so i found some resources:
viewtopic.php?p=19443&highlight=#19443
http://www.mare.ee/indrek/ephi/pef2/
and straight from emc2:
http://www.emc2fusion.org/QuikHstryOfPolyPgm0407.pdf
"WB-6, 2005, R = 15 cm, B = 1.3 kG, E = 12.5 kV, clean recirc truncube with minimal spaced corner interconnects, multi-turn, conformal can coils, uncooled, cap pulsed drive, Ie to 2000 A, incorporated final detailed engineering design constraints."
that leaves me with some questions:
1.) given the magrid is formed by a resistance-less wire of radius 0 and total length l meters
what is the electric current density (per dl), in amps, to produce the magnetic field?
the field is listed as 1.3kG (killiGauss)
the radius of wb-6 is listed as 15cm so l = 2*pi*15cm*6 coils*0.01 meters/cm.
2.) given same wire, what is the electric charge density (per dl), in coloumbs, to produce the electric field?
the field is listed as 12.5 kV.
3.) 2000 Amp Ie, does that mean that the electron guns are pumping out 2000/(1.602176487*10^(−19)) electrons a second? is that per electron gun or total (presumably total)? what is the initial radail velocity of these electrons? zero?
4.) what about ions or was the above "ion energy" - in which case, then what are the electron gun rates?
5.) what is the net total charge of the plasma (in coloumbs)?
6.) about how many particles are in the plasma? or total charge of the hydrogen ions? or grams of hydrogen ions? (i can convert).
7.) beta=1 conditions, to achieve wiffle-ball effect. how do i calculate the current, charge, and ion and electron quantities for beta=1 conditions?
questions about WB6 parameters
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happyjack27
- Posts: 1439
- Joined: Wed Jul 14, 2010 5:27 pm
WB-6 (sorta) simulation run, what i got and what i don't got:
configuration: perfect cuboctahedron, injection at zero energy on faces.
scale = 0.15 m
coil current density = 24kA (=0.1 Tesla per this page)
coil charge density = ???
# of ions in flight = ???
# of electrons in flight = ???
chamber radius (loss channel) = ?? 2x polywell radius = 0.30 m ??
coil radius (loss channel) = ???
injection
max. injection rate (total charge of particles in coloumnbs) per second per gun = ????
average alignment error of guns (i.e. radial dispersion of initial ion/electron position in meters) = ???
average velocity error of guns (i.e. radial dispersion of initial ion/electron velocity in meters/second) = ???
i need these number in order to run a simulation of a polywell that's even in the right ballpark. i know the particle count is going to be way high so i'll have to scale the parameters. but i'm dead in the water without anything to start with.
configuration: perfect cuboctahedron, injection at zero energy on faces.
scale = 0.15 m
coil current density = 24kA (=0.1 Tesla per this page)
coil charge density = ???
# of ions in flight = ???
# of electrons in flight = ???
chamber radius (loss channel) = ?? 2x polywell radius = 0.30 m ??
coil radius (loss channel) = ???
injection
max. injection rate (total charge of particles in coloumnbs) per second per gun = ????
average alignment error of guns (i.e. radial dispersion of initial ion/electron position in meters) = ???
average velocity error of guns (i.e. radial dispersion of initial ion/electron velocity in meters/second) = ???
i need these number in order to run a simulation of a polywell that's even in the right ballpark. i know the particle count is going to be way high so i'll have to scale the parameters. but i'm dead in the water without anything to start with.
I'm not sure where you got some of the numbers. I'm to lazy to answer each point individually, so I'll just ramble off my figures.
I understand, WB 4 worked up to ~ 1300 Gauss, I think WB8 [EDIT- should be WB6] stayed closer to 1000 Gauss.
The WB6 coils consisted of 200 turns of heavy copper wire (12-14 gauge?)
The current was ~ 2000 amps through the magnet wires, giving ~ 200,000 amp turns [EDIT (boy, my cognition was faulty yesterday) should be 400,000 amp turns]. The voltage was from marine 12 volt batteries in parellel. I don't know if there was any serial connections, so the voltage was ~ 12- to as much as 60 volts?). I generally assume 12 volts, which gives a power of ~48,000 Watts driving the magnets.
