For tokamaks, betas of larger than 0.05 or 5% are desired for economically viable electrical production.
[citation needed] The same term is also used when discussing the interactions of the solar wind with various magnetic fields.
The amount of energy released by the fusion reaction when it occurs may be greater or less than the Coulomb barrier.
Generally, lighter nuclei with a smaller number of protons and greater number of neutrons will have the greatest ratio of energy released to energy required, and the majority of fusion power research focusses on the use of deuterium and tritium, two isotopes of hydrogen.
Even using these isotopes, the Coulomb barrier is large enough that the nuclei must be given great amounts of energy before they will fuse.
Although there are a number of ways to do this, the simplest is to heat the gas mixture, which, according to the Maxwell–Boltzmann distribution, will result in a small number of particles with the required energy even when the gas as a whole is relatively "cool" compared to the Coulomb barrier energy.
In the case of the D-T mixture, rapid fusion will occur when the gas is heated to about 100 million degrees.
These considerations are combined in the Lawson criterion, or its modern form, the fusion triple product.
Systems using only magnets are generally built using the stellarator approach, while those using current only are the pinch machines.
The most studied approach since the 1970s is the tokamak, where the fields generated by the external magnets and internal current are roughly equal in magnitude.
Given that the magnets are a dominant factor in reactor design, and that density and temperature combine to produce pressure, the ratio of the pressure of the plasma to the magnetic energy density naturally becomes a useful figure of merit when comparing MCF designs.
is always much smaller than 1 (otherwise thermal pressure would cause the plasma to grow and move in the vacuum chamber until confinement is lost).
[4] Ideally, a MCF device would want to have as high beta as possible, as this would imply the minimum amount of magnetic force needed for confinement.
Spherical tokamaks typically operate at beta values an order of magnitude higher.
Shafranov and Yurchenko first published on the issue in 1971 in a general discussion of tokamak design, but it was the work by Wesson and Sykes in 1983[7] and Francis Troyon in 1984[8] that developed these concepts fully.
is the external magnetic field, and a is the minor radius of the tokamak (see torus for an explanation of the directions).
Experiments on the DIII-D machine (the second D referring to the cross-sectional shape of the plasma) demonstrated higher performance,[10] and the spherical tokamak design outperformed the Troyon limit by about 10 times.
A common example is the interaction of the solar wind with the magnetic fields of the Sun[12] or Earth.
[12] Active regions have much higher beta, over 1 in some cases, which makes the area unstable.