Hello,
I think I have solved another Polywell Problem. I wanted to run it by everyone here. It regards Bussards last machine. That machine had two numbers which seemed inconsistent:
1. A “Ring Current” 2,000 Amps
2. Field at the axis: 0.13 Tesla (1,300 Gauss)
Both numbers are from Bussards Google presentation. The problem is these numbers did not fit together. Using the Biot-Savart law for the axis if you come at the problem from one number you cannot get close to the other:
Axis Field = (1.25663E-6*Current)/(2*0.127 Meters)
Axis Field = (1.25663E-6*2,000)/(2*0.127 Meters)
Axis Field = 62 Gauss
-Or -
1,300 Gauss = (1.25663E-6*Current)/(2*0.127 Meters)
Current = 26,276 Amps
These numbers do not fit, unless you multiply by the number of turns in the ring? If so, I calculate there were 13.1 turns of the wire each coil. That would make sense.
The current in WB-6's rings
The magnetic field is dependent on the amp turns, not the amps or turns ( number of wire loops) alone. There are other complications depending on whether there is an iron core, etc.
In WB6 there were 200 turns and ~ 2,000 amps for a total of ~ 400,000 amp turns. You could get the same field with 1 amp through 400,000 turns or 400,000 amps through 1 turn. Thicker wires means you can pass more amps with the same heating, but the number of turns goes down proportionately. This is why super conductors (or at least cooling to liquid nitrogen temperatures) is so attractive. You can have more windings without any or much less resistive heating.
My recollection of WB6 tests were that there were several tests with ~ 0.1 Tesla B fields and one abridged test at ~ 0.12-0.13 T which ended when the copper windings shorted to the case. WB4 operated at up to ~0.3 T.
Dan Tibbets
In WB6 there were 200 turns and ~ 2,000 amps for a total of ~ 400,000 amp turns. You could get the same field with 1 amp through 400,000 turns or 400,000 amps through 1 turn. Thicker wires means you can pass more amps with the same heating, but the number of turns goes down proportionately. This is why super conductors (or at least cooling to liquid nitrogen temperatures) is so attractive. You can have more windings without any or much less resistive heating.
My recollection of WB6 tests were that there were several tests with ~ 0.1 Tesla B fields and one abridged test at ~ 0.12-0.13 T which ended when the copper windings shorted to the case. WB4 operated at up to ~0.3 T.
Dan Tibbets
To error is human... and I'm very human.
Dan,
This bothered me. The numbers did not fit. So, I came at it another way and I have something that works. Let me know what you think. First, at Google, the power supply was described as 240 RV batteries. I figure these batteries are 12 volts and 100 Amp Hours. You can get batteries into the several hundred amp hours but, Tom Ligon mentioned amperage of ballpark 60 amps and the math works out if it is a hundred. Plus, these are common enough to purchase. Next, I argue the batteries were wired in series. This makes a high voltage (2880 volts), low current power source, which is what we want. A source like that will be used up quickly, but that is ok, since the machine is only pulsed for a few microseconds.
If you have a high voltage, low current source, you are going to use thin wire in the coil. A thin wire, high turn, electromagnet work better for high voltage, low current power sources. Also, I would argue Bussard is going to use thin copper wire, because it is more flexible. Based on photos of the 2005 machine, I do not expect the individual wires to be insulated. So, now I can apply the Biot-Savart law for the field in the middle of the ring, and the math works.
Axis Field = (1.25663E-6*Current*Turns)/(2*0.127 Meters)
Axis Field = (1.25663E-6*200 turns *100 Amps)/(2*0.127 Meters)
Axis Field = 989 Gauss or ~0.1 Tesla
So the current through the rings would be 20,000 amps*turns not 2,000. I also tried solving this by trying to find what the wire cross section would be, if it were wrapped 200 times inside a ring which is 2.25” in diameter – but for various unknowns that was a dead end. I also tried to find the Ohms/100 feet by calculating that the wire was at least ~80 feet in length and using ohms law – that was also a dead end because I cannot know the total resistance of the system. In any case, this model system (200 turns, 100 amps, 2880 volts, 1,000 Gauss field) works well enough.
This bothered me. The numbers did not fit. So, I came at it another way and I have something that works. Let me know what you think. First, at Google, the power supply was described as 240 RV batteries. I figure these batteries are 12 volts and 100 Amp Hours. You can get batteries into the several hundred amp hours but, Tom Ligon mentioned amperage of ballpark 60 amps and the math works out if it is a hundred. Plus, these are common enough to purchase. Next, I argue the batteries were wired in series. This makes a high voltage (2880 volts), low current power source, which is what we want. A source like that will be used up quickly, but that is ok, since the machine is only pulsed for a few microseconds.
If you have a high voltage, low current source, you are going to use thin wire in the coil. A thin wire, high turn, electromagnet work better for high voltage, low current power sources. Also, I would argue Bussard is going to use thin copper wire, because it is more flexible. Based on photos of the 2005 machine, I do not expect the individual wires to be insulated. So, now I can apply the Biot-Savart law for the field in the middle of the ring, and the math works.