The potential well was derived from the potential on the cases of the magrid. This was ~ 12,000 Volts, and gave a working potential well depth of ~ 10,000 Volts. The electron guns were at low voltage (~12 volts) and at ~ 40 amps durning the brief time that neutrons were being produced, which was when B was presumed to =1. The total electron current is difficult to figure, because the gas from the puffer was mostly ionized (releasing their electrons) through a cascading secondary process. And during/ after this ionization time these secondary electrons were progressively heated from their birth energy of perhaps 100 eV, up to near the e- gun provided electron energy of ~ 10,000 eV. Ignoring this secondary electron contribution (at least from an energy input perspective, the secondary electrons get all of their energy from the injected E-gun electrons, so I don't think it would change the input power values. My guestimate for WB6 input power during Beta = 1 steady state conditions was ~ magnet power (48 KW) plus the electron gun current * the magrid cassing potential (40 A * 12,000 V or 480 KW)= 520 KW. This is consistant with the expected power scaling needed to exceed breakeven in a 3 meter diameter machine at ~ 10 Tesla.
The radius to the midplane of the magrid casings was 15 cm. The magrid casing minor radius was ~ 17% of the total or ~ 2.5 cm radius or 5 cm diameter.
Up until WB6, I think the computer models run by EMC2 assumed infinitely thin magrids, that did not have any cross sectional area that the escaping electrons could hit, so electron gyroradii concerns in the cusps was ignored until the eureka moment that lead to the design of WB6.
Also, though I cannot defend it, I believe the relavent magnetic field strength was taken from the cusps between the magnets, not the coil center point cusps, so the distance to the center of the coils was irrelevant. I assume this was justified by the much smaller losses through the point cusps. The edge or funny cusp losses still dominated even though there was greater local fields in these areas.
Dan Tibbets
I understand, WB 4 worked up to ~ 1300 Gauss, I think WB8 [EDIT- should be WB6] stayed closer to 1000 Gauss.
The WB6 coils consisted of 200 turns of heavy copper wire (12-14 gauge?)
The current was ~ 2000 amps through the magnet wires, giving ~ 200,000 amp turns [EDIT (boy, my cognition was faulty yesterday) should be 400,000 amp turns]. The voltage was from marine 12 volt batteries in parellel. I don't know if there was any serial connections, so the voltage was ~ 12- to as much as 60 volts?). I generally assume 12 volts, which gives a power of ~48,000 Watts driving the magnets.
The potential well was derived from the potential on the cases of the magrid. This was ~ 12,000 Volts, and gave a working potential well depth of ~ 10,000 Volts. The electron guns were at low voltage (~12 volts) and at ~ 40 amps durning the brief time that neutrons were being produced, which was when B was presumed to =1. The total electron current is difficult to figure, because the gas from the puffer was mostly ionized (releasing their electrons) through a cascading secondary process. And during/ after this ionization time these secondary electrons were progressively heated from their birth energy of perhaps 100 eV, up to near the e- gun provided electron energy of ~ 10,000 eV. Ignoring this secondary electron contribution (at least from an energy input perspective, the secondary electrons get all of their energy from the injected E-gun electrons, so I don't think it would change the input power values. My guestimate for WB6 input power during Beta = 1 steady state conditions was ~ magnet power (48 KW) plus the electron gun current * the magrid cassing potential (40 A * 12,000 V or 480 KW)= 520 KW. This is consistant with the expected power scaling needed to exceed breakeven in a 3 meter diameter machine at ~ 10 Tesla.
The radius to the midplane of the magrid casings was 15 cm. The magrid casing minor radius was ~ 17% of the total or ~ 2.5 cm radius or 5 cm diameter.
Up until WB6, I think the computer models run by EMC2 assumed infinitely thin magrids, that did not have any cross sectional area that the escaping electrons could hit, so electron gyroradii concerns in the cusps was ignored until the eureka moment that lead to the design of WB6.
Also, though I cannot defend it, I believe the relavent magnetic field strength was taken from the cusps between the magnets, not the coil center point cusps, so the distance to the center of the coils was irrelevant. I assume this was justified by the much smaller losses through the point cusps. The edge or funny cusp losses still dominated even though there was greater local fields in these areas.
Dan Tibbets
Last edited by D Tibbets on Sat Nov 20, 2010 6:57 pm, edited 3 times in total.
