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for a 5 MW reactor, assuming anode circumference is 5cm, that yields Area ~2e-4 m² facing the plasmoid, so we blast thru that 20 MW/m² limit by a factor of 1250.

i’m starting to think about radical designs.

if it can handle even a single transient shot, then how about triggering several anodes in a round-robin fashion? then each one gets some cool-down time. but i’m not confident that it can.

the anode is beginning to look like a big welding rod, here. maybe a design that can tolerate ablation? it gets used up in the process, just like a welding rod, or electrodes from an electric arc furnace, but we keep pushing it in from underneath.

“A typical alternating current furnace has three electrodes. Electrodes are round in section, and typically in segments with threaded couplings, so that as the electrodes wear, new segments can be added. ” — http://en.wikipedia.org/wiki/Electric_arc_furnace

graphite then becomes the most reasonable choice. though this does beg the question: carbon ions will get into the plasmoid on subsequent shots. are there any undesirable reactions we should be aware of?

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how does one become an accredited investor? what’s the process?

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i started dreaming up an advanced material..
perhaps: take graphene nano-ribbons, allow them to twist nicely, spin them into thread, weave this on the bias, and stretch it over the anode, like a tea cosy. then it would conduct electricity along the surface, but allow thermal penetration to the interior, and remain very strong at high temperatures.

http://www.springerlink.com/content/e092tm31km023064/

but then i realized two things:

first, graphene is basically single-layer graphite, which is stable at high temperature and used in refractory materials and high-voltage electrodes. in graphite, the layers are ~.33 nm apart, so we could use coatings of 100 layers of that, maybe, or just make the whole electrode from ordinary graphite. it’s a bit crumbly, but ought to be better in vacuum.

but, the show-stopper:
it’s going to react with the protons in the plasma, producing hydrocarbons and maybe compromising the anode integrity (not sure).

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jamesr wrote: The trick will be arranging that power circuitry to deliver the constant 50/60Hz 3phase output, as the pulse rate goes up and down to match power demand from the local/national grid.

that’s just about like keeping a flywheel at constant speed

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Allan Brewer wrote:

Using Ohm’s law (apologies if I am being naive) for 1MA through a 20nm skin of the copper electrode does indeed give an answer, in the expected range, of around 2MW of heat from the anode and about the same from the cathodes. Beryllium has twice the resistivity so would double the heat “problem” (and increase the power required to initiate each shot?).

can you give the area and the length also, for us to check?

I used 20nm skin x circumference of 5cm diameter anode to give area, and 15cm of length. In practice the length varies during the pinch cycle, and I guess the length of feed cable from the capacitor bank will also heat, but approximate calculation only.

Feed cables wont be too significant a problem because capacitors are mounted around the outside edge of a flat sheet.

okay, 5 cm circumference gives 1e-9 m² as the area. resistivity of copper ~ 16.78 nΩ·m, yielding 2.5Ω for 15cm length; beryllium ~ 36 nΩ·m, giving 5.4Ω for a 15 cm length; Yes, now i see it. but it’s important to note that skin depth changes through the pulse.

Graphene electrical resistivity may be less than 5e-4 nΩ·m; and its in-plane thermal conductivity, around 5e3 W/(m·K), is greater than diamond. I am starting to like this a lot.

Shall we put a graphene coating on everything, then? Now all we have to do is figure out how.

http://pubs.acs.org/doi/abs/10.1021/la101698j
http://nanopatentsandinnovations.blogspot.com/2010/01/fabrication-process-for-large-area.html

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Allan Brewer wrote:
Using Ohm’s law (apologies if I am being naive) for 1MA through a 20nm skin of the copper electrode does indeed give an answer, in the expected range, of around 2MW of heat from the anode and about the same from the cathodes. Beryllium has twice the resistivity so would double the heat “problem” (and increase the power required to initiate each shot?).

can you give the area and the length also, for us to check?

