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Two DPFs firing at each other is about 30 years old. The concept evolved into what is known as the hypocycloidal pinch. It has promise for increased pinch lifetime but the energy input is much greater.

The energy cost for PF device to accelerate particles is far greater than a particle accelerator. Medical applications will likely use advanced accelerator technology like plasma wakefield accelerator in the coming decade.

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There are publications by LPP that suggest the temperature was achieved. The measurement leaves some questions but it is a good first look at it. They used the hard x-rays generated by the pinch to estimate a temperature. The potential problem is the high energy gamma rays created when neutrons interact with the stainless steel vacuum vessel. I’ve encountered it in the past and it can screw up measurements. The measurement I’m waiting to see is the soft x-ray spectrum of continuum radiation from the deuterium. Folks have done it before and it provides a pretty reasonable estimation of the temperature. It tends to be a little on the cold side so it is a good lower bound. The density again has been estimated. You really need to do an x-ray transmission measurement to measure the line density and infer the actual density from x-ray images of the pinch itself. Nether has been done so the conditions for D-T breakeven have been inferred rather than measured. This does not mean the results to date are not promising, but more needs to be done. The other option is to load the machine with DT and go for it. It would be a huge political win to show breakeven. The cost of the experiment would be enormous as T is involved but a successful demonstration might eliminate some of the funding problems. Big risk, big reward. The other option would be to move the machine to a national lab for the test. It would be distracting and difficult but again, big risk, big reward. You could also get some DOE buy in as their lab made fusion viable.

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Similar problem with XRAM. You need switches that can do the job. Opening switch technology at the ~1MA level has not worked correctly using plasma based switching i.e. gas switches. Solid state systems tend to have a problem with the voltage spikes from the switch opening and the pinch. Building large solid state stacks is possible but costly. A single component failure is enough to take out an entire stack. Advanced materials like silicon carbide or diamond might save the day but they are a few years off at least for the systems we are talking about.

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The LLNL approach is likely going to use hydrogen for the beam. You can’t fuse protons very easily in a PF.

The part that no one is talking about is that the former team leader of the LLNL team went to DARPA recently and has pushed this concept for five years. Now his former team has funding for the project. Hmmmm. Good science or good networking.

The simulation tool is owned by private company so it can be bought. You need a lot of computational power to run it.

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You are correct that the largest piece is the capacitors. Super capacitor technology is advancing quickly but they are the wrong kind of capacitors. The capacitors for FoFu require low inductance, fast discharge current and high voltage. Super capacitors tend to be low voltage, slow discharge capacitors. It is challenging to reduce the size of high voltage capacitors that can discharge as needed in FoFu. Other technologies may replace capacitors but a FoFu reactor will still need shielding. I can imagine a 5 MW reactor with everything fitting in a 1 car garage but much small than that is unlikely.

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The main concerns are slew rate (rate of change of the current), voltage hold off and price.

Slew rate: SCR’s are very limited in slew rate for a PF. The common solution is to use saturatable magnet cores that choke the current until they saturate. The cores need to be reset after every shot but that is known technology.

Voltage hold off: SCR switches are limited to a few kV so a stack is required. Firing multiple switches in series is challenging but not impossible. The problem is the voltage from the pinch which can be 1.5-10X the charge voltage of the bank. This means the switches must be crow barred to prevent damage. SCR’s conduct in only one direction so a reverse current shuts them off which can create problems.

Cost: Solid state PF devices exist up to the ~300 kA scale (look up Science Research Lab). The pulse power cost ~$1M at this level with an 8 kV charge and operation at 80 Hz. Scale up is non-linear so a pulse power system at 40 kV and 3 MA is going to cost far more than $10M.

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Arcing is derived from a combination of things like questionable contacts between metal surfaces and imperfections in the metal surface like protrusions and oxidation. Destructive arcing is not uncommon in high current devices like FoFu-1. The contact problem is challenging at these high currents in the geometry the FoFu-1 operates in. The ring that “chews the sheath” concentrates current into a limited number of dense filaments. To do this it must be thin. The contact between the jagged ring and the cathode plate must be nearly perfect so the massive current can flow a negligible impedance. Arc occurs when either it is easier for current to flow in the gas or when the impedance of the contact is high leading to local heating leading to higher impedance leading to more heat until the local spot melts and you get metal plasma.

