[asymmetric_implosion]

A few comments:

1) the notion of pre-heating the fuel a pinch device is being tried right now at Sandia National Lab. It is call MagLif.
2) The neutrons from fusion, D-D or D-T, are such high energy that they will pass through a plasma of sustainable volume. Even ITER cannot contain its neutrons and it is many times larger than a pinch. The same is true for a NIF fuel pellet that is extremely dense but small.
3) Preheating a plasma in a pinch is not a positive attribute. You want cold fuel to start with. If the fuel is hot, it is difficult to compress to even higher temperatures as radiation becomes an important loss mechanism. Even pre-heating at MagLif is only 100 eV at most. Pre-heating is also an energy intensive process. It might cost more than it benefits.

[asymmetric_implosion]

It doesn’t happen in every system. The ions from fusion are very energetic but they are distributed evenly in every direction. The reason the ions are directed because of the voltage difference between the anode and cathode.

[asymmetric_implosion]

You can try and fire switches at different times but the jitter in the switches tends to be too great to control. You also run into issues with different voltages in the circuit at different times. They are pulse shaping systems that fire switches at different times but they cannot respond at the nanosecond scale at the MA level.

[asymmetric_implosion]

Focus fusion and other plasma focus devices are inertial confinement devices. Inertial confinement relies on the momentum of the matter to hold the fusing system together. PFs use a magnetic field to accelerate and try to confine the matter but in the end the field cannot hope to win. One way to look at the problem is with pressure. The magnetic field has a pressure associated with it. As the current increases the magnetic field increases and as the inner radius of the plasma column decreases, the magnetic field increases. Magnetic pressure increases with magnetic flux squared. The kinetic pressure is your normal density times Boltzman constant times temperature. When you strike the plasma, the magnetic pressure overwhelms the kinetic pressure and pushes the mass forward just like pushing a door shut. When plasma reaches the end of the electrodes, the magnetic field can press the plasma into a cylindrical object commonly called a pinch. Within this pinch region hot spots which are sometimes called plasmoids and other regions form due to instabilities in the compression process. One average, the density increases and kinetic energy of the moving plasma is converted to thermal energy as the pinch stagnates. You can go in any radial direction as the magnetic pressure is pushing you toward the center. The stagnation is caused when magnetic pressure and kinetic pressure equalize. Before stagnation, the current starts to drop sharply due to electrical changes in the circuit as a result of changing the plasma shape. Thus, kinetic pressure eventually overwhelms the magnetic pressure and the pinch explodes. To increase fusion time you must hold up the current, which has not proven to be positive. You want the rapid drop in current. If you push more mass but the plasma is colder and less likely to reach the conditions of interest. The fusion lifetime for a PF device appears to be fixed at ~10 ns.

[asymmetric_implosion]

The beams are a result of runaway particles in the dense plasma region. Runaway particles are ion and electrons that are accelerated well above the temperature of the system. For example, if you have a 1 keV plasma, you expect to find most of the particles with energies less than 10 keV. If you find an abundance of particles at 100 keV you have a runaway situation. The cause is complex but ions move away from the anode (center electrode) and electrons move toward it. While it is a nice diagram to show the two beams are truly separate, recent published articles show ions travel in both directions and electrons seldom let ions travel without tagging along. This means you have ions and electrons in both beams but the contributions are not equal.

[asymmetric_implosion]

Lerner wrote: Right–we have a Rogowksi coil built into the machine to monitor the current and it does indeed show the current oscillating at the same frequency as the voltage. Although all the grounds are connected, the Rogowski coil in grounded to the ‘scope while the high voltage probe is grounded to the support structure. The ratio of current to voltage oscillations and the frequency of the oscillations combine to give us evidence that the current is moving back and forth between the top and bottom transmission plates–they have the right inductance and capacitance for this. The energy is mostly radiated out the edges of the plates, creating a big RF noise source which we spent a long time shielding against the first year of FF-1’s existence.

