Re-Analysis of Texas Data Shows High Stability of Plasmoid and Helps to Build Simulations

Lerner took as an example a single shot from the Texas experiments, shot 81206, which was one of the shots having the highest quality data.  We had data for the total x-ray power, the electron temperature, and the ion beam current.  We were able to determine the peak density of the plasmoid from the relative number of neutrons produced by the main deuterium-deuterium reaction and those from the secondary reaction occurring when tritium produced in the fusion reaction in turn reacted with deuterium, to produce a higher-energy neutron. We also knew the plasmoid current had to be at least 1.2 MA for the magnetic field to be strong enough to confine the tritium nuclei long enough to react.  For the plasmoid to have lasted as long as it did, we know the cyclotron radiation had to be trapped, and thus the ratio of cyclotron to plasma frequency could not be more than 2.

Lerner wanted to see if he could model these results with a simple picture of a plasmoid in which the plasmoid is producing the beams. Energy is flowing from the plasmoid magnetic field into the beams and the electron beam is heating the plasmoid electrons. Using the observed values, at each 2ns time period, of the x-ray emission and temperature and the observed beam current, the model computed the density, radius and magnetic field of the plasmoid, given the initial mass and magnetic energy of the plasmoid.

The goal was to see if there was a model that could meet the known constraints for density, plasmoid current and cyclotron/plasma frequency ratio. This proved to be the case.

Figure 1 show the plasmoid radius, which declines during the pulse, as the beams evacuate the particles and the magnetic field compresses the remaining plasma. Density rises to a peak and magnetic field rises as well (figures 2 and 3). This occurs even as the number of particles in the plasmoid drops (figure 4) as the particles exit by the beams, and as the x-ray power goes through a peak (fig 5).  X-ray power first rises with increasing density and temperature, but then falls with the decreasing volume of the plasmoid.

These results, which need to be further refined, are encouraging in two ways. First, they show the great stability of the plasmoid, since the time scale of the compression, of the order of 15 ns, is 500 times longer than the time it takes a typical ion to orbit the plasmoid. The inward pressure of the magnetic field and the outward pressure of the plasma have to be balanced to better than one part in ten million for this stability to be maintained.  This occurs because the “force-free” structure of the plasmoid is the lowest-energy structure that the plasma can generate. In force-free structures, the ions and electrons move in the direction of the magnetic field at every point. This eliminates the Lorentz force, which depends on the angle between a particles motion and the magnetic field. In the plasmoid the average angle between a particle’s direction of motion and the magnetic field direction must be less than one hundred thousandth of a degree.

Second, it is also encouraging that density of the plasma continues to rise as the plasmoid shrinks. This will maintain a high level of fusion reactivity thought the plasmoid life.

This analysis will be used to modify the existing LPP plasmoid simulation and to start building a new 1-D simulation that will include a radial profile of the plasmoid.

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.