Engineering help requested

[Lerner]

There are a number of challenges with moving from a successful experiment to a working prototype generator that we can already start working on, if we have some volunteer help. So for the New Year, we are inviting engineers and scientists who want to donate their time to this project to help with the problems outlined here.
1) Conditions in the generator chamber—how to keep the boron from depositing on the electrodes?
Our current calculations indicate that in a generator boron will not be mostly in a vapor state. We won’t be leaving enough energy in the plasma in the chamber to vaporize all the boron and we estimate the operating temperature will probably be around 3500 K, well below the boiling point of boron. At the same time, as we understand it, it looks like most, if not all, hydrogen-boron compounds will be unstable at this high temperature, so the boron would be cool into a mist of fine liquid droplets. We want to know, first of all if this picture is accurate, or if there will in fact be enduring hydrogen-boron volatiles. Second, we want to know how to avoid allowing the boron to deposit on the electrodes. This is undesirable as boron is a strong electric insulator and removing it with the current pulse will almost certainly create high enough local temperatures to erode the underlying beryllium electrodes as well. Presumably the motion of the gas within the chamber will keep most of the mist from freezing out on the electrodes, but we need to know under what conditions this will occur—how much motion is needed—will this actually happen naturally or will we need to work to keep the motion up?
This analysis will be useful for our current experiment as well. Ideally it would be good to pump the boron out before it can deposit on the electrodes. How could this be possible? Can we somehow keep it swirling around until it can be pumped out? In an experiment, the boron would presumably freeze out to a fine dust.
2) What are the limits on cooling the electrodes? How hot can the outside of the electrodes get before weakening the beryllium? How fast can the heat be removed by compressed helium?
3) Are there way to increase beryllium’s strength and ductility?
4) Can we concretize the design of the ion beam convertor? Should it be both inductive and electrostatic, or will this push up the cost too much?

[Francisl]

I suggest using jets to create a laminar flow of cool fuel along the surface of the electrodes. That would cool the surface of the electrodes and block the boron particles from touching the electrodes. Vacuum pumps would have to exhaust the chamber to maintain the proper pressure and remove the boron particles. The exhausted fuel could be cleaned, cooled and recycled.

[asymmetric_implosion]

A couple of questions/comments:

1) If the operating temperature is 3500 K and the melting point of Be is <1600K and vapor point is 2800K are you planning on vapor electrodes? Not impossible but probably pretty challenging at a high repetition rate. Our Z-pinch friends use gas puff technology all the time.

2) I assume that the generator is still running at 200 Hz. If so, you have a 5 ms window for particle deposition. Most sonic processes occur on the ~1 ms scale so particles may not be too bad. I’d be more worried about chemistry between Boron and Be. Laminar jets are probably going to be terribly upset by the returning shock from the gas returning to the vacuum created by the pinch process.

3) What is the pump lifetime you require? Pumping particles through any turbo is very bad news. Rotors spinning a speed of sound hitting particles is like bullets hitting a wall.

4) Be is typically alloyed with aluminum to increase aluminum’s strength.

[Lerner]

First, I want to emphasize I am talking about two different situations—the generator pulsing 200Hz and our experiment, firing a few times an hour.
For the generator, I think that solid electrodes are possible. Cooling rates of 1 kW/cm^2 are considered achievable today. At 3500 K, blackbody radiation would be at that level, so you could keep electrodes much cooler, say around 1100 K. If I have done the calculations right—and I invite you to do them yourselves–neither conduction nor convection with any reasonable internal gas velocities can cool the gas anywhere near as fast as radiation, so they can be ignored. In addition the entire heat content of the 0.7 g of gas in the chamber is only 8 or 9 kJ so if you cool it all the way down to the electrode temperature in 5 ms, you still only get 1.5 kW/cm^2 for a 10 cm radius spherical vacuum chamber.
However, if the droplets of molten boron hit the electrodes and stick, they would presumably freeze on to it and probably cause localized melting. So clearly it would be really good to keep them away or prevent them from sticking. The question is how can we calculate that?
Now obviously we can’t be pumping boron mist through a pump so I am not talking about evacuating the chamber in a generator. I suspect there should be some good way of letting the helium produced slowly leak out and new fuel leak in.
The pumping-out idea is for the experiment, when we would be pumping out cooled boron dust. No doubt that would not be good for the roughing pump, (the turbo would be turned on later) but we are talking about thousands of shots, not billions.
I have not looked up boron-beryllium chemistry as yet. Does anyone know about that? My guess is that, again, very few compounds are stable at these temperatures.

[Francisl]

Another thought that I had is that right after the electrical discharge the particles will have an electrostatic charge. An electrostatic precipitator inside the chamber could be formed by having a residual charge on the electrodes with respect to a collector plate outside the path of the plasma front. My guess is that the maximum particle concentration will be close to the pinch area so a collector could be placed close to that area.

