The Focus Fusion Society › Forums › Lawrenceville Plasma Physics Experiment (LPPX) › Steps towards FF-1 Feasibility › Reply To: Great News!
Joeviocoe wrote: Would any voltages greater than 60 kV be even relevant to LPP’s DPF?
It depends on the optimum load design for the PF. As I said before, every PF regardless of size has to contend with to 10-20 mOhm of impedance in the flowing plasma. It is an artifact of the self similar physics of the PF rundown. You desire a roughly 100 km/s plasma speed during the coaxial rundown. The geometry is coaxial so the time rate of change of inductance (dL/dt) is 2E-7*ln(b/a)*v_axial. b is the cathode radius and a is the anode radius. For most PF devices, the ratio of b/a is between 1.5 and 2. Thus ln (b/a) is between 0.4 and 0.7. This leads to 8E-3 to 14E-3 Ohm. Some additional impedance always crops up so it is common to use 20 mOhm as the upper limit for machine design. If you use 20 mOhm, you need 60 kV just to drive the coaxial section during the axial rundown at 3 MA. Consider the other impedance like the bank resistance (<10 mOhm), bank inductance (~20 nH), bank capacitance (10-1000 uF) and inductance/resistance of the plasma (time varying). At a minimum you need to double the minimum voltage to achieve your desired current with a reasonable tolerance. Using this data, it is clear you might need more than 60 kV even at the 2 MA level. The last published paper from LPP has data at 1 MA and ~40 kV on the bank [PoP paper]. The scaling to 2 MA is fairly linear unless the cap bank size went up.
I was suggesting a scheme to minimize consumables (switches) by using transformers. To minimize the number of switches, you need to increase the primary voltage. Step downs of 2:1 are known at the 1 MA level but 4:1 would be better. If you require 100 kV to drive the load, then you need 400 kV on the primary. It seems a bit ridiculous at first glance, but >1 MV is very common in large pulse power. The trick is gas switches are used so you have the lifetime problem. The difference is by using a 4:1 transformer you need 1/4 the switches if you have a 400 kV switch (not easy). By replacing consumables with non-consumables (Transformer cores) you might find an advantage in cost in the long term. This approach works well at low currents but it might now work as well at high currents. More to be done.
As delt0r has said, there are other alternatives like the LVA. Each system has merits and problems. It will come down to cost and lifetime in the end. If the LPP’s cost model works for 1 month operation, then you need 5E8 shots between shutdown. Solid state can do it if it doesn’t fault. In fact it could possibly run for a few months which leaves the anode as the limiting factor. State of the art solid state pulse power for a PF is at 260 kA, 8 kV and 80 Hz. It is a big leap to 3 MA, 60 kV and 200 Hz but one that might be necessary.