The Farnsworth Multipactor

[Wilfried Heil]

Farnsworth's original idea for a fusion reactor was to trap and heat a deuterium plasma with electron beams. The electrons would then "multipact", i.e. oscillate through the plasma. Hence the same electrons cross the plasma many times, and together they create a deep potential well which in turn traps ions.

This multipacting can happen in high powered vacuum tubes, if the electron transit time coincides with half the RF oscillation period and the electrons impact on a surface, which emits secondary electrons. It is an effect that one usually tries to carefully avoid, as it is destructive to the tubes.

The principle of Farnsworth's multipacting fusor looks exactly the same to me as that of Bussard's Polywell, except that the electrons which create the well are guided by electrostatic rather than magnetic means. The ions are trapped electrostatically in both cases.

I quote Richard here:
>Having spoken with all the techs and engineers in person on the Farnworth team for many hours of interviews in person in Fort Wayne and over any number of phone interviews over the years, Farnsworth refused to accept that his electron bombardment idea was not all that valid. As such, They, to the man, told stories of the tedium between 1960 and 1964 of no results, numerous modifications to the idea and concept, alterations of the device, several un-named complete device retoolings, etc. , with no neutrons in evidence.
>It was only with the arrival of Hirsch in his final year of his doctoral work, (summer of 63), as a guest worker that he, somehow, got Farnsworth to alter the design to an ion machine. With no results to that point, ITT was working on canceling the entire program and Farnsworth knew it. ITT and the Admiral decided to permanently hire Hirsch to give the entire effort a Phd somewhere in its midst. 1964 saw the first neutrons of even moderate significance. ITT decided to continue funding at a bit higher level.

Let's ask the question in a different way. Given our understanding of today, what would be needed to make a multipacting fusor work?

The natural choice would be a high powered, pulsed device. I envision something like a reflex klystron with several intersecting beams. Maybe the performance will not be at the level of the ion accelerating fusor with a gas target, because the fusion rate depends critically on the depth of the potential well, but the 3 detected neutrons per blast that Bussard claimed for the Polywell should be attainable. This is not intended as a power generating fusor, but as a proof of principle that fusion can be done in this way.

The big advantage is that it can be scaled up, and there is no grid in the place where it is least desirable.

I see no fundamental reason why the "Multipacting Fusor" can't work.

[Chris Bradley]

Wilfried Heil wrote:
> I see no fundamental reason why the "Multipactor" can't work.

Isn't the basic issue for Polywell or multipactor quite simply that if it is electrons that are 'attracting' the ions, then the electrons and the ions will do exactly that - that they will preferentially meet up?

If an ion is whizzing its way in towards a cloud of electrons, why would it bump into an ion first???

I would expect plenty of fast neutrals would be generated, with resultant fusion from fast-neutral in collision with embedded neutrals in the chamber walls, if fusion results at all.

On the face of it, it would seem self-evident that you need to aim towards the oft naively-proposed configuration of having 'all ions'. In realistic terms, that, at least, means the potential well must be formed by fixed structures that aren't going to move into the path of the ions and, preferably, that could also actively reject electrons from mixing in the same space that the ions mix in, as far as possible.

I guess this was Hirsch's successful step - forget about inviting the electrons to the party, it's all about the ions!

If electrons can 'freely roam' along with the ions, we're not actually talking about a generally-cold/locally-hot device anymore but a glorified thermalising device. The problems with such devices are the well-established un-results of 50 years' worth of magnetic confinement studies.

best regards,

Chris MB.

[Carl Willis]

Hi Wilfried,

I've thought about the idea of having a transit-time resonance with ions in the conventional fusor--basically making it a one-drift-tube linac operating on radial bunches of ions. During the positive swing of an alternating drive voltage, the synchronous ion bunch drifts at high velocity inside the grid. During the negative swing, the ions are outside the grid, feeling a field that pulls them back in. (This was originally what I thought the Park-Nebel "POPS" concept was all about. Turns out that's a different phenomenon.) You could in theory do this with electrons too, but they move much faster.

