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?).tombo wrote: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.
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