Axis Field = (1.25663E-6*Current*Turns)/(2*0.127 Meters)
Axis Field = (1.25663E-6*200 turns *100 Amps)/(2*0.127 Meters)
Axis Field = 989 Gauss or ~0.1 Tesla
So the current through the rings would be 20,000 amps*turns not 2,000. I also tried solving this by trying to find what the wire cross section would be, if it were wrapped 200 times inside a ring which is 2.25” in diameter – but for various unknowns that was a dead end. I also tried to find the Ohms/100 feet by calculating that the wire was at least ~80 feet in length and using ohms law – that was also a dead end because I cannot know the total resistance of the system. In any case, this model system (200 turns, 100 amps, 2880 volts, 1,000 Gauss field) works well enough.
What do you think is "thin" wire?
As for insulation, the wire was insulated. If it was not, it in effect would be a single turn machine. Also, the insulation was the failure reason for WB-6. The firing shock caused it to rub on the casing and it grounded out after wearing through the varnish after a few shots.
Magnets are simple, you really are making this harder than it needs to be.
Think amp-turns and leave it at that.
This is a 30cm diameter coil. It is like counting m&m's in a jar. How many turns do you think?
I would estimate about 3cm (1/10 of total diameter) and probably about 200 turns from the photo. The wire is also most definately insulated, as you can see the varnish in the photo.
As for insulation, the wire was insulated. If it was not, it in effect would be a single turn machine. Also, the insulation was the failure reason for WB-6. The firing shock caused it to rub on the casing and it grounded out after wearing through the varnish after a few shots.
Magnets are simple, you really are making this harder than it needs to be.
Think amp-turns and leave it at that.
This is a 30cm diameter coil. It is like counting m&m's in a jar. How many turns do you think?
I would estimate about 3cm (1/10 of total diameter) and probably about 200 turns from the photo. The wire is also most definately insulated, as you can see the varnish in the photo.
The development of atomic power, though it could confer unimaginable blessings on mankind, is something that is dreaded by the owners of coal mines and oil wells. (Hazlitt)
What I want to do is to look up C. . . . I call him the Forgotten Man. (Sumner)
What I want to do is to look up C. . . . I call him the Forgotten Man. (Sumner)
The marine batteries provided high amp currents to the magnet copper wire, not low currents. Again the current was reported as ~ 1000-2000 amps. From the picture it is obvious that the copper wire was fairly thick. I don't know the gauge, but assuming a square cross section magnet can and 200 windings (also reported) a rough estimate of the wire thickness is ~ 4 mm. I have not converted this to gauge, and have not calculated the total resistance for ~1.2Km of wire to wind all six of the magnets (200 windings *~ 1 M/ winding * 6 magnets). Using Ohm's law ( A= V/R) it can easily be calculated how much voltage is needed to push the 2000 Amps through the wire at room temperature. I generally assume the batteries were arranged in both parallel and series. ~10 batteries in series and these banks were then combined in ~ 20 parallel banks. That would provide the amps and necessary voltage and account for the number of batteries. The gauge of the wire and thus the final resistance is uncertain.
Note that at liquid nitrogen temperatures the resistance of the copper wire would be ~ 6-8 times less depending on the purity of the copper.
I assume that WB4 had a similar number and gauge of copper windings. The WB4 case was square and ~ 7.5 cm wide so there was more internal volume. I guess that the extra volume was filled with the water cooling system. The thermal mass was greater than in WB6 and the water carried off a modest to large amount of the heat so I guess that the magnets could be run as long or longer than in WB6, even with 3 times the peak magnetic field (three times the current in this example).
This bring up a point, the ~240 batteries may be the number used in WB4. Some of these would have been idled in WB6 (or a current limiter or a different series- parallel arrangement used).
Note also, that WB4 and WB6 were copper windings hooked up in series through all of the magnets. In WB4 the coolant flow needed to pass through all six magnets and the coolant flow had to be fast enough to handle all of the heat from the six magnets. The arrangement where each magnet is mounted separately (standoffs from the vacuum vessel wall) and cooled separately means the coolant flow only has to handle a single magnet. This eases engineering concerns and allows for more room in the casing for magnet wire windings, thus greater magnet strength. This is another advantage to mounting the magnets separately instead of having then connected through nubs (that carry the connecting wire and coolant flow between magnets).
Dan Tibbets
Note that at liquid nitrogen temperatures the resistance of the copper wire would be ~ 6-8 times less depending on the purity of the copper.
I assume that WB4 had a similar number and gauge of copper windings. The WB4 case was square and ~ 7.5 cm wide so there was more internal volume. I guess that the extra volume was filled with the water cooling system. The thermal mass was greater than in WB6 and the water carried off a modest to large amount of the heat so I guess that the magnets could be run as long or longer than in WB6, even with 3 times the peak magnetic field (three times the current in this example).
This bring up a point, the ~240 batteries may be the number used in WB4. Some of these would have been idled in WB6 (or a current limiter or a different series- parallel arrangement used).
Note also, that WB4 and WB6 were copper windings hooked up in series through all of the magnets. In WB4 the coolant flow needed to pass through all six magnets and the coolant flow had to be fast enough to handle all of the heat from the six magnets. The arrangement where each magnet is mounted separately (standoffs from the vacuum vessel wall) and cooled separately means the coolant flow only has to handle a single magnet. This eases engineering concerns and allows for more room in the casing for magnet wire windings, thus greater magnet strength. This is another advantage to mounting the magnets separately instead of having then connected through nubs (that carry the connecting wire and coolant flow between magnets).
Dan Tibbets
To error is human... and I'm very human.