[Francisl]

Another thought occurs to me. Normal chemistry will be complicated by the intense photo-ionization in the chamber. I don’t know if that will create compounds faster or lead to their decomposition.
It would be interesting to coat some samples of beryllium with boron and beryllium/boron compounds and expose them to intense x-rays to see what would happen. That could be a good experiment for a university lab.

[meemoe_uk]

Well here’s an amateur’s rough design. If its no good, you can tell me why and I can learn something!

Are we allowed to move the anode away from the cathode?
– The barriers have orifices to allow fluid circulation.
– The cathode edge ( and ideally its whole cylinder ) is positioned out of direct line from the fusion zone
– If need be, the anode can be simply shielded from direct line of the fusion zone too.

Attached files

[asymmetric_implosion]

@Lerner: I’m still a bit confused. What is 3500 K? If the gas is 3500K I don’t see a problem holding the electrodes as 1100 K or less with some creative thermal engineering. If the metal is 3500 K, I don’t understand the logic. Your calculation of the heat transfer from what I presume is the gas is likely inaccurate. The results appears to assume that you can remove heat at 1.5 kW/cm^2. All heat flow is driven by temperature differences in the system and the convection of the gas if the gas is the hottest element. Radiation is important for a time but convection could also play a role as the gas is extremely turbulent and should be directed at the chamber and the inner anode diameter. The decay of the electron population is also important. Electrons will carry away and radiate away heat.

My piece of advice is design a larger vacuum spool so you can address the shock problem with CF gasket leading to vacuum issues if you still believe it a problem. This will allow for a large gas buffer and throw away volume. If you are interest in dealing with gas based nucleation, I would suggest looked at our semiconductor friends. They have these problems and deal with them. Probably a good start.

[asymmetric_implosion]

meemoe_uk wrote: Well here’s an amateur’s rough design. If its no good, you can tell me why and I can learn something!

Are we allowed to move the anode away from the cathode?
– The barriers have orifices to allow fluid circulation.
– The cathode edge ( and ideally its whole cylinder ) is positioned out of direct line from the fusion zone
– If need be, the anode can be simply shielded from direct line of the fusion zone too.

You have designed a Z-pinch. You have lost the axial flow of plasma that stabilizes the plasma focus and allows for reproducible operation. The cathode is a lesser problem than the anode in a plasma focus. The anode takes the brunt of the energy from the expanding pinch plasma. This can lead to metal vaporization, melting, etc, of the electrode. The cathode will vaporize but a much smaller extent as the current is distributed over a larger area.

The proximity of the electrodes is a key problem for any pulse power based approach that directly flows current into the plasma. Tokameks and laser systems remove this complication by taking away electrodes. The move to the tokameks was driven by the electrode problems in long, slow Z-pinches. The materials problem of the PF is non-trivial and needs a serious research effort. A few teams have only scratched the surface and as is usually the case, the answer is not the same for every application. For example, the LPP need for high x-ray transmission of the anode is driving the use of Beryllium. Folks working on neutron generators and lithographic x-ray sources are less concerned about x-ray absorption in the anode and favor long lifetime operation so they choose materials like SS-304, molybdenum and tungsten alloys.

The message at the end of the day is the electrodes are a consumable. You can only extend their life so far given the limits of available materials. The alternative is to choose inexpensive materials that can be replaced rapidly. I favor frequent replacement as complex engineering system may not buy much increase in operational lifetime for a significant cost sink. Another trade study to be completed.

[Lerner]

@Lerner: I’m still a bit confused. What is 3500 K? If the gas is 3500K I don’t see a problem holding the electrodes as 1100 K or less with some creative thermal engineering. If the metal is 3500 K, I don’t understand the logic. Your calculation of the heat transfer from what I presume is the gas is likely inaccurate. The results appears to assume that you can remove heat at 1.5 kW/cm^2. All heat flow is driven by temperature differences in the system and the convection of the gas if the gas is the hottest element. Radiation is important for a time but convection could also play a role as the gas is extremely turbulent and should be directed at the chamber and the inner anode diameter. The decay of the electron population is also important. Electrons will carry away and radiate away heat.

My piece of advice is design a larger vacuum spool so you can address the shock problem with CF gasket leading to vacuum issues if you still believe it a problem. This will allow for a large gas buffer and throw away volume. If you are interest in dealing with gas based nucleation, I would suggest looked at our semiconductor friends. They have these problems and deal with them. Probably a good start.

Yes, the gas is 3500 K . Even if convection is important, the heat flow out is limited by how much heat we are putting in, which is , I calculate about 6-8kJ per shot. If there is a lot of heat transferred by convection, than the average gas temperature will be lower than 3500 K, which assumes radiation is the main coolant.
If you have sources from semiconductor people that would know about forming mists and keeping particles away from surfaces, can you share them?

[gianfranco]

ELECTRODE COOLING. Electrode cooling could become much easier by reversing feed polarity to the Cell (assuming this is technically possible and allowed by the electrical connections of capacitor & switches).

