Replacing Electron Guns

[MSimon]

I recently read that 13.56 MHz is used to ionize gases in plasma reactors. So with POPS modulation we may get density enhancement and ionization together in one package.

[Stefan]

The main purpose of the electron guns isn't ionizing the gas, it's replacing the electrons lost to the grid (so the net charge stays negative) and heating the electrons coming from the fuel so they can produce a deep well.

[MSimon]

The main purpose of the electron guns isn't ionizing the gas, it's replacing the electrons lost to the grid (so the net charge stays negative) and heating the electrons coming from the fuel so they can produce a deep well.

In an operating reactor - electron losses to the grid are replaced by "fusion" electrons. Electrons left behind by alphas.

Electron guns supply no significant energy (by comparison) in any case. That is the purpose of the grids.

I do envision electron guns as part of the start up process.

[Stefan]

In an operating reactor - electron losses to the grid are replaced by "fusion" electrons. Electrons left behind by alphas.

True, in an operating reactor with sufficient Q the alpha current could compensate all the electron losses.

However in a working reactor the electrons lost are high energy, unlike the electrons gained by ionization of the fuel.
If the new electrons aren't brought to high energy too, the well depth will decrease.
I don't see how this energy should be supplied to those electrons without electron guns.

Electron guns supply no significant energy (by comparison) in any case. That is the purpose of the grids.

I don't quiet understand what you are saying here.
Energy is supplied by a current between the grids and the electron guns, in what other way are the grids supplying energy?

[MSimon]

It is the potential difference between the electron guns and the grids that supplies the energy.

If the electrons are left behind in the center they will be at high potential vs the grids. Just as they would be if shot in from an external electron gun.

[Keegan]

Hey Stefan, It took me quite some time to get. After start up, electrons that get left behind by the alphas speeding off, gain high energy through collisions. This process happens amazing fast.

Kinda blew me away when i realized that the machine can seed its own virtual cathode. Not something i think alot of people realize yet.

BTW i should have posted reactor discussion here instead of contaminating Dr. Mikes lovely thread

[drmike]

BTW i should have posted reactor discussion here instead of contaminating Dr. Mikes lovely thread

I don't think it matters where we discuss things. There's so much going on it's pretty hard to describe in any simple way!

I could argue that the alpha's don't have anything to do with the electrons other than local collisions on their way out. And I could prove it with some simple scattering theory. The trick is to pick the right assumptions! I can also see how the alpha's can raise the total electron energy with slightly different assumptions. That's why "back of the envelope" only gets so far. We need the real experiments to tell us what actually happens!

[Stefan]

If the electrons are left behind in the center they will be at high potential vs the grids. Just as they would be if shot in from an external electron gun.

If the well depth isn't increasing the electrons in the center won't gain more potential energy than they had in the first place.
Increasing well depth doesn't sound like steady operation.

The potential energy the alphas give to the electron population by leaving the well is the same the coresponding ions took from it when dropping into the well.

After fusing the alphas have the kinetic energy of the source ions (proportional to the well depth) plus the fusion energy. Leaving the well costs them the energy the ions got dropping down.
When they left the well they still have all of the fusion energy, apart from the energy lost to collisions on the way out.
So this (probably rather small) energy is the only part of the fusion energy going directly to the electrons, the rest is carried by the alphas.

After start up, electrons that get left behind by the alphas speeding off, gain high energy through collisions.

Hmm, the electrons gain high energy through collision as soon as they get in contact with the confined high energy electrons, but this has nothing to do with the alphas.
Or are you talking collisions with alphas here?

[Keegan]

Hmm, the electrons gain high energy through collision as soon as they get in contact with the confined high energy electrons, but this has nothing to do with the alphas.
Or are you talking collisions with alphas here?

Stefan my last post was badly worded. I came across this table of ionization of elements that led to a little confusion because it was in kj/mol. I had to make sure that all the electrons got ionized at our drive energy and had to do a little maths.




