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Joe:

Hybrid Mmagnets (Combination of superconducting magnets and normal magnets) hold records of 100 T or 1E6 Gauss in a pulse mode. Pulse current drivers like the plasma focus and Z-pinch are one of the few methods to produce such strong fields in a somewhat controlled way. Other methods are explosively driven like nuclear detonations. Annually, a meeting is held on Megagauss fields which are common in the Z-pinch community using 1 MA to 24 MA drivers to report results on 1E7 and 1E8 Gauss experiments. The reproducible demonstration of Gigagauss fields had yet to be shown. The Focus Fusion concept argues they are necessary but making a measurement of these fields directly is very challenging. Diagnostics are only now becoming available to do what is needed and they require very specific axillary facilities that are likely to exceed the cost of FoFu-1. It is likely that Gigagauss fields will be inferred from another measurement before directly measured. The problem with measurement by inference is the interpretation. Someone sees a plasmoid while others see a Rayleigh-Taylor neck or so called hot spots. To achieve a Gigagauss field using a 1 MA drive pulse, you need a pinch diameter of ~2 microns. Typical observed pinch diameter are more like 5 millimeters. The problem is more complex than this simple calculation but features less than 10 microns are required to achieve such a high field unless you are using other techniques like flux compression.

Dave:

Black body losses are not that significant in a deuterium plasma because most of the electrons are unbound leading so-called free-free radiation instead of free-bound radiation. Free-bound transitions are more frequent and generally more potent because you can excite a bound electron leading to a photon emission to return to ground. It can be rapidly excited again. In the free-free mode, you need specific interactions to generate radiation. Also, deuterium plasma is optically thin. Remind your engineer friends that a black body is the most efficient emitter of radiation at a given temperature which means it takes the most power to sustain a black body at a given temperature. Gray body and white bodies (optically thin bodies) are much easier to heat to high temperature given a fixed power input. Emissivity for plasma can be quite low or large depending upon the conditions of interest. This is a complex matter is plasma physics requiring very complex diagnostics and very intricate numerical simulations.

I would add to Jamesr’s comment about brems. Brems emission is typically related to electron temperature or energy. In pinch devices, the electron temperature is naturally lower than the ion temperature. It is commonly reported in published literature since 1958. Pinch plasma is one of the few plasma types to have hotter ions than electrons. That is a huge advantage to accessing p+11B fuel. If you can further suppress the electron temperature or increase the ion temperature using strong magnetic fields, you can benefit further.

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Francisl wrote: On a related topic, since tungsten electrodes will be used, can the tungsten ions be used to measure the energy levels in the different parts of the plasma wave and pinch as suggested by this article?
http://www.sciencedaily.com/releases/2009/09/090909111623.htm

My understanding is the Be will be used as electrodes. Be would fully strip if it could reach the pinch. Very little electrode material seems to make it into the pinch plasma. Measurements of high Z materials in deuterium pinches seldom reveal anything other than deuterium. Some people intentionally dope Z-pinches with high Z gases to measure the state of the plasma. For example, Ar pinches are commonly doped with Cl. The Ar lines become optically thick in pinch plasmas making the measurement of temperature and density more difficult. Cl is close to Ar so it doesn’t radiate away too much energy but it remains optically thin so you can measure temperature. It is a common trick. Other people dope deuterium plasma with Ne, Ar and Kr to enhance the radiation yield by cooling the plasma. It is counter-intuitive but cooling the imploding plasma is actually beneficial in some situations. There are several papers on deuterium doping. Plasma focus diagnostics typically operate in the visible, soft x-ray (>200 eV) and hard x-ray (>10 keV). EUV is not typically examined because the spectrometer are costly and must operate in vacuum without filters. Debris from the pinch and plasma can damage the camera if one is not careful. Visible emission can be measured through a window. Soft x-ray is penetrating enough that thin filters can protect a CCD or other recording medium. X-rays are penetrating enough to leave the vacuum through a thin x-ray window.

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It is a nice piece of basic plasma science. It might apply for higher Z atoms like Ne and Ar that are partly ionized before imploding into a pinch but low Z gases like H and He are already fully ionized before they become dense plasma. I would venture a guess that boron is fully stripped of electrons before imploding.

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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.

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The most common example of this approach is so-called planar wire arrays. Rather than arrange a group of wires in concentric cylindrical shells, they are arranged in two straight planes or other planar geometries. The JxB force drives the wires to some central axis. The problem appears to be that the wires arrive at different times. Rather than getting all the mass arriving on the axis at the same time which leads to a dense pinch, you have waves of mass arriving. You can’t compress the plasma as tightly leading to a cold pinch which is bad for the application of wire arrays (soft x-ray production). Planar wire arrays are one of the fads of the Z-pinch community right now so the literature is filled with tomes on the subject.

