WB-8 article

[happyjack27]

Rick on simulation challenges:

3-D Particle-in-cell is extremely expensive. Resolution goes like (N)**.5 where N is the number of particles. You have multiple timescales and multiple spatial scales to resolve. This means supercomputers.

N^(0.5)??? if that's the computational time complexity, then that's fantastic!! a brute-force all pairs n-body sim's comp time is roughly N^2, which is of course MUCH MUCH worse.

and then there are methods of approximation like having 1 simulation particle represent thousands of real particles, or just using a simulated tiny wiffleball, and/or really high mag fields, etc.

as far as "super-computers" go, well, there's a law in computer science, and it goes like this: _algorithm triumps hardware_. e.g. if an N^2 algorithm can do 100 particles at a rate of 1 picosecond/second with $x of hardware, to sim 200 particles at that rate would cost $x*(200^2-100^2)/(100^2). which, needless to say, would be _A LOT_ of money, quite regardless of what "x" is.

now if instead you can find, say, an N*log(N) algorithm, well, what an N^2 algorithm can do on a machine that costs $N^2, an N*log(N) algorithm can do on a machine that only costs $N*log(N), and when N is very large (which it usually is), the payoff ratios can become downright astronomical.

so when i hear "that would take a super-computer!" my immediate reaction is: "...or a normal desktop computer and a bit of cleverness."

[happyjack27]

.....Then throw in considerations of the electrons being dragged along to a modest extent by the ions, the effects of resultant complex potential wells with virtual central anode formation, etc, and the dynamics become increasing complicated to model.

or you can simply numerically _simulate_ it instead of trying to mathematically _model_ it, i.e. use an high temporal-resolution n-body langrangian method that just uses the basic em-force equations.

then all these effects are included for free.

as per my simulation runs in the theory forum.

[D Tibbets]

Direct calculation would, I guess, simplify (and eliminate erroneous tangents). I have very little mathmatical and programing skills to appreciate the significance of various approaches.
Several questions though, how far have you gone with your equipment and skills? Modeling on scales in what proportion to a real machines? 1 part in a billion, one part in a ziptillion? Are you confident that your alogrhythms are accounting for electrostatic (or perhaps I should say electrodynamic) and magnetic interactions in a spherical geometry(or at least a two dimensional disk geometry- which is what I believe Joel Rogers depended on)?
I think I recall that you are achieving > 1 Teraflops with your graphic card driven setup. How optimistic are you that you can use alogrhythms to speed up the runs at accecptable precision and accuracy to get some standard of reliability? For that matter, what is the required reliability limits to make useful predictions?
What are your quality control procedures. Do you depend on basic formulas and assumptions, then let it fly?
With the impressive but task limited equipment, can you use short runs from some set beginning conditions, check the results, then do another run and take a stepwise iterative approach to building up a picture while avoiding erroneous tangents that might build up with longer runs?

Have you attempted target directed simulations? IE: take claimed results and manipulated the simulation to achieve those results, and then try to defend those manipulations?
Claimed results, like annealing, ion containment lifetimes greater than time to ion fusion lifetimes, cusp confinement electron lifetimes (50-60 transits), Wiffleball effect, electron recirculation claims, etc?

Finally, what would it take equipment wise to utilize you code if you wish to share it? If you worked out some type of iterative approach or internet shared collective approach which I have heard would be difficult for this kind of problem) could you farm out subsets of the problem?

In any case, what you have already presented is impressive and appreciated.

Dan Tibbets