-Carl

[Dustinit]

It seems interesting that allot of people think that an electron meeting an ion will form a fast neutral. This is only the case for slow ions and low energy electrons. I read an article recently that described the process of stripping all the electrons from a uranium atom in a high current electron beam. Imagine the charge a bare nucleus of uranium would have and at the same time is in a sea of high energy electrons.
I recall it was called EBIS.
a quick google turned up this article,
http://www.osti.gov/bridge/servlets/pur ... /64977.pdf

I see no reason to pulse the electron beam, This should operate steady state with the electron beam as the focal point. Ions will simply fly through the beam and out the other side.

Dustin

[Frank Sanns]

Somewhere in this forum was a thought that I had about using multiple grids that were tied together with an RF oscillation. The idea would be exactly drift tube design on a 3 dimensional level. It would be much like fission and critical mass but with fusion and critical mean free path for fusable neucleii and electrons.

I have kept my eyes open for a large vessle that I could retrofit with multiple grids but the budget and the practicallity for me to do it personally is still outside of my means. Too bad as I think there would be some interesting results for a varity of reasons. Anybody have an old stainless steel chemical process tank they could loan out for a few months????

Frank Sanns

[Brett]

I'd been kind of thinking about something like that: If you magnetically contain the electrons in the center of the fusor, and try to keep a DC field in place, you need to continually pump up the field to compensate for the fact that the electrons WILL leak, since you can't make a spherical field, and they're going to jump field lines anyway during collisions.

But if you magnetically contain the electrons, and then feed in RF at the natural oscillation frequency of the ions, you don't have a DC field driving the electrons to leak from their magnetic containment. Half the time you've got an excess of ions in the center, and the electrons are trying to leak IN, not out. On average, there's no field to cause the electrons to escape the containment. AND you don't need your spherical cathode, the bane of recirculating ions.

To work, you'd need a field strength where the radii of the electron motion is much smaller than the dimensions of the fusor, but the radii of the ions is much larger, so that they effectively don't notice it. Quite possible since the latter is about 1800 times larger.

My thought was that this might let you put the magnetic coils outside the vacuum chamber, since you don't need really good containment, just a residence time significantly shorter than the ion oscillation period. Maybe using that coil design that looks like the stitching on a baseball.

That's what I'd like to try eventually, when I'm in a position to build a fusor. Getting laid off, and moving to another state, has set that back a few years...

[Chris Bradley]

The generalisation that applies here is to say that you get recombination when the electron's velocity is the same as the ion's. This make simple, mechanistic sense - a bit like the stunt where the parachutist drops into the back of an open top car. If the differential speed is too big, then they'll stay apart.

This simple model can therefore also explain why a fast ion will pull the electron off stationary neutrals (which will be persistent in any such device). An electron orbiting around a nucleus will have a probability of having a suitable velocity for charge-sharing, so if the ion comes up on the neutral in a certain position and direction then it can charge-share that electron.

But it is very very bad in a reciprocating GC/LH system. As the ion passes on through, the electrons will 'latch on' to its electric field and follow the ion out of that central region like little lost doggies. At some point, the ion will slow down to head on back.

It seems logical to me, then, that in this set-up there will ALWAYS be a point where an ion will slow down to the speed of the local electrons.

So, having free electrons seems a dead duck to me. Richard's little historical note there on Farnsworth's wanting early efforts only serves to convince me yet further, if the Polywell has not already done so. I think electro-static fields generated by electrons to force reciprocating ions to collide is a busted myth.

The fusor gets by this problem by accelerating free electrons out as quickly as it can. It is a heavy price to pay in energy terms, but it gets you to fusion.

What other means might there be to avoid GC/LH systems from ending up with slowing ions that can recombine? I hope there may be several - any ideas anyone? - but the only one I have come up with in 25 years thinking on it is to keep them moving fast by getting them orbiting in a circle rather than trying to pass them back-and-forth through the same space. This is a solution I am currently investigating.

