Heat produced by Focus Fusion and cooling

[vansig]

Here’s another:

“The microstructure and mechanical properties of ultrafine-grained ferritic alloys containing nanoclusters (NCs) are investigated. The NCs (diameter ∼3nm) as well as the grain size (∼200nm) remain stable at 1000°C. Substantial Hall–Petch strengthening occurs at room temperature. Surprisingly, the creep rate at 800°C is up to a factor of 10^8 slower than that predicted for diffusional creep. Possible reasons are the high NC coverage as well as Cr and W enrichment at the grain boundaries, and inhibition of self-diffusion.”
— http://tinyurl.com/2c7enbn

[Aeronaut]

Sounds very promising except for the ferritic material, which should act like an X-ray magnet relative to even copper.

[jamesr]

I was thinking more that if the anode had a 10 to 20nm thick skin of something like carbon in some highly conductive configuration (eg graphene) then this would mitigate the surface vaporization and lessen the joule heating due to the large current flowing in the skin compared to beryllium.

The surface layer would still have to be thin relative to the absorption depth of the X-rays. So it would be a trade off between the lower Joule heating and the increase X-Ray absorption drive heating.

Then if the anode skin temp can rise to say 1200K and so the coolant exit temperature can rise to 900K then the Brayton cycle becomes viable

[Brian H]

vansig wrote: Here’s another:

“The microstructure and mechanical properties of ultrafine-grained ferritic alloys containing nanoclusters (NCs) are investigated. The NCs (diameter ∼3nm) as well as the grain size (∼200nm) remain stable at 1000°C. Substantial Hall–Petch strengthening occurs at room temperature. Surprisingly, the creep rate at 800°C is up to a factor of 10^8 slower than that predicted for diffusional creep. Possible reasons are the high NC coverage as well as Cr and W enrichment at the grain boundaries, and inhibition of self-diffusion.”
— http://tinyurl.com/2c7enbn

Yes, that sounds very good, doesn’t it? 100,000,000 times better, actually, than expected. 😉 :cheese: :coolgrin:

[Allan Brewer]

jamesr wrote: I was thinking more that if the anode had a 10 to 20nm thick skin of something like carbon in some highly conductive configuration (eg graphene) then this would mitigate the surface vaporization and lessen the joule heating due to the large current flowing in the skin compared to beryllium.

I thought that with these very large currents the majority of the current flows on the outside of the electrode rather through the conductor anyway??

[jamesr]

Allan Brewer wrote:
I thought that with these very large currents the majority of the current flows on the outside of the electrode rather through the conductor anyway??

Exactly – that’s the problem. The current flows through a thin surface layer & hence all the resistive heating is concentrated there. Although it is the fast rise time (ie frequency) or the current flow that causes it to flow in the skin.

[Aeronaut]

And the X-ray burst hits the anode right as it’s temperature is peaking?

[vansig]

but the xrays should emanate in random directions as the pinch compresses, so it is more about the electron exit beam, that strikes the dimple in the anode. carbon nanotubes, or even colossal carbon tubes, would conduct both heat and electricity very well along their axes, if aligned parallel to that beam.

when it comes to x-ray absorption, carbon is also a light element, so isn’t very bad a choice.
its heat-conductive properties and strength might more-than make up for increased x-ray absorption.

the electron exit beam is very much like the focus area of an electron beam welder; there’s some very interesting info about these at http://www.hps.org/publicinformation/ate/q143.html

[Aeronaut]

Sounds promising for the thermal, electrical, and mechanical loads. Do you think this would enable smaller electrode diameters?

[Allan Brewer]

Could we do some clarification as to where the heat actually arises in the FF device because there seem to be some diverging statements:

(1) ELECTRODE RESISTANCE Some of the postings refer to the resistance in the surface layer of the anode, and I assume here we are addressing the simple electrical resistance in the anode to the 100KJoule input to initiate the pinch. “The current flows through a thin surface layer & hence all the resistive heating is concentrated there” What about the cathodes – will there not also be resistive heating there? – Can we cool those? – are they thick enough for Helium flow?

