## Numerical Simulation of a Polywell

I also believe we're talking about octuple or higher precision math because of the nature of the integrals being used.

An example: one thing that is still being discused is the wiffle-ball efect, is it real or just another case of hopeful thinking? A simulated experiment specificaly designed could shed some light:

Let's say we model a cube made with perfect mirrors (for particles), and substitute one face of it for a magnetic field. Inside we let loose a population of charged particles. The goal would be to compute the field resulting from the interaction between the external magnetic field and the field created for those particles, and then compute the loses. We could play with, at least, the shape and power of the B field, and with the number, mass, charge, initial movement direction, and speed, of the particles (they dont even have to reflect the properties of any real particle).

Giving up on reproducing the conditions inside a polywell in simulations doesn't mean they are completely useless.

charliem wrote:Ok, a full computer simulation of a polywell is not doable but that does not mean that they are completely worthless. It is still possible to build virtual experiments involving particular (and very interesting) aspects of it. There are people here that have been doing exactly that with B and E fields for some time.

An example: one thing that is still being discused is the wiffle-ball efect, is it real or just another case of hopeful thinking? A simulated experiment specificaly designed could shed some light:

Let's say we model a cube made with perfect mirrors (for particles), and substitute one face of it for a magnetic field. Inside we let loose a population of charged particles. The goal would be to compute the field resulting from the interaction between the external magnetic field and the field created for those particles, and then compute the loses. We could play with, at least, the shape and power of the B field, and with the number, mass, charge, initial movement direction, and speed, of the particles (they dont even have to reflect the properties of any real particle).

Giving up on reproducing the conditions inside a polywell in simulations doesn't mean they are completely useless.

I'm reading the Feynman Physics lectures on electrostatics/magnetics and it is clear that such a computation is devilish hard for the reason that a particle's magnetic field is purely relative. If there is no relative motion between two particles there can be no magnetic field interaction between them. And even then the motion must be cross product and depends on relative velocity.

Which means that to compute the magnetic field the relative motion between each and every particle and the distance between them must be known. Three numbers for position. Three numbers for velocity. A number for mass. A number for charge. Probabilities of interaction vs distance and relative velocity. Probabilities of result once an interaction takes place.

The electric field is much simpler. Even the "static" field created by the magnets is simpler. The movement of charges in wires allows for lots of simplifications because the motions of the charges is constrained.

Bussard has created one of the most difficult calculable problems known to man. Which is why so many here have said: build it and see what happens. The equations of motion are simple under conditions of no interaction - which given the low probabilities is a fair approximation of device operation. So start with that.

Once we have seen what happens in a real machine simplifying rules of thumb can be developed.

As has been pointed out simplifying assumptions can be made even with our limited understanding to get at aspects of the problem. The static magnetic field. The static electrostatic field.

I'm not sure that the whiffle ball is calculable. It may need to be handled with rules of thumb. When those are known.

Engineering is the art of making what you want from what you can get at a profit.

I dont think its impossible, but I agree that, most probably, it's a case of a "non tractable" problem, in the computer science sense. That is, when you augment its size (in this case the number of particles), then the number of operations the computer have to perform is disproportionally higher (an example of this concept: if you go from 1 to 10 particles, and then the number of operations goes from 15^1 to 15^10, this would be a very "non tractable" problem).

Well, that means the problem cant be solved for any realistic number of particles, but we can still try to solve it with a few.

¿Enough to obtain something valuable for all the effort? I dont know, all I'm saying is that I think it's worth a little more thought before throwing it way.

If you can do things like assume the Wiffle Ball, the well, and make other simplifying assumptions then a few thousand particles traipsing around a simulation could be useful.

i.e assume the reaction field etc. What happens to a few particles. From that assume densities and compute reaction rates.

Doing it right will depend on feedback from experiments.

Paul Dietz says - simulation first experiments later. I think that because of the nature of the problem they must be done in tandem.

http://www.classicalvalues.com/archives ... ed_sc.html

Feynman talked about such problems in relation to aeronautics in book one of The Lectures.

http://www.amazon.com/gp/product/020102 ... 0201021153

He said the more accurate the simulation the more complicated the "laws". You have one for wing drag. Another for fuselage drag. A third rule for combined drag.

So what do we need to know? Wiffle Ball currents and particle distribution. Charge density in the well. Do we get a layered field or is it more like a vacuum tube with continuous flow?

