[asymmetric_implosion]

Some heavy ion fusion folks talk about using neutral beams but as far as application goes, neutral beams are the province of tokameks. IEC devices create conditions that drive fast ions like an electrostatic accelerator. The plasma focus creates fast ion beams to drive fusion as well. Laser fusion, reverse field configs and many other concepts are driving toward purely thermal fusion which does not want ions or electrons that deviate from the thermal spectrum.

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How so? The ion heating in a plasma focus is derived from the kinetic energy of the fast moving ions rather than electron heating of the ions which is more like the case for laser fusion and tokameks. PF devices and Z-pinches are one of the few devices that allow the ion temperature to exceed the electron temperature. In any case, PF fusion as described in literature relies on instability driven ions more like a particle accelerator rather than a thermal bath of ions fusion like in a tokamek or laser fusion pellet. In my way of thinking a cold ion and electron population may actually be a good thing as the kinetic pressure of the plasma is lower so you can compress more mass as long as you can still generate the fast ions you need, you win.

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I forgot that the number of generators to get 2.3 TW (mean electrical demand in US) is huge at 5 MW per generator or 460,000 generators. If they are running all the time you can produce about 8% of the helium used in the US in 2008 (193 million standard cubic meters). I couldn’t find a newer number in my five minute hunt. Not enough to get from A to B but it would help if helium recycling efforts step up. You need something like 7-10X the electrical power output in the US to supply the helium using p+11B reaction. Not easy to do given that electrical demand and helium demand are both rising. If helium recycling is implemented and wasteful uses of helium are eliminated, it might be possible for LPP to produce a significant amount of helium say 30%. The real savior would be high temp superconductors as the biggest single He user is for superconducting MRI machines according to Wikipedia. That would cut out 22% of the helium demand alone.

[asymmetric_implosion]

Hmmmm. Lets do the math.

PF reactor will produce a net of 66 kJ per shot according to Sankey diagram on LPP website. With 8.7 MeV/reaction, that requires, 4.75E16 reactions per shot to produce the fusion energy. Each reaction produces 3 helium atoms so 1.4E17 atoms per shot. You fire 200 shots per second giving you 2.8E19 atoms per second. For reference, your average helium tank in party store for balloons holds 300 cubic feet or 8.5 cubic meters of helium at standard pressure and temperature. The standard pressure and temperature density of helium is 2.7E25 atoms/m^3. The total number of atoms to fill the bottle is 2.3E26 atoms. Using the production rate, it will take more than 90 days to fill a single bottle from a 5 MW PF reactor as proposed by LPP. I can’t speak for anyone else but we use a helium bottle every month and we are a very small lab. You would probably be able to produce the world’s total electricity needs many times over before you could produce enough helium to sustain the current demand.

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The regular issue companion to this special issue on pulse power also has some new results from Kansas State’s PF device.

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It seems a bit unfair to think that the tokamak was selected without any competition or data on other concepts. Pinch based fusion concepts were in the works since the 1950’s but none panned out. Laser based fusion, colliding ion beam concepts and other ideas were examined before the tokamak was declared the winner. Admittedly, technology and modeling have come a long way since the tokamak was declared the most likely to succeed, but it wasn’t in the absence of other concepts.

Down-select is the natural process of technology development. You can’t run all the ponies forever. I think models like those developed by the semiconductor industry could successfully be applied to fusion. For the first period a pot of money is divided up among the candidates but all data is shared in the group. At the end of first period, the most promising concepts are chosen and funded as competitive entities with schedules, time lines, etc for some period. The winner, if you have one, becomes the focus for the last period until it is viable. I think the real threat of killing a project will help the teams focus on the real problems and not get caught up in side lights that seem to drag these projects off course. It might also encourage informed risk taking that is uncommon in the existing fusion programs.

The real problem is finding unbiased reviewers that can provide adequate technical assessment without being bound by political trappings. On might argue that ITER and NIF continue to exist as much due to their potential as capable marketing. I think the science of NIF is starting to win out over the marketing. ITER might lose out for budget reasons and a lack of a central bank account so where are we left? New diagnostics and side technologies were developed but we fell short of the goal. Key problems were identified that could hamper fusion in any form such as materials. Some information was gained which are goals of a science program but the energy program failed.

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R. E. Beverly III & Associates does customize switches for the user application. They built the original switches on FoFu-1. 🙁

Pseudo-sparks are possible. I don’t know enough about them to give stats on performance. My guess is that their lifetime is not going to be the 1E9 shots you need to feel good about them. Gas based switches are inherently limited by the cathode erosion. You can increase the cathode area and optimize materials (which is largely done if I understand it correctly). Large switches tend to be high inductance which limits current for a given charge voltage which means more switches or increased voltage. I’ve heard mixed reviews from folks that use pseudo-sparks; some love them and some hate them.

