IOn Guns, Pressure and Mean Free Paths..etc.

[DaveC]

I originally had this attached to my comments, in the Fusor Construction, but they more properly belong here..

To increase the neutron generation rate, we require higher ion DENSITY. And you need that density at the region of intended collision. There seems to be at least two ways to go from here.

One is the classical colliding focused ion beam approach.. the so called Gunned Fusor. Here you want well focused ion beams to collide (or at least pass by each other in the smallest possible volume. This gives a high ion density at the collision zone and a low density everywhere else. To minimize beam spread before the target region, we need minimal gas injection, to allow the lowest possible average pressure, to minimize collision with neuturals.

The other approach is to intentionally go after neutral collision. Richard Hull has mentioned on several occasions that the neutron production appears to come from outside the poissor region in the standard Farnsworth Fusor..from collision with neutrals. Thus firing a beam of high energy ions into neutral D2 gas at rather high pressure, would assure a fairly high probablity of collision. (How else do the ions lose their energy?) The key is to have the first collision (the one at highest energy) be the one that consumes all the kinetic energy. Given the great disparity in energies between the ion and neutrals, the ions will tend to deflect with little energy loss until they collide nearly head on.

It's tempting to apply simple kinetics here and see a fused atom/ ion stopped dead in its tracks and particles (neutrons, protons and etc) carrying away the excess energy. Not sure if one can really do that.

Ideally neutral gas densities would need to keep the ion mean free path less than fusor diameter (or length), thus minimizing ion impacts on the fusor walls and the consequent heating and Xray generation.

Given the high ion velocity (read that as temperature) the mean free paths of D+ ions will be much longer than those for the room temperature neutrals.

A rough estimate is the square root of the energy ratios which for 20keV ions compared to 300K neutrals is about sqrt of(20,000/.025) or 894. Call it 1000,for ease of estimation. So the high energy ion has a mean free path of about 1000x the Room Temperature mean free path for any given pressure.

Using about 10^-5 cm MFP for deuterium at STP, the MFP for the high energy ion is about 10^-2 cm and thus to get it stopped just before the wall of a 20 cm diameter fusor, requires a pressure of around about 1/2000 of an atm. , or about 500 microns. Quite a bit higher than we have been thinking.

The challenge will be to get the ion gun to work at these pressures.

But... since the only interaction volume is actually along the beam path itself, then only this region needs to be at the higher pressure... or.... needs to be there at all!... ERGO we are back to the linear type of fusor.

I do not have all the details sorted out yet, but offer these ideas for intellectual fodder.

Dave Cooper.

[Richard Hull]

Good thinking Dave! I believe that the D-neutral fusion was ancillary to the desired D-D fusion in the papers I read and compete with it only when the applied voltage was over 100kv on the normal fusor. ( a Miley group paper, I believe). The reason this assisted was due to the very high applied voltage and the fact that there was so much volume involved where neutral-d collisions could occur.

Of course what you propose is a liner type gas target system.

I like the idea of the extra density of the reactant gas, but the ion gun would, of course have to be the total accelerator and the extractor would have to work at nearly 60kv or above!! This I have never heard of. The gas target area would have no electrode in it. This means differential pumping or a very tricky gun aperture control system. I would probably take it on as a diff pumped system.

Still, it is very interesting, the two order of magnitude more dense gas target.

Richard Hull

[3l]

Hi Dave:

The gas liner idea would be interesting to try.
A heck of a lot easier than frozen D2 targets.
You would need some kind of face plate to hold the gas that would not impeed the ions.
That way you could use standard type filament guns.
But I'll wager RF will be needed as filaments burn out at at the production rates you are talking about.
It might be tough to implement as a solid target turns to silly putty at 80kv and 1 ma at the beam area. You would need to sweep the beam around to prevent melt down in the liner area.
That's what some neutron tubes and the dymatron neutron source implement to save their targets from melting. The dymatron puts 22kw of ion beam on the target, I imagine a linear fusor will have equal if not greater power requirements.

Happy Fusoring!
Larry Leins
Fusor Tech

[DaveC]

I am thinking of an RF barrier discharge ion source. More details shortly. It may be necessary to use a very thin window.. to isolate the higher pressure gas from the lower pressure ion gun region. or...with good focus, aim the ion beam down a slightly larger than capillary diameter tube being used for the differential pumping line.