To error is human... and I'm very human.
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happyjack27
- Posts: 1439
- Joined: Wed Jul 14, 2010 5:27 pm
thanks for that. making sure i undesstand correctly. voltage being relative, and the plasma being neutral, a well of 12kv and a charge on the magrid of 12kv are essentially the same thing. so you guys put 12kv of positive voltage on the magrid casing. i need figures in coloumbs per meter (assumng single-turn). how do i convert from voltage to coloumbs per meter?
(on a side note, and to make sure i got the reasoning right: from what i've seen of simulation runs i figure the charge isn't just useful in creating a well, it's usefull in attracting electrons, thus keeping the electrons from flying off into the chamber walls. the magnetic mirroring keeps them from actually hitting it, so as long as the mirror effect overwhelms the attraction, it's all good.)
also, if i am to understand correctly, you started with just electrons. you kept filling it with electrons until it seemed there was some kind of pressure balance between the b-field strength and the plasma density (i.e. electron particle count). it would be very usefull for simulation purposes to know how i would measure that.
so anyways in that this was a pulse mode machine, you'd hit that level and then you'd send your ions in. on that note, how far were the guns from the center, in relation to how far the coils were from the center? twice the distance? coplanar?
i suppose my most important questions right now is hwo to convert voltage on the magrid to coloumbs per meter of a single-turn coil, and how to adjust particle count to get beta=1.
(on a side note, and to make sure i got the reasoning right: from what i've seen of simulation runs i figure the charge isn't just useful in creating a well, it's usefull in attracting electrons, thus keeping the electrons from flying off into the chamber walls. the magnetic mirroring keeps them from actually hitting it, so as long as the mirror effect overwhelms the attraction, it's all good.)
also, if i am to understand correctly, you started with just electrons. you kept filling it with electrons until it seemed there was some kind of pressure balance between the b-field strength and the plasma density (i.e. electron particle count). it would be very usefull for simulation purposes to know how i would measure that.
so anyways in that this was a pulse mode machine, you'd hit that level and then you'd send your ions in. on that note, how far were the guns from the center, in relation to how far the coils were from the center? twice the distance? coplanar?
i suppose my most important questions right now is hwo to convert voltage on the magrid to coloumbs per meter of a single-turn coil, and how to adjust particle count to get beta=1.
I think the e-gun distance from the center was ~ 1.5 times the radius of the magrid. This was a compromise. If too close it interferes with cusp confinement, if too far away the efficiency of electron injection suffers ( the obtainable potential well depth suffers).
Magnetic mirroring, I believe, refers to charged particles oscillating back and forth along magnetic field lines, not the magnetic turning , or Lorentz (?) force that diverts the path of a charged particle away from the magnet surface. If the magnetic field is constant (and strong enough) the particle will assume some distance from the magnet where it's direction is parallel to the magnetic field, where it continues to mirror (or bounce) back and forth as it gyrates along a field line. It becomes much more complicated with variations in the magnetic field strengths, interactions between opposing magnetic fields, and more than one particle. Without cusps, if the particle is not traveling too fast and hits the magnet on first approach, the effective confinement is limited by diffusion through the field by the particles. This is driven by collisions between the particles. In ExB drift diffusion, one of these particles is knocked exactly one gyroradii closer to the magnet, while the other is knocked exactly one gyroradii further away. This is why Tokamaks have to be so big. You have to have a magnetic field thickness that can tolorate this random walk process long enough to reach useful fusion output that exceeds the cost of placing the energetic particle (ion in this case) in the system. In a Tokamak, I have heard values of ~ 800 seconds confinement times being needed. In the Polywell , I have heard values of as little as ~ 20 milliseconds.
Also, in the Polywell, only the electrons need to be magnetically confined for some acceptable time (perhaps ~ 0.1 millisecond), That, plus the recirculation allows for the acceptable effective confinement times of a few milliseconds or more. These electron confinement times come from WB6 type machines. A large (3 meter diameter) machine might confine the electrons for longer times, I'm unsure on this point. Assuming electron losses dominate the input energy picture, and using the claimed scaling laws, the electron confinement times in a fixed magnetic strength would be be r^3 / r^2. EG: size increase from 30 cm to 300 cm, is a change of 10X. So the confinement time increase would be 10^3/ 10^2= 10 x increased confinement time or ~ perhaps 1-2 ms and ~ 20 ms with recirculation
If the size is maintained and the magnetic field strength is increased, a different set of scaling laws apply, and this part confuses me. I think I have heard of effective electron confinement times of several seconds being possible in a production type machine. Also, I'm unsure how these prolonged electron confinement times interact with the thermalization times.