I offer you this bit of optimism. FrancisL found a paper on using a transformer PF that I wrote a year or so back. The idea, in principle, can be expanded to a 3 MA machine. The transformer ratio would probably drop from 6:1 to 3:1 to keep the voltages reasonable for thyratron switches or pseudo-sparks, if you prefer. This reduces the switch count by 3. Take the $136.5K and divide by 3 to get a number slightly less than the money generated from electricity. Now you have to address the capacitors which are truly limited to 1E8 shots. I don’t know of a way around it in a high current cap. I know 1 kHz caps exist and they are used commercially at the 50 kV level and currents of ~10 kA so there already is a market to drive the development. One might argue that caps are not required if you use inductive energy storage methods but those require some work as well.

My point is not to say it is impossible to produce cost effective fusion. The point is that a great deal of science is required to make it cost effective. Step 1 is showing gain. Step 2 and so on will use the requirements of a gain configuration to develop the energy conversion, materials, pulse power and eventually the business plan.

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A lot of science needs to be done before you can claim to understand the economics because you don’t know what you need to make the system work. Gain is a necessary but not sufficient condition to produce a viable fusion power plant.

I agree that gain would push the supporting technologies like switches and capacitors (yeah, these guys burn out faster than the switches). The potential pitfall is pushing beyond fundamental physics limitations of materials. Many of the problems with the switches and capacitors are material wear and failure. Thyratrons are already pushed to their limits on the material side by using hydrogen as the source gas to limit ion damage on the cathode and refractory materials when merited. There is nothing left that can be done. Diamond switches, which have been mentioned on this site a few times, are difficult to trigger because of the large band gap that makes them large voltage hold off. The purity of the material is just getting good enough to approach the theoretical hold off limits.

Information on Thyratrons is available from the vendors, English Electric Valve and L-3 Communications Electron Devices. The bulk sales rates are just guesses based upon the limited numbers I buy. The cost per J for the solid state number is based upon a plasma focus built by SRL that stored ~2 kJ and cost ~$2M to run at 80 Hz and 200 kA.

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While the actual accelerating structure is only 3.3 cm, the laser that drives the acceleration is the size of a two car garage. The huge advantage of LPA is size of the accelerating gradient typically measured in V/m. The LPA could reach 100E9 V/m while the best RF structures will never exceed 100E6 V/m due to material limits. Whether the LPA will be man portable like a power tool or vehicle portable is yet to be determined. It is exciting work doing some really great physics.

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@Zapkitty: I have no problem with science for the sake of science. I support the astrophysics and nuclear physics folks. I think they do amazing work. My problem is hiding behind some practical application in the near term. Inside and outside the gov’t folks invest in science for the sake of science. They seem to hate being lied to. If you tell me that you are interested in exploring the feasibility of a gain reaction from a PF, I don’t have a problem with it. If I reviewed a reasonable proposal I would probably green light it. Don’t write a proposal that says in five years I will have working reactor regardless of the fusion reaction. It is unrealistic. I take the LPP project as an example. They are two years in and there are problems with arcing and pulse power. Every project has these glitches. Some take days to resolve, some take years. ITER, NIF and all the alternative confinement concepts will suffer these problems before they can answer the question of whether they work or not. It is these unknowns that make estimating the economics very difficult. You speak of turbines which I agree are costly, but the economics are well known and cost effective as we currently use them and electricity cost are not obscene.

If you believe that aneutronic fusion is so economically viable I give you this economic calculation for consideration. FoFu reactor in production must run at 200 Hz. The only switch that exists that has a hope of operating in the regime is a thyratron which carries 11 kA per switch at voltages of interest (<100 kV). For a 3 MA PF, you need 273 units for this device rounding up for decimal places. A typical thyratron costs $3500. Imagine you can buy them in bulk for $500, so you need $136.5K per burn out. Each switch lasts 5E7 shots. At 200 Hz each switch lasts 69 hours so at 5 MW, the energy generation is 347 MW-hrs. Using the US average cost paid by the consumer of $0.133 per kW-hr ($133 per MW-hr from http://www.bls.gov/ro9/cpilosa_energy.htm), the plant makes $46151 while it costs $136.5K. Hmmmm. Even if you double the money made by selling the heat from the reactor you are still coming up short. I would argue this is a blue sky calculation so the real system would cost more per 69 days. This neglects any people to work on the plant, ES&H, other parts that might fail like electrodes or capacitors, etc. This is a doomed business proposition on micro-economics alone. If you want to argue about the cost of carbon in the atmosphere and long term effects, it is all good and well but sell the technology as necessary to save us from global flooding and wars. People might consider paying 50% more for electricity if they know it's going to save lives, provide energy independence, etc. And yes, I do consider a gov't subsidy a cost to the people.