So it looks like you only need 670.99 eV to strip Boron's 5 electrons (2,3) which is far below the fusion cross section we are targeting. Guess it never hurts to check these things. So your right. The electrons gain energy through collisions pretty much as soon as they enter the machine core.

Even though they are talking about Dueterium the Final WB6 lab Notes have some fascinating descriptions of ionization time scales. Fact; low energy electrons have a larger collisional cross section that high energy electrons.

However, as this initial ionization proceeded, the low energy electrons (at ca. 100 eV)
produced by such ionization of each neutral atom of D, then collided with other D atoms, and
ionized them in an exponentially-growing cascade. This is especially important to note, because the
cross-section for ionization by low energy electrons is much larger than by fast electrons (e.g. at the
injection energy of ca. 12-12.5 keV). At low energy the cross-section is approximately (sigmaizn) =
1E-16 cm2, while at the high drive energy of injection the cross section is of order 0.3-1E-17 cm2.
The e-folding time for this cascade is about 2 usec (microsec). Since the stable density attainable by
the injected electrons is only about 1E9/cm3, while the neutral gas density is in the range of 2-
5E12/cm3, the cascade must increase the electron density by roughly 4000x to reach nearly total
ionization. This is only about 9 e-foldings, thus the entire secondary low-energy ionization process
requires only about 20 usec to complete.

As this process proceeded, the increasing and large density of initially-low-energy (i.e.
“cold”) electrons thus produced was “heated” by (the very rapid) collisions with incoming fast
injected electrons. The electron/electron energy exchange collision time in the ionizing plasma is of
the order of 1-2 usec, so that the “cold” electrons are readily “heated” by collision with the incoming
injected electrons. The energy required to excite and energize the initially “cold” electrons resulting
from the first “fast” electron ionization, is supplied by the incoming injected electron current,
however, the total rate at which this can occur is limited by the input power of the injected beam.
Thus the increasing density of initially-cold electrons will rise until a power balance is reached.
Analysis of this process shows that injection currents of 10-40 A, at the injection energy of 12-12.5
kV, provides enough power to yield almost complete ionization of the neutral D gas (by this twostep
– cold/hot –process) at a density of ca. 0.5-1E13/cm3, equivalent to a pressure (at STP) of about
3E-4 torr.

At these currents the complete ionization process takes place in less than 0.5 msec, by which
time the electrons will nearly all be at the injection energy, because of the rapid 1-2 usec heating by
electron/electron collisions during the process. With full ionization of the internal fill gas, the
beta=one condition is reached (first with cold electrons) and maintained, as all the electrons are
driven to injection energies by electron/electron collisions. The potential well is maintained, and the
ions thus produced are able to make fusion reactions at or near the center of the well, by colliding
with other ions at the bottom of the well

But can Alpha particles energize electrons or ions upon exit via collisions ? That is an excellent question Dr Mike. They talked about cross section shrinking with Delta Energy above. Im guessing the collision cross section would drop significantly when your dealing with MeV energies. So they could, but it would be very small and possibly negligible. Anyone up for a bet ?

Btw if you only need 670eV to fully ionize boron this is fantastic news to DIYers. Possibly one could start studying Boron ion cloud dynamics with drive energies of >1kev. Which means off the shelf MOT transformers..... although expect bugger all fusion.

[drmike]

Back in the 1920's Langmuir noticed that electron-electron and electron-ion collisions did not match the measured equilibrium time. In fact, taking everything he could into account, he found the discrepancy to be on the order of 1e16 times faster than expected. This has since been known as "Langmuir's paradox".

It turns out it's a good thing, you can just assume you have a Maxwellian distribution of energy essentially instantly.

For beam-plasma interactions the times quoted are correct - but the assumption is that you have a true beam of electrons like that coming out of a TV tube. The electron sources I saw in WB-6 are not beams, they are going to be a lot more diffuse and I would expect the energy distribution to be Maxwellian almost instantly. But it would be good to see probe data to be sure.

