Yup, me too. But reading the details is interesting - they all assume a velocity distribution of some kind at each space point, then compute the flow from that assumption.
Argh.
I'm increasingly skeptical this can be modelled in any meaningful way with the processing power available today. It's starting to remind me of the global warming models, none of which predicted our unprecedented temperature drop this year. Too many variables to track.
Not that this has anything directly to do with anything in this thread, but I was just amazed by the resume (PDF) of the principle author of the qd library, David H. Bailey. He's won numerous awards in mathematics, including one for "Algorithm of the Century" for the discovery of the PSLQ algorithm, which itself found a means to calculate arbitrary binary digits of the number pi without first calculating its predecessors, using only a simple polynomial.
Some of these results have profound implications. The pi formula raises questions about the long-held but never proved assumption that pi's digits are random. The Feynman-diagram results suggest unsuspected relationships among formulas associated with fundamental particles.
tonybarry wrote:Tip of the day ... code for clarity, not for speed.
Code for clarity before speed. If you can get speed without losing clarity, go for it.
MSimon wrote:One of the things that makes C code more difficult to read than English is that calls are so expensive. So you get big (often difficult to test) modules instead of small (easy to test) ones.
Judicious use of macros and inline functions can help there. Sloppy use can bloat code size like crazy, but done right they can speed things by avoiding the function call overhead. Depending on the C compiler and target machine, function calls can be made using registers to pass parameters rather than the usual stack, another speed boost. As far as function calls being expensive, that's often as much the underlying hardware as the language. You want fast calls, get a stack based machine.
scareduck wrote:Not that this has anything directly to do with anything in this thread, but I was just amazed by the resume (PDF) of the principle author of the qd library, David H. Bailey. He's won numerous awards in mathematics, including one for "Algorithm of the Century" for the discovery of the PSLQ algorithm, which itself found a means to calculate arbitrary binary digits of the number pi without first calculating its predecessors, using only a simple polynomial.
Some of these results have profound implications. The pi formula raises questions about the long-held but never proved assumption that pi's digits are random. The Feynman-diagram results suggest unsuspected relationships among formulas associated with fundamental particles.
Wow. Just, wow.
That is incredible. I wonder if it has string theory implications.
drmike wrote:What I don't understand yet, is why Bussard put the electron sources at cusps instead of at the face of each coil. Hopefully I can find out with a model!
Hey Mike. This topic was briefly discussed a little while ago. I cant find the exactl link but basically one can inject electrons into coil centres or into the line cusps. The reason WB6 had its electron guns feeding into the line cusp was that it improved the virtual cathode formation. If you look at all the EMC2 experiments the earlier ones all injected electrons via the coil face. I guess after experimenting using different set ups they must of found that the line cusps axis improved virtual cathode formation.
It kind of makes sense when you think about it. If you look at some of Indrek's magnetic field renderings, the way the fields squeeze together as you aproach the coils on the cusp axis could seem to exhibit some sort of focusing mechanism. Your always fighting the Child Langmuir Space Charge Limit to get the electrons into the core, possibly this could improve things. Exactly what factor of improvement the cusp axis has over the coil face is unclear. Whether this improves the rate that one can form a virtual cathode, or simply improves virtual cathode stability is also unclear. Most certainly intelectual property of EMC2.
scareduck wrote:Not that this has anything directly to do with anything in this thread, but I was just amazed by the resume (PDF) of the principle author of the qd library, David H. Bailey. He's won numerous awards in mathematics, including one for "Algorithm of the Century" for the discovery of the PSLQ algorithm, which itself found a means to calculate arbitrary binary digits of the number pi without first calculating its predecessors, using only a simple polynomial.
Wow. Just, wow.