To be fair, FoFu-1 and other PF devices operate in the arc regime naturally. Ideally, the arc covers a large fraction of the anode and cathode diameters. Imperfections in this distributed arc can lead to poor performance. Various tricks are used to help the arc homogenize such as doping with a higher atomic number gas, electrode geometry and pre-ionization. There is a significant body of literature on the subject. For example, alpha radiation sources were found to be an excellent pre-ionization source leading to improved reproducibility. Lower current PF devices have demonstrated improved neutron yield when the deuterium fuel gas is doped by a few percent by mass of gasses like Ne, Ar and Kr. By altering the electrodes to converge to a point, the neutron yield and reproducibility were also improved. Erosion is a natural consequence of exposing a metal to a plasma. The rate of erosion is important. In a pure metal system without a fuel gas you can evaporate mass at the rate of 10-100 micrograms per Coulomb of charge transferred. In the case of a PF, there is a fill gas the reduces the electrode erosion but it cannot be eliminated. The rate of erosion appears to be manageable when the arc is distributed.

The difference between FoFu-1 and other PF devices is the jagged ring. It is theorized that distributing the current flow in the arc in a non-uniform way around the cathode diameter improves fusion yield. The data set that supports this theory is growing. While a non-uniform current distribution may be preferable for fusion yield, it may be unstable. Can the instability be managed? Time will tell. The severity of damage from local arcing will increase with current. Arcing is driven by current density in the system. Resistive dissipation of power increased with the square of the current. Therefore, contact resistance must be dropping significantly as current increases to avoid potential arcs. This is commonly achieved by increasing the length of contacts and compressing the interface between the two contacts to the point of deformation of the metal. It is fairly common to use a soft metal like silver or indium in the interface to minimize contact impedance. As current increases, the contact impedance must increase. In principle, a 100 kA PF device can tolerate a contact resistance of ~100X the contract resistance of a 1 MA PF. At 3 MA you require a nearly 1000X reduction in tolerable contact resistance. I believe LPP stated the need of a contact impedance of ~1 uOhm. That is challenging. To make matters worse it must be uniform. Any local high impedance spots could be a significant problem. Not any easy problem to solve moving forward.

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The graph is ion energy.

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Vlad: You need to be a bit careful using temperature and ion energy seemingly interchangeably. Temperature is key in thermal fusion devices. In principle, you can have a cold plasma that produces neutrons very well in a pinch. Pinch devices exploit the instabilities to produce non-thermal ions, ions that don’t conform to a thermal distribution. It is of these ions that efficiently produce neutrons. Small PF devices which have temperatures of less than 1 keV can produce neutrons well beyond the expectations of thermal calculations. LPP hypothesizes that their configuration to place a lower limit on the ion energies. If the LPP approach works, energies below 200 keV would not be relevant to the problem. It’s not clear how far the lower limit can be pushed up but the higher the better for p+11B.

As far as the “honest” calculation goes, a great deal of engineering is required to prove that the energy from RLC ring can be recycled. I’ve looked into using energy recovery technology for a small PF device in the past. State of the art technology was nearly enough to work at the 60 kA level. At 3 MA, it seems unlikely with current materials.

Francisl: The MAGLIF concept implodes a pre-magnetized, 100 eV plasma into a pinch. The initial magnetic field is flux compressed limiting the heat transfer of electrons and partly trapping alpha particles. The approach relies heavily on a thermal DT plasma. The density and magnetic field should suppress fast ions that the LPP approach relies on.

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D+3He might be an easier path than p+11B at first but you could not claim an aneutronic success. My gut feeling is something like half your yield with very large error bars would be from D+D. One could argue that breakeven in itself is a big deal and it is. My opinion is a pinch device has reasonable odds of making it to breakeven first but it won’t be a PF. LPP is working toward or may have recently reached a 1 J fusion yield. With something like 50 kJ stored in the capacitor bank the Q is 5E-4. An experiment at Sandia using Z is my bet right now. They have better funding and more resources in terms of people. They also see an opportunity as NIF is pushed to the back burner. The MAGLIF experiment that will continue this year is quietly demonstrating some of the key technologies needed for their concept to work with D-T. I suspect when they fire fully loaded shots with D-D instead of D-T, they will reach a Q~0.1 very quickly. If their theory holds it will not be easy but a path forward to fusion will open up. Sandia has done a pretty good job of keeping the results low key and focused on science milestones as well as managing expectations with the funding agencies. NIF grossly over-promised and now they are paying for it.

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D+3He is a little easier to access than p+11B but you are likely to produce a number of neutrons from D+D. 3He is in short supply so not a good long term choice as it is derived from tritium or some lunar digging. p+11B works best above 600 keV.

