Conditions for Fusion

In addition to providing a sufficiently high temperature to enable the particles to overcome the Coulomb barrier, that temperature must be maintained for a sufficient confinement time and with a sufficient ion density in order to obtain a net yield of energy from a fusion reaction. The overall conditions which must be met for a yield of more energy than is required for the heating of the plasma are usually stated in terms of the product of ion density and confinement time, a condition called Lawson's criterion.

 Lawson's criterion for fusion nτ ≥ 1014 s/cm3 deuterium-tritium fusion nτ ≥ 1016 s/cm3 deuterium-deuterium fusion
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Confinement Time for Fusion

Confinement time in nuclear fusion devices is defined as the time the plasma is maintained at a temperature above the critical ignition temperature. To yield more energy from the fusion than has been invested to heat the plasma, the plasma must be held up to this temperature for some minimum length of time. Calculations of that minimum time are

 τ = (2 x 1014)/n s deuterium-tritium fusion τ = (5 x 1015)/n s deuterium-deuterium fusion

where n is the ion density in the plasma. The product of the ion density and confinement time required for fusion is called Lawson's criterion.

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Ion Density for Fusion

Even given a high enough temperature to overcome the coulomb barrier to nuclear fusion, a critical density of ions must be maintained to make the probability of collison high enough to achieve a net yield of energy from the reaction. The density required for a net energy yield is correlated with the confinement time for the hot plasma, so the minimum condition for a productive fusion reaction is typically stated in terms of the product of the ion density and confinement time, called Lawson's criterion. The calculated values are

 nτ = 2 x 1014 s/cm3 deuterium-tritium fusion nτ = 5 x 1015 s/cm3 deuterium-deuterium fusion
 Discussion of Coulomb barrier Why is this temperature too high?
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Lawson's Criterion for Fusion

Once a critical ignition temperature for nuclear fusion has been achieved, it must be maintained at that temperature for a long enough confinement time at a high enough ion density to obtain a net yield of energy. In 1957, J. D. Lawson showed that the product of ion density and confinement time determined the minimum conditions for productive fusion, and that product is commonly called Lawson's criterion. Commonly quoted figures for this criterion are

 Lawson's criterion for fusion nτ ≥ 1014 s/cm3 deuterium-tritium fusion nτ ≥ 1016 s/cm3 deuterium-deuterium fusion

The closest approach to Lawson's criterion has been at the Tokamak Fusion Test Reactor (TFTR) at Princeton. It has reached ignition temperature and gotten very close to Lawson's criterion, although not at the same time.

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