Thanks for the pointers. Reminds me of my BigFloat project of many years ago. Software arbitrary precision for pure math
Keegan wrote:It kind of makes sense when you think about it. If you look at some of Indrek's magnetic field renderings, the way the fields squeeze together as you aproach the coils on the cusp axis could seem to exhibit some sort of focusing mechanism. Your always fighting the Child Langmuir Space Charge Limit to get the electrons into the core, possibly this could improve things. Exactly what factor of improvement the cusp axis has over the coil face is unclear. Whether this improves the rate that one can form a virtual cathode, or simply improves virtual cathode stability is also unclear. Most certainly intelectual property of EMC2.
But the cusps have higher mirror reflection, so less current should enter.
Maybe the electrons follow around and enter the face anyway and you get more simply because putting sources at the face get nothing in on the cusps. It definitely does not make sense to me - more squeeze of field implies better confinement which implies less electron density into the center.
At least I'm getting a good handle on how to model the electron source. I hope to get something "flowing" real soon.
I'm definitly having too much fun. I found a nice formula for evenly spaced charge source areas on the surface of a sphere, their centroids and radial vectors as well. Next step is to track these "phase particles" in a vlasov formula (which means no collisions, just electrodynamics). This is really a very different approach than I've seen in most of the literature, but mostly because this is a really well defined problem in terms of boundary conditions. Should be interesting to see what happens (and just how hard it actually is to compute too.)
I'll write it up once I get into debugging code. I suspect I'll need a break once it stops being "fun" and starts being "work".
Well, the qd library work is not going as well as I had hoped. Even though the package passes its limited tests, the demo program in the accompanying PDF doesn't even compile! I passed a note on to the maintainers, and have yet to hear anything substantive back yet (other than "thanks for the note"). My C++ is a bit rusty and the language continues to evolve since I used it at all (about ten years ago now), so I'm at least learning things. I'm hoping to come up with some patches to get certain functions that will be needed working.
Good luck with it! I've had bad luck in too many cases - where what I wanted to do wasn't part of the design of some package. But if the demo doesn't compile, you really have to wonder if it is worth the effort to fix things. If it's fun, it's worth it! Some times the challenge alone is enough.
Well, I finally gave up doing some of the conversions that should be part of the package last night (assignment in particular from qd_real to dd_real -- just drop down and use the explicit function for that). I started rewriting electron_fluid.c to see what comes out and so far it's all compilation errors but I think it ought to be pretty soon that I can at least get it to compile.
Well... whew! I finally got a version running (it's running right now). Still likely has some lint (in fact I know it does) but there shouldn't be any horrors. No results at the moment -- I expect that will take some fraction of the night -- but this should give us results down to 54 decimal places if I'm correct.
drmike wrote: It definitely does not make sense to me - more squeeze of field implies better confinement which implies less electron density into the center.
I understand. The only way it makes sense is that i have worked in aerospace and know how "illogical" fluid flow is. Convergent ducts accelerate fluid flow. Looking at one of Indrek's renderings it seems the line cusps are a convergant duct.
Congrats scareduck! It will be interesting to see what you get.
For fluid flow, using MHD models is useful up to a point. For the start up condition of pure electrons, an MHD model doesn't apply. I do think we can model the start up condition fairly easily with brute force though, it really is a major advantage that the polywell has over other systems. And the fun part is that I get to pull out my books and look at conformal mapping to get the E field off the electron sources. I think I should be able to reduce a 3D problem down to 1D, then use the mapping to figure out what it should be in 3D.
Once I know where the electron blobs are, adding ionization and scattering and making things more fluid will make sense - especially secondaries generated by collisions. At that point you've got both ions and electrons and an MHD type model should work.
The flow field of a nozzle comes from physcial interactions that are "straight". The flow field from a cusp is going to be really weird because the physical interactions are cross products. Good diagnositics are going to be hard to build, but I think they will be mighty useful. It would be great to "see" the flow as it happens!
Kind of a newbie here. I wrote a few thoughts about the Polywell concept on my newly created weblog. I spoke some about modeling. In reality, this part is basically a summary of what I have been learning in an advanced thermodynamics course.
