Reply To: Military Effects

[asymmetric_implosion]

Ferret wrote: Well, that’s exactly what happens when more pinches are formed. The total current has to provide a high enough intensity to each pinch. This can be done if the current is high enough and it is quite constant during the formation of pinches. The pinches would then be hot even if the plasma sheath were not moving at the same speed, as long as the plasma feeding each pinch arrives at the same time. Since the pinches separate due to plasma instabilities, how could the distance at which they form be estimated? On the other side, the number of pinches may also depend on the current intensity, which is a factor in plasma instabilities.

Let me put it this way, if you build a pulse power circuit you will always get more radiation yield (fusion, x-ray, etc) from a single pinch rather than groups of pinches in parallel. This is a well studied and well understood problem. People have suggested this in various forms for years and every experiment has proven this is a bad approach when maximizing yield is king. When you want to increase the current on a plasma focus or other pulse power device, you generally need to increase the charge voltage. One can argue that you can streamline the pulse power system but there is a limit. Say you operate near the minimum bank impedance such as FoFu-1, you can only increase your current to support multiple pinches at the previous single pinch current by increasing the bank voltage. In a capacitor bank, the energy stored increases with the square of the voltage (E_stor=0.5*C*V^2 where C is the capacitance, V is the voltage and E_stor is the energy stored). It turns out that the peak current is linearly related to the charge voltage in an RLC circuit (and yes, the trend holds with the dynamic properties of the plasma as long as you don’t screw around with the electrodes too much). Take the two relationships together and your current increases with square root of energy. Take the case of two pinches running in parallel. You want to push 3 MA through each pinch. Compared to a 3 MA single pinch circuit, you need to store 4 times the energy to drive the total current of 6 MA. By splitting the current in two paths, you get a yield twice the 3 MA value because you have two pinches. Overall, you multiply Q by 0.5 because you have increased the energy stored by 4 and increased the yield only by 2. (Q=Yield/Store).

Now, take the case of increasing the pulse power to 6 MA with a single pinch. Using conventional scaling laws with Y~I^4, the yield for a 6 MA machine with a single pinch is 16X larger than the 3 MA machine with a single pinch. You still increased the stored energy by a factor of 4. The net result is multiplying Q by 4 on the single pinch at 6 MA.

Regardless of your geometry, planar, multiple cylinders arranged in a pattern, etc, you always lose in Q. You also make the electrode heating problem worse by adding more energy. You’ve increased the dissipation area by ~2X and increased the energy by 4X.

The other point you state about the plasma will break up into pinches due to instabilities is not correct. Consider the modes of plasma formation. You start with a glow discharge, like fluorescent light bulbs. It is largely homogenous. As you increase the current, the gas becomes susceptible to other forces like JxB, the force that drives implosion and pinch formation. The plasma will constrict into an arc. Now, you may say that is what I’m talking about but step back. The plasma carried during the axial phase is already an arc. How can an arc break up into many arcs? The opposite is usually observed. If you start with multiple arcs, they tend to coalesce into a single arc. Why would a planar geometry drive the plasma in the opposite direction. One observes regions in a pinch that are different from other regions but the structure is still a single pinch. If you want, the pinch can be thought of as a group of micro pinches in series. An individual arc can carry huge currents well into the mega amp range without any problems so it doesn’t need to break up. It will be susceptible to instabilities like Magneto Raleigh Taylor (m=0) and kinking (m=1) but it tends to stay together as a single body. I can explode or re-strike but it is still a single current carrying structure. If you want to start with multiple arcs and implode each of them into pinches, it is a large breakdown voltage with a fast rise time that matters. This approach is used in low inductance, high current switches to create multiple arc channels. The spec for the switches I use is 4 kV/ns with breakdown at 20 kV. You would need something similar to create multiple arcs in a plasma focus.