Generator testing concept

[Francisl]

Lerner wrote: Just to clarify–we don’t think we have tested the new tungsten “teeth” and our published results pre-date using them. We do think our results are due to the small size of the electrodes and the axial field coil we are using. I agree that neutralization of the current is a potential problem but how much of one it is needs to be determined experimentally.

asymmetric_implosion’s link led me to this paper by S Lee and S H Saw: Nuclear Fusion Energy- The Dawning of the Fusion Age
Section 5.5 “Operating the Plasma Focus Beyond Neutron Saturation- Ultra High Voltage and Current-steps” talks about the next generation of plasma focus devices using higher voltages for greater success.
I’m really just speculating here but I think that in effect the LPP device is benefiting from higher voltages. By carefully reducing power losses and using smaller electrodes I’m guessing that a smaller percentage of the capacitor charge is used in the axial phase and this leaves more charge and consequently more voltage for the radial and pinch phases. If a higher voltage translates to higher temperatures and if this is combined with the axial magnetic field, then a more efficient fusion process could be occurring. This could explain their progress and point a way to future experiments.
Does my reasoning make sense or is it bogus?

[asymmetric_implosion]

Francisl wrote:

Just to clarify–we don’t think we have tested the new tungsten “teeth” and our published results pre-date using them. We do think our results are due to the small size of the electrodes and the axial field coil we are using. I agree that neutralization of the current is a potential problem but how much of one it is needs to be determined experimentally.

asymmetric_implosion’s link led me to this paper by S Lee and S H Saw: Nuclear Fusion Energy- The Dawning of the Fusion Age
Section 5.5 “Operating the Plasma Focus Beyond Neutron Saturation- Ultra High Voltage and Current-steps” talks about the next generation of plasma focus devices using higher voltages for greater success.
I’m really just speculating here but I think that in effect the LPP device is benefiting from higher voltages. By carefully reducing power losses and using smaller electrodes I’m guessing that a smaller percentage of the capacitor charge is used in the axial phase and this leaves more charge and consequently more voltage for the radial and pinch phases. If a higher voltage translates to higher temperatures and if this is combined with the axial magnetic field, then a more efficient fusion process could be occurring. This could explain their progress and point a way to future experiments.
Does my reasoning make sense or is it bogus?

40 kV operation is not uncommon in PF devices at the 1-3 MA level. In fact, some PF devices operate up to 300 kV. Voltage alone is not an important quantity. The plasma focus is a current driven device. Most key processes are a result of current or rapid changes in it. Take a 1 MA device. If one does some basic circuit analysis, a typical metal resistance is 2-5 mOhm. The capacitors have a resistive effect called effective series resistance (ESR) of up to 0.2 Ohm per unit so one typically puts a bunch in parallel or buys low ESR caps but it can add 10 mOhm. The axial run down phase has an equivalent resistance of 10-20 mOhm. The impedance due to capacitance and inductance is another factor but let’s neglect that for now. Taking only the resistive looking terms, you need between 10 and 20 kV just to drive the current due to resistive terms. Depending on your capacitor bank and inductance you need more. It is difficult to build a 1 MA PF below 20 kV. Thus 30 or 40 kV gives you a safe window. If you are truly concerned you can go higher in voltage.

The normal mode of operation in a plasma focus is to have the plasma reach the end of the axial phase when the current is at maximum. Maximum current means the capacitor bank charge is very small or ideally, zero. Thus, higher voltage does not leave more charge to use during the radial phase. It means that the rise time (time to peak current) is probably different because you changed the capacitance to achieve some desired current. In a circuit dominated by capacitance (C) and inductance (L) the rise time is given by Pi/2*sqrt(LC). If you desire a fast rise time L and C must be small. In many practical devices, L cannot be smaller than 10 nH. C is determined by the desired rise time and operating voltage window you can tolerate. Higher voltage means more problems with operation in air, component cost goes up unfavorably, component lifetime tends to go down and safety becomes a bigger problem.

This part is new and something I’m working on with a hope of publishing later this year if the reviewer and I can agree. Plasma focus devices seem to perform well when the voltage generated by the pinch is large compared to the voltage used to charge the bank. When the ratio of these terms is large, the fusion yield is large. When the ratio is small, the fusion yield is small. The higher ratio implies that the mean ion energy that drives the fusion is higher, which is a good thing. Fusion cross sections grow quickly with ion energy.