These short confinement times are acceptable, because of the density advantage of the Polywell over the Tokamak. The narrow energy spread in the particles helps also as almost all of them can participate in the fusion process, instead of only 1-10% of the particles in a thermalized Tokamak plasma.
The density is claimed to be ~ 1000X greater. This results in a fusion rate ~ 1,000,000 X greater. 800 sec necessary ion confinement time in a Tokamak / 1,000,000 X fusion rate advantage for the Polywell results in a necessary confinement time of ~ 0.8 ms to achieve the same fusion rate per unit volume. This allows the Polywell to be much smaller due to both of these effects, electrostatic confinement of ions by magnetically confined electrons, and greater fusion rates. This also illustrates the importance of the Wiffleball effect (density enhancement) necessary to allow smaller and much cheaper Polywells.
Dan Tibbets
Magnetic mirroring, I believe, refers to charged particles oscillating back and forth along magnetic field lines, not the magnetic turning , or Lorentz (?) force that diverts the path of a charged particle away from the magnet surface. If the magnetic field is constant (and strong enough) the particle will assume some distance from the magnet where it's direction is parallel to the magnetic field, where it continues to mirror (or bounce) back and forth as it gyrates along a field line. It becomes much more complicated with variations in the magnetic field strengths, interactions between opposing magnetic fields, and more than one particle. Without cusps, if the particle is not traveling too fast and hits the magnet on first approach, the effective confinement is limited by diffusion through the field by the particles. This is driven by collisions between the particles. In ExB drift diffusion, one of these particles is knocked exactly one gyroradii closer to the magnet, while the other is knocked exactly one gyroradii further away. This is why Tokamaks have to be so big. You have to have a magnetic field thickness that can tolorate this random walk process long enough to reach useful fusion output that exceeds the cost of placing the energetic particle (ion in this case) in the system. In a Tokamak, I have heard values of ~ 800 seconds confinement times being needed. In the Polywell , I have heard values of as little as ~ 20 milliseconds.
Also, in the Polywell, only the electrons need to be magnetically confined for some acceptable time (perhaps ~ 0.1 millisecond), That, plus the recirculation allows for the acceptable effective confinement times of a few milliseconds or more. These electron confinement times come from WB6 type machines. A large (3 meter diameter) machine might confine the electrons for longer times, I'm unsure on this point. Assuming electron losses dominate the input energy picture, and using the claimed scaling laws, the electron confinement times in a fixed magnetic strength would be be r^3 / r^2. EG: size increase from 30 cm to 300 cm, is a change of 10X. So the confinement time increase would be 10^3/ 10^2= 10 x increased confinement time or ~ perhaps 1-2 ms and ~ 20 ms with recirculation
If the size is maintained and the magnetic field strength is increased, a different set of scaling laws apply, and this part confuses me. I think I have heard of effective electron confinement times of several seconds being possible in a production type machine. Also, I'm unsure how these prolonged electron confinement times interact with the thermalization times.
These short confinement times are acceptable, because of the density advantage of the Polywell over the Tokamak. The narrow energy spread in the particles helps also as almost all of them can participate in the fusion process, instead of only 1-10% of the particles in a thermalized Tokamak plasma.
The density is claimed to be ~ 1000X greater. This results in a fusion rate ~ 1,000,000 X greater. 800 sec necessary ion confinement time in a Tokamak / 1,000,000 X fusion rate advantage for the Polywell results in a necessary confinement time of ~ 0.8 ms to achieve the same fusion rate per unit volume. This allows the Polywell to be much smaller due to both of these effects, electrostatic confinement of ions by magnetically confined electrons, and greater fusion rates. This also illustrates the importance of the Wiffleball effect (density enhancement) necessary to allow smaller and much cheaper Polywells.
Dan Tibbets
To error is human... and I'm very human.