I normally have a hard time getting math and code to give me consistent results. But it looks like the electron_fluid.c code stabilizes within 2 rounds. I used gnuplot to check the output, so it just looks ok, I have not really checked the numbers for accuracy yet.
Of course, this is for very cold electrons and an arbitrary distribution in space. Even if the code is wrong, the fact that it reaches a stable solution so quickly means doing reasonable time steps should not be too bad a problem.
The main thing I have to expand on is the assumption of uniform Maxwellian temperature. Normally the temperature along the field line is different than the temperature perpendicular to field lines. It will be interesting to see how hard it will be to let the code figure that out. But I suspect I'll run out of ram and cycles first.
I still have a long ways to go, but it sure is nice to see the computer give me a self consistent solution. I'll be a happy sleeper this evening - especially after shoveling all that snow!
Virtual Polywell
I tried a couple of electron temperatures just to see what would happen. With 0.1 and 1.0 I get the same density integral. I think it is because the potential is a function of space, but the density really isn't, so it gives the same number. I'll continue to check that I'm doing it right.
The interesting thing is the potential distribution changes a lot. At 0.1, I get around -0.3 for the peak potential, but at 1.0 it jumps up to -40. These are all relative to the MaGrid voltage, and I assumed a fixed number of electrons with a fixed radius (which are all parameters, so their ratio is all that's important).
When I start letting it explode, I need to be more careful about my assumption of Maxwellian velocity distribution. u (dot) u X B is zero, but only if the velocity is uniform. The velocity of the fluid across field lines has got to be a lot less than the velocity along field lines, so back to the books and time to remember all the math....
The interesting thing is the potential distribution changes a lot. At 0.1, I get around -0.3 for the peak potential, but at 1.0 it jumps up to -40. These are all relative to the MaGrid voltage, and I assumed a fixed number of electrons with a fixed radius (which are all parameters, so their ratio is all that's important).
When I start letting it explode, I need to be more careful about my assumption of Maxwellian velocity distribution. u (dot) u X B is zero, but only if the velocity is uniform. The velocity of the fluid across field lines has got to be a lot less than the velocity along field lines, so back to the books and time to remember all the math....
Antenna / waveguides ? Or modulating the HV to the coils ? This has been flogging my noggin for sometime.
Increasing and decreasing the probability of alpha's being at certain radians of the reactor at certain times. Now wouldn't that be nice.
Agreed. They would get obliterated by alphas sooner or later. One might be able to get away with waveguides, if they were coated with boron for a period of time. Somehow i just cant imagine a Yagi inside a Polywell.MSimon wrote:I'd like to see you get a 6 MHz Yagi into one of these jobs. Or a 6 MHz waveguide.
Increasing and decreasing the probability of alpha's being at certain radians of the reactor at certain times. Now wouldn't that be nice.
Purity is Power
Replacing Electron Guns
Thanks David!
I think modulating the coils is what we are stuck with.
I recently read that 13.56 MHz is used to ionize gases in plasma reactors. So with POPS modulation we may get density enhancement and ionization together in one package.
I think modulating the coils is what we are stuck with.
I recently read that 13.56 MHz is used to ionize gases in plasma reactors. So with POPS modulation we may get density enhancement and ionization together in one package.
Engineering is the art of making what you want from what you can get at a profit.
Re: Replacing Electron Guns
Yes Simon 100% ! I got really excited when i realized the other night that we could use the RF for ionization(for the 2 colour start up) to drive POPS as well. I also imagined using quarter wave fuel rods, the tips of these would ionize and introduce our fuel into the reactor core exactly like the GMR video last page. This way we could kill 3 birds with one stone.MSimon wrote:I recently read that 13.56 MHz is used to ionize gases in plasma reactors. So with POPS modulation we may get density enhancement and ionization together in one package.
I have been trying to CAD some of my sketches up and what i really like about all of this is that the numbers are finally starting to join together. The polywell has been, so far to me, a dimensionless dream like entity. Now if we need waveguides at a certain frequency this gives us some hard numbers as a reference point and im already starting to see some solid relationships between different parts of the reactor.
I used to think 13.56 Mhz was a magical number used in plasma generation tied to something like ECR. It just seems like it is more of a industrial standard to minimise RF interference, just like all microwaves are 2.4ghz.