The previous logic to these devices has been that it is the fast ions that need to be all pushed into the same space to get fast-fast collisions, but the reality that the fusor illuminates is that fusion is much easier with fast-ion/slow-neutral. So keeping the ion velocity continually high through a back-ground medium seems a much more logical place to go after the fusor. For me it is as if the fusor is screaming out this solution!!

best regards,

Chris MB.

[philstro]

Hello Wilfried,

Is it true that we have a very sketchy notion at best, as to what the actual multipactor configurations were that Farnsworth was trying? Other than they were using concentric cylinders with picture tube guns until Hirsch, who used concentric spheres and eliminated the gun. What do we know now that was not known then? There is not really a lot of theoretical physics in this is there, it is mostly Edison type trial and error.
Your proposal is essentially to operate a klystron (or magnetron) with a sparse deuterium atmosphere inside, and to modulate or oscillate the anode voltage to provide a maximum at the moment, or slightly before, the deuterium ions converge on an electron bunch? That seems like it would work. Actually doing it would be a huge challenge. I guess you would need a radar transmitter or second klystron somehow triggered by the first. Why would you call it a multipactor since it is not using a secondary electron multiplying effect; just the spiraling bunches created by cavity resonance? If the device was large enough, i.e., lower frequency, you might be able to use an ordinary radio or TV transmitter for the anode voltage.
The polywell is another thing where it is hard to know just what they are doing. Are they shooting the electrons in, in a steady stream? The pops proposal was to use a time varying current in the magnetizing coils. Their anode was DC on the metal shells around the coils, is that correct? The fact that they (apparently) did not foresee blowing up a coil by discharging huge capacitors into it, coupled with all the hype and claims based on five neutrons leaves me skeptical of the whole polywell project.
However, the idea of using some magnetic means to help create a virtual cathode looks very good (to me). That would be especially so if you did not have to resort to superconducting coils or huge capacitors. These things strike me as fun, but impractical. Too bad there is not some other way besides electrons, to create a deep negative potential well.

Regards,
Phil Strohbehn

[Chris Bradley]

Phil Strohbehn wrote:
> However, the idea of using some magnetic means to help create a virtual cathode looks very good (to me).

You do seem to be in the majority on this.

I'm not aware of anyone else's expressed view that having free electrons around will kill the very thing being attempted.

I patiently await, in my minority, convincing evidence that a field generated by electrons can ever produce any detectable fusion at all. I just can't see how ions can survive as they reciprocate through the electrons.

best regards,

Chris MB.

[philstro]

Hi Chris,
Imagine an air hockey table with sideboards, full of ping pong balls (fluidized bed of electrons). You drop a bowling ball (D ion) in. Will even one pp ball be smashed? No, very low probability.

If you could eliminate the inner grid you could run at power levels that otherwise would vaporize the grid. Possibly in a larger vessel one could use a consumable electrode in the center with some magnetic confinement to help define the cathode.

Either way you are consuming a lot of power keeping the electrons moving therefore never coming close to net energy. But maybe you could make more neutrons.
Regards,
Phil Strohbehn

[Brett]

"I just can't see how ions can survive as they reciprocate through the electrons."

It's not a mystery: If the relative velocities are high enough, the probability of an electron/ion collision neutralizing the ion becomes vanishingly low, because the collision involves so much more energy than is necessary to strip an electron off. The electron won't "stick".

At least that's the theory, of course you're going to lose *some* of the ions to neutralization.

[Chris Bradley]

Phil Strohbehn wrote:
> Imagine an air hockey table with sideboards, full of ping pong balls (fluidized bed of electrons). You drop a bowling ball (D ion) in. Will even one pp ball be smashed? No, very low probability.

I would counter this analogy by saying I imagine that the bowling ball would punch a hole right through the table (!), and the ping pong balls would trickle out of the hole, following it. This is what we are taking about, the ion punching right through this table of electrons. What stops the electrons leaving the table through the same hole/direction that the ion leaves it?