OK, all grounds are connected. This by definition is a ground loop. Ground loops generate noise on signals by floating the grounds at different parts of the circuit leading to noise on the ground side rather than the power side. I don’t doubt you see oscillation in the current at some level but you also have to contend with ground loops.

IF you are seeing the current oscillating at a higher frequency than the initial frequency of the system (contributions from L, C and R for short circuit) then you have to have a transmission line like system. Typically, a ~1 us pulse system does not behave like a transmission line. You usually have to be much faster. One might argue that the fast behavior of pinch can do it but you see it on the trigger as well. The trigger should be reasonably clean as there is negligible current in the system. If you see oscillation at breakdown, it tends to be high voltage noise in my experience. It could be something else but I suspect if you can make the noise go away with a better selection of the ground point of the HV probe. It is a simple experiment that could tell the difference between a paper and a problem.

[asymmetric_implosion]

A rogowski coil is a magnetic coil. It is used to measure the time derivative of the magnetic field and converts it to a voltage. When placed around the anode, the rogowski coil is related to the current in the anode.

My observation on previous PF devices is the rogowski coil is a pretty clean signal when properly shielded outside the detection region. High voltage probes are more problematic. Most HV probes require a local ground in addition to the digitizer ground. The local ground is really the problem. A few volts of noise on the ground can lead to artificial signal at the digitizer by affecting the ground rather than the primary signal you wish to measure. I’ve notice noised coming into the system when the HV probe is not attached. Depending upon the location of the probe the noise can vary greatly. Large PF systems have a harder time keeping the ground lead short so they tend to produce noisier HV probe signals. When the ground lead is very short the noise is minimized and the best measurement is realized.

[asymmetric_implosion]

Are the rog coil and the HVP on the same ground?

[asymmetric_implosion]

Alternative hypothesis on the ringing: The voltage probe is the victim of a ground loop. I’ve run across it before and by changing the way the ground is done can alter the amount of ringing.

The hypothesis on the voltage spike is right on. There are a few published papers relating the depth of the current bite with the voltage spike.

[asymmetric_implosion]

The short history of the PF: The main objective of PF devices early in their history was to produce large bursts of radiation. It was initially believed that could reach fusion gain conditions. However, the bumps on the road cropped up quickly when devices were scaled up to a few MA current levels. The typical characteristics of a plasma focus are:
1) a low repetition rate device firing a few shots per hour.
2) Cathode radius is 2-3X the anode radius.
3) Operating pressures between 1 Torr and 10 Torr.
4) Simple RLC circuit to drive the system.
5) charge voltage of ~20 kV on the capacitor.

Plasma focus devices have been built that are high repetition rate, high pressure or lower/higher charge voltage.

The information you are seeking depends highly on the design. Typically you iterate on the design when you have some goals in mind. Typical goals are the radiation yield of the system, the system inductance, the charge voltage and the repetition rate. I believe all other criteria are derivatives of these inputs. Typical scaling of the device depends upon the radiation yield (Y) proportional to the current to a power. Y=a*I^n. n is typically around 4 but varies from 3 to 5. The proportionality constant a can vary widely. I don’t believe ‘a’ is truly a constant but that is a story for another time. When you know the yield and derive ‘a’ and ‘n’ from others work, the peak current is known. With a peak current, you can use models to estimate the capacitance knowing the target inductance and charge voltage. The physical size of the system is largely driven by the capacitors and the inductance. The electrode design is driven by the rise time of the current pulse which is driven by the capacitance and inductance. The repetition rate drives the wall plug power (kVA) to power an instrument and the parts selection. Do you want a capacitor that survives a few days or a few years. The electrode material and thermal management are driven by the total power into the system. Single shot machines seldom thermally manage the electrodes or vacuum chamber. Repetition rate systems typically challenge the thermal management systems on the W/cm^2 basis. Electrodes tend to be small and they tend to get hot relative to the power input. This is typically the point when one starts to iterate seriously. Some experiments might feed into the iterations. If you want to design a machine, best of luck. I think you will find the folks that operate machines are generally very helpful and supportive.