Purity is Power
Yeah. It really struck me that RF may give us the answer to the electron gun problem. i.e how to keep the electron guns out of the beam space. It may be that electron guns may only need to be used during startup.
The deal here is to virtualize as much as possible. It lowers the losses.
POPS is going to be in the 50 KHz to 400 KHz range with full size machines. Ionization should not be a problem even with those frequencies. What will be a problem is 1/4 wave fuel rods. Even at 14 MHz (20 m) you need a 5 m rod - impractical. I kind of like laser bursts on a suitable B11 target suitably placed. At this time I have no suitable answers.
The deal here is to virtualize as much as possible. It lowers the losses.
POPS is going to be in the 50 KHz to 400 KHz range with full size machines. Ionization should not be a problem even with those frequencies. What will be a problem is 1/4 wave fuel rods. Even at 14 MHz (20 m) you need a 5 m rod - impractical. I kind of like laser bursts on a suitable B11 target suitably placed. At this time I have no suitable answers.
Engineering is the art of making what you want from what you can get at a profit.
I guess it all comes down to core frequency. I can still picture a funky VHF test reactor that might work some magic where the numbers line up.MSimon wrote: POPS is going to be in the 50 KHz to 400 KHz range with full size machines. Ionization should not be a problem even with those frequencies. What will be a problem is 1/4 wave fuel rods.
Based on the electro static dificulties of having a 4Mev Electrical Grid at the perimeter for direct conversion. Simon, what is your estimation of the overal diameter for a net power machine ?
Purity is Power
I ran a cross a reference to diamagnetic field in Krall and Trivelpiece yesterday. It is in a section of text about single fluid plasma models where the fluid is all electrons. The model is pure theory, but relates to some of the "angular momentum" comments I've seen some of the papers that are off shoots of polywell and similar fusion ideas.
If you take a uniform B field and put a tube of electrons on it with uniform density across the diameter of the tube, then you can look at the rotational velocity of the electrons as a single value - the cyclotron frequency. That rotation is a current which creates a diamagnetic field - it is bucking the external field. While they comment on it, they also say that for small enough currents it does not disrupt the flow of the tube.
I think Bussard is using an MHD type single fluid model with the assumption that it is slightly negative, so there are more electrons in the mix. The over all plasma looks like a pure electron fluid, but the density is low, and the mass is high. For rough estimiates it is a perfectly valid way to look at things.
I also got a chance to review a lot of the math I've been doing and compare it to the single fluid model. The main problem I've had so far is knowing I'm not including the electron reaction to the external magnetic field and wondering if purposefully ignoring the internal magnetic field is correct. The two are tied together - in the process of ignoring the diamagnetic field (electron fluid current generated field) I also ignored the external field.
So in a sense, the electron_fluid.c code isn't wrong for a MaGrid charged up - it is definitly wrong for what the Polywell is supposed to be. I'll be grinding on that for a while yet.
As for the antennas - take a look at Fractal Antennas. You can get a lot of antenna into a pretty small place even for large wave lengths. This is RF design and electromagnetic field theory on steroids - it really is a ton of fun!
For a power plant we can use any frequency we want - we just have to make sure we are shielded properly to the outside world (and safe for the plant workers as well). If we can pick off the shelf parts that's great, but I don't think the design should be held to that.
If you take a uniform B field and put a tube of electrons on it with uniform density across the diameter of the tube, then you can look at the rotational velocity of the electrons as a single value - the cyclotron frequency. That rotation is a current which creates a diamagnetic field - it is bucking the external field. While they comment on it, they also say that for small enough currents it does not disrupt the flow of the tube.
I think Bussard is using an MHD type single fluid model with the assumption that it is slightly negative, so there are more electrons in the mix. The over all plasma looks like a pure electron fluid, but the density is low, and the mass is high. For rough estimiates it is a perfectly valid way to look at things.
I also got a chance to review a lot of the math I've been doing and compare it to the single fluid model. The main problem I've had so far is knowing I'm not including the electron reaction to the external magnetic field and wondering if purposefully ignoring the internal magnetic field is correct. The two are tied together - in the process of ignoring the diamagnetic field (electron fluid current generated field) I also ignored the external field.