Brett Bellmore wrote:
> If the relative velocities are high enough, the probability of an electron/ion collision neutralizing the ion becomes vanishingly low

To a point, without endless caveats, I agree.

But as the ions slow down at the end of their tracks, having just stirred up a dust-cloud of electrons in their wake behind them, they will pass through zero velocity. If the electrostatic force between the ions and the electrons was enough to pull the ions in, why is it not strong enough to pull the electrons out to the ions by the same route?

So the probability that they DON'T neutralise appears to me to then become vanishingly small? Keep the ion velocity high and I will go with the story, but this doesn't appear to be the principle in these devices. Maybe I am missing some essential understanding on this?

best regards,

Chris MB.

[philstro]

Hi Brett,
One of the fusor concepts as I understand it is that you have monoenergetic ions travelling in toward the negative potential well created by the electrons. Meaning that they are all coming in at a speed determined by the anode voltage instead of a broad distribution of speeds.
Regards,
Phil Strohbehn

[Brett]

"If the electrostatic force between the ions and the electrons was enough to pull the ions in, why is it not strong enough to pull the electrons out to the ions by the same route?"

Two points:

1. At the outside, where the ion energies approach zero, we don't much care if the ions are being neutralized, they're also being created at the same rate. We care about it when they're at high energy, because if they're neutralized then, they continue on out of the center with their energy intact, and deposit it into the vacuum chamber wall. And the system loses energy. As well as electrons from the center.

2. If, as in the Bussard concept, you're containing the electrons by a magnetic field, electrons are about 1800 times more effectively contained, because of their higher charge to mass ratio. 3600 times more than deuterons, in fact.

[philstro]

Hi Chris,
In my understanding of glow discharge mode of fusor operation there is a continuous flow of electrons from the cathode to the anode so yes, some if not many electrons will be in the “wake” of the ions as they recirculate. Due to their much lower mass wouldn’t the electrons be travelling much faster? In the potential well however, there is a dense grouping or space charge of electrons which as a whole (not individuals) tend to stay there. The lumped charge from that grouping is what attracts the ions. The charge gradient increases as the inverse square of the distance for the ions as they “roll down the hill” toward the cathode until they “fall off the cliff” in the area of strongest negative charge. Since they are coming in from all directions some collide and occasionally fuse.

For the positively charged ions that have conserved their momentum by not colliding, most of them, they travel through the cathode and back toward the anode which repels them back in again. Neutral D2’s are being continuously let into the chamber by the gas valve and some are being formed by electron capture. Some or most of these will be re-ionized (their electrons stripped off) by the high anode voltage.
Regards,
Phil Strohbehn

[Chris Bradley]

Brett Bellmore wrote:
> 1. At the outside, where the ion energies approach zero, we don't much care if the ions are being neutralized, they're also being created at the same rate.

hmmm... I will go with you to a certain degree - if ions reach some point in the field and are neutralised right at the point where they are lab-stationary, then, OK, it would be a legitimate argument that they have just given up their energy back to the electric field. But in reality they surely must be giving up some fractions of their energy each time this goes on and these devices just can't afford to do this. If we take the 50keV deuterons calculated in the other recent post, a cross-section of 70mb in a vacuum of one micron (and I think the Polywell is meant to run at significantly harder vacuums) means it has to 'normally' travel approx 1/(1E19/m3).(70E-31m2) = 14 million kilometers before it gets to fuse. Being stopped after each stroke just doesn't fill me with confidence - these ions have to really get a move on to cover that distance!

Just consider the cost of replacing the electrons, let alone the ions. 13eV per electron on 14E9m/chamber_size occasions. That'll add up to a stack of input energy.

