MSimon wrote: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.
Simon, would be true if at a lower energy level (which is a BIG Guess). At a high energy level and when the ion density is far lower than the electon density (again a guesstimate do not have the numbers or the math), i guess before the ion drags any electron there would be collisions that destroy this "drag".
The idea is that at a very high energy level and at a reasonable density, we would have the electrostatic attraction effect which causes the drag you mentioned to be nullified by the collisions that are happening. i.e. Fdrag <<< Fcollisions, because Nelectron >> Nion (density is far lower; large ion density destroys the well) and Eelectron >>> 1KeV; Eion >> 1KeV (because of the well). I assume that the fluid should have uniform viscosity, i.e. the plasma flows can be modeled forgetting the electrostatic interaction between the ions and the electrons.
Next step is to see if I can actually compute anything from it. That I found a reference to Krall using the magnetic potential in a side note lets me think this isn't that far off. The trick is that it only covers the intial set up, following things over time is going to be very difficult.
Nelectron >> Nion (density is far lower; large ion density destroys the well) and Eelectron >>> 1KeV; Eion >> 1KeV (because of the well). I assume that the fluid should have uniform viscosity, i.e. the plasma flows can be modeled forgetting the electrostatic interaction between the ions and the electrons.
A couple of points:
Nelectron >> Nion - I do not believe that is true. At least if you accept the quasi neutrality claim ie (Nelectron - Nion)/Nelectron ~= 1E-6
Also it appears that the ions tend to self oscillate coherently (all beams synchronized to reach the core at the same time). I'm not sure a purely fluid dynamical model can get that. I think you need PIC for that.
A new approach to modeling partially collisional plasmas that provides a smooth transition from the fluid (Coulomb collision dominated) to the fully kinetic PIC (collisionless) limit is presented. In addition to the usual quantities of mass, charge, and velocity, each particle carries an isotropic Maxwellian velocity distribution. Higher resolution of velocity space is achieved by generating more particles using a procedure that preserves the first four velocity moments. This velocity space fragmentation is essential for capturing non-Maxwellian plasma behavior. The model developed here allows the efficient simulation of partially collisional plasmas by reducing both the number of particle pairings required per time step and the number of particles needed to retain non-Maxwellian plasma behavior. The method produces reasonable results when the time step is large relative to the collision frequencies and works in the limit of one particle per species per cell. Particle merging can be exploited to control the number of particles in a natural way. The collision process is fully three-dimensional and conserves energy and momentum exactly. Results from 3v and 1d3v simulations are presented and compared with previous multi-fluid and fully kinetic PIC simulations.
The mesh also introduces a periodicity in the potential which results in an unphysical coupling between the field and particles. This may be just a minor nuisance or it may result in a situation in which the particles keep on acquiring more and more energy from the field, ultimately leading to a meaningless simulation. The storage requirements for a three dimensional electromagnetic particle simulation can just be met by present day desktops computers, but the time needed to follow the particles for, say, many hundreds of plasma periods would be of the order of several weeks in a typical time sharing computer installation.
Engineering is the art of making what you want from what you can get at a profit.
Hmm. (Why is there not a 'beard-stroke' emoticon? I really need that!)
That new method sounds good. I bet it's harder to implement though; probably more coding. I wonder how much we can find out ~ it just by mining the internet?
MSimon wrote:Nelectron >> Nion - I do not believe that is true. At least if you accept the quasi neutrality claim ie (Nelectron - Nion)/Nelectron ~= 1E-6
Even with p-B11? A neutral pure boron plasma would have five times as many electrons as ions, and a neutral boron/proton plasma in equal numbers would have three times as many electrons as ions.
In terms of pure number density that's true, but in terms of charge density you have the same amount of charge. So there is 5 times as much charge at a point for Boron, you can track z*N and get the balance.
Mass density is the kicker. The ions don't respond to the high frequencies the way electrons do, so in some sense you can figure out the ion trajectories independently.
