Here are Dr. Park's answers for questions 7-10.
7. Is there a reconciliation between this machines low Beta cusp confinement numbers and those claimed for WB6? WB6 was ~ 60 passes , while this machine was ~7 passes. Given that simple biconic mirror confinement was quoted as ~ 5-8 passes (in the older patent application), the numbers for this machine ('Mini B' as it has been called here) seem small. Is the increased magnet spacing distance combined with the overall smaller size (relative differences magnified) significant, despite the increased B field strengths?
- First, I won’t be able to answer this question. This is because we do not know much about the WB-6 results. As you may know, an intense arcing event destroyed the WB6 device after only a handful of shots (3 shots were completed according to the staff who worked with Dr. Bussard on WB-6). In addition, I have no idea about where the 60 passes came from.
Instead, I will do my best to explain the plasma confinement in WB-7, WB-8 and Mini-B here. The understanding we gained from executing WB-8 and mini-B experiments is critical for us to move forward and I would like to share that part here.
We built the WB-7 as a replica of WB-6 in most aspects. We ran about 2,000 shots on WB-7. As for WB-8, we got another several thousands shots.
At a low beta cusp, the electron confinement time is proportional to E^(-0.875) – see page 16 of my presentation from 2014 US Japan IEC Workshop at U. Wisconsin (link
) where the theoretical cusp-mirror loss rate is given.
So, for the same device size and the magnetic field strength, the cusp electron confinement time for ‘cold’ 10 eV electrons is 310 times better compared to the confinement time at ‘hot’ 7 keV electrons.
One example of seemingly good cusp confinement for cold electrons is the electron density decay time measurement (correlates with the electron confinement time) in page 10 of the same presentation for WB-8. It is ~180 microseconds for an estimated ‘cold’ electrons with a temperature of ~3 eV.
By the way, testing showed that there was no difference in the observed density decay time times for various grid bias voltages. This result is probably the most direct demonstration of why the magnetically insulated grid approach failed to produce a potential well. Grid bias had no impact on electron dynamics. If the potential well is formed with the grid bias, we would have seen the significant changes in electron dynamics from increasing bias voltages. In addition, no neutrons were observed when the grid was biased up to 20 kV in WB-8, while the plasma density is much higher for WB-8 compared to WB-7 (where we saw significant neutrons at 13-14 kV bias), providing another clear example of failed ion heating (from the lack of potential well formation) using magnetically insulated grid approach.
For a high beta cusp, the theoretical scaling law predicts electron confinement time is proportional to E^(-1.5.). In this case, the electron confinement time at 10 eV would be 18,000 better than at 7 keV.
“Mini-B” (in our nomenclature, we used the term, WBX) confinement time was given for 7 keV electron beam, not for the cold electrons at 3 or 10 eV. Poor confinement for a 7 keV electron beam in a smaller sized cusp machine like Mini-B is expected for a low beta case based on the cusp-mirror loss theory. In addition, there is no reason that the electron confinement in a hexahedral cusp is significantly better than for a biconic cusp in the case of low beta based on the cusp-mirror loss theory. Also note that the magnet spacing is not critical.
Back in 2008, we estimated electron confinement time for the WB-7 to be about 7 microseconds. The conditions are: 1 kG nominal cusp magnetic field, 8 cm plasma radius, grid bias at +13 kV, grid current at 42 A (electron current), and avg. electron density at 1.7x10^12/cc. The idea behind the electron confinement time estimate was that in steady-state, the grid current (which can be viewed as electron loss) would be equal to the total number of electrons divided by electron confinement time. Coincidentally, an estimated WB confinement time for 13 keV electrons in the WB-7 size device is about 4 microseconds.
This estimate had a number of shortcomings. The major ones are:
- We don’t know the energy of lost electrons to the grid. For example, were they at ‘cold’ 10 eV, ‘hot’ 13 keV, or something in between when they were in the bulk plasma? In addition, how their energy would have varied as they moved toward the metal surface since we do not know the electric field distribution near the grid surface and the metal joints (connecting “nubs”) between each grid coil.
- We don’t know where the loss of electrons occurred. The measured loss current is the electron current (assuming no secondary electron emission) to the entire coil surface (not intercepting the magnetic field lines) and to the metal joints connecting the coils (intercepting the field lines). In general, the plasma motion (in particular electron motion) is almost always along the field lines rather than across the field lines. So, how you would weight the surface area to analyze this grid current distribution was not a trivial question.
- We don’t know the loss rates along the other cusp openings that were not blocked by the metal joints. These losses would not show up as the grid current. So, we are ignoring significant part of electron loss by using only the grid current as the measurement data.
Despite these shortcomings, we nonetheless estimated the electron confinement time back in 2008 because that’s all the data we had at the time. They are poor man’s results (it is almost always a bad idea to analyze your data without detailed plasma diagnostics) and in retrospect it was a mistake that should not happen again.
One excuse was that I had only one year to build and operate the WB-7 device from scratch in a completely empty space, to produce neutrons, and to make physics measurements to understand the WB physics with the help of a ‘motley crew’ of physicists, engineers and technicians on a shoe string budget. We told the review panel exactly how we got this result with the related shortcomings and explained to them we needed to have a better measurement regime. They understood our situation and provided their findings to the Navy. Somehow, that was good enough for the Navy to take a chance on EMC2 (probably three reasons in retrospect: high energy price, technical competency, and honesty), in addition to the scientific merits of the Polywell concept, although I don’t think we fully understood how remarkable the Polywell approach was at that time. It was more of a seasoned physicists’ gut feeling based on perceived elegance. That’s why, to this date, I am grateful for the support from the Navy.
