Lawson criterion

The Lawson criterion ( according to John Lawson ) is a physical condition linked to the necessary for a self-sustaining nuclear fusion reaction minimum values ​​of certain variables. It was originally formulated for the fusion of deuterium and tritium ( DT) with magnetic plasma confinement, but basically also applies to other fusion fuels and entry methods. The criterion is fulfilled in many stars at relatively low temperatures and very high pressures, which are not available on the earth. All earthly attempts to reach the Lawson criterion, have failed so far because the plasma volumes are too small and therefore their thermal power loss is too large. Was to be achieved it with the original design for ITER, but this was not granted in this size. When his successor DEMO it should be possible.

The criterion is obtained from a DT plasma from the balance of the generated plasma, carried by the alpha particle fusion power and the power dissipation of the plasma.

The criterion is obtained from a DT plasma as follows: left that are produced during the fusion reaction neutrons, since they are electrically neutral, the plasma immediately and their kinetic energy of 14.1 MeV is then the energy of the reactor. The electrically charged alpha particles remain in the plasma and give their kinetic energy of 3.5 MeV at this from, so they heat the plasma with a power. At the same time, the plasma loses energy by bremsstrahlung and transportation, the power loss. In equilibrium, ie the alpha particle heating must be as great as the energy loss. Where a DT plasma this condition, " ignite " it "burns " then without further energy input and in turn provides energy as kinetic neutron energy. The criterion should not necessarily be fully met for the operation of a magnetic confinement fusion reactor; a certain constant necessary external heating ( eg with a few percent of the recovered energy neutrons ) would even have the advantage of an additional control possibility of the reaction has to offer (see also fusion by magnetic confinement ).

The equilibrium

A without external energy supply " burning " fusion requires that the power loss is not greater than the proportion of remaining in the plasma fusion power. The latter is in a DT plasma

With the particle densities of the two reactants, which over the velocity distribution of the particles averaged reaction rate ( particle velocity multiplied by the velocity-dependent cross section ), the equity attributable to the alpha-particle part of the energy released per fusion and plasma volume.

The thermal energy contained in the plasma is

The electron density of the Boltzmann constant and temperature.

Radiation and Teilchentransportvorgänge cause a power loss. The quotient of the thermal energy and the dissipated power has the dimension of time and is referred to as energy confinement time:

To achieve the automatic firing must apply:

Are with the assumption that both reactants are present in equal amounts, ie have the same particle density and virtually completely ionized

Follows the Lawson criterion:

At a given temperature, therefore, results in the minimum value of the product of particle density n and energy confinement time for automatically burning fusion reaction. This product is a function of temperature, the bit is different for each of the fusion reaction, but always has an absolute minimum. For the DT reaction, for example, one obtains

Wherein the minimum is at a temperature of about 25 keV.

The triple product

The so-called triple product is usually used as a measure for reaching the firing condition in place of. The Lawson criterion is then

.

This has the advantage that the minimum of a function of the temperature is about 14 keV ( with ) the value of which is approximately required in order to operate a nuclear fusion reactor.

Losses by bremsstrahlung

In particular, highly ionized impurities in the plasma ( for example ) can lead to a loss of energy by bremsstrahlung. The necessary for ignition value of Tripelproduktes is therefore higher.

The bremsstrahlung losses are given by

With the constants and the effective charge (the sum runs over all ion species of the plasma ).

For a self running fusion reaction, this results from the condition ( in which case only describes the loss by transport processes ), the criterion

.

Without impurities, that is,, This results in the minimum of the value. If the plasma, for example, 0.5 % contamination, that is, as the value of the Tripelproduktes increased to the minimum. So it is difficult to achieve the necessary conditions for ignition.