Contents: Return to Home Page
Fusion Concepts Controlled Fusion Methods Modern Research Efforts
Conceptual Overview Inertial Confinement Reactors Inertial Confinement Research
Conditions for Fusion Magnetic Confinement Reactors Tokamak and Stellerator Research

Conditions for Nuclear Fusion


Overview

In summary, nuclear fusion is a process that takes place when the distance between two atomic nuclei is small enough for the attraction from the short-ranged yet incredibly powerful strong force to overcome electromagnetic repulsion between atomic nuclei from Coulomb's force. This is the basic condition required for fusion between nuclei. In an actual fusion reactor, specifically some variety of magnetic confinement reactor, a very large number of fusion reactions will occur in a heated plasma simultaneously. A description of ideal fusion conditions within a heated plasma will entail a great deal of complexity, so quantities such as ion density and reaction confinement time become relevant conditions alongside the temperature required for the reaction to ignite.
In order to obtain a net yield of energy from nuclear fusion after a critical ignition temperature has been achieved, the reaction must be confined for a sufficient time at a high ion density. In 1957, J.D. Lawson showed that the minimum conditions for productive nuclear fusion as the product of the ion density and confinement time. This product is known as Lawson's criterion. The aim of modern day experimental fusion reactors is to produce the conditions required to achieve Lawson's criterion. The following sections describe the implicit and explicit conditions involved with Lawson's criterion and the challenges they present to fusion researchers.

Energy Barriers

As mentioned before, the primary condition that must be met for a fusion reaction is set by an energy barrier from electromagnetic repulsion between like- charged nuclei given by Coulomb's force. This energy barrier is called Coulomb's barrier. Because Coulomb's barrier originates from electric potential energy, given as U=(kq^2)/r where r is the distance between the two particles, Coulomb's barrier is simply as the electric potential at the distance R where the strong force attraction becomes dominant. If the charge of the fusing particles and the minimum distance for fusion R are known, then it's possible to calculate the temperature required to have an average thermal energy of each particle to overcome the height of Coulomb's barrier. However, the temperature calculated by this method will actually be lower than the actual critical ignition temperature of fusion because of non-uniform energy distribution and also quantum tunneling effects.
The methods used to reach this critical ignition temperature vary between reactor design, but are generally divided between two schools of thought.
Inertial confinement reactors work around the problem of confining a high temperature material altogether by blasting nuclei with massive amounts of energy and taking advantage of their inertia.
Magnetic Confinement Reactors work with heated plasma, so in order to heat the plasma to the critical ignition temperature a variety of methods have been proposed. For tokamaks, the steering magnetic fields also induce an electrical current within the plasma. The current causes collisions between plasma, electrons, and ions in the form of electrical resistance, and this resistance produces heat. More specifically, the heat caused by resistance in the current is called Ohmic Heat. As the temperature of the plasma increases further, the overall resistance it provides decreases. Therefore, Ohmic heating is insufficient as a sole heating method.
Two additional methods exist for adding energy into a magnetic confinement reactor - neutral beam injection and high-frequency electromagnetic waves.
Neutral beam injection consists of accelerating deutirium particles to a desired energy level. Afterwards, these ions are processed by a device called an "ion beam neutralizer" which removes their electrical charge. Once the particles do not have any charge, they can be ejected into the main fusion reactor and, through rapid collision, transfer their energy to the plasma as a whole.
Energy is also carried by High-frequency electromagnetic waves which are introduced into the plasma to increase the total energy and temperature of the system. This heating method can be optimized for heat transfer by matching the frequency of the wave to the frequency of plasma ions and electrons in three spatial dimensions of the reactor.

Confinement Time and Ion Density for Fusion

Confinement Time of fusion is defined as the time elapsed while the plasma is maintained at a temperature above the critical ignition temperature. In order to yield more energy than what was put into the plasma, the plasma must be kept at this temperature for some minimum amount of time that depends inversely on anther quantity called Ion Density. Ion Density is the critical density of ions in a plasma such that the probability of collision is high enough that there is a net yield in energy. This density correlates to the confinement time for fusion, so these two quantities are often expressed together as a product of confinement time and ion density called Lawson's Criterion, named after J.D. Lawson who first stated it.