Bussard’s Polywell concept is a theoretically new way of producing power, but that is the only thing alien about it. In a physical sense, it is merely a construct of both mass and energy streams. While the conservation of mass and the conservation of energy is not respected in the Polywell itself, it is respected everywhere else. However, this lack of respect should not be a hindrance since nuclear reactions are understood just as chemical reactions are. In an analogous sense, the Bussard Polywell, and its auxiliary equipment, is just a chemical plant. Raw materials come in, are purified, proceed to a reactor, and through a separation process produce both waste and product streams. The figure below shows a simplified model of the Polywell system.
The mass stream containing raw materials can consist either a mixture containing the reactive fuel, or a purified form of the reactive fuel. The choice would depend on economies of scale, and in-house technological advantages. In short, the choice would depend on economics. The reactive fuel itself would be boron, in the ideal case, since it would produce no lasting radioactive byproducts, as Dr. Bussard suggested.
Depending on the purity of the raw materials, the priming stage may range anywhere separation equipment to a unit to ensure that the reactor feed is at the correct temperature and pressure. In the latter case, no purification would be needed. In the former case, the separation equipment would need to be combined with equipment to ensure the correct temperature and pressure of the reactor feed.
Around the reactor itself, a vacuum pumping system would be necessary. However, it is not shown on the diagram. It is important though that the net mass efflux of air into and out of the reactor be zero. In the ideal case of course, this steady state condition would be maintained at very low concentrations of air to avoid interactions of the reaction within the reactor with the air surrounding the reactor.
In the post processing stage, products from the reactor would need to be dealt with. Doing this, would require a second set of separation equipment to extract unreacted portions of the reactor feed from reacted portions.
In addition, the waste would need to be conditioned such that it is safe to release to the environment or sell as an end product. In the case of boron as a reactor feed, the waste would be helium. This of course has a wide range of uses ranging from balloon animals to cryogenics. In other cases, when deuterium and tritium are used as a reactor feed neutrons will need to be dealt with.
It should be noted that understanding the behavior inside the Polywell is of critical importance to understand the flow rates exhibited in all other stages of the system. In the chemical plant sense, we would need to know the kinetics of the reaction. However, since we are dealing with a nuclear reaction, kinetics is instead called neutronics. That is we need to know how much of the reactor feed is converted during one pass through the reactor by understanding the nuetronics. To do this, we need to predict the number of collisions of the particles if we assume that fusion only occurs during collisions. Therefore, we need to know the dynamics of the system. Rather than running endless experiments, it would be useful to understand mathematically this behavior so to limit the number of experiments needed. Allen and Tildesley suggest the following algorithm for understanding the relation of computer simulations with experimental results. The figure below presents a modification of a flow chart given in chapter one of their book.
Here is the reason for the relations in the diagram:
When we consider plasma within the Polywell, we can analyze it in two ways. Either we can view it experimentally or we can make some sort of hypothesis about how it will behave and make use of the hypothesis. The hypothesis is normally used in one of two ways: either by simulating the position and movement of each particle within the plasma over time, or by predicting the number of positions that all particles can exist in along with the probability of existence of each position in a time where all positions are realized. Assuming these two methods are equivalent is saying that plasma is ergodic. In the first case, the simulation is a dynamics simulation. It is similar to molecular dynamics. One program that does molecular dynamics is LAMMPS. In the second case, theories are made to describe the behavior. The theory just described for this case is statistical mechanics. One important daughter of statistical mechanics is the Monte Carlo simulation. As the name implies, Monte Carlo is a random simulation that generates possibilities for positions of the particles. One should note that a Monte Carlo simulation is computationally easier than tracking the position of countless particles as in the dynamics simulation. However, due to its removal from the reality of the situation that dynamics simulations more easily entail, the predictions that are produced may not always be needed. What is needed for statistical mechanics to work, and therefore Monte Carlo to work, is the correct partition function describing the number of positions and the probabilities of these positions. Monte Carlo, and its parent statistical mechanics, must therefore be compared to the dynamics simulation. However, the dynamics simulation may not reflect reality either, so it must therefore be compared to experimental data. One must note that the data from the experiment may not reveal everything about the behavior of the system itself. In the case of movement of electrons within the plasma, one cannot measure both the position and the velocity accurately. In measuring one, the other is perturbed by the act of performing the measurement. This lack of ability of measuring both quantities accurately is known as the Heisenberg Uncertainty Principle. However, if a dynamics simulation can model the velocities and positions of electrons, and these dynamics can be related to a reading from experimental data that is dependent on these dynamics, then some idea of the positions and velocities can be deduced. One should note though that this idea may not be exact since many measurements such as temperature and pressure are based on averages over all particles. From statistics, one realizes that the average can be the same while the distribution of the velocities and positions changes. Statistical mechanics can help with this problem since it can be related to dynamics simulations. However, a statistical mechanics model may be related to a dynamics model and even match the experimental results but still not match the exact positions and velocities of the actual system. I cannot give the solution to the answer this problem. However, it is likely that it does not need to be known. I believe only the probability of collisions of particles needs to be known.
Sources:
M.P Allen and T.J Tildesley; Computer Simulation of Liquids,
Oxford University Press, 1989
Inspired by:
Chandler, David; Introduction to Modern Statistical Mechanics,
Oxford University Press, 1987
