New theoretical work shows how FF-1 gets ions to 1.8 billion C. Iranian group- independently confirms LPP theory (Apologies for length of this important item!)
Theoretical insights and calculations by LPP’s Chief Scientist Eric Lerner and our new summer graduate student, Ahmad Talaei of Utah State University, as well as work by an independent group of physicists at Amirkabir University of Technology in Tehran, have provided a long-sought explanation on how FF-1 has managed to achieve record breaking ion energies, four times hotter than LPP’s earlier theory had predicted. The new theoretical improvement will help us to understand and more efficiently guide further experiments. This work and the independent confirmation of our theoretical calculations by the Iranian group reinforce our confidence that our high temperatures will indeed be able to ignite the ideal fusion fuel, hydrogen-boron.
Since we first observed the 160 keV energies of the ions (equivalent to 1.8 billion C) over a year ago, we had been puzzled as to why they were so much higher than the 40 keV we had predicted. We knew that the earlier predictions, based on theories developed by Australian physicist Heinrich Hora, were only approximate and needed a better physical foundation. But we had not, until now, come up with an improvement.
The first big step to the solution came May 15, with the publication online in the Journal of Fusion Energy of a paper by the Iranian team, S. Abolhasani, M. Habibi, and R. Amrollahi, “Analytical Study of Quantum Magnetic and Ion Viscous Effects on p11B Fusion in Plasma Focus Devices.” The paper studied in greater detail the quantum magnetic field effect originally applied to the DPF by Lerner, for the first time independently confirming our calculations showing that ignition and net energy gain can be achieved with pB11 (hydrogen-boron) fuel, the key to obtaining aneutronic fusion energy. Above: Eric and visiting grad student Ahmad Talaei during a visit to Princeton’s physics library
But in addition, the paper applied to the plasma focus device a process studied by British physicist Malcolm Haines to explain high ion energies achieved in the Z-machine. That process, called “ion viscous heating” works like this: as the plasmoid contracts, ions moving inward at different velocities start to mix together, so that their ordered velocity of motion is converted into the random velocity of heat. By analogy this is a bit like trying to rapidly stir a vicious liquid like honey. The resistance of the liquid to rapid changes in velocity—its viscosity—converts kinetic motion to heat and the liquid warms up. The formulae derived in the paper indicated that this viscous heating could possibly explain FF-1’s high temperatures.
But there was a second puzzle to be solved. The viscous process heats only the ions—the heavy nuclei—not the electrons. If the electrons are too cold, collisions between them and the ions would rapidly cool the ions. So what heated the electrons up hot enough so they would not cool those ions too fast? We had known for many years that the electron beam could not directly heat the electrons in the plasmoid enough. The very fast-traveling electrons in the beam don’t stay near other particles for long enough to effectively heat them by collisions. Some other process must help—but what could it be? Lerner had puzzled over this for years and Dr. Hora’s theory gave only a very partial answer.
On June 10, Lerner thought of a possible solution. The electron beam will induce currents in the plasmoid electrons, just as any rapidly changing current induces other currents in a surrounding conductor (we intend to use this same process to capture the energy of the ion beam with a coil of wire). But since the plasmoid has a much greater density of electrons that the beam, the same current will be distributed over more electrons, and they will be moving much slower than the beam electrons. These slower electrons will have the time to undergo collisions and convert their kinetic energy to heat. Following up on this hypothesis, Talaei found a dozen important papers on this same process of electron beams heating plasma by induced currents, although none applied directly to the plasma focus. Curiously, all the papers dated from the 1970’s, the same fertile period that gave rise to the first research on the magnetic field effect.
When we combined the formulae from these papers for electron temperatures with the formulae from the viscous heating paper and plugged in the observed values for plasma density, radius and current from FF-1’s experiments, the predicted ion energy came out to 170 keV—in terrific agreement with our best observed results of 160 keV. Of course more experiments will be needed to fully confirm that this theoretical explanation is right, but this combination of processes is clearly a possible explanation.
Interestingly, the effectiveness of the ion viscous heating declines rapidly with increasing density of the plasmoid and smaller plasmoid size, while the effectiveness of the induced current heating rises for smaller, denser, plasmoids. So as we increase plasmoid density we expect to see a temporary decline in temperature, and then a subsequent rise back to the levels needed to burn pB11. Fusion yield will continue to rise, as the higher density and thus higher burn rate will more than compensate for the temporary decline in T.
Long as this tale already is, we will have more to say on this heating story in the future!