One might argue that a planar sheet of gas is different. My concern is that when the sheet breaks up into a few pinches, you are splitting the current between each pinch. Say you get an equal division of current in two pinches. The radiation yield (neutrons, alphas, x-ray) scales with the current to some power (Yield=a*Current^n). In the equation, n tends to vary from 3-6 for fusion and a is all over the place (1E-4 to 0.1). The typical value of n is around 4. You divide the current into two equal pinches sharing half the current. Thus, each pinch is emitting ~6% of the radiation a single pinch with all the current. You have two pinches so you get a total of ~12% of the radiation yield from a single pinch in a concentric geometry if a is the same. The exact value of a is not easy to get. My feeling, but not proven, is a will drop for the parallel pinch case because you are dividing the pinch inductance into a parallel paths reducing what is commonly referred to as the current bite. Small current bite tends to correlate with small a. The problem is far more complicated but you need to read the published literature for a more complete description.

If you argue you can drive more current per shot, you might have a hope of increasing the yield by increasing the number of pinches. However, you can drive more current in a cylinder than you can a set of parallel plates for the same gap between anode and cathode due to inductance.

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dennisp wrote: I was going to ask you about your previous post mentioning momentum…if there’s a simple explanation, why does that force the nucleus to split? Why couldn’t the proton just stick to the boron and give it a push, like a bullet hitting a block of clay?

I understand there will be energy that has to go somewhere…the clay heats, but the carbon could, as you say, emit a gamma.

(As I’m sure you can tell, my physics training only extends to a couple semesters.)

While the gamma can carry momentum to balance the reaction, imagine the state of the 12C nucleus after absorbing the proton. The five protons and six neutrons were dancing around in their quantum mechanical happy place. Balance between the electromagnetic force and strong nuclear force is achieved. Suddenly, some jerk from out town shows up. He has both strong nuclear attributes (attractive over short distances) and electromagnetic attributes (repulsive over long distances) and he’s not afraid to show it. By the time the proton gets close enough for the strong nuclear force to gab onto everyone the electromagnetic force is pushing on the other protons. The neutrons have to stay near the protons to maintain balance so they start to move as well. Like a desperate person falling, the out-of-towner grabs what he can. For some reason, grabbing another proton and two neutrons is the most favorable. The remaining nucleons suddenly find their peace disrupted. Factions grow up in the 8Be nucleus and talks break down. It is far easier to divorce than stay together. Every now and then, the protons course is such that it can grab onto everyone or enough neighbors to stick. At that point, a photon is released to conserve momentum and energy.

If you imagine the case of a neutron going into the nucleus, it has only strong nuclear properties. It can cozy up to the other nucleons. Trying to find its place in the group it fights the other nucleons. Depending on the instability in the nucleus to start with, it can lead to some particles expelled (host of neutron reactions), an invitation to stay (neutron comes and photon goes) or the Jerry Springer show breaks out (fission). Protons and photons can do the same thing but the energy requirements tend to be much larger. Photons of sufficient energy are rare. Protons are charged particles and they are repelled by other charged particles in the nucleus.

Protons reacting with nucleons are throwing a ping-pong ball into the wind. You cannot say the ping-pong ball collided with the wind in the ball hitting the wall sense. Instead, you say the ping-pong ball was continuously deflected. Take a golf ball and throw it into the wind. You won’t notice much change relatively speaking.

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Dennisp: I don’t agree with you analogy. Carbon-12 has many possible exit channels to release its energy such as re-emitting the proton, emitting a gamma or falling apart. The brick does not have the same option. There are reasons the carbon-12 is not stable and energy plays a role as I said above. The ability to conserve momentum is the reason. Energy and momentum are linked quantities. If you look at the fission of U-235 by neutrons it produces the largely stable U-236 after absorbing the neutron. The time of stability is 12C->4He+8Be; 8Be->2*4He. p+11B is a bit unique in that it takes advantage of the stability of He-4 for it’s location on the periodic table. He-4 has a binding energy per nucleon of 7 MeV/nucleon. Fe-56 has binding energy per nucleon of 8.7 MeV/nucleon (near top of the charts). 11B is 6.9 MeV/nucleon. The general trend is binding energy per nucleon increases with Z until you reach Fe. After Fe, binding energy per nucleon decreases leading to less stable nuclei. p+11B moves toward stability by reducing product atomic number rather than increasing it. Why work harder when you can work smarter? Why gain atomic number per product when losing atomic number per product is more favorable?

Look at the reactions below. Which ones are the most alike?

D+T->5He->4He+n
D+D->4He->p+T
n+235U->236U->Xn+products (Too many to list, X~2.3)
p+11B->12C->4He+8Be->3*4He

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mchargue wrote: So far as I know, fusion is defined by: (the mass of the reaction products) < (the mass of the mass of the reactants) The difference is released as energy.

Total mass is always lost in an exothermic nuclear reaction. Fission meets the same conditions. Fission and fusion are subclasses of exothermic reactions. My opinion is the names came about to satisfy someone with the desire to classify things until only a few were in each category. The holy grail of nuclear energy is an exothermic nuclear reaction that does not produce neutrons but can produce a controllable chain reaction. p+11B meets the neutron condition. We shall see if it can meet the chain reaction condition.

