I'll bring my fusor down to Raliegh, NC for the North American Science Fiction convention (NASFic) for the August 6-8 weekend. My fusion talk is presently scheduled for 11 AM Saturday morning.
http://www.reconstructionsf.org/
I'm tweaking my usual talk to cover Amateur Fusion and Polywell Fusion, with the question of how possible it is for amateurs to go beyond fusors and on to Polywells. Yes, the publicity Prometheus got recently did inspire this, but I've been trying to get the guys at fusor.net interested in trying since about 2007.
Here's a question for you math whiz types. The t-shirt I will be wearing is one I just ordered this morning with my custom art. It starts "What part of " and a bunch of equations follow "Don't you understand?" The first equation is Poisson's, del curl = f, and the diffeq 3-D version that looks much more impressive. When I was in college in EE, we studied partial differential equations in the Sophomore year, and the Juniors got into Laplace transforms (and I presume Laplacian operators like del). I'm not sure when Physics majors tackled this level of calculus, but I presume their development was similar, maybe a little earlier.
So, at what level are these topics studied today? Would you guys say that undergrads with a strong calculus background are equipped to tackle the math of electrodynamic fusion machines? I'm presuming they only need to follow what is in existing publications, not derive it all from scratch.
Tom Ligon speaking at NASFic ...
Yep. Strong calculus should be fine. Maxwell's obviously. The nuke fizz (fusion collision cross sections etc) will need some stats exposure..
Throw them in the deep end and the young ones swim fine I find, just keep a life buoy handy. Some thrive on the challenge ... the gee whiz and dangerously unknown territory is what drives the best of them.
Throw them in the deep end and the young ones swim fine I find, just keep a life buoy handy. Some thrive on the challenge ... the gee whiz and dangerously unknown territory is what drives the best of them.
I only went as far as Calc I (business school), and my stats exposure was from PoliSci. In terms of things I've run into that required some study to get my head around, I would tend to agree with Icarus that the stats exposure is especially important. I think, as Bussard said, the big issue is vacuum tube physics, which apparently no one studies anymore.
Of course, Polywell is strictly hobby-level for me, and I haven't done any calc since grad school, and most of that was just for tutoring undergrads. So what do I know.
Of course, Polywell is strictly hobby-level for me, and I haven't done any calc since grad school, and most of that was just for tutoring undergrads. So what do I know.
n*kBolt*Te = B**2/(2*mu0) and B^.25 loss scaling? Or not so much? Hopefully we'll know soon...
My calculus is not too bad (I can read it but solutions are much harder) and I recently learned curl from reading Feynman "Lectures". It is amazing how little math you actually need to be a tolerably good engineer.WizWom wrote:We covered del, curl, and multivariant calculus in Calc III last semester. Differential equations will cover that bit in more depth, but we touched on them in Physics II for deriving the repercussions of Einsteins's special theory of relativity.
I was just reading a "solution" to the capacitor charging problem from a rectified AC source that assumed perfect sine waves (sin, cos, tan, cot, etc.). Perfect transformers, and perfectly resistive loads. Well of course the solutions are exact to umpteen decimal places.
In the real world waves are not sine, rectifiers are not perfect, loads are not resistive (power converters can have negative resistance), and all parasitics are not accounted for. And you only need a solution good to 10% or so in any case: the tolerance of the capacitors.
For all the above reasons algebraic and trig approximations are good enough for most things. MathCad or MathWorks can handle the rest. Or you can time slice ala Pspice. Or hire a mathematician.
Then you iron out the kinks in the lab. Just like we are doing for Polywell.
I think the design equations that will be useful for Polywell are more likely to come out of the lab than out of theory. Still the exercise is useful. If nothing else those doing it will be warmed up so that when we actually know something the work will be familiar.
Engineering is the art of making what you want from what you can get at a profit.
Simon,
There's a lot to be said for finite element modeling, too. Simpler math but a whole lot of it. And it is easier to adapt to complex topologies.
Yes, most engineers spend 99% or more of their calculating time adding, subtracting, multiplying, and dividing, after setting up the equations to their satisfaction with a bit of simple high-school algebra.
But I would like to refine my calculus skills to the point that I can easily follow the theory papers. I think I understand the principles tolerably well, but Engineering Technologists went lighter on the math in our Junior year, and once powerful tools are compressed to single-operator shorthand, following the derivations is a bit harder than it would be if we didn't have to teach ourselves a year of calculus.
