Well, I take it back. A fully self consistent set of equations that includes radiation is impossible to set up with initial conditions, let alone attempt to solve! The reason is that the particles all have retarded fields associated with them, and figuring out where everything came from to start with is simply insane to attempt to model.
For a non-relativistic plasma, we can safely assume that every particle's field fills the whole volume of the reactor and is just centered on the particle. Maxwell's equations work just fine in determining radiation of all kinds - interparticle to whole system waves.
Time to grind out some more code. I'll be using a lot of ideas everybody has given me to compute the magnetic vector potential - should be pretty quick this time. It should also be an "interesting" result.
Virtual Polywell
I put up yet another file - this one computes the vector potential. I used a plotting program to catch some obvious bugs, but it still doesn't seem quit right at zero angles on the z axis. It should be exactly zero for all radius values, but isn't, so I think there are stil minor bugs.
Next step is to use the vector potential to find the electron distribution for an arbitrary radial distribution, and then feed that to the fluid following code. It should be interesting because to start with there won't be any electron current. But as it explodes, it will create its own B field which should warp things quite a bit. In order to do any calculations at all, I may have to just assume everything stays Maxwellian. For electrons, that's not a bad assumption really, most experiments have that behavior. But polywell's aren't your average plasma experiment either.
Thanks to everyone who gave me hints from previous runs - it definitly helped with this one!
[Edit: Found and fixed a couple more bugs, new upload done. Next step is to see how magnetic potential affects the previous integrals over electrostatic potential.]
Next step is to use the vector potential to find the electron distribution for an arbitrary radial distribution, and then feed that to the fluid following code. It should be interesting because to start with there won't be any electron current. But as it explodes, it will create its own B field which should warp things quite a bit. In order to do any calculations at all, I may have to just assume everything stays Maxwellian. For electrons, that's not a bad assumption really, most experiments have that behavior. But polywell's aren't your average plasma experiment either.
Thanks to everyone who gave me hints from previous runs - it definitly helped with this one!
[Edit: Found and fixed a couple more bugs, new upload done. Next step is to see how magnetic potential affects the previous integrals over electrostatic potential.]
Got a clue while shoveling water today (yeesh - freezing rain turning to slush/ice is a pain in the back!!) Since I'm working with potentials, I can shift things by constants and it won't matter - the fields are found from derivatives anyway. So it's a matter of picking the right constants. I think....
Just having a place to "think out loud" is a great help. Thanks for setting up this discussion board, it's a lot of fun to read.
One of things my kids don't understand about "science" is that it takes 100 mistakes before you find the 1 right answer. Floundering around in what appear to be good ideas and then turn out to be dead ends is the normal process. Having a place to flounder around in public is what makes the net so cool to me.
I'm definitely having fun - and I'm definitely making mistakes
But I think eventually we'll get some good ideas on how prove the Polywell is a go (or no go as the case may be). I'm certainly hoping it can be proven to work!
Thanks for being here.
One of things my kids don't understand about "science" is that it takes 100 mistakes before you find the 1 right answer. Floundering around in what appear to be good ideas and then turn out to be dead ends is the normal process. Having a place to flounder around in public is what makes the net so cool to me.
I'm definitely having fun - and I'm definitely making mistakes
But I think eventually we'll get some good ideas on how prove the Polywell is a go (or no go as the case may be). I'm certainly hoping it can be proven to work!Thanks for being here.
long url
Many experiments carried out in the last decade have confirmed
long-standing claims that plasma confinement in toroidal
devices strongly depends on the electric and magnetic fields
at the plasma edge [1–5]. The former fields are related
to the observed anomalous particle transport at the plasma
edge, which has been shown to be largely controlled by lowfrequency
electrostatic drift waves [2]. The steep density and
temperature gradients existing in the plasma edge give rise to
diamagnetic currents across the confining toroidal magnetic
field so generating drift waves propagating in the poloidal
direction.
Engineering is the art of making what you want from what you can get at a profit.
That all makes sense to me now. So there's the state of the art - it is a 2D and crude approximation that tries to see how edge effects blow everything apart in a tokamak.
The polywell is going to have the same problems on the edge, but it has a major advantage with the electrostatic field being helpful compared to the tokamak. I think the real trick will be attempting to make the electron/plasma currents radial with little rotation too. That will be difficult near the coils. But again, that's an advantage over the tokamaks - the polywell can tolerate chaotic motion in the system so long as there is a general compression wave often enough to generate net power.
Plasma physics is challenging. That's why so many people like it.
The polywell is going to have the same problems on the edge, but it has a major advantage with the electrostatic field being helpful compared to the tokamak. I think the real trick will be attempting to make the electron/plasma currents radial with little rotation too. That will be difficult near the coils. But again, that's an advantage over the tokamaks - the polywell can tolerate chaotic motion in the system so long as there is a general compression wave often enough to generate net power.
Plasma physics is challenging. That's why so many people like it.
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laksindiaforfusion
- Posts: 22
- Joined: Sat Feb 16, 2008 9:48 pm
- Contact:
Dumb Suggestion:
Dr. Mike:
I appreciate how much you have progressed in this area. I have not read you work in the entirity (i have been around this site only for 2 days), so here isa rather dumb suggestion:
Let us first define the ionic motion in the electron concentration, now if they concentrate at the center and form a virtual anode as per Dr. Bussard, then we can move forward and define the properties of the electron concentration.We would also need to look at whether the conditions at the virtual anode are suffecient for the ions to fuse.
