OK, like many others I suspect, I'm getting bored with AGW, no news, no ideas etc.

I was looking at the possibility of formation of a potential well at the (approximate) centre of a polywell. I came up with a bunch of integral equations which looked quite horrific ... and then I thought, wait aminute, isn't that what we used to use analogue computers for?

Given the advances in analogue electronics generally, since the late 60s early 70s, wouldn't an analogue model help quite a lot with progressing (or otherwise) the theory of the Polywell?

## How about analogue computing?

### How about analogue computing?

Insanity Rules!

There was a recent science news article somewhere about lasers being used to force circular or spherical bubbles into squarish shapes (transiently) that had me also thinking about analog computing, but I'm not able to locate it now.

For Polywell, the combined electric and magnetic fields in 3D are probably not suitable for mechanical analog computing, but I'd be happy to be proven wrong. As far as electronic analog computers, they'd have to be able to simulate the "full bounce-averaged Fokker-Planck equations" IIRC from earlier posts on this forum.

There is a building-block approach to analog electronics that's very interesting and might have some application to this problem:

D. Grundy and J. Raczkowicz, "Structured Analogue Electronics", Electronics World & Wireless World, 97, pp. 965–969, November 1991

http://ieeexplore.ieee.org/xpl/freeabs_ ... 5&index=12

shorter is sweeter

Plasma physics has always been this way. I would like to know of any plasma experiment that has done what it was, a priori, predicted to do.

Show me an accurate simulation of a 1-D gas discharge in a cylinder..... even that simple arrangement defeats MHD and kinetic theory, so how is any theory gonna hit Polywell's arrangement?

DeltaV wrote:As far as electronic analog computers, they'd have to be able to simulate the "full bounce-averaged Fokker-Planck equations" IIRC from earlier posts on this forum.

Modified:

As far as electronic analog computers, they'd have to be able to emulate some behavior coarsely approximating the "full bounce-averaged Fokker-Planck equations" which coarsely approximate the actual Polywell behavior.

I'll let you and Rick Nebel (if he ever posts here again) duke it out over the validity of any particular approach to Polywell theory, modeling and simulation.

http://www.aa.washington.edu/research/PSI/

http://www.aa.washington.edu/research/PSI/research.html

"The PSI-Center's primary objective is to develop predictive capability for "Concept Exploration"-level experiments, so that one can design and model new experiments in fusion science and in other areas of plasma science, but without actual construction."

I'm with chris.

The difficulty is that plasma is chaotic. Small deviations (in both the simulations and reality) lead to unexpected effects. This leads to divergence between models and reality.

Nick Krall was discussing a Polywell simulation (in a private e-mail) and said you need a a very low density of gas and an electron imbalance of a "gazillion to one" to get the electric fields to work in a Polywell. That means that the you need a a simulator with enough significant digits to represent the system to a factor of a billion gazillion to be able to run a large number iterations. That says 128 bit or 256 bit numbers plus an exponent.

Once you can cross confirm simulations with reality you may be able to simplify the code. Until then it is just shots in the dark.

The difficulty is that plasma is chaotic. Small deviations (in both the simulations and reality) lead to unexpected effects. This leads to divergence between models and reality.

Nick Krall was discussing a Polywell simulation (in a private e-mail) and said you need a a very low density of gas and an electron imbalance of a "gazillion to one" to get the electric fields to work in a Polywell. That means that the you need a a simulator with enough significant digits to represent the system to a factor of a billion gazillion to be able to run a large number iterations. That says 128 bit or 256 bit numbers plus an exponent.

Once you can cross confirm simulations with reality you may be able to simplify the code. Until then it is just shots in the dark.

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

MSimon wrote:I'm with chris.

The difficulty is that plasma is chaotic. Small deviations (in both the simulations and reality) lead to unexpected effects. This leads to divergence between models and reality.

Nick Krall was discussing a Polywell simulation (in a private e-mail) and said you need a a very low density of gas and an electron imbalance of a "gazillion to one" to get the electric fields to work in a Polywell. That means that the you need a a simulator with enough significant digits to represent the system to a factor of a billion gazillion to be able to run a large number iterations. That says 128 bit or 256 bit numbers plus an exponent.

Once you can cross confirm simulations with reality you may be able to simplify the code. Until then it is just shots in the dark.

Perhaps oddly, I too agree with Chris that a simulation is no substitute for a real experiment.

MSimon's point about the required dynamic range is the killer for an analogue simulation: with that required range some of the variables would be below the noise floor.

Sad really ... there was I thinking how neatly I could get the integrations to run really quickly (but not very accurately) as opposed to lots of slow clunky code in the digital version. Ah well!

Insanity Rules!

Analog computer for beam control:

"Programmable VLSI Extended Analog Computer for Cyclotron Beam Control"

http://www.cs.indiana.edu/pub/techreports/TR441.pdf

DeltaV wrote:My hope for analog simulation of Polywell would be for qualitative, not quantitative, results. The SAE method maps everything into logarithms and has a very wide dynamic range IIRC, due to the inherent characteristics of semiconductor junctions. I can't find it on the web though; it's been too many years since I read the 1991 EW&WW article to recall details.

Analog computer for beam control:

"Programmable VLSI Extended Analog Computer for Cyclotron Beam Control"

http://www.cs.indiana.edu/pub/techreports/TR441.pdf

Control is one thing (you are dealing with a feedback system and one or two orders of magnitude of signal).

Measuring the output of an analog computer can be done to 16 bits (12 to 14 ENOB) at 100 MHz sampling. And 24 bits (16 to 20 ENOB) at 100 KHz sampling.

SNR of the very best analog amps is 120 dB. Resistor noise (even at 50 ohms) degrades that. You can increase the noise by running more than optimum current (more electrons more noise) or increase it by reducing current from optimum (Shott noise).

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

Noise can improve the signal-to-noise ratio of many nonlinear dynamical systems. This “stochastic resonance” (SR) effect occurs in a wide range of physical and biological systems. The SR effect may also occur in engineering systems in signal processing, communications, and control. The noise energy can enhance the faint periodic signals or faint broadband signals that force the dynamical systems.

http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdf

DeltaV wrote:Noise is not always a bad thing. Which does not mean it wouldn't be bad for a Polywell simulation.Noise can improve the signal-to-noise ratio of many nonlinear dynamical systems. This “stochastic resonance” (SR) effect occurs in a wide range of physical and biological systems. The SR effect may also occur in engineering systems in signal processing, communications, and control. The noise energy can enhance the faint periodic signals or faint broadband signals that force the dynamical systems.

http://citeseerx.ist.psu.edu/viewdoc/do ... 1&type=pdf

Sure. You can add a bit by taking 4X as many samples and doing a decimation. For two bits you need 16 samples. Three bits 64 samples. etc.

So you gain accuracy and lose speed. Real fast.

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

### Re: How about analogue computing?

mad_derek wrote:OK, like many others I suspect, I'm getting bored with AGW, no news, no ideas etc.

I was looking at the possibility of formation of a potential well at the (approximate) centre of a polywell. I came up with a bunch of integral equations which looked quite horrific ... and then I thought, wait aminute, isn't that what we used to use analogue computers for?

Given the advances in analogue electronics generally, since the late 60s early 70s, wouldn't an analogue model help quite a lot with progressing (or otherwise) the theory of the Polywell?

One small problem. 1E-6 greater electrons than ions. Analog computers don't do well with those kinds of ratios.

There is one kind of computer that can solve those problems exactly. They are called experiments.

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

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