Dave Cooper

[Frank Sanns]

Dave,

Early on I did a calculation on mean free path and what I thought the life of a deuteron might be. I came up with numbers very similar to yours but I abandoned them because of the statements of many here that ions don't last more than a recirculation cycle of a couple or less. I felt that the expertese of the many outwayed the delusions of the one. This was not the case and it is NOT a criticsm of the group. Quite the contrary. This is a fantastic proffesional, open minded group but there are a few preconceved notions that can limit our approaches. I think we all need to work though our own math and follow our particular approaches based on our own conclusions. And even a mistake sometimes can make for a good new discovery. It is all good and I am feeling much more optimistic about the RF approach, collisions with neutrals, and a few other approaches that I have wanted to persue. I had started to cool off thinking they were dead ends but now I feel that they are well worth the effort.

Thanks Dave and everybody else!

Frank S.

[DaveC]

Frank - I remember your calculations, and I believe, that these values are more or less correct ballpark values. The spoiler to our accuracy is the ambiguities of the high energy ion's mean free path, and whether the usual methods of calculating mfp are completely valid for these much higher "temperature" particles.

At this point in my ignorance, I am inclined to think they are more correct than not. So... issues reduce to....whether the ions deposit their energy in a narrow region of space... as they are known to do in solids..

The so-called "Proton Therapy" used by some cancer research hospitals (Loma Linda University Hospital in Redlands CA is one expample) has this particular advantage of being able to very accurately target the region both as to width and penetration depth.

I also know electrons can be deposited deeply into dielectric materials in a fairly well defined sheet. I once had some PMMA about 1 cm thick with a sheet of charge deposited at the midpoint in thickness. It was done at MIT using their 5 MEV Van de Graaff driven accelerator. The charged pieces were shipped to me packed in dry ice and retained some of the initial charge, despite an overnight trip across country.

So allowing for the effects of much lower density in the fusor gas, one would expect a broadening of the energy exchange region, compared to that in a solid.

This raises the issue of the definition of the mean free path when a particle (the deuteron) is not in thermal equilibrium with the other particles.

Some good things to consider theoretically and practically.

Dave Cooper

[badflash]

I would think you would use the nuclear cross section for the energy the particle has. This is how it is done in nuclear reactors with fast moving neutrons. Of course this gets a little dicey if the particle is under constant accelleration until it hits the higher densiity region inside the inner grid. With reactors, the calculations are simplified by breaking the energy regions up and using effective energies & cross sections. Basically fast, resonance region, and thermal.

The mix of ionized and non-ionized particles makes this pretty messy. Propably need to come up with some models, them figure out a way to validate them experimentally.

[DaveC]

Well said Jack! You have put the descriptive terms on the basic complexities, there are to address.

Dave Cooper

[Richard Hull]

I know that the electron travels much farther at reduced pressures and elevated energies. Spangenburg gives a specific equation for this modified MFP in his book on vacuum tubes. I just know that I have left it in a former post here!

Unfortunately, I would think that at our lower energies, the deuteron is so large and moving so slow that the MFP might not improve by more than a factor of four, which has always been my rule of thumb under 30 Kev. At normal temps, using the equilibrium equation and normal fusor pressures for fusion, the mean free path would be on the order of 30mm but I have figured on 120 mm which is about 1.5-2 trips, but this is only a maximum for ~60% of the deuterons the other 40% go farther than this. I would opt for the longest ion going maybe a meter with the bulk being under 250mm at 30kev and 10u pressure.

Richard Hull

[DaveC]

Because in the common fusor, there is no specific ion source, the Deuterons have a wide range of energies, having been created at various radial distances out from the central grid structure. Thus there is not a mono-energetic ions flux, but a rather borad energy distribution. Stated in thermodynamic te rms, there is a broad temperature distribution.

The higher energy ions would travel farther between collisions. Also... the longer the fusor is in operation, at constant pressure, the hotter the neutrals become, thus increasing the mean free path of all gases and ions.

The key thing to recognize is the role played by maintaining constant gas pressure. As the fusor temperature increases, normally, with constant gas density, the pressure would rise according to PV = nRT. But when the gas pressure is maintained constant, then the gas density goes downward as the fusor temperature increases. The reduced number of molecules allows longer mean free paths.