If the next argument is that next gen switches need to be developed, I agree. Those are 10-15 years away at the current pace. The Army is driving the development pretty hard for their applications but that darn physics keeps cropping up in a disagreeable ways. Even with the next amazing step, the cost of solid state which offers 1E10 shots per cycle costs ~$1000/J. FoFu power plant will requires something like 100kJ stored to produce 3 MA reliably so a capital investment of $100M in the pulse power alone. It runs at 200 Hz for 1E10 shots or 13888 hrs. Again, a 5 MW power plants so you make, $1.9M using $133 per MW-hr. This assumes the replaceable materials cost, people, ES&H ,etc less than 2% of the initial capital investment in the pulse power to make money. You might have a leg to stand on with economies of scale if you can amortize the cost of the plant over many years. The cost of solid state pulse power is not going to drop below $100 per J in the near future so you will be right on the edge of economically viable in 10-15 years with some gov’t subsidy to hide the cost.

This neglects all the really complicated issues like source reproducibility over the long run, beryllium chemistry with hydrogen and boron, electrode erosion, neutron production, etc. It really doesn’t matter which subsystem is the cost driver, it is the total cost that matters or return on investment. Fusion might have better efficiency of conversion, more compact geometry, no carbon, but as an energy source it costs more than anything we have now even in the most promising case. When all is said and done, it will cost more than this simple calculation while the cost of energy will only increase by 10-20%.

Should we pursue fusion science? Sure. Fusion energy comes after fusion science is proven and proper cost modeling is possible with all the factors considered. Is economics the only reasonable driver? No, but those decisions are above my pay grade.

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My question is how do they know that alternative concepts are economically competitive? This has been the bane of the mainline ICF and MCF programs for years. Claims of clean, cheap energy without a configuration that is capable of producing more energy than it takes in. Doesn’t it seem premature to assume the economics are known before the physics is demonstrated to work? Doesn’t engineering the system need to be done to understand the components and people that are the real cost of fusion? This will provide the inputs to decide if carbon free energy from fusion is worth the investment.

It frustrates me to no end that national lab folks talk about clean, cheap energy as a way to keep pouring money into programs they know are not viable for producing energy. I guess the folks at the top of these programs lost sight that they were once credible researchers that knew that science strives to be an objective process. While not as satisfying, it is just as important to know what doesn’t work. One can conclude with our current level of technology that fusion from NIF and ITER may be beyond us. Are other concepts going to meet the same end? I don’t know but isn’t it time to state honestly that the fusion program is more about hunting and pecking for what might be possible i.e. science rather than producing energy? If a concept produces net energy, the engineering and economics will come on their own.

Astrophysics and particle physics seem to stay funded when one can easily argue in tough times they have little practical value such a creating sustainable jobs worldwide, improving energy efficiency, reducing need for carbon based fuel, etc. They stand on quality of their work and people continue to support them. I’m not sure what it says about fusion but I don’t think the commentary is good.

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DHS was interested in a compact neutron source at high repetition rate. The larger machines are not of interest to them for their applications. Others have proposed it and it never worked out. Too many neutrons per shot at high current leading to detectors getting swamped in neutrons and can’t see the signal. DHS has moved onto advancing technology that can impact their mission in the short term. Long term, active interrogation scheme development is on hold unless you are a university and then they want very different technology like exotic particles or out there detection schemes.

As far as the transformer goes, it requires some thought to scale up. When the transformer PF was designed, the thought was to build a 300 kA system as the next step for another group. The transformer has some nice properties but the mass and need for oil are downsides. Eric contacted me about using the transformer system for his PF or next gen PF. It is possible but I haven’t looked at it in the necessary detail. Modeling the transformer PF is a bit more complicated due to the transformers and the approach to transformer core saturation. I don’t think the cores in the RSI paper are saturating but there is some evidence that the transformer geometry is affecting the pinch behavior. There is another paper in IEEE Trans plasma sci on the device (Bures Plasma Focus Neutron Generator, 2012). Another paper is in the works dealing with 10 Hz operation and materials. It have the first round of comments on the paper. I am in the process of rebutting them and making corrections. A paper looking at scaling which includes the RSI transformer PF (internally called AASC PF-2) and FoFu-1 is due out in Physics of Plasmas in Dec 2012. I posted the keys graphs about the scaling law in the generator testing thread about a week or so ago.

I’ve said before that our machines are similar to LPP and John Thompson is the reason. John and I worked together for two years. One of the things he taught me was high current pulse power design. John consulted for our group and LPP for a while before he joined another company.

-BB

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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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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) 

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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.

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