Doing that hat would give us an idea of the pressure that the electrons would exert on the magnetic field. I assume that the motion of the electrons would cause a magnetic field which would neutralize the magnetic field caused by the polywell magnets. This creates a diamagnetic region inside the electron concentration. From there we can get the dimensions needed for the polywell and perform simulations with your code.
I can work on the problem of an ion moving thru and electron potential well. I am reading up on some of the physics and i assume we can get some rough approximations.
Is this a sane approach?
I appreciate how much you have progressed in this area. I have not read you work in the entirity (i have been around this site only for 2 days), so here isa rather dumb suggestion:
Let us first define the ionic motion in the electron concentration, now if they concentrate at the center and form a virtual anode as per Dr. Bussard, then we can move forward and define the properties of the electron concentration.We would also need to look at whether the conditions at the virtual anode are suffecient for the ions to fuse.
Doing that hat would give us an idea of the pressure that the electrons would exert on the magnetic field. I assume that the motion of the electrons would cause a magnetic field which would neutralize the magnetic field caused by the polywell magnets. This creates a diamagnetic region inside the electron concentration. From there we can get the dimensions needed for the polywell and perform simulations with your code.
I can work on the problem of an ion moving thru and electron potential well. I am reading up on some of the physics and i assume we can get some rough approximations.
Is this a sane approach?
The believer's burden and a skeptics purpose
I believe we will need beam forming grids in the "dead space".drmike wrote:That all makes sense to me now. So there's the state of the art - it is a 2D and crude approximation that tries to see how edge effects blow everything apart in a tokamak.
The polywell is going to have the same problems on the edge, but it has a major advantage with the electrostatic field being helpful compared to the tokamak. I think the real trick will be attempting to make the electron/plasma currents radial with little rotation too. That will be difficult near the coils. But again, that's an advantage over the tokamaks - the polywell can tolerate chaotic motion in the system so long as there is a general compression wave often enough to generate net power.
Plasma physics is challenging. That's why so many people like it.
:D
BTW plasma physics is a lot like post modernism. There are no wrong answers. At least in theory.
Engineering is the art of making what you want from what you can get at a profit.
Maybe. If the dynamics are set up right, we may be able to haveMSimon wrote: I believe we will need beam forming grids in the "dead space".
virtual grids form and disolve exactly when they need to.
Ha! Don't tell my wife that.BTW plasma physics is a lot like post modernism. There are no wrong answers. At least in theory.
She can't define "art", but she knows itwhen she sees it! And some people will always say "that's not right" because the approximations are different than what they assume.
It's more like all the answers are wrong. We gotta build it and see what reality says!
Re: Dumb Suggestion:
I'm attacking from the other direction. Bussard said that there is a slight negative balance to the system, so I am trying to see how a pure electron distribution behaves. Once I've got that, I'll start attacking the ion distribution.laksindiaforfusion wrote:Dr. Mike:
I appreciate how much you have progressed in this area. I have not read you work in the entirity (i have been around this site only for 2 days), so here isa rather dumb suggestion:
Let us first define the ionic motion in the electron concentration, now if they concentrate at the center and form a virtual anode as per Dr. Bussard, then we can move forward and define the properties of the electron concentration.We would also need to look at whether the conditions at the virtual anode are suffecient for the ions to fuse.
The main reason for doing electrons first is that they are light and fast. It is more sensible to model them as a fluid, and then add the ions later. I will probably keep the ions as fluid too, and only look at individual reactions once the global picture makes sense.
Pressure is one way to model it. I'm not using an MHD type model, I'm looking at particle distribution functions and tracking each species as its own fluid. Partly because it is more complete, and partly because it is more challenging. But we will have boron, hydrogen and electrons all mixing at high speed. Making sense of what is going on is non-trivial.Doing that hat would give us an idea of the pressure that the electrons would exert on the magnetic field. I assume that the motion of the electrons would cause a magnetic field which would neutralize the magnetic field caused by the polywell magnets. This creates a diamagnetic region inside the electron concentration. From there we can get the dimensions needed for the polywell and perform simulations with your code.
I think looking at an MHD model makes a lot of sense. The idea behind the MHD model is that the whole plasma acts as a unit. You have only one fluid to deal with and it gives you bulk properties. It is definitely a good place to start.I can work on the problem of an ion moving thru and electron potential well. I am reading up on some of the physics and i assume we can get some rough approximations.
Is this a sane approach?
One of the difficulties with the fluid approach is that some think that ions dragging electrons around is an important phenomenon.
The interfluid viscosity is going to be greatest when the particle velocity of the ions matches that of the electrons.
How do you decide in the fluid model when the intermixed fluids stop acting as a unit?
We are very constrained right now by having too many possibilities. We need experiments to restrict our choices.
The interfluid viscosity is going to be greatest when the particle velocity of the ions matches that of the electrons.
How do you decide in the fluid model when the intermixed fluids stop acting as a unit?
We are very constrained right now by having too many possibilities. We need experiments to restrict our choices.
Engineering is the art of making what you want from what you can get at a profit.
Re: Dumb Suggestion:
IIRC Bussard's calculations were based on an MHD model.drmike wrote:I'm not using an MHD type model, [...]
I think looking at an MHD model makes a lot of sense. The idea behind the MHD model is that the whole plasma acts as a unit. You have only one fluid to deal with and it gives you bulk properties. It is definitely a good place to start.
Re: Dumb Suggestion:
Yes, I think so too. Certainly seems like a single fluid model from what I read.scareduck wrote: IIRC Bussard's calculations were based on an MHD model.