And personally? I'd like to be able to do away with the puff gas system. I'd like to be able to keep a constant density in the system and also possibly time a gas feed from a grid to start up. Any way. Those are some of the things I'd consider in an experimental machine. And some of the things I want to find out.

i.e assume the reaction field etc. What happens to a few particles. From that assume densities and compute reaction rates.

Doing it right will depend on feedback from experiments.

Paul Dietz says - simulation first experiments later. I think that because of the nature of the problem they must be done in tandem.

http://www.classicalvalues.com/archives ... ed_sc.html

Feynman talked about such problems in relation to aeronautics in book one of The Lectures.

http://www.amazon.com/gp/product/020102 ... 0201021153

He said the more accurate the simulation the more complicated the "laws". You have one for wing drag. Another for fuselage drag. A third rule for combined drag.

So what do we need to know? Wiffle Ball currents and particle distribution. Charge density in the well. Do we get a layered field or is it more like a vacuum tube with continuous flow?

And personally? I'd like to be able to do away with the puff gas system. I'd like to be able to keep a constant density in the system and also possibly time a gas feed from a grid to start up. Any way. Those are some of the things I'd consider in an experimental machine. And some of the things I want to find out.

Engineering is the art of making what you want from what you can get at a profit.

### PARSEC - Density functional theory

greetings all,

I've be lurking for a short while. Didn't have much to contribute but found it all very interesting and hopeful. I just bumped into some simulation software that might be interesting, though its beyond my ability to know how suitable it is. Perhaps too fine grained but it seems to deal somewhat with many-bodied electron and atom interactions in electrostatic and electromagnetic fields.

Rather than repeat these, the description is here...

http://parsec.ices.utexas.edu/about/index.html

http://en.wikipedia.org/wiki/PARSEC

The interesting thing I note from http://en.wikipedia.org/wiki/Density_functional_theory is that:

+ quantum mechanical theory used in physics and chemistry to investigate the electronic structure (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases.

+ the properties of a many-electron system can be determined by using functionals, i.e. functions of another function, which in this case is the spatially dependent electron density.

+ generalizations to include magnetic fields

or perhaps http://en.wikipedia.org/wiki/Time-depen ... nal_theory is more appropriate:

+ quantum mechanical theory used in physics and chemistry to investigate the properties and dynamics of many-body systems in the presence of time-dependent potentials, such as electric or magnetic fields.

for which http://www.tddft.org/ links to some simulation software

cheers, Ben

I've be lurking for a short while. Didn't have much to contribute but found it all very interesting and hopeful. I just bumped into some simulation software that might be interesting, though its beyond my ability to know how suitable it is. Perhaps too fine grained but it seems to deal somewhat with many-bodied electron and atom interactions in electrostatic and electromagnetic fields.

Rather than repeat these, the description is here...

http://parsec.ices.utexas.edu/about/index.html

http://en.wikipedia.org/wiki/PARSEC

The interesting thing I note from http://en.wikipedia.org/wiki/Density_functional_theory is that:

+ quantum mechanical theory used in physics and chemistry to investigate the electronic structure (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases.

+ the properties of a many-electron system can be determined by using functionals, i.e. functions of another function, which in this case is the spatially dependent electron density.

+ generalizations to include magnetic fields

or perhaps http://en.wikipedia.org/wiki/Time-depen ... nal_theory is more appropriate:

+ quantum mechanical theory used in physics and chemistry to investigate the properties and dynamics of many-body systems in the presence of time-dependent potentials, such as electric or magnetic fields.

for which http://www.tddft.org/ links to some simulation software

cheers, Ben

In theory there is no difference between theory and practice, but in practice there is.

This is more into quantum mechanics than what we're interested in. Our particles are zooming so fast around that we can pretty much ignore quantum mechanics.

Do you know why electrons don't fall into the nucleus of the atom but stay at some distance off and at fixed energy levels forming layers? I mean they are of opposite charge and so are attracted - why won't the electrons fall in? Classical billiard-ball mechanics can't describe this. Only quantum mechanics offers a model for it.

The rules of quantum mechanics also allow us to determine how multiple atoms form molecules through bonds (ionic, covalent, etc) and more importantly how chemical reactions happen.

However the multi-body Schrödinger equation is another thing quite impossible to solve, either analytically or numerically (efficiently; find a way and you'll get the Nobel). So to get over this hardship all these tricks have been invented. Like the Hartree-Fock method or the Density Functional Theory. Unfortunately they are not perfect.

