Demonstrating over 100 keV confinement in a dense plasma

High Energy Ions:  Trapped or unconfined?

While researchers have known for a many years that the dense plasma focus produces high-energy ions, with energies well into the range where pB11 fuel will burn, some fusion researchers have long held that the high-energy ions are not trapped, but travel freely in unconfined beams. 

These beams, according to this model, collide with the diffuse, cold background plasma in the vacuum chamber to produce the observed fusion reactions. 

By contrast, we and other DPF researchers have long contended that some of the high energy ions are indeed trapped for relatively long times in dense plasma spots—the plasmoids [see animation for visualization of this theory]. 

Both sides agree that high-energy beams are also produced by the device.  The question is if any of the hot ions are confined—moving in closed loops, not straight lines.

This argument is critical to the viability of the DPF as a fusion generator, because only if some ions are trapped, circulating around and around within a dense plasmoid, can they heat the fuel up sufficiently to ignite a self-sustaining burn that will consume most of the fuel in the dense plasmoids.  A diffuse beam alone, traveling on a one-way trip through cold and much less dense background plasma, will not be able to do that.

Evidence

Previous experiments by LPP at Texas A&M University in 2001, and by other groups of researchers, have accumulated evidence that the hot ions are indeed trapped.  But clear proof has been lacking that would rule out the unconfined beam model.  LPP now has provided that clear proof. 

One big piece of that proof came from a recent re-analysis of shots we fired back in March.  These shots achieved high fusion yield, over 10¹¹ neutrons, but with relatively modest currents, between 600 and 700 kA.  We wondered how these high yields could be explained by a beam running through the background plasma.  How much energy would it take to generate such a beam?  Because the background plasma is diffuse, with a density of only 6.6X10¹⁷atoms/cubic centimeter, a very powerful beam would be needed to produce so many fusion neutrons.  We calculated that at least 9 kJ of energy would be needed to produce such an ion beam, about one third of all the energy fed into the capacitors.

But not all energy fed into a DPF is available at any given instant. Only the energy stored in the magnetic field created by the current is so available. In turn, only part of this energy is drawn into the pinch and therefore can drive the beams. We found that the energy needed for this hypothetical beam was more than double all the energy available for forming it, so it could not exist. 

We could measure the amount of this energy drawn from the DPF’s circuit during the pinch by examining the drop in the current.  The energy carried by a current is proportional to the square of the current times the inductance.  (Inductance is a basic electrical quantity which is explained briefly at the end of this report.)  From our Main Rogowski Coil, one of our instruments, we could measure the drop in current.  But what was the inductance of the total circuit?

In the past month, LPP engineer Fred van Roessel had measured the inductance of the entire DPF device by matching the current output curves from several shots with standard electrical models.  He checked those results by calculating the inductance of some key components, such as the switches.  So we knew how much inductance we had, and thus could calculate the total energy in the pinch as less than 4 kJ—far less than was needed for the hypothetical beam, even at 100% efficiency.  So a beam through the background gas could not produce this many neutrons.

The shots back in March only reached about 70 keV of energy.  In September, however, we had two shots that our time-of flight detectors showed had over 100 keV ions.  Could we be sure of this result?  It came from measuring the difference in the neutron arrival times at two detectors set at different distances—11 meters and 17 meters.  The more the neutrons spread out, the greater their range of velocities and thus the greater the range of velocities of the ions (deuterium nuclei) that fused to produce the neutrons.  More velocity means more energy, so this is a measure of the ions’ energy.

With just two detectors of neutrons, we could not be positive that something was not introducing an error.  For example, what if there were really two neutrons pulses?  We needed data on neutrons as measured closer to the source.

Figure 1. Ready for its close-up. This graph shows the output of the photomultiplier tube (PMT) located only 1.28 meters from the machine’s axis. This is close enough so that the neutrons from fusion reactions do not have time to spread out due to their different velocities, so they reveal the shape of the neutron pulse as it originated. This shot, 12241009, has a single x-ray peak, the one on the left. It is filtered heavily by 6mm of copper so only relatively high-energy x-rays, above 80 keV, can get through. This reduces the x-ray peak enough so we can see the neutron peak, the broad one on the right. We can identify it as a neutron pulse because of its timing relative to the neutron pulses observed at the same time at a much greater distance by the near and far Time-of Flight PMTs. This graph shows clearly the single-pulse shape of the neutrons and confirms the high energy that we have calculated for the ions producing the neutrons.  This particular shot achieved “only” over 40 keV, but other shots in September achieved over 100 keV.

On our last day of shots in December, on December 24, we got clear neutron signals from one of our PMTs located at only 1.3 meters from the axis of the machine.  Thanks to a reduction of noise, to 6 mm of copper shielding to cut back on the X-ray signal, and to the reliable firing of the device (more of that below), we have clear evidence that we are not getting double neutron pulses and that our measurements of ion energy are reliable. (see Fig. 1)  This is a second major piece of the evidence for the confinement of 100 keV ions.

Our ICCD images, obtained in October, show that the region where the ions are confined is only about 120 microns or less in radius.

In addition, our neutron bubble detectors, located along the axis of the device, as well as horizontally, show that there definitely are somewhat more neutrons moving in the axial direction than horizontally.  This means that the motion of the ions cannot be totally random as in a thermalized plasma with no circulating beams.  Instead, the only explanation of all the data is a circulating beam of ions, constituting a large fraction of the ions in the plasmoid, that encounters the most dense plasma as it flows up along the central axis of the plasmoid, thus producing the most neutrons in the axial direction, but many in all other directions.

This model has allowed us to calculate the plasma density in our best shots to be in the area of1-4 X 1020 ions/cubic centimeter, more than 100 times the fill pressure of the gas we started with.

We will be working on the technical paper describing this important result in January and hope to complete it during the month.  We think that it will add considerably to the credibility of the Focus Fusion project, and thus ease future fundraising.

Technical note:  What is Inductance?

Inductance is a measure of how much magnetic energy is stored in a circuit (or part of a circuit) for a given amount of current.  All currents produce magnetic fields, and these fields contain energy.  The current itself supplies the energy to build these fields.  The inductance of an object is the ratio of the amount of magnetic energy to the square of the current (to be precise, twice that ratio).  The bigger the inductance, the large the magnetic field of a given current, so the slower that current must build up.  Inductance is affected by how strong the magnetic field produced is—and thus how concentrated the current is—but also by the total volume of space affected by the field.