Reply To: would nuclear energy really be accessible to all?

[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.