The ultimate goal here is to get an ab-initio solution, that is a solution from first principles without using any empirical data. That is we know the masses of electrons, protons, neutrons and from that alone using quantum mechanics can determine all the properties of matter.

Or, well, that's my impression. So the links you offered are more about condensed matter physic. But I'm not an expert really. Interesting stuff this though.

- Indrek

### APE - Relativistic Density Functional Theory

> Do you know why electrons don't fall into the nucleus of the atom

Similarly, why don't the positive ions combine with the electrons in the centre. You could look at the mass of the electrons in the centre of the Polywell as one big atom, with other atoms wizzing by. Perhaps some condensed matter approximations could work (not that I know anything about it.) Though that analogy doesn't hold up completely when the ions go wizzing through the middle of the "atom".

I read this about pseudopotentials (wikipedia)...

The pseudopotential is an attempt to replace the complicated effects of the motion of the core (i.e. non-valence) electrons of an atom and its nucleus with an effective potential, or pseudopotential, so that the Schrödinger equation contains a modified effective potential term instead of the Coulombic potential term for core electrons normally found in the Schrödinger equation. In this approach only the chemically active valence electrons are dealt with explicitly, while the core electrons are 'frozen', being considered together with the nuclei as rigid non-polarizable ion cores.

Indrek, I think it was your simulation that showed a single electron moving in a polywell. Very interesting how it wandered around. With a large mass of eelctrons gathered in the centre, I would imagine that all the electrons bump off one another and don't actually move very far individually. My idea is that for the mass of electrons in the centre, within a certain shell radius, treat them as a single group, and statistically along the surface of the shell, electrons pop out such that they can be treated like valence electrons to interact with the magnetic fields. The probability would be different at different points of the shell due to the cusps.

> Our particles are zooming so fast around that we can pretty much ignore quantum mechanics.

So then this caught my eye int he manual at http://www.tddft.org/programs/APE/

APE is a computer package designed to generate and test norm-conserving pseudo-potentials within Density Functional Theory. The generated pseudo-potentials can be either nonrelativistic, scalar relativistic or fully relativistic and can explicitly include semi-core states. A wide range of exchange-correlation functionals is included.

When performing atomic calculations APE can solve either the Kohn-Sham equations, the Dirac-Kohn-Sham equations or the scalar-relativistic Khon-Sham equations. Valid options are:

+ schrodinger: Kohn-Sham equations.

+ dirac: Dirac-Kohn-Sham equations.

+ scalar_rel: scalar-relativistic Kohn-Sham equations.

- Ben

Similarly, why don't the positive ions combine with the electrons in the centre. You could look at the mass of the electrons in the centre of the Polywell as one big atom, with other atoms wizzing by. Perhaps some condensed matter approximations could work (not that I know anything about it.) Though that analogy doesn't hold up completely when the ions go wizzing through the middle of the "atom".

I read this about pseudopotentials (wikipedia)...

The pseudopotential is an attempt to replace the complicated effects of the motion of the core (i.e. non-valence) electrons of an atom and its nucleus with an effective potential, or pseudopotential, so that the Schrödinger equation contains a modified effective potential term instead of the Coulombic potential term for core electrons normally found in the Schrödinger equation. In this approach only the chemically active valence electrons are dealt with explicitly, while the core electrons are 'frozen', being considered together with the nuclei as rigid non-polarizable ion cores.

Indrek, I think it was your simulation that showed a single electron moving in a polywell. Very interesting how it wandered around. With a large mass of eelctrons gathered in the centre, I would imagine that all the electrons bump off one another and don't actually move very far individually. My idea is that for the mass of electrons in the centre, within a certain shell radius, treat them as a single group, and statistically along the surface of the shell, electrons pop out such that they can be treated like valence electrons to interact with the magnetic fields. The probability would be different at different points of the shell due to the cusps.

> Our particles are zooming so fast around that we can pretty much ignore quantum mechanics.

So then this caught my eye int he manual at http://www.tddft.org/programs/APE/

APE is a computer package designed to generate and test norm-conserving pseudo-potentials within Density Functional Theory. The generated pseudo-potentials can be either nonrelativistic, scalar relativistic or fully relativistic and can explicitly include semi-core states. A wide range of exchange-correlation functionals is included.