Allan Brewer wrote:
Finally just to note that thermal radiation from the plasma & plasmoid cannot be calculated using the Stefan-Boltzmann law (gives a silly answer) – I leave the physics of the emissivity of high temperature plasma to experts.

yes, ion temperature of 6.5×10^9 kelvin would seem to yield about 10^32 watts/m²; but, we should note that excitation isn’t exactly uniform in all directions (longitudinal >> transverse vibration, so maybe take the cube root? or the square root?), and quantization effects due to the strong magnetic field could also play into this.

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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?

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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

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Brian H wrote:
Yeah — 160 tons of FF, a ton or 10 of helium, and maybe 160 lbs. of fuel? No problemo! :cheese:

nope. two capacitor banks, one vacuum chamber, 80 anodes x 20 kg each, and 80 shares of a bigger onion x20 kg each.
plus shielding, under twenty tonnes for the lot..

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zapkitty wrote:
A wild-ass guess says that we’re looking at 400 MW or more in excess of primary power needs to enable a switch to jet-style propulsion.

that’s just 80 anodes, tessellating a spherical shell, cooled by 160 kg/s of helium in a closed cycle. hardly any challenge, at all 🙂

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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

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jamesr wrote: I think, for a Brayton cycle you would need the helium temperature to be higher.

This may be eventually achievable with some fancy materials technology to allow the anode surface to run hotter without boiling off.

curiously, 565°C (838K) is the usual upper limit for the Rankine cycle, due to the creep strength of stainless steel.
— http://www.engineersedge.com/material_science/creep.htm

to run the anode surface hotter, creep limit is really the property we want to know. for 90-day service, that would be specified as something like “creep rate of 0.01 in 2000 hours at operating temperature of X”

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digh wrote:
Perhaps the heat energy could be recaptured for helium cooling with a Brayton closed cycle gas turbine.

possibly. note, that the temperature ratio is 800:373, just over 2:1, which i’m not sure is all that good, but the pressure ratio could be increased with intercooling… “wherein the working fluid passes through a first stage of compressors, then a cooler, then a second stage of compressors before entering the combustion chamber.” in this case, what they call the “combustion chamber” is the space inside the anode just beneath the tip, where the cooled, high-pressure helium gas squirts from the artery.

some people might quibble about terms, since this is not really internal heat generation, (meaning internal to the working fluid), but it’s all based on the same principles.

also, the turbine could run the compressor pumps, and further heat be rejected with combined cycle, using water and steam, running counter-current to the higher-temperature helium flow. it all seems very expensive, though.

the compressor, even a compact one, will be bulky. check http://www.grcompressor.com/

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Ok. but i’m using the exit temperature of the helium, and holding that at 800K for these calculations. so the anode surface will climb a little higher than 800K.

next, i’m getting that at 373K, the volume of 456 mol/s helium is ~14 m³/s (at ~1atm pressure), which would need to become supersonic to pass through the artery.

PV=nRT
= (456) (8.314) (373)
= 1.414 x 10^6 m³ Pa
= 13.9 m³ x 1 atm

(edit: corrected)
speed of sound in helium = ~1137 m/s at 373K;
1137 m/s x Area = 14 m³/s
Area = 0.0122 m²;
= a 12.5 cm diameter tube. since the injection nozzle is smaller, so then the pressure must increase until enough coolant goes through.

Seems like pressure will climb to ~175 atmospheres (the typical pressure in a fuel injector), and/or the gas velocity will become supersonic.
Can it do this?

Or will that exceed the structural strength of the beryllium anode?

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jamesr wrote: The anode would have helium gas pumped through, in order to keep its surface below 800K or so. The outside of the vacuum chamber and other parts (eg. the capacitors) can be conventionally water cooled.

for 5MW of cooling to an exit temperature of 800K, I’m getting that ~2 kg/s of helium gas would need to be pumped.

delta-T = 527° (800K – 373K, if the secondary coolant is water);
Helium heat capacity = 20.786 J·mol−1·K−1
5MW / 20.786 J·mol−1·K−1 / 527° = 456 mol/s
= 1.8 kg/s

If the anode is constructed to enable co-axial flow, of cool helium up through the centre (~1cm diameter “artery”), and to exit back down along the adjacent layer, closer to the surface (“veins”), what is the max flow rate?

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