When I was referring to mass, I should have said atomic number (Z). In my experience, fusion usually means one product has a higher Z than either one of the reactants. Fission leads to products that are both lighter (smaller Z) than the heaviest reactant.

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Zap: Your definition seems pretty arbitrary. U-236 is stable in a small fraction of events when a gamma is emitted. If I understand the reaction correctly, C-12 does the same thing in a small fraction of events from p+B-11. The C-12 does not break apart due strictly to energetics. Conservation of momentum is the reason. Can’t conserve momentum in the reaction without a minimum of two particles ejected. If we could avoid two particles, D+D-> He-4 would work and our cold fusion friends would be very happy. 🙂

The definition I’ve run across (Mayo, Intro to Nuclear Concepts for Engineers) is about producing a heavier particle than the initial pieces with a smaller partner (Again momentum conservation). By this definition, p+B-11 is fission. The two products are an alpha and Be-8 which quickly decays by two alpha emission. Fission does not require neutrons. Proton fission is a known quantity. It is terribly inefficient but it does exist with high Z elements. One can choose the banner to carry by shaping the definition for their purpose. I have no problem with fission so I don’t mind calling it fission. I know many on this site don’t share my feelings so they unite under the fusion banner. I find it funny that the unknown of fusion energy is more appealing to some than the known of fission. Fission is far from perfect but we know the problems. Fusion energy is still a mystery and the unknown unknowns are still many.

In the end it doesn’t matter; a nuclear reaction without neutrons is still sweet.

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The switch is practical. Ideas like the HCP were turned into multi-channel switches like the MMCS switch that is used in some linear transformer driver systems. They are high current, high voltage switches with very low inductance. The problem is the rep-rate is limited to a few Hz at most.

I think the HCP is feasible to build and test. The key unknown is whether it will be able to sustain fusion as long as the x-ray pulse.

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The key question is how thick do the walls have to be to survive. Circulating liquid metal is an efficient cooling approach but Li is a pain. I’ve never worked with it myself but the couple folks that I know that work with it complain about it constantly. I believe high pressure He is the stated cooling method for electrodes because it is easy to clean up. I’ve used water as a coolant on lower power systems and water can be a challenge at times. We looked at metal heat pipe technology and it wasn’t practical for size reasons. Flowing Li might work if the pumps, etc exist. A potential downside is activation of the flowing Li by a flux of neutrons. Helium doesn’t have that problem.

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I wish them luck. Many PF sources and pinch sources have competed for EUV lithography. The only one still standing (has funding) is a liquid tin Z-pinch system.

ZaP Flow Z-pinch is nothing more than a PF with constant gas injection and a really long power pulse.

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People have tried two PF’s facing each other on and off since the 1970’s. The tale is one of woe. It led to the design of the hypocycloidal pinch. Rather than two concentric cylinders, the hypocycloidal pinch uses three ring electrodes. The rings are stacked in a cathode-anode-cathode configuration. A plasma is generated by flashing an insulator, like a PF, at the larger diameter. The plasma runs toward the center like a Z-pinch but it turns the corner at the of the rings and implodes. The pinch lifetime was observed to last for 10-100X longer than any pinch device at similar densities (~1E19 /cc). As a general rule, a pinch can hang together longer if the density is lower. A single NASA tech report was written and the idea was abandoned. I don’t know why. I would post the report but it is huge. I’ve wanted to test this idea in more detail as the beam damage and x-ray deposition should be significantly reduced due to geometry. The key problem that I observe is the energy stored in the pulse power is much larger than a PF so the energy released per shot must be larger.

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Q>1 is a necessary but not sufficient condition for a fusion reactor. Electrode failure in a PF has been a problem for many PF applications at repetition rate. Plasma facing in general is a huge area of research. A breakthrough could benefit many applications from high current switching on the grid to fusion. LPP may not have the resources to explore this right now but it is probably worth discussing the issue to see if anyone has any bright ideas.

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You have lost all the benefits of a PF and replaced them with all the problems of other fusion concepts. The problem with the HyperV concept and other similar concepts is the limited compression ratio. Using low density mass to push instead of a magnetic field limits your coupling to the strong shock limit for deuterium which is a compression of 4:1. By driving the plasma with a magnetic field one can achieve compression ratios of 10:1 or greater. In this configuration you also limit you ability to produce the instabilities that most consider necessary to produce the fast ions required to drive fusion in a PF. In the case of LPP’s approach with a quantum magnetic field effect, you need the high compression to generate the intense magnetic fields required to achieve the plasmoid.

In defense of hyper V they plan to use high Z gases as a tamper which will allow higher compression ratios but it is difficult to believe they will achieve a large compression ratio. The other problem for HyperV is the lack of support in DOE right now which was the dominant if not sole source of funding. Their big supporter was transferred to another project area and the new project manager isn’t as supportive of their approach. Last I heard, the entire concept was bad news at DOE.

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