As a fluid model, I don't think it matters either way, we can ignore the individual particles
and just look at the net overall behaviour.
The paper Simon quotes is quite interesting. Their model is about velocity space, not physical space (3v vs 3d). And they assume uniform velocity distribution per particle. That's exactly what I assume in my derivation.
It would be really interesting to get the data on the present Polywell experiments and
find out what the actual spatial distribution is. A better imprical model combined with good
physics can help us a lot.
Sure sounds like that AMD/ATI Firestream would be useful to a lot of plasma people.
Oh yeah - I agree with that beard stroke emoticon!!
drmike: Here is another thought : for charge neutrality Nions approx = Nelectrons for D, and Nions = (1/5)Nelectrons.
But boron is 11*1836 times heavier than an electron and a D is some 2*1836 times heavier than an electron... so Columb collisions would completely rock the electron but not so much for an ion.
Now if that means that the ion velocity/lifetime in the same field would be way different than the electron velocity/lifetime ==> for a small time dt can the ions be treated as stationary and the electrons moving rapidly around them bouncing off the ions, whereas the ions take it slowly and the movements can be captured in a lower resolution timescale.
I dont know if this is what Simon and others meant here.
I am still reading up on a lot of my undergrad physics (i am a semiconductor EE grad , and it means i am way different from the vacuum tube EE grad ) so bear with me
MSimon wrote:Nelectron >> Nion - I do not believe that is true. At least if you accept the quasi neutrality claim ie (Nelectron - Nion)/Nelectron ~= 1E-6
Even with p-B11? A neutral pure boron plasma would have five times as many electrons as ions, and a neutral boron/proton plasma in equal numbers would have three times as many electrons as ions.
You are correct. I should have used charges not particles.
Engineering is the art of making what you want from what you can get at a profit.
Edit: AMD either issues a Modified: header on their HTML that's the same as the request time, or else they don't issue one at all, so it's hard to tell how old their SDK registration page is. Interesting to me that they now support Mac OS X for the first time I can remember.
I will be pretty happy with 125 GFLOP double precision at $1000! 15 years ago I was thinking about building that level of processing power for a million dollars. Even if AMD is late on what they thought they could do initially, it will be worth waiting for.
You can think of plasmas in lots of ways. The reason is that there is a lot going on. Each sub component is sort of independent of the others for certain time scales. So you can ignore ion motion totally for very high frequency electron motions, and you can ignore high frequency electron motions for general ion motion, at least for a while.
A friend of mine once related his country of China to a plasma. From the outside, you see things happening slowly. From the inside, you feel all the
tension of individual people pushing and shoving and fighting each other.
No matter what view you take, it is hard to tell what will happen next.
You can think of plasmas in lots of ways. The reason is that there is a lot going on. Each sub component is sort of independent of the others for certain time scales. So you can ignore ion motion totally for very high frequency electron motions, and you can ignore high frequency electron motions for general ion motion, at least for a while.
Would that mean computational savings; like "ionstateupdate()" function can be called say in every 100 calls for "electronstateupdate()" function.
Another way to put it is: the ion motion can updated in simulation after letting it be where it for a time interval t', and counting the vector sum of all columb collision forces in that interval and then update the position with the motion caused by the vector sum of all the electron collisions during t'. That way we can model both the plasmas together.
laksindiaforfusion wrote:
Would that mean computational savings; like "ionstateupdate()" function can be called say in every 100 calls for "electronstateupdate()" function.
Another way to put it is: the ion motion can updated in simulation after letting it be where it for a time interval t', and counting the vector sum of all columb collision forces in that interval and then update the position with the motion caused by the vector sum of all the electron collisions during t'. That way we can model both the plasmas together.
Yes, that would work. It would be a PIC simulation with different update rates. You could do the same thing for the H vs B ions as well, updating the B once every 10 times you update H becuase it has 10 times the mass.
) so bear with me 