Ionization cross section is going to change with charge - the effective diameter of each orbital will shrink (on average), but the there are usually resonances which have much larger cross sections at specific energies. Since we've got a large distribution of energy in the electrons, I would think ionization of all the Boron happens fast. I've actually got several books on the topic of how to compute ionization cross sections - it's fun physics. But measurement is the trump card! In general, the cross section falls with energy because the DeBroglie wave length is inversely proportional to velocity.

The same thing is true of alpha-ion and alpha-electron cross sections. The alphas have small cross section at higher energy.

On top of all that, the plasma acts as a shield. As the particles swarm around, they prevent long range interactions from really having any effect. So as the alphas blast out from the center, there will be a tube around them that gets affected, but not much else will be. That total energy will then be disapated around the plasma fairly quickly, and I'm sure it can be estimated with the standard physics assumptions.

A smaller but also interesting problem is the fact that all accelerating charges radiate. The electrons rotating around the B field radiate, and as the ions and electrons move around each other they also radiate. This is not the same thing as Bremstrallung (braking radiation), but it is an energy loss that a real reactor needs to account for.

That's why I like this problem - there's a lot of physics in it!!

[MSimon]

*
http://www.physics.usyd.edu.au/space-pl ... esses.html

*

Langmuir waves are electrostatic waves that exist in a weakly magnetized plasma with dispersion relation
ω2 ≈ ωpe2 + 3k2Ve2, where ω is the wave angular frequency, ωpe is the electron plasma frequency, k is the wave number and Ve is the electron thermal speed. These Langmuir waves may interact with other waves such as ion acoustic waves, other Langmuir waves and radio waves (wave-wave processes), or with the electrons and protons in the plasma (wave-particle interactions). Such interactions are responsible for many physical processes that take place within a plasma such as the flattening of electron beams and in radio emission.

Often, the rates and efficiencies of these processes are not proportional to the energy density (∝ E2) but instead on higher powers of E. They are then nonlinear phenomena. Examples include nonlinear wave particle scattering processes, such as scattering off thermal ions (STI), nonlinear wave-wave processes, solitons (solitary waves) and other localized structures.

Here is another good one:

Beams in Plasmas

http://books.google.com/books?id=rQN3lP ... k#PPT11,M1

It seems to me that calling the waves that naturally occur in plasmas "instabilities" has got people thinking about plasmas the wrong way.

Self organizing principles is better.

[Keegan]

A smaller but also interesting problem is the fact that all accelerating charges radiate.

I just found a comprehensive treatise on that subject. Wow.

Despite Feynman's assurances, there is no general agreement in the literature about whether a uniformly accelerated charge radiates (in classical electrodynamics)

Oh and thanks Simon, ^"Physics of intense beams in Plasmas" has a great account of the Langmuir Paradox and his assumptions in the first chapter. All completely readable.

[drmike]

The true form is that it is proportional to the 3rd derivative or "jerk", but as long as the there is a 3rd derivative there is radiation. And obviously if there is anon-zero 3rd derivative to position, there is a second non-zero derivative which is acceleration.

Jackson takes the Lagrangian from the same ideas that Rohrlich uses. The idea is to make classical electrodynamics consistent. Radiation is obviously a quantum effect since radiation is photons, but that's just too hard to deal with sometimes.

I have a thesis from the mid 1990's which uses quantum field theory to compute plasma dynamics in a low density system. It's really interesting. I'm not sure how useful it is though.

Which takes us back to the idea of assumptions. How you start determines what you will derive. This is why experiments are so important. It's impossible to know all the details. But it is also important to know how to ask what to measure - the act of measurement can change the experiment if it is not done carefully!

It's safe to say that particles in a plasma have chaotic motion and therefore they have a 3rd derivative to position and will radiate. If we design things right, the total radiation can be a lot smaller than the power we generate. Unless we're really smart and make all the power come out as radiation which is easily converted to useful work!!