Off the wall question:

[D Tibbets]

OK, I was shooting from the hip on the scaling comments above.
I’ve been looking a 1/r^2 for each dl in the numerical integration for too long.
Yes it does simplify to 1/R at the coil center which is the most important point.

But I stand by my model because it agreed with the analytical solution for a square turn to better than 1% when I turned the current off to the other 5 turns. (I must say I was very pleased to see that result.) I also stand by it because I’ve been much more careful with it than I was with my above comment.

Starting with a current that gives 1.00 T at the center of the square coil then turning off the other 5 coils I get 1.86 T. I.e. the other 5 coils decrease the field at the center of each of the coils by 46% from what they would each create alone. (See table on the thread Optimal Size for Magrid Casings)
Most of the effect is from the adjacent coils not from the opposite coil.
The other coils increase the field at the highest field point by 5.6%.
So we have to push the materials roughly twice as hard as you would think by naïvely assuming no effect from the other coils.

Which SC can do 100 T? I see MgB2 listed at 74 T.

Running the numbers through the model: (3 m dia truncube square plan form coils, 100mm diameter conductors)
For 100 T (per MSimon above) at the highest field point on the conductor surface, the field at the center of the square turn is 5.74 T at 1.99e7 amp-turns. (The field at the center of the square turn is weaker than at the center of the triangular virtual turn.)
For 74 T (MgB2 thin films per Wikipedia) at the highest field point on the conductor surface, the field at the center of the square turn is 4.24 T at 1.47e7 amp-turns.
For 55 T (MgB2 fibers per Wikipedia) at the highest field point on the conductor surface, the field at the center of the square turn is 3.16 T at 1.10e7 amp-turns.

So, if we can get up to those fields & currents then we are still in the running.

I don't know how adjacent magnetic coils would decrease the magnetic field strength in the center of one coil. The field strength should be solely dependent on the amp turns. Certainly the field geometry could be distorted, though I cannot visualize the effect on the face cusps (More diamond shaped instead of circular?).

If I understand the 100 mm to be the minor diameter of a magrid coil, then that size would be small in a 3 meter diameter machine. If the 10% ratio of WB6, WB7(?) is kept, then the minor radius would be 300 mm. Again, I'm uncertain how this would effect the magnetic field drop off. The distance from the center of the minor radius coil crossestion to the center of the major radius would not change, but the distance from the inner border of the minor radius coil crosection to the center would be less.

And, on the original question of size- no one has mentioned the size needed to support a superconducting magnet - multiple insulating and cooling layers. This engeenering limit may be more significant than the theoretical limit based on the gyroradius issues. Also, little mention of the ratio of the magrid size to the vacuum vessel size that needs to accomidate all the collection grids, guns, pump assemblies, etc. I'm guessing that the size of these structures would add to a greater percentage of the total size as the magrid was shrunk. So these 'external' structures may limit the final size as much or more than the magrids.


Dan Tibbets

[MSimon]

Which SC can do 100 T? I see MgB2 listed at 74 T.

I'd have to do some digging to find it. It may be specially doped MgB.

But 74T is good enough for now.

[tombo]

I don't know how adjacent magnetic coils would decrease the magnetic field strength in the center of one coil. The field strength should be solely dependent on the amp turns. Certainly the field geometry could be distorted, though I cannot visualize the effect on the face cusps (More diamond shaped instead of circular?).

That is just how the numerical integration comes out.
But, If you visualize the field from the adjacent coil without the coil in question energized then you see the field coming out through it. (assuming all coil fields point in)
Turn both coils off. Turn on the coil in question. Then when you turn the adjacent coil on, by superposition the field at the center of the coil is reduced.
I suppose it must go up elsewhere, i.e. around the edges, to balance the Maxwell equation.

If I understand the 100 mm to be the minor diameter of a magrid coil,

yes of the conductor

then that size would be small in a 3 meter diameter machine. If the 10% ratio of WB6, WB7(?) is kept, then the minor radius would be 300 mm.

I'm using a baseline WB100 design put forth by MSimon as it currently stands. As I understand it.

Again, I'm uncertain how this would effect the magnetic field drop off.

Me too. Hence the numerical integration based on Kiteman's spreadsheet.

The distance from the center of the minor radius coil cross section to the center of the major radius would not change, but the distance from the inner border of the minor radius coil cross section to the center would be less.

And, on the original question of size-

Yes we have strayed, sort of. I think the upshot is that we are hard up against existing superconductor materials with the 3 m diameter machine.

no one has mentioned the size needed to support a superconducting magnet - multiple insulating and cooling layers. This engineering limit may be more significant than the theoretical limit based on the gyro radius issues.

Agreed. Last I heard it was on the order of 200 mm minor diameter of the casing for insulation and coolant only (no load bearing structure). but we may be able to do better if the alphas are significantly confined to cusps.

Also, little mention of the ratio of the magrid size to the vacuum vessel size that needs to accommodate all the collection grids, guns, pump assemblies, etc. I'm guessing that the size of these structures would add to a greater percentage of the total size as the magrid was shrunk. So these 'external' structures may limit the final size as much or more than the magrids.

Yes, the arc breakdown issue for 2MV collectors etc.

And the radiation shielding.

And the heat engine to recover the big chunk of energy not directly convertible. And the heat dissipation. Heat exchangers tend to be big.

And as the fields go up the forces go up and we will hit material strength limits much sooner than we would hope for. (See BillyCatringer's work.)

And those direct converters: The only picture of a fully thought out one that I have seen has a 3 m dia polywell with 4 converter channels a hundred meters long each. IIRC

Gut feel: At this point I think we will be lucky to get it to work with a 3 m dia PW in a building 30 m on a side and 3 stories deep. Plus facilities & offices buildings.

[tombo]

Which SC can do 100 T? I see MgB2 listed at 74 T.

I'd have to do some digging to find it. It may be specially doped MgB.

But 74T is good enough for now.

OK for forward planning.
The real question (for near term projects) is what field and current at what temperature can they actually deliver in quantity now.

[MSimon]

Which SC can do 100 T? I see MgB2 listed at 74 T.

I'd have to do some digging to find it. It may be specially doped MgB.

But 74T is good enough for now.

OK for forward planning.
The real question (for near term projects) is what field and current at what temperature can they actually deliver in quantity now.

The field is moving rapidly. If it is experimentally verified this year it will be commercial in 3 to 5 years.

[icarus]

The field at the center of the coils changes again when you add in the Wiffle-ball effect, i.e., push-back from electron plasma pressure.

I seem to recall it goes up ... and quite significantly so if it is a large wiffle-ball ... of course it depends upon assumptions you make regarding size and shape (geometry) of the plasma.