Phil Strohbehn wrote:
> Hi Chris,
> In my understanding of glow discharge mode of fusor operation there is a continuous flow of electrons from the cathode to the anode

Because the fusor generates its field from rigid structures, it 'forces' both electrons and ions into specific positions. This means it can, quite effectively, keep them apart.

> Due to their much lower mass wouldn’t the electrons be travelling much faster?

In a fusor, absolutely. You'd get a few hundred electrons flowing off the grid to the anode for each and every reciprocation of just one ion. It's a heavy cost, but they stay separated due to fixed structures, a feature this multipactor or the Polywell do not appear to enjoy.

best regards,

Chris MB.

[Wilfried Heil]

The physics of fusion hasn’t changed over the last 50 years, but we may have a better grasp now on the engineering requirements which have to be met to actually make D+D fusion in an electrostatic potential well possible. We also have much better means to simulate at least parts of the processes involved, like the current and beam power required for the formation of a deep enough potential well.

Close reality checks with experimental data would be needed as well. Otherwise, the results can be so far from reality that it may be better to build a machine and then try to analyze it later.

Here is how I presume it could work:

- The simplest multipacting fusor would just have two parallel plates, or parts of a sphere, to which a high voltage RF is applied. When the electrons are in resonance with the RF, at a predetermined voltage and frequency, they will hit the opposing plates on each transit and produce secondary electrons. This multipacting effect causes the number of oscillating electrons to rise exponentially.

- The advantage to use multipacting to generate electrons is that no other electron or ion source will be needed, and the reciprocating current can be several hundred times higher than the current supplied by the plates, which only needs to replace those electrons which are lost from the beam.

- When the electron beams are focused, they will create a negative space charge region in the center of the chamber. This will then attract and accumulate ions, which can move freely around inside of the potential well.

- The ions don’t feel much of the RF due to their large mass, only the electrons oscillate. Hence the ions will not see any net forces from the electrodes at all, just the potential well in the center of the chamber.

- This is intended to be a thermal fusion machine with electrostatic trapping of the plasma! If the plasma in the potential well is thick enough (relative to the surrounding neutral gas), then the ions will acquire a maxwellian energy distribution. If the ions are too few to thermalize, then they will also oscillate through the virtual cathode and interact mostly with the background gas. So there is a threshold of the plasma density which must be exceeded, in order to obtain a thermal plasma. Below this threshold, the device will operate just like an IEC fusor.

- The electrons are only needed to set up the potential well and to heat the plasma. They will interact very little with the gas as long as they are fast enough. When they slow down, they will be repelled by the central space charge region and drift to the grounded outer shell. On the other hand, they cannot transfer much energy to the ions either, so that the heating of the plasma will occur over multiple collisions at random.

The multipacting resonance frequency can be calculated from the following formula:

f_osc = k * sqrt(V) / d in [Hz]

with k = 7.5E4 [s^-1 * m * V^-1/2] (experimental parameter, the theoretical one is slightly lower)
V - RF amplitude in [V]
d - distance between the plates in [m]

In the fusor which I have here, with a distance between plates of 89 mm and an RF amplitude of 10 kV, the multipacting frequency would be around 85 MHz. This is not a sharp resonance, but a fairly broad peak with a half height full width of +/- 10% of the oscillating frequency or +/- 20% of the voltage.

Carl - I also have an RF feed to the HV terminal of my fusor, which can be superimposed on the high voltage DC. This runs at a few MHz and seems to generate ions that keep the discharge alive at fairly low pressures. I have not noticed any effect on the fusion rates yet.

Phil - The reason for using a Klystron-like setup would be that it is self resonating. So there will be no need for an external oscillator, feedlines and matching networks, if the oscillator can be an integral part of the fusor. The frequencies for the electron multipacting resonance will be relatively low (for a Klystron), in the range of several 100 MHz at an operating voltage near 100 kV.