"Given del curl equals f, it should be intuitively obvious that ...." (explosion of symbols floods the page).
While at EMC2, the Physics PhDs could handle the math, and I was free to figure out how to control the output of a bank of thirty RV batteries in series, apply filtering to satisfy the Nyquist criterion to a data acquisition system, protect delicate analog inputs from the spikes that plague a high voltage lab, design and build a nanoamp electrometer amplifier that could float at umpteen thousand volts and communicate its data via fiber optics, couple microwave oven power into a vacuum chamber to produce ECR, troubleshoot IGBT switching power supplies, and myriad other things the physicists were totally clueless about.
But now that my job seems to be to explain Polywells to the world, I'm embarrassed at all the math I never learned.
There's a lot to be said for finite element modeling, too. Simpler math but a whole lot of it. And it is easier to adapt to complex topologies.
Yes, most engineers spend 99% or more of their calculating time adding, subtracting, multiplying, and dividing, after setting up the equations to their satisfaction with a bit of simple high-school algebra.
But I would like to refine my calculus skills to the point that I can easily follow the theory papers. I think I understand the principles tolerably well, but Engineering Technologists went lighter on the math in our Junior year, and once powerful tools are compressed to single-operator shorthand, following the derivations is a bit harder than it would be if we didn't have to teach ourselves a year of calculus.
"Given del curl equals f, it should be intuitively obvious that ...." (explosion of symbols floods the page).
While at EMC2, the Physics PhDs could handle the math, and I was free to figure out how to control the output of a bank of thirty RV batteries in series, apply filtering to satisfy the Nyquist criterion to a data acquisition system, protect delicate analog inputs from the spikes that plague a high voltage lab, design and build a nanoamp electrometer amplifier that could float at umpteen thousand volts and communicate its data via fiber optics, couple microwave oven power into a vacuum chamber to produce ECR, troubleshoot IGBT switching power supplies, and myriad other things the physicists were totally clueless about.
But now that my job seems to be to explain Polywells to the world, I'm embarrassed at all the math I never learned.
Regarding accuracy of ten percent, for estimation purposes even twenty percent is fine.
While Dr. Bussard was perfectly capable of the high-end calculus and theory, he developed the theory in partnership with Dr. Krall. Dr. Krall confessed to me that he was scared of labs, whereas Dr. Bussard was a great bridge between theory and application.
The hairy-bear numbercrunching ws handled by the computer codes. Once those handled the complex modeling, out popped some relatively simple relationships for several key "gains", such as Gwb (wiffleball gain). So handling a particular case or an idea for tweaking the theory was reduced to a remarkable session at a whiteboard or chalkboard. Doc would stand there with the Plasma Formulary in one hand, chalk in the other, pieces of calcium carbonate flying every which-way, numbers going up to one or two decimal places. It was adding, subtracting, multiplying, and dividing, occasionally a square or square root. All the calculating was done in his head, and the result was typically within ten percent of what you would get following up with a calculator. Occasionally the result would be off by a factor of three (which I learned was failure to put pi in to one of the irksome conversions necessitated by switching from CGS to MKS units, something physicists of a certain age seem to thrive on.
While Dr. Bussard was perfectly capable of the high-end calculus and theory, he developed the theory in partnership with Dr. Krall. Dr. Krall confessed to me that he was scared of labs, whereas Dr. Bussard was a great bridge between theory and application.
The hairy-bear numbercrunching ws handled by the computer codes. Once those handled the complex modeling, out popped some relatively simple relationships for several key "gains", such as Gwb (wiffleball gain). So handling a particular case or an idea for tweaking the theory was reduced to a remarkable session at a whiteboard or chalkboard. Doc would stand there with the Plasma Formulary in one hand, chalk in the other, pieces of calcium carbonate flying every which-way, numbers going up to one or two decimal places. It was adding, subtracting, multiplying, and dividing, occasionally a square or square root. All the calculating was done in his head, and the result was typically within ten percent of what you would get following up with a calculator. Occasionally the result would be off by a factor of three (which I learned was failure to put pi in to one of the irksome conversions necessitated by switching from CGS to MKS units, something physicists of a certain age seem to thrive on.
I don't know if they are still using microwave ovens, but there's a lot to be said for a kW of microwave power for $40.