When performing atomic calculations APE can solve either the Kohn-Sham equations, the Dirac-Kohn-Sham equations or the scalar-relativistic Khon-Sham equations. Valid options are:

+ schrodinger: Kohn-Sham equations.

+ dirac: Dirac-Kohn-Sham equations.

+ scalar_rel: scalar-relativistic Kohn-Sham equations.

- Ben

In theory there is no difference between theory and practice, but in practice there is.

MSimon wrote:Free E/M field simulator:

http://www.mwrf.com/Article/ArticleID/2 ... ftware.com

From the web page:

The no-charge three-dimensional (3D) planar electromagnetic (EM) simulator is an excellent training and learning tool for those new to the analysis capabilities of EM simulation software.

It looks like its a Printed Circuit Board simulator

http://www.sonnetsoftware.com/products/ ... tures.html. Perhaps not useful for simulating the Polywell core. Could be useful for the design of the control electronics later on. Looks like great functionality for a free tool. It would have been very useful last year when I had a unit to design a PCB to minimise susceptibility to elctromagnetic noise to measure very small signals. Thanks, I will pass the link on to the lecturer.

-Ben

In theory there is no difference between theory and practice, but in practice there is.

BenTC wrote:MSimon wrote:Free E/M field simulator:

http://www.mwrf.com/Article/ArticleID/2 ... ftware.com

From the web page:

The no-charge three-dimensional (3D) planar electromagnetic (EM) simulator is an excellent training and learning tool for those new to the analysis capabilities of EM simulation software.

It looks like its a Printed Circuit Board simulator

http://www.sonnetsoftware.com/products/ ... tures.html. Perhaps not useful for simulating the Polywell core. Could be useful for the design of the control electronics later on. Looks like great functionality for a free tool. It would have been very useful last year when I had a unit to design a PCB to minimise susceptibility to elctromagnetic noise to measure very small signals. Thanks, I will pass the link on to the lecturer.

-Ben

Well there are simple things you can do:

1. All measurement is done differentially

2. The signal traces must be parallel and close together with constant impedance.

3. The signal should be buried between two quiet ground planes and if you are really finicky the ground planes should be stitched together with vias.

BTW are you familiar with the Tayloe detector? It is one of my very favorite low noise detectors. It is a sampling (rather than mixing) detector. You can look up Dan Tayloe and e-mail him. He is very gracious.

Of course if your PC board doesn't allow you to follow the rules an EM simulator is good. Or a spectrum analyzer with a small loop pick-up and possibly a LNA (to make a LNA first get an LNA) for signal boost.

Engineering is the art of making what you want from what you can get at a profit.

### Tayloe low noise detector

I had not heard of the Tayloe detector. I guess you mean this. Very interesting concept. Its been 15 years since I've done quadrature math but the generalised concept is still there. I'll file it for later reference. Thanks.

In theory there is no difference between theory and practice, but in practice there is.

### Re: Tayloe low noise detector

BenTC wrote:I had not heard of the Tayloe detector. I guess you mean this. Very interesting concept. Its been 15 years since I've done quadrature math but the generalised concept is still there. I'll file it for later reference. Thanks.

Yeah. That is the one.

If you have questions Dan will talk to you.

BTW the detector responds to the 3rd harmonic of the center frequency so a front end filter is required. But the dynamic range and linearity are excellent. I'd build this into an instrument that needed a linear detector. In fact I have it in mind for some Polywell control problems that may show up with pB11.

Let me add that the odd harmonics are reduced by 1/n where n is the harmonic number. So the 3rd harmonic would be 9.5 db down, the 5th would be 14 db down. etc. With nulls at the even harmonics.

Also I'm into FIR (Hilbert) filters for SSB. Very good CODECS can be had now for very cheap (all that iPod stuff). And a fast enough DSP is not very expensive either.

Just stuff I like to think about when Polywell starts hurting my head. i.e. Electronic snacks.

Engineering is the art of making what you want from what you can get at a profit.

Let me add that the proper way to bias the Tayloe Mixer (due to the way the selector works) is to run it with plus and minus supplies so the input can be at DC ground. It is cheap enough. At least for instruments. An LM317L for the positive and the equivalent negative part (with a very simple ckt to keep the differential voltage constant i.e. 3.3V) and away you go. That way you can properly balance the op amp resistors without injecting Power supply noise.

Engineering is the art of making what you want from what you can get at a profit.

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