Dave Cooper

[Richard Hull]

I hope that you are not suggesting that as some point in the fusor that there are a significant percentage of 30kev neutrals which is absurd. One such neutral in a quintillion would be a huge number. Secondly, such neutrals, by definition, can have no source and no focus in the collisional sense. As there is no way possible to characterize the gas temperature in the fusor the equation can't be quantitatively solved but only qualitatively arrived at. I figure 4X over STP gas for MFP is about right for a full 30kev deuteron which is, in itself, rare in a 30kv applied, fusor. At least it has a mission as it has an origin, a focus and is fully, electrostatically directed, unlike the missionless, brownian limited, bumbling, be-dazed, neutrals.

Speedy, tiny, lightweigh 1/3th C electrons only have there paths extended by a factor of 30 or so. A huge Ion like a deuteron at a mere 30kev would be a real slow mover.

I guess someone needs to figure out or find someway to measure the gas temp in the inter-grid volume for the question to be answered to any degree of satisfaction.

Richard Hull

[Richard Hull]

I just posted a cool URL as part of a mean free path FAQ on the vacuum forum. All MUST check it out.

Dave Cooper put me on the quest.

It turns out that he is right on the temp idea but without any knowledge on our behalf of what the hell actually is in a running fusor, we are as muddled as we ever were inspite of a new insight.

It turns out that the less than ideal gas law has a special equation for mean free path and this URL has a solver built into it.

I punched in some numbers. here is the result.

The mean free path of a D neutral in a gas of itself at 300 kelvin at 10 micron's pressure is about 70mm, as I guessed.

Amazingly the deuteron is so microscopic that in a gas of its fellow deuterons, only, all with only an average energy of 1000ev, (~10,000,000 kelvin) the mean free path is 10e 13 meters!!!! (That's 60 billion miles!!!)

This is, of course, meaningless in the fusor as every gas atom would have to be a deuteron. Impossible. And, the temperature inside would be a real 10,000,000 degrees.

I likewise assumed, as Dave might desire, a 70,000 kelvin heated neutral gas temperature in a 10 micron fusor. This is still less than only 6ev per molecule of neutrals. The mean free path jumps to nearly 16 meters. If this were the case, virtually every moving neutral would forever result in a wall collision (they would be doomed to this fate) and never impact with microscopic, nearly five order of magnitude smaller, deuterons.

It turns out that any neutral that ever acquires a kinetic energy of over 0.1ev will virtually always impact the fusor chamber's wall and virtually never hit another brother neutral and certainly never impact with a micro deuteron, on a statistcally notable level!

Again, we know nothing about the fusor's interior! It s internal gas temperature?.....The ratio of the species contained in it..........The energy ranges of significance with in it. Calculations are just not viable without good data. The data we might hope to obtain via experiment would be an averaged intergrated data which might hide some significant and novel processes.

It's a crap shoot guys!

Richard Hull

[DaveC]

Have to check out the URL,,,, but I did get the 16.8 m path length for 6eV neutrals.

With the fully ionized Deuteron, D+one is dealing with a very tiny cross sectional area... and very high speed.... So the 10^13 m mean free path, while surprising initially, is right in line.

I am just beginning to think along these lines in more detail...It is probably ok to consider that any ion thus formed, will have a long mean free path...but.... couldn't really be much longer than Fusor diameter. Unless a mechanism is asserted that reflection and riccochet could occur without neutralizing the ion. And THAT I just don't find credible. Sooo.. the ions mean free path at high energy might well be only limited by the fusor size.

There much here to consider.

Dave Cooper

[DaveC]

Just a bt more on the long mean free path idea of ions.

My last post.. suggested the Fusor diameter as the practical limit to mean free path. Obviously, that would ONLY be true if the path were rifle straight. A curved path could easily circle the fusor for a number of orbits... maybe a big number!.

But this is not a new idea either... didn't Farnsworth have the "recirculation" idea as an integral part of his design.??

So Methods to create ion trajectories that curve significantly should be on our design, and theory dicsussion agendae.

Dave Cooper

[badflash]

A curved path for charged particles at high speed is self defeating. They emit energy is you try and that doesn't help the cause.