With polarity reversal the Anode would be grounded and the troublesome alumina insulator would be eliminated. The Anode could be built from a solid cylindrical block of metal, flanged thru the top chamber wall to an external heat sink which could be convection cooled, air cooled or liquid cooled, according to technical convenience & engineering constraints.

The Cathode would become a “floating cathode”. The top wall of the chamber could be made with a thick circular plate of Teflon, for limited mechanical elasticity, covered by a plate of Alumina carrying as many “towers” as needed to hold as many cathode bars. The cathode bars would be made of thick tubing joined on top by the cathode joining ring, also made of tubing. On the ouside of the top wall we would have the electrical connections (negative) to each cathode tube. In addition half the cathode tubes would receive liquid coolant under pressure (non-toxic transformer oil). The coolant would reach the top cathode joining ring and tru it reach the other half of the cathode tubes which would then discharge the coolant back to the cooling system. Any convenient method could then be used to stabilize coolant temperature to the required value and perhaps obtain Energy Recovery.

For example a “solid” (no insulator) Beryllium Anode with a thermal length of 10 cm and with the tip at 1,100 °C (Berillium melting point 1287°C) will dissipate almost 5,5 kW if the cold end is kept at 10 °C. Thermal length measured from center length of Anode and cold end. A single hollow Berillium Cathode bar with a wall thickness of 3 mm and a thermal length of 10 cm, if cooled by a suitable flow of oil at 100°C could be easily be kept at 600°C while dissipating heat in excess of 10 kW.

BORON DUST PROBLEM. My proposal is to employ an injector and a getter. The injector will be served by a calibrated injector pump which will deliver a metered quantity of Boron powder to the injector. This arrangement limits the quantity of Boron into the Chamber. The getter is a simple metal ring fitted near the inner bottom of the chamber connected thru an insulator to a low power positive HV supply (30 kV is a good guess). At the beginning of a discharge cycle the injector will supply the limited quantity of Boron powder. At the end of the ignition cycle and during recovery (say at plus 20 uS) the HV PSU will switch on and the getter will easily capture both Boron dust at zero charge from the Anode and at negative (residual charge) from the cathode. It should not be difficult to automatically recover Boron dust after a convenient number of cycles, because extra Boron dust will be localized at the bottom of the chamber.

[Francisl]

@Lerner: If you have sources from semiconductor people that would know about forming mists and keeping particles away from surfaces, can you share them?

This link may help.
Silicon Semiconductors Chamber Cleaning

Here is another link of contacts.
FABVANTAGE CONSULTING

[Alex Pollard]

Lerner wrote:
For the generator, I think that solid electrodes are possible. Cooling rates of 1 kW/cm^2 are considered achievable today. At 3500 K, blackbody radiation would be at that level, so you could keep electrodes much cooler, say around 1100 K. If I have done the calculations right—and I invite you to do them yourselves–neither conduction nor convection with any reasonable internal gas velocities can cool the gas anywhere near as fast as radiation, so they can be ignored.

This presentation casts doubt on aspects of Black Body theory.

[Francisl]

Here is a link to a calculator for this example: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/stefan.html

Here is a link to high power tests on beryllium: http://www.iop.org/Jet/fulltext/JETR96002.pdf

[dzhkzhnyr]

Hi Dr Lerner,

If I have any worthwhile input, it’s most likely to be on your first question. If you’d be interested, I think I could generate some phase diagrams for boron-hydrogen under reactor-relevant conditions. I’ll try to make a phase diagram of boron-hydrogen around 3500K, and 10-1000 Torr.

Edit:

I’ve attached Pressure vs Temperature and Temperature vs Composition phase diagrams.

The data describing the thermodynamics of these systems comes from SGTE’s “SSUB4” database.

This modeling describes solid and liquid boron’s Gibbs energies as two functions, both of which are essentially polynomials. The gas phase is described as 10 ideally interacting species, each of which also has its own sort-of-polynomial function Gibbs energy.

Thermo-calc, the software these plots were produced in, takes those descriptions and finds the lowest energy combination of species to make the gas phase, and the lowest energy combination of phases to meet the pressure/composition/temperature conditions.

So, for example, at 3500K, it’s found that out of 1 mole of substance, .913 moles are in the gas phase, and .086 moles are liquid boron. Further, the gas phase is made up of .480 moles Boron, .439 moles Hydrogen, .073 moles H_2, .005 moles BH, and .001 moles B2, along with trace amounts of other compounds, e.g., 1.58e-6 moles of BH3.

This P-T(log P vs 1/T) diagram was created at a fixed composition of 50:50::boron:hydrogen, but could be generated at other compositions as well, and the T-X(T vs mole fraction B) diagram was created at 100 torr, but could also be created at other pressures.

All T units are Kelvin, all P units are Pascals.

Attached files

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