FoFu-1 does well because it is able to produce a large voltage at pinch time. The small electrodes are an important part of the equation. It also seems that LPP is able to compress their pinch more tightly than most machines.

[Francisl]

asymmetric_implosion wrote:

This part is new and something I’m working on with a hope of publishing later this year if the reviewer and I can agree. Plasma focus devices seem to perform well when the voltage generated by the pinch is large compared to the voltage used to charge the bank. When the ratio of these terms is large, the fusion yield is large. When the ratio is small, the fusion yield is small. The higher ratio implies that the mean ion energy that drives the fusion is higher, which is a good thing. Fusion cross sections grow quickly with ion energy.

FoFu-1 does well because it is able to produce a large voltage at pinch time. The small electrodes are an important part of the equation. It also seems that LPP is able to compress their pinch more tightly than most machines.

Please let us know when your paper is available for viewing. I’m already thinking of questions.

[asymmetric_implosion]

The quick and dirty of it… Neutron yield (Y) in a pinch device increases with the peak current (I) by a power law with a form Y=a*I^d where d is between 3 and 5. The coefficient a is not a constant (observed from experimental data). So, what parameters affect a? The answer is that the ratio of the pinch voltage to the charge voltage or more commonly measured the ratio of the minimum in the time derivative of the current to the maximum of the time derivative of the current (See graphic labeled Fig 5 for locations of these points). As the dI/dt ratio grows, Y divided by I^d grows leading to more favorable fusion yield (See graphic labeled Fig 7). The larger Z-pinch devices like Z and S-300 don’t fair well by this model while plasma focus devices generally do OK. FoFu-1 and AASC PF-2 do very well. The value of d from general least squares fitting using the 8 machines is 3.79. Want a better fusion source, maximize the ratio of pinch voltage to the charge voltage…well for D-D reaction anyway. D-T might have a maximum due to the low peak in the cross section at 100 keV.

Attached files

Fig7.tif (217 B)  Fig5.tif (162 B) 

[Francisl]

asymmetric_implosion wrote: The quick and dirty of it… Neutron yield (Y) in a pinch device increases with the peak current (I) by a power law with a form Y=a*I^d where d is between 3 and 5. The coefficient a is not a constant (observed from experimental data). So, what parameters affect a? The answer is that the ratio of the pinch voltage to the charge voltage or more commonly measured the ratio of the minimum in the time derivative of the current to the maximum of the time derivative of the current (See graphic labeled Fig 5 for locations of these points). As the dI/dt ratio grows, Y divided by I^d grows leading to more favorable fusion yield (See graphic labeled Fig 7). The larger Z-pinch devices like Z and S-300 don’t fair well by this model while plasma focus devices generally do OK. FoFu-1 and AASC PF-2 do very well. The value of d from general least squares fitting using the 8 machines is 3.79. Want a better fusion source, maximize the ratio of pinch voltage to the charge voltage…well for D-D reaction anyway. D-T might have a maximum due to the low peak in the cross section at 100 keV.

That is some impressive work. I hope it gets published.
Can you use this model to predict the limits of your sampled machines?

[annodomini2]

While my question was innocently intended, it seems to have generated some interesting discussion.

Keep up the good work! 🙂

[asymmetric_implosion]

Francisl wrote:

That is some impressive work. I hope it gets published.
Can you use this model to predict the limits of your sampled machines?

Thanks. I think the reviewer and I agree on the big picture stuff but there seems to be some details that we can’t come to terms on. I think the last revision will be enough middle ground to get published in Physics of Plasmas. If not, there are other journals. I have a back up in mind already.

The goal of the model is predictive capability for future experiments and future machine designs. I’d like to include more than 8 machines but this is all the data people were willing to share. The part I’m still working on in a follow paper is the electrode geometry requirements. The model as is does not recognize when the electrode geometry becomes impractical. This is a trade off depending upon the application. If you are doing a one shot and done application like Z at Sandia you can tolerate electrodes that will mechanically fail on each shot. If you are working at repetition rate, you need to the electrodes to survive for long periods. This model might play a role in making those decisions. The dI/dt traces (shown in Fig 5 of last post) can be predicted using pretty basic models that take the computational power of Excel.

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