[Frank Sanns]

Dave,

Yes! Yes! Yes! Curved paths conserve energy. There will be synchrotron radiation but at our low energies it should be no where near the factor of everything crashing into solid objects and dissipating ALL of thier energy with every pass.

I like the resonant RF idea from a circulating ion and resonance stand point but it uses just as much energy to slow down the charged particles as it does to just let them strike the wall except that they have the chance of phase bunching and increasing the odds of collision as they bunch up at the center.

A figure 8 cylotron is also an interesting approach. Let there be two counter rotating and independent paths of electrons and deuterons. Each wil have thier own orbit and will circulate. This removes the chance for recombination of electrons with the deuterons giving longer ion life. Plus, when the 2 deuteron nodes from each loop of the figure 8 collide, those that miss or just graze by, will still keep thier energy and go into the next loop pass.

Yes much to explore, so little time.

Frank S.

[Jon Rosenstiel]

Frank,
You've probably seen this, but just in case you haven't, here's the link:
http://fti.neep.wisc.edu/iecworkshop/agenda.html
Go down to Session 4 and click on the second item's pdf. (Effects of cathode structure on neutron production in IEC devices). See page 13, Ion Trajectories.

Jon Rosenstiel

[DaveC]

If I may use Jack's response and Frank's and Jon's as comparisons to illustrate the need for careful calculations....

The energy, radiated by a charged particle, is significant witness the radiation from a Magnetron from a uWave oven. The power produced there is a large fraction of the input power. We should be able to quantify this in terms of trajectory radius, and keV. IT would be a very useful result to have at hand in these discussions.

Actually, some of the ions, (those launched with the proper initial directions) will not collide with the inner grid wires but will be curved by the field into a spiralling open curved path. The conference the Jon referred to, is very interesting... I think we should all have that Conference paper for reference... Many thanks Jon, excellent citation.

In typical Japanese thoroughness, they determined that the grid structure details have little or no effect on neutron production and only a minimal effect on V-I characteristics for a fixed pressure, and similarly minimal differences in kV vs pressure effects for fixed input current. All good examples of carefully taken data. The more open the gird, the more easily modeled ions can circulate... no surprise here either. But conjecture is now replaced with experimental result.(aka... fact).

The modeling setup is tedius, and can only take us so far... models are always better than the quality of our experimens... the surfaces of the model is perfectly smooth, the curvature impossibly uniform, the metal's work function a true constant, etc and etc.... None of this is true in the actual experiment, so our results WILL differ. But the theory provides some expectations, targets and predictions with which we can flog our experimental technique into obedience, or illustrate that a showdown is demanded...meaning the theory is inadequate to describe the results.

Some good information and ideas here.

Dave Cooper.

[Frank Sanns]

Jon,
Thanks for the reference. I do remember reading it a couple of years ago. Nice work but I wish they would have had larger grid size differences to at least see some differences. I hate when everything equals out. Then you have no idea of the sensitiviy of detection of a variable. I think I will reread the paper again. The mind is getting foggy and I forgot about that one. Thanks.

Dave,

A magnetron produces the energy from electrons. Becasue they are 2000 times less massive than a deuteron, they are accelerated to a higer velocity at the same eV. Sychrotron radiation is proportional to the velocity^4/radius^2 so a little bit in velocity really jumps up the loss.

For a 15 KeV deuteron, the velocity is around 1.3E6 meters/sec. The equation for sychrotron radiation is:

Power=(2*K*e^2*)/(3*c^3)*(v^2/r)^2 so for a deuteron whirling around in a 6 inch (0.17 meter) radius cyclotron, that is around 10^-28 watts/deuteron. At one amp at 15 kv that is 6.3e18 deuterons/second. The loss then would be <1 millionth of the 15Kw or <1mW.

Frank S.

[Richard Hull]

I figured that our stuff is so slow that any turning radiation via synchrotron would be insignificant. The fusor avoids a lot of hassles common to big accelerators.

Frank's deuteron current figures would be in the tenth of an amp range which is something we have never witnessed in a fusor.

Our fusing deuteron current in a 10e5n/s fusor is normally about 100 fempto amps while I would imagine the fusible but missed deuteron current is on the order of a few tens of picoamps and the total deuteron current is about a few milliamps. This is all for the simple fusion, of course.

Richard Hull