[jamesr]

imflux wrote:

Hmm, What I am saying is, create fission in the plasmid, which would then ignite fusion?

My point what that you would never get a plasmoid form in the first place. If you had a dpf with some heavy, elements in the gas (fissile or not), and then discharged the capacitors through it. The gas would ionise to form a plasma at a few thousand degrees, the plasma would sweep down the electrodes as per normal. But by the end rather than having concentrated lots of energy in the plasma & magnetic field to drive the pinch & compression, all the energy would have already been radiated away as bremsstrahlung x-rays. The plasma would just die out with nothing much happening once the capacitors had discharged.

Even if this didn’t happen the density of a good plasmoid with just deuterium only gets upto the number density (or avg atomic spacing) of that of a normal liquid. To get a volume the size of the plasmoid to go critical with uranium or plutonium would need densities orders of magnitude higher.

[jamesr]

Adding any heavy ion species into a plasma makes it cool rapidly due to bremsstralung radiation. This goes up as Z^2 where Z is the charge on the ion. So if you added in even a small amount of uranium and it became anywhere near full ionized, ie Z->92 then the rate of cooling would go up by ~8000x preventing the plasma ever achieving fusion temperatures. It’s bad enough trying to cope with boron with Z=5.

You could have a hybrid deuterium or D-T device where fissile material (or actinide waste product you want to get rid of) surrounds the DPF device to react with the neutrons. This would be similar in concept to various accelerator driven sub-critical reactor designs that are being proposed.

[jamesr]

I thought of using Comsol, which is a general purpose physics modeling program, that can combine thermal, electrical and many other phenomena together in one simulation. However until recently they could not easily handle plasmas. They have now just released a new module http://www.comsol.com/products/plasma/ which may make it easier.

It won’t be up to the task of modeling the later stages of the pinch & plasmoid, but may be sufficient for a mock-up of the axial & first part of the radial phase. To let a full 3D simulation run any further would need the inclusion of higher order terms in the equations and serious amounts of computing power.

[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…

[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.

[jamesr]

KeithPickering wrote:
There are no commercially available plasma switches that can handle the current requirements. Hence the need for multiple switches that must fire simultaneously.

I guess that then begs the question – What would it take to design a switch that can handle the load?

[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.

[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

[jamesr]

Can somebody tell me why there needs to be more than one switch?

They are all wired to the anode on the other side of the switches. One big switch has to handle the whole current load, but it completely eliminates synchronization issues.

[jamesr]

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.

[jamesr]

vansig 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?

I love this kind of quick & dirty calculation. It lets you get a grasp on what are fairly intangible concepts and bring them into reality.

The outer surface or the anode would get that hot, but there would be a steep thermal gradient down to the cooling “veins” running through it. So their inner wall temperature, even if they are only 1mm below the surface would be quite a bit less. Hence the volume of coolant, I reckon, would probably be a bit more than your estimate.

[jamesr]

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.

The easiest way may be to go to DC then generate the nice stable sinusoidal mains frequency from that, but its not necessarily the most efficient.

[jamesr]

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.

[jamesr]

The core of a conventional fission reactor, such as a PWR has around 3500MW being produced in a volume of around 3 cubic meters. A fast breeder reactor is even smaller – hence they need to use a more efficient coolant (liquid sodium). But you can get that order of head out of a small volume. It’s just a case of pumping through a large enough volume of coolant fast enough.

A PWR for example pumps around 11tonnes of water through it ever second!

[jamesr]

I know several of my friends from my masters course are now working on accelerator driven sub-critical and fission-fusion hybrid designs. I think they are definitely viable way of disposing of the longer lied actinides.
But I do wonder at the cost and benefit of them. I still think the best way of getting rid of the waste is to just wait 50-100 years for the short live stuff to decay then drop the rest, encased in concrete, into an ocean trench.

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