Simulation Results

Posted by Admin on Feb 01, 2004 at 06:10 PM
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The holy grail of fusion research is net energy production, more energy out than in. Recent simulations of the focus fusion device show that net energy production may be achievable with our next set of experiments at the University of Ferrara (on hold due to funding issues). Additionally, power generating reactors must achieve net electricity production which takes into account the inefficiency of converting fusion energy output (high energy particles and x-rays) to electricity.

For conventional Deuterium-Tritium reactor designs that produce heat to run a steam generator this is a big problem because of the low efficiency of the steam generator. However, focus fusion will generate electricity directly from its charged particle beam and x-rays at high efficiency. So for focus fusion reactors net electricity production is not far beyond net energy production.  Here’s the story as found in the Newsletter:

Preliminary Simulation Runs

Lawrenceville Plasma Physics has completed preliminary runs of a simulation of plasmoids that burns proton-boron (pB11) fuel. Overall, the simulation results broadly confirmed that net energy production is possible with a small focus fusion device.  The simulations were better than expected in that good energy production seems possible at a current of 2 MA (mega-amperes), well below the 3 MA we thought would be needed. This makes it more certain we can reach very near these conditions with the device we are planning for the next set of experiments. On the other hand, the ratio of beam energy to x-ray energy is not quite as good as expected, so some capture of x-ray energy (again by direct conversion) is likely to be necessary.  These are conservative estimates, so the results can only become better with more precise modeling.

How the simulation works

The simulation is zero-dimensional—that is it models the plasmoid, the dense, magnetically self-confined plasma structure, as a homogenous entity.  It tracks the changes in magnetic field, radius, and the particle-density, energy and temperature of both the ions and electrons. In the current models, the time step is 3.1 picosecond long, so a thousand or two thousand time steps are used for each simulation of several- nanosecond-long plasmoid lifetimes.

The program simulates the formation of the plasmoid as the magnetic field rises, compressed by the pinch at the plasma focus, when the plasma sheath reaches the end of the electrodes.  After a sine-like rise in magnetic field, the radius of the plasmoid is then assumed to be constant, with the magnetic field containing the plasma. This sequence produces an x-ray pulse that looks similar to those we obtained in the Texas A &M experiments.

The simulation models a number of physical processes: the production of the electron and ion beams; the heating of the plasmoid electrons by the electron beam; the emission of x-rays by the electrons; the heating of the ions by the electrons, and of the electrons by the ions.  As well, it models the generation of 2.9Mev alpha particle by thermonuclear fusion reactions as the ions heat up and the heating of the ions by the alpha particles (helium nuclei).  The simulation demonstrated that very little of the energy from the alpha particle directly heated the electrons.

The magnetic effect that reduces the heating of the electrons by ions was also included in the formulae used for the simulation.  Finally we also modeled the transfer of energy from the ions back to the magnetic field, as the heated ions push against the confining field.

The one phenomenon that we did not model was the non-thermal, collective heating of the ions by the electrons. This is the heating that occurs by the wave-like interactions of large numbers of electrons and ions, not the collisions of individual particles. It is clear that this heating takes place, as collisional heating is too slow to heat up the small plasmoids we created at Texas A and M with their density of about 3x1021/cc.  Although the plasmoids in the simulation have much higher density, so heat up rapidly by collisional heating, non-collisional processes may be at work as well. We don�t as yet have a good model for this. Since this heating can only enhance the difference in ion and electron temperatures, leaving it out make our calculations conservative. The situation is likely to be BETTER than the simulations imply.

Since the sum of the input energy, the magnetic energy, the thermal energy of the particles, and the energy emitted by the beams and the x-rays must remain constant, we were able to use this conservation of energy to check the simulation for errors and correct them.

Simulation results

We’re still exploring the parameter space so the conclusions here are preliminary. First, peak currents of 0.75MA provide a very measurable burn of pB11, with secondary neutrons (those produced by alpha-boron collisions) amounting to 3x1010. Above that, fusion yield rises rapidly with current.  Holding the final B field at 6GG, the simulation showed that the ratio of fusion yield/gross input energy rose from 0.067% at 0.75MA to 5% at 1M to 24% at 1.5MA. 

The magnetic effect became rapidly dominant above 1.1 MA. While at 0.8 MA, the electron peak temperature was 660keV and the ion peak temperature was only 85keV, at 2 MA, the situation was reversed, with ion temperature peaking at 1,380 keV and electron temperature at 62 keV. (The ion temperature would be the equivalent of 15 billion degrees K.) As a result, thermonuclear power peaks at 3 times higher than x-ray power.

In the simulation, break-even (more energy out of the plasma than in) occurs at around 1.5 MA, an easily achievable current. At 2 MA, energy output should exceed energy input sufficiently for net energy production with reasonable conversion efficiencies.

Unfortunately, early in the pulse x-ray power exceeds thermonuclear power as the ions heat up, and late in the pulse x-ray power again exceeds TN power when fuel is exhausted.  In addition, some of the of the fuel does not get burned, as it is emitted in the beam before the ions get hot enough to burn.

The net result is that for the examples studied, some recovery of the x-ray energy, as well as of the ion beam energy,  is essential for net energy production.  The best case studied so far is for I of 2.0 MA, cathode radius 3.3 cm, final magnetic field 12 GG.  This example produced a beam that carried 97% of input energy and x-rays that carry 57% of input energy.  In practical terms this mean that if the beam energy recovery efficiency is 90%, net energy production will require x-ray energy recovery rates above 22 %, which is easily achievable.(Some of the examples studies are summarized in Table.1) Total thermonuclear yield is 54% of gross input energy.

Table 1 Simulation examples

A practical energy-producing combination would be 80% beam recovery and 80% x-ray recovery for an overall efficiency of 43%. In this example net electric energy production would be 3.1kJ per pulse or 3.1 MW for a 1kHz pulse rate.

More research in the literature is needed to look at effect x-ray-to-electricity direct conversion schemes.  The simplest is to have the x-rays emit electrons from thin metallic foils, with the electrons captured on wires held at negative voltages.  While a production reactor would have to be completely surrounded with x-ray collection sheathes, the small physical size of the reactor should preclude any large increase in capital costs due to the x-ray collection device.  We’ll look at ways to use the sharp-pulsed nature of the x-rays to improve collection efficiency.

It seems clear that for high efficiency, x-ray collection will be needed. However, at this point we can’t rule out that net energy production from the beam alone is still possible. As mentioned above, the present simulation excludes non-collisional ion heating, which will improve the situation. Including such heating will be the next step in developing the simulation.

What is already clear from the conservative simulations is that it is possible to get a beam that has energy equal to energy input, it is clearly possible to get break-even (more energy out than in) and it is possible to get net energy production with reasonable conversion efficiency.

For those interested, some plots from the 2 MA, 12 GG run are attached to this newsletter.

Note on plots:

For each, time step is 3.1 ps, so total plot is 20ns.

1) proton/electron temp (unitless ratio)
2) beam power (units are 0.32 TWO)
3) fusion power (units are 0.32 TWO)
4) ion temp(eV)
5) electron temp (eV)