Attached fig shows the cross sections for the fusion contenders.

Attached files

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Isn’t this a computational or theoretical grant? What is the theory you are going to pursue or develop? Rule #1 of federal grant writing; respond to the topics. If you are an experimental person proposing an experimental study, this type of grant is unlikely to be successful. Worst case, it is rejected without review because it is considered unresponsive.

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Spallation sources rely on very high energy protons (~1 GeV) to work. A PF alpha particle or proton source is unlikely to exceed 10 MeV with most of the particles of interest far below this value. The PF would serve as an intense ion source but you need the particle accelerator in front of it to accelerate to the desired speed.

If you want to go to an (alpha,n) reaction with something like Be it is possible but you have to deal with a target accepting a high instantaneous power, low average power situation which makes the target difficult to thermally manage where the beam impacts the target. I’ve damage steel with a plasma focus ion beam.

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The short answer is the PF is unlikely to make an impact on sub-critical fission systems. Current plasma focus devices operate at a peak of ~1E12 neutrons per shot (DD) at ~2MA. If one assumes the 100X gain by going to DT and it is a big if, you need more than 3X the current. A 7 MA driver running at repetition rate has not been demonstrated. I don’t know of a plasma focus that has operated above 3 MA. The electrode erosion, vacuum chamber design, confirmation that the fast ion beam does not substantially exceed the peak in the DT fusion cross section, next generation pulse power technology beyond the requirements of FoFu-1 and years of engineering failure analysis make this approach unlikely. The accelerator systems are much closer to reality with countries like India pouring money into ADS. An accelerator like SNS could be viable for an ADS. The operational time needs to improve but many of the problems are known and could be addressed.

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Brian: Pun on the name is cute. But the humor aside, I know the technology exists because I have worked with it for the last five years. I have a few peer reviewed publications in the area of plasma focus devices and how to build their pulse power systems that I’ve listed below. Brian, too, by the way.

Brian L. Bures, Mahadevan Krishnan, Robert E. Madden, and Florian Blobner, “Enhancing Neutron Emission from a 500J Plasma Focus by Altering the Anode Geometry and Gas Composition” IEEE Trans. Plasma Sci. Vol 39 No 4 pp 667-671 (2010)
B. L. Bures, C. James, M. Krishnan and R. Adler “Application of an impedance matching transformer to a plasma focus” Rev. Sci. Instrum. 82, 103506 (2011); doi:10.1063/1.3648117
Brian L. Bures, Mahadevan Krishnan and Robert E. Madden “Relationship between Neutron Yield and Macro-scale Pinch Dynamics of a 1.4 kJ Plasma Focus over Hundreds of Pulses” IEEE Trans. Plasma Sci. Vol. 39 No 12 pp 3351-3357 (2011) doi: 10.1109/TPS.2011.2170588
Brian L. Bures, Mahadevan Krishnan and Colt James “A Plasma Focus Electronic Neutron Generator” IEEE Trans. Plasma Sci. Vol 40 No 4 pp 1082-1088 (2012)
Brian L. Bures and Mahadevan Krishnan “An alternative scaling relationship for neutron production in Z-pinch devices” Physics of Plasmas Vol 19 No 11 112702 (2012)

I’m not a novice talking without some background. I’ve been in the trenches with PF devices making them work. If you have a specific complaint about my disingenuous comments related to switch choice or vacuum technology I’d be happy to talk about it. That is what the forum is about.

There is a huge difference in funding levels. No one denies that. One selling point of the PF is that it is an easier, faster, cheaper path to fusion. Many millions have been spent on PF device develop and it is far behind the tokamek right now in terms of Q. It could be made up if the device begins to work correctly. That is the part I find frustrating. The tantalizing data that is out there needs some backbone to it and a working device could provide that data. Time will tell. The PF has enjoyed application based funding for some years that can viewed as tech base development for FoFu-1. The Z-pinch community has already addressed many of the pulse power problems as they operated at much high voltages (1-6MV) and currents (1-20 MA) routinely with rise times of less than 200 ns while FoFu-1 operates with >1 us rise times with 1-3MA of current at 35-45 kV. Even with this tech base I’m sure that the PF program is poorly funded by comparison to the tokamek program. I think one could find passionate advocates in the plasma and fusion community if the proof of concept experiments were completed successfully. Use existing tech to prove the physics works and then push for the state of the art tech to make it pretty. This has been the approach of many successful science programs turned into useful things like commercial products.

The politics of fusion are really opinions so I can agree to disagree. Time will provide the answers.

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