Lawson criterion

High temperature is an important requirement for the attainment of fusion reactions in a plasma. The conditions necessary for extracting as much energy from the plasma as went into it is the Lawson criterion, which states that the product of the ion density and the confinement or reaction time must exceed 10 s/cm in the most favorable cases (173). If the coUisions are sufficiently violent, the Lawson criterion specifies how many of them must occur to break even. Conventional magnetic confinement involves fields of as much as 10 T (10 G) with large (1 m ) plasmas of low densities (<10 particles/cm ) and volumes and reaction times of about 1 s. If the magnetic flux can be compressed to values above 100 T (10 G), then a few cm ... 

Lawson criterion - [IHERMODYNAMICS] (Vol23) - PLASMA TECHNOLOGY] (Vol 19) -for fusion energy pUSION ENERGY] (Vol 12)... 

In order to achieve an overall positive energy balance the D-T plasma has to be heated to the ignition temperature of 5 keV and confined for a sufficiently long time4). Energy breakeven is usually expressed in terms of the Lawson criterion which states that the product of the plasma density, n, and the energy confinement time re has to exceed a critical value which is a function of the plasma temperature4 8). 

By the end of 1977 Tokamak devices had achieved nre values in excess of 1019 m-3 s and ion temperatures of 2-3 keV. In the early summer of 1978, temperatures in excess of 7 keV were achieved in the Princeton large torus, PLT, using auxilary neutral beam heating9). Other confinement systems such as magnetic mirror devices and intertial confinement are also operating currently below the Lawson criterion but there has been continued development and substantial progress is continually being made. 

Lawson criterion (see below). Temperatures of 10 K have been reached with electron beams, and fusion neutrons produced. With a repetition rate of 100 pellets s, a power output of 1 — 10 GW would be achieved. Difficulties which have hanq )ered the development include problems of shielding against the 14 MeV neutrons and of extraction of the released kinetic energy. 

Lawson criterion A condition for the release of energy from a thermonuclear reactor first laid down by J. D. Lawsonin 1957. It Is usually stated as the minimum value for the product of the density (Ug) of the fusion-fuel particles and the containment time (t) for energy breakeven, i.e. it is a measure of the density of the reacting particles required and the time for which they need to react in... 

The minimum of the L-function occurs at temperature about 25 keV (approximately 250 million K) and has a value of approximately 1.5 x lO s/m. Substituting this value into O Eq. (60.5), one gets the so-called Lawson criterion (Lawson 1957)... 

In the above treatment, it was assumed that alpha heating compensates all the losses from the plasma. This condition is called ignition. One can set similar Lawson condition for various Q = Pf/Pioss values. Abundantly used is the case when the total (alpha + neutron) fusion power reaches the losses, that is Q = 1. This condition is called breakeven. In a given experiment, the value of the product n tE and its deviation from the minimum requirement is a measure of fusion performance. From the above derivation, it is clear that the actual value of the number before the factor 10 s/m in the Lawson criterion depends on the plasma temperature. In the early decades of controlled fusion research, the fusion performance of the plasmas was so far from the Lawson criterion that its use was satisfactory. In the recent years, however, the use of another quantity cailed fusion triple product TiU tE became more popular, because it also contains the ion temperature T and describes the Lawson criterion off the optimal temperature as well ... 

Looking at the Lawson criterion, one can immediately see that there are two basic ways to satisfy it ... 

For inertial confinement fusion, a criterion equivalent in meaning to the Lawson criterion but different in form is applicable, wbicb considers time integrated quantities during the whole fusion bum process rather than the steady-state conditions in the original Lawson criterion. For the simple calculations below, uniform compression of a pellet is considered. Suppose that ignition and fusion bum conditions are attained when the pellet containing Nq atoms has a radius of Rq. 

From this time on, the pellet freely expands with the sound speed, which is = y/k Te/nti. To get the corresponding Lawson criterion, it shall be assumed that the pellet consists of a 50-50% deuterium-tritium mixture and the fusion rate is constant during the expansion as a first approximation, the consumption of fuel during the explosion shall not be taken into account. Tbe number of reactions in the whole pellet during time df is Nf = NDrtj<(TV>dt. The bum fraction f i.e., the ratio of the burnt fuel to its initial quantity) during the expansion time is... 

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