When I was there we had bought a very expensive tunable TWT system, intended to run to higher frequencies. The problem I had with ECR in WB3 was the 2.45 GHz topology in that machine was pretty deep inside the cage. You really want the ECR to happen close to the inner MaGrid surface to take full advantage of the volume. As you go to higher and higher magnetic field strength, you need correspondingly higher frequency microwaves to hit the resonance where you need it. I never saw that unit actually put to use, though.
So instead of $40 for 1 kW, you wind up with $70,000 for 200 W. And then you are scared to use it because you might break it.
They may very well be using ECR, and another possibility is hitting the ions with ICR, which allows lower frequencies.
ECR did show up visibly as a bright layer, but it might actually not be necessary to excite it particularly hard. At a given magnetic field strength, energetic electrons will automatically gyrate at the ECR frequency there. If you want to enhance it at a particular frequency, set up the geometry to encourage that frequency. That's how a magnetron works ... ECR in a tuned cavity. A Polywell is a magnetron of sorts.
I strongly suspect there is some density measurement going on by beaming lower-powered microwave chords across the chamber. WB7.1 would seem to have sufficient budget for diagnostics of that sophistication.
When I was there we had bought a very expensive tunable TWT system, intended to run to higher frequencies. The problem I had with ECR in WB3 was the 2.45 GHz topology in that machine was pretty deep inside the cage. You really want the ECR to happen close to the inner MaGrid surface to take full advantage of the volume. As you go to higher and higher magnetic field strength, you need correspondingly higher frequency microwaves to hit the resonance where you need it. I never saw that unit actually put to use, though.
So instead of $40 for 1 kW, you wind up with $70,000 for 200 W. And then you are scared to use it because you might break it.
They may very well be using ECR, and another possibility is hitting the ions with ICR, which allows lower frequencies.
ECR did show up visibly as a bright layer, but it might actually not be necessary to excite it particularly hard. At a given magnetic field strength, energetic electrons will automatically gyrate at the ECR frequency there. If you want to enhance it at a particular frequency, set up the geometry to encourage that frequency. That's how a magnetron works ... ECR in a tuned cavity. A Polywell is a magnetron of sorts.
I strongly suspect there is some density measurement going on by beaming lower-powered microwave chords across the chamber. WB7.1 would seem to have sufficient budget for diagnostics of that sophistication.
I didn't know what ECR & ICR were, so wikipedia helped out.
ECR = Electron cyclotron resonance
definition pretty much the same definition as ECR.
Edit: spulling
ECR = Electron cyclotron resonance
ICR = Ion cyclotron resonanceElectron cyclotron resonance is a phenomenon observed both in plasma physics and condensed matter physics. An electron in a static and uniform magnetic field will move in a circle due to the Lorentz force. The circular motion may be superimposed with a uniform axial motion, resulting in a helix, or with a uniform motion perpendicular to the field, e.g., in the presence of an electrical or gravitational field, resulting in a cycloid.
The ECR ion source makes use of the electron cyclotron resonance to heat a plasma. Microwaves are injected into a volume, at the frequency corresponding to the electron cyclotron resonance defined by a magnetic field applied to a region inside the volume. The volume contains a low pressure gas. The microwaves heat free electrons in the gas which in turn collide with the atoms or molecules of the gas in the volume and cause ionization.
definition pretty much the same definition as ECR.
Edit: spulling
Last edited by BenTC on Sun Aug 01, 2010 4:18 am, edited 1 time in total.
In theory there is no difference between theory and practice, but in practice there is.
You got it, Ben. And the likelihood of a neutral atom crossing a region of ECR in a Polywell is << the lifetime of a snowball in Hell.
Neutrals are bad in a Polywell as they tend to charge exchange with fast ions, resulting in slow ions and useless fast neutrals. The key is achieving the ionization where it does the most good.
Neutrals are bad in a Polywell as they tend to charge exchange with fast ions, resulting in slow ions and useless fast neutrals. The key is achieving the ionization where it does the most good.
Speaking of bad neutrals, I'm guessing that WB6 did not have any ECR ionization implimentation to ease the problems with neutral gas injection in that small machine. How much would such efforts effect the neutron production and/or the arcing time limits? Did WB3 or 4 (or 5) show any advantages if such efforts were implimented?
Dan Tibbets
Dan Tibbets
To error is human... and I'm very human.