal B fields would thus be much stronger. Would this contrast of the B field inside and outside of the can play a role in presenting a smooth contour B field outside of the can?
In a solenoid with a cylindrical magnetic wire winding, how close do the windings have to be to prevent the concave- convex wobbling in the B field relative to the plasma? I presume a solenoid/ cylinder with parallel walls could be vulnerable to macro instabilities due to local variations in the plasma pressure (due to various plasma characteristics). As such, a small local bulge could occur and then grow due to the favorable energy balance. How much convexity is required to prevent most of these local excursions from occurring? I think cylindrical B fields of this nature are vulnerable to macro instabilities. Would this slightly- to mildly diverging near cylinder help? Combined with separate end opposing ring magnets it starts to look like thee three ring magnet magrid that I have describe before . And, except for the central curvature, like old and discarded cylindrical with end cap designs.If the 'cylinder, or big ring if you prefer, might still allow for central focus (it does as demonstrated by some magnetic modeling I have done before and presented here) provided the length of this curving cylinder is not to long and appropriate B field strengths are applied to this central curving 'cylinder' or fat or oval minor radius magnet and the opposing end magnets. I like a central donut or torus magnet that has a length of ~ 1.5 to 2 times the length/ radius of the opposing end magnets. Also having a greater radius from the midline of the 'cylinder' for the central magnet helps with central focus into the previously mentioned torus, near sphere or dumbell core. I don't know if this central magnet to end magnet length along the cylindrical axis could be pushed past this ratio.
Note that the Lockheed design has elements of this and I originally thought that it was essentially the same. But emphasis on circulating FRC type flows/ recirculation between cusps and lack of a potential well are a major divergence from my concept.
Dan Tibbets