(2) ELECTRON EXIT BEAM Then some of the postings refer to the electron exit beam from the plasmoid ( “so it is more about the electron exit beam, that strikes the dimple in the anode“). But Eric in the thread about the anode said “We hope that when the DPF is optimized almost all of the e-beam energy will be deposited in the plasmoid, leaving very little in the exiting beam.“. So perhaps that would not be a major source of heat? And indeed there are ideas for extracting that energy (“This is quite a big area (referring to the target for the e-beam) – so I would think if the it were replaced by a fine mesh, rather than a simple hole, that let most of the electrons pass through to another small chamber behind the anode, they could be slowed down as you describe (extracting their energy in the process). “

(3) PLASMOID Does the plasmoid itself radiate heat to all adjacent parts of the device? – presumably depending on temperature, surface area and lifetime of the plasmoid?

(4) CAPACITORS We know there will be resistive heating in the capacitors, which can be addressed by water cooling.

Could our engineers and physicists assign rough percentages as to which of the above sources (or others) gives us the “4-8 MWatts ” of inefficiency heat??
(Apologies if I have misrepresented anybody)

[jamesr]

Allan Brewer wrote:

Could our engineers and physicists assign rough percentages as to which of the above sources (or others) gives us the “4-8 MWatts ” of inefficiency heat??
(Apologies if I have misrepresented anybody)

I’m not sure I can go as far as percentages but here are a few figures from analysis done by Doug Olsen in 2003 (not verified):

For a copper anode, if the current is treated as a 1/4 sinusoidal rise to 600kA in 2us the skin depth is ~0.18mm. Integrating the current as a function of radius gives a maximum temperature rise of ~26C at the surface – for one shot. This diffuses into the bulk of the anode over time so after 40us or so the surface has dropped to 15C above its pre-shot temperature.

Replacing the thermal and electrical conductivities with those of berylium, and increasing the current profile to rise to 3MA in 1us (giving a skin depth of 0.2mm). Starting from a 20C ambient temperature, the surface temperature rise is ~400C after one shot. after 100us the heat is conducted into the bulk and so the surface drops to 200C above its pre-shot temperature.
The colder the coolant, the faster the surface temperature will drop and the sooner you can have another pulse.

One of the main issues from this localized surface heating is the thermal expansion and stresses put on the material. Essentially the rate of thermal expansion of the surface exceeds the yield point of the material. So it cannot expand & contract with cooling without undergoing significant fatigue. Potentially causing surface cracks & flaking off of the surface layer after repeated shots. The thermal stresses are on top of the pinch stress caused by the magnetic field created by the current.

For comparison the half-depth absorption of berylium to 100keV X-rays is ~6mm. So the X-rays heating is distributed much further into the anode than the ~0.2mm depth of the resistive heating.

The electron beam heating is focused on a small area in the centre of the anode. I don’t think you can do anything to stop these vaporising the surface & creating a pit. Not really a heating problem; more of a wear rate & pollution of the plasma for the next shot.

[vansig]

jamesr wrote:
For a copper anode, if the current is treated as a 1/4 sinusoidal rise to 600kA in 2us the skin depth is ~0.18mm.

my intuitive feeling is, that this rise, (DC pulse from 0 to full current), matches the shape of a 1/2 wave better, since skin depth begins at zero, and increases with time.. and that 1 µs is closer to the actual rise time. this would yield somewhat smaller skin depth (~50% less?)

does that make sense?

[benf]

Perhaps one of you could come up with a graphic simulation of heat propagation through the cycle. I see a 3D motion animation presentation for this. Gathering all the factors and with different materials employed…. Sounds like a science project. I’m not up to it, but maybe you all are. This is a really interesting thread that’s dealing with the crux of potential risks as energy levels increase. You can’t know for sure how it will all play out without going through the experimental phase, but it doesn’t hurt to have foresight.

[jamesr]

benf wrote: Perhaps one of you could come up with a graphic simulation of heat propagation through the cycle. I see a 3D motion animation presentation for this. Gathering all the factors and with different materials employed…. Sounds like a science project. I’m not up to it, but maybe you all are. This is a really interesting thread that’s dealing with the crux of potential risks as energy levels increase. You can’t know for sure how it will all play out without going through the experimental phase, but it doesn’t hurt to have foresight.

I was going to have a go at this a while ago, but other work seemed to always get in the way. Maybe its time I tried again…

[benf]

Jamesr, I understand that what’s easy for me as a lay person to think of isn’t so easy to do. I looked up thermal radiation in Wikepedia and it shows a set of formulas for calculating. With your background I’m sure you see that as just the beginning of the daunting issues involved. I would think it would be a valuable tool to have the visual modeling of data to be able to show effects of different design configs. and material choices. Maybe LPP has done something along these lines already?

[Author]

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