So in a sense, the electron_fluid.c code isn't wrong for a MaGrid charged up - it is definitly wrong for what the Polywell is supposed to be. I'll be grinding on that for a while yet.
As for the antennas - take a look at Fractal Antennas. You can get a lot of antenna into a pretty small place even for large wave lengths. This is RF design and electromagnetic field theory on steroids - it really is a ton of fun!
For a power plant we can use any frequency we want - we just have to make sure we are shielded properly to the outside world (and safe for the plant workers as well). If we can pick off the shelf parts that's great, but I don't think the design should be held to that.
The models and the underlying assumptions are maddeningly variable. I was re-reading Nevins early this morning (the wife had to get up before the crack of dawn for a run), and I ran into this:
The Wikipedia entry (linked above) says the theorem "describes the increase in the entropy of an ideal gas". You could call the returning ions a lot of things, but it's not clear that an "ideal gas" is one of them.Ion-ion collisions are an obvious mechanism for reducing the ion anisotropy. It follows from the Boltzmann H theorem that ion-ion collisions will drive the system to an equilibrium ...
The frequencies, like some of the physical ratios, are predetermined. POPS is fixed by drive voltage, ion mass, and reactor size.For a power plant we can use any frequency we want - we just have to make sure we are shielded properly to the outside world (and safe for the plant workers as well). If we can pick off the shelf parts that's great, but I don't think the design should be held to that.
The fractal idea could reduce size. I doubt the reduction at 400 KHz is going to be enough to matter.
Theses days, if you can describe it with G codes, it is off the shelf. Any thing made with a PC board is "custom" off the shelf.
Engineering is the art of making what you want from what you can get at a profit.
No kidding!! I'm amazed at what you can do over the net even. Some of these companies give you the software to create a model and they include all the machines that can make it along with the price and accuracy. It's flabbergasting!These days, if you can describe it with G codes, it is off the shelf.
I've been pounding thru math and physics and boy is it fun. I started from the Lagrangian and derived a whole lot from scratch. It's beautiful modeling, it will be interesting to see if it even comes close to anything realistic. I'll try to type it up over the next few days when I think I've got it close to right.
Heh. Yeah, the H-thereom is pretty coarse. The longstanding critique of "not necessarily valid for large perturbations" and "ignores many-body effects in the potential energy" are also in the wiki. I also keep thinking of the MIT beam-bunching findings.You could call the returning ions a lot of things, but it's not clear that an "ideal gas" is one of them.
The Singularity is near!Some of these companies give you the software to create a model and they include all the machines that can make it along with the price and accuracy.
I hope I'm not heading for any singularities - I think it'll hurt!
I posted another math pdf describing how the particle distribution function is modified by the magnetic field. I've never seen plasmas attacked this way before, so I suspect it is much more difficult than it looks. Sure is fun physics though!
I posted another math pdf describing how the particle distribution function is modified by the magnetic field. I've never seen plasmas attacked this way before, so I suspect it is much more difficult than it looks. Sure is fun physics though!
The physics is really interesting. The math is amazing. I actually found analytical solutions to integrals over velocity, at least at time=0. And it's all because I just started from scratch.
I think I can add in radiation terms and still have a fluid description, but it means going back a few steps in how particle distributions are derived. Starting with un-solvable formulas will at least tell me which assumptions are being made. It may not help with politics, but it should be clear how the physics came about.
I think a "classical physics" approach is perfectly fine for the Polywell. The only place we need a quantum description is in the center where fusion takes place, and a "classical nuclear physics" description should work just fine as well. A relativistic description of electron velocities might be important if we get energies over 200kV. That would definitely be a pain.
I think I can add in radiation terms and still have a fluid description, but it means going back a few steps in how particle distributions are derived. Starting with un-solvable formulas will at least tell me which assumptions are being made. It may not help with politics, but it should be clear how the physics came about.
I think a "classical physics" approach is perfectly fine for the Polywell. The only place we need a quantum description is in the center where fusion takes place, and a "classical nuclear physics" description should work just fine as well. A relativistic description of electron velocities might be important if we get energies over 200kV. That would definitely be a pain.