[asymmetric_implosion]

D-D fusion can be aneutronic when a third body is present like another atom. Momentum conservation requires two products so He-3 and n or p+H-3. There is a very rare reaction <1E-12% of the time that can lead to He-4+ gamma but it is not worth mentioning. The aneutronic D-D is one of the hopes of cold fusion folks. Evidence does not support that this reaction can favor the aneutronic branch in the presence of current materials or conditions that can be reproduced.

[asymmetric_implosion]

The PF, when working properly, is a series RLC circuit. All components contribute to the R, L and C. The C is dominated by the capacitor so other capacitance can be neglected in most PF devices. There are a number of different R and L contributors to the system. A gas switch typically triggers the systems and it is a dynamic resistor and inductor. The resistance falls from >100MOhm to <0.01 Ohm in less than 50 ns. The inductance stabilizes based upon the switch geometry for the rest of the pulse. It is typically 50-100 nH. The feed plates contribute both R and L depending upon their geometry and conductor choice. The electrode region is most accurately modeling as a time varying and time varying R. There are a number of models that exist like the model by Sing Lee. I've posted the link to Lee's model a number of times on this forum. When I have the measured time derivative of the current and the voltage at the electrodes, I prefer to derive R and L as they vary with time. There are very complex numerical models that address the physics in detail but they are beyond the reach of the average person due to the processing power required to run them. Lee's model is probably the most accessable model for the average person (only need Excel) while maintaining some meaningful accuracy. Just a warning, garbage in and garbage out. You need to know a bit about PF devices before you just start throwing numbers in the model. It is not valid over a wide range of parameters.

[asymmetric_implosion]

Frank,

Some important differences between the Jacob’s ladder and the PF. The Jacob’s ladder climbs mainly due to convection; the arc is hot while the surrounding gas is cold. The travel speed is limited by typical convection speeds. In the PF, the plasma motion is driven by the magnetic pressure behind the sheath. Like a balloon, the sheath blows up as the pressure increase and pushes the plasma along the channel between the cathode and anode. Magnetic pressure can only exist where there is current flowing so the pressure is concentrated between the anode and cathode.

The plasma focus circuit is a simple design on paper. You want a high voltage capacitor, a low inductance circuit and a low resistance circuit. The mechanical part of the system must withstand the current pulse which for most small plasma foci is easy enough. The optimum electrode design is typically a cathode diameter that is double the anode diameter. The anode radius is optimized when the Lee’s drive parameter is 70-90 kA/cm-sqrt(Torr). D=I_max/(a*sqrt(P), where D is the drive parameter, I_max is the peak current, a is the anode radius and P is the deuterium gas pressure in Torr. You cannot choose the pressure arbitrary. It must be between 1 and 20 Torr for most systems. The pinch effect is demonstrated from systems of a few amps to 26 MA. There a practical problems of small pinch devices. Pinch devices above 100 kA are easy enough to produce and literature is fully of devices of this scale.

Good luck learning about PF device.s

[asymmetric_implosion]

The purpose of the axial field per Slutz’s original paper is to limit Rayleigh-Taylor instabilities during implosion and to confine pre-heated electrons. The instability arises due to a light fluid, the magnetic field, pressing on a heavy fluid, the plasma or a metal can. The axial field is compressed which changes the radial implosion velocity profile. The other consideration for the MagLif is to preheat the fuel to 100 eV with a laser.

The helical electrodes are an old idea but they have problems. The biggest challenge is forcing the plasma to stay connected to the electrodes. If you build a helical electrode the plasma current is still radial with an azimuthal field. The bulk of the force is still in the axial direction. The force will push the plasma along the helix and it may skip the valley and jump to the next hill in the helix. The initial axial field is the best way to add some angular momentum to the plasma.

[asymmetric_implosion]

The ideas are nearly identical during the radial compression. Both system are trying to compress magnetic flux and stabilize the implosion. Both will add some measure of angular momentum to the implosion. In both cases, the applied fields are small compared to the induced fields from the current. In both cases, the compressed field reduces electron transport and keeps the plasma hot.

[Author]

Posts