>Is it true that we have a very sketchy notion at best, as to what the actual multipactor configurations were that Farnsworth was trying?
Yes, unfortunately, because it didn't work as intended. One of the relevant patents is for a multipactor ion source, and the earlier fusors were electron gunned and used multipactor surfaces in a spherical arrangement. The secondary electrons were to be emitted from the vacuum vessel's shell and then accelerated inwards through a grid. More of what has been tried should be known to Richard from his interviews.

Chris - The fast electrons will have little interaction with the ions, but some will recombine of course. So there will be a small current from the virtual cathode in the center to the outer shell, just like in a fusor. I think most of the fusion will happen from interactions between ions and the neutral gas and not by embedded fusion with fast neutrals. But granted, if we see any fusion at all, we’ll have to determine where it is taking place.

Brett - quite correct that the interaction between fast electrons and matter drops off quickly at higher energies. A program which simulates this nicely for ions is SRIM.

I don't really expect any wonders from this, but I'm curious if it is possible to get fusion by trapping deuterons with e-beams, just as Farnsworth had intended to do. What I would like to see is an utterly inefficient IEC fusor with a virtual cathode at first and then one which can hold a small thermalized hot plasma later on.

I've added a sketch of the principle, though I have no idea if this is related to anything which Farnsworth did.

[Chris Bradley]

Sounds like you are simply generating an RF induced plasma. What particle density are you hoping for here? I suspect your Debye length will be far too small for any electrostatic behaviour at the temperatures this is likely to reach. I don't know if there is some plasma wave frequency that would mean it has some chance of working but I'd guess that'd be in the GHz for any plasma density where detectable neutrons would be generated.

This sounds like it is going in quite a different direction to IEC?

[Wilfried Heil]

>Sounds like you are simply generating an RF induced plasma.
The multipacting effect does not rely on a plasma, but on the proper phase angle between the electron beam and the RF. The electrons then create ions as a welcome byproduct. Because the electrons loose very little energy per pass and we don't want to dump the beam after a single transit, we'll keep them oscillating.

>I suspect your Debye length will be far too small for any electrostatic behaviour at the temperatures this is likely to reach.
The ions don't need to follow the RF. The objective is to contain a hot plasma within a small area for thermal fusion.

>This sounds like it is going in quite a different direction to IEC?
Inertially confined electrons which in turn confine the plasma - within a space charge region. In contrast to the standard IEC design with a central grid, the electrons now have a purpose.

[Chris Bradley]

Sorry, I don't understand your scheme. Are you thinking that the electrons will be contained in the centre, between the two electrodes, thus pulling the ions in to the centre aswell?

[Brett]

If I'm reading it correctly, the notion is that because this cloud of electrons is being yanked back and forth between two electrodes which are concentric spherical segments, they will be converging on that common center during that trip back and forth, leading to a sharp concentration of electrons there.

Of course, while the field lines emerge perpendicular to the electrodes, and thus pointing directly at the common center, they will rapidly diverge, and the effect would be closer to two flat electrodes, with no significant focus at the center.

[Wilfried Heil]

Sorry if that was confusing. I've added a sketch to illustrate the principle.

Brett - if you get a chance to admire one of the old Crooke's tubes with curved electrodes, you can see that the electrons fly off at a vertical angle from the surface, towards a focal point. The field diverges, but the electrons continue straight ahead anyway.

[Chris Bradley]

So why wouldn't it just form a discharge plasma between the electrodes in the top and bottom regions? There wouldn't be any of the multipacting going on there, so plasma would just hang around there, in its little Debye cocoon and quite unconcerned about the electrons' antics in the middle of the device? I don't see why ions would want to tend to head towards the centre of this arrangement?

[Wilfried Heil]

>So why wouldn't it just form a discharge plasma between the electrodes in the top and bottom regions?
It will, unless the Paschen product p*d is too small for a glow discharge. We have to work below a specific pressure because we want to avoid this. Likewise, there will be no discharge between the spherical electrodes and the outer vessel, because the product p*d is too small here as well.

[Chris Bradley]

How can this reach fusion temperatures then, if this plasma is not confined away from all parts of the reaction vessel?