In comparison, WB-8 and WB-mini measurements did not have those shortcomings. In WB-8, the observed electron loss can be easily explained by the cusp mirror loss theory. Of note is that we never produced a high beta in WB-8 though we might have done so if we were given an opportunity to continue the project for another 6-12 months. In Mini-B, the electron confinement enhancement is clearly measured from low beta to high beta, which provided the breakthrough for the Polywell concept to move forward.
8. The reported neutron counts for the relatively large reaction space in WB-7 seem modest compared to simple amateur fusor reports with only modestly higher voltages, and this is ~ 3 orders of magnitude less than that claimed for WB6. Was deep potential wells obtained in WB7,and 8? You mention that deep potential wells were obtained in 1995, how about in WB7 and/ or 8?
We could not confirm if we had a potential well in WB-7. We definitely did not have the potential well in WB-8. The neutron rate of WB-7 was 1x10^6 neutrons/s compared to 1x10^9 neutrons/s from WB-6. Though those two devices operated at comparable grid bias voltages (12 kV for WB-6 and 13 kV for WB-7), the grid current was 4,000 A for WB-6 compared to about 40 A for WB-7. It was because in WB-6, the power system had no control whatsoever to protect the device from catastrophic arcing. The neutron data for WB-6 came when the arcing occurred and destroyed the device by dumping the entire amount of stored energy from the high voltage capacitors into one metal joint. On the other hand, the WB-7 was designed with the modern pulse power system with the protection circuit to suppress arcing and limit the current. This resulted in much lower grid current for WB-7 compared to the catastrophic arcing case of WB-6.
Assuming that both devices had similar ion energy and confinement time, WB-6 would have produced about 100 times more neutrons if the fusions were from the beam ion to target neutral reactions and 10,000 times more neutrons if fusions were from the beam ion to bean ion reactions. So, I don’t see any inconsistency between the WB-6 and WB-7 results though this comparison is only qualitative in nature.
Despite modest neutron yields per input power (e.g. the peak power of WB-6 was ~50 MW, 4,000 A at 12 kV: Thus it is no surprise why the WB-6 failed after just 3 shots). WB-6 and WB-7 are probably the only known gridded fusion devices that produced neutrons while operating with a positive bias voltage. The performance difference between a positively biased potential well machine (a virtual cathode) and a negatively biased gridded device (Fusor) can be attributed to the following simple reason: The electron, being a lighter species, moves ~60 times faster than deuterium ions for the same kinetic energy. This in turn results in a much larger loss current to the grid for a positively biased grid system compared to the negatively biased grid system. As a result, WB-6 and WB-7 would have greatly underperformed in neutron yields per given input power against comparable fusors unless the electron loss rate is greatly improved via WB (and assuming there was a potential well).
That’s why Mini-B results are so important. Now we know that a high beta cusp can provide a means for electron confinement good enough for a fusion reactor, which in turn can make the electrostatic ion acceleration and confinement a reality. Throw in the inherent plasma stability of cusp, we may have one of the most attractive fusion concepts.
9. What is the next proposed test machine going to look like, and what will be the biggest engineering challenge in its construction?
We plan to build a series of Polywell machines in the next phase. A spindle cusp, hexahedral cusp and the dodecahedron cusp. It is the right time to investigate this part of the physics now that we tackled the Wiffleball. This part is also related to investigating the possibility for p-11B. In addition, we absolutely plan to focus on the formation of a potential well with sufficient electron beam power and sufficiently good electron beam confinement. All previous WB devices (from WB-1 to WB-8) utilized a magnetically insulated gridded system, thus lacking the proper electron beams. That needs to be changed. We plan to have at least 10 MW of electron beam power to produce a potential well. Following in the tradition of WB-8 and Mini-B, we plan to make all the key measurements required to fully understand the physics of Polywell. If all goes well, we should have demonstrated the following in 3 years:
- A potential well depth of ~ 5 kV or higher (equivalently, average ion energy of 5 keV)
- Sufficiently good electron confinement in a high beta (without good enough electron confinement even 10 MWs is not going to be enough).
- Electron confinement time scaling data over 2-3 orders of magnitude. At present, the electron confinement from Mini-B is about 1-10 microseconds. In the next machine, we expect an electron confinement time between 1-10 milliseconds. If we can validate the scaling physics over 2-3 orders of magnitude, we can extend the scaling law to a power producing reactor.
There are some expected engineering challenges for the next phase (I won’t go into details). However, I don’t think it is going to be worse than the WB-8 where we had to come up with a design for 1) minimum 50 kV insulation, 2) cryogenic operation at liquid nitrogen temperatures, 3) UHV compatibility, 4) thermal loading over 1 MW/M^2, and 5) mechanical strength to handle over 30 metric tons of compressional and substantial shear stresses for each coil support at the same time in one package. What we did not discuss much is how simpler it is to design a Polywell device not utilizing magnetically insulated grid approach.
10. What are your thoughts on the proposed test plan and regimes for this new machine?
I can’t wait to build and test the new devices. If we can form a potential well at ~ 5 kV by extending the WB confinement to 1-10 millisecond range, the expected plasma parameters are on the order of: 5 keV ions at 6x10^13 cm-3 density using 10 MW of input power and 5 kG magnetic fields. At that point, the Polywell device can favorably compete with advanced tokamaks (e.g. EAST from China except for pulse duration) while being a much smaller size device and operating with lower magnetic fields. In my view, if one can come up with a device that can outperform the tokamak, that will be the beginning of the end for the decades old quest for practical fusion power (otherwise, we are back to square one and have to wait for tokamak to get significantly more economical).