rate (reactions per volume per time) of fusion reactions is where is the fusion cross section, is the relative velocity, and denotes an average over the Maxwellian velocity distribution at the temperature . The volume rate of heating by fusion is times , the energy of the charged fusion products (the neutrons cannot help to heat the plasma). In the case of the D-T reaction, . The Lawson criterion requires that fusion heating exceeds the losses: Substituting in known quantities yields: Rearranging the equation produces: The quantity is a function of temperature with an absolute minimum. Replacing the function with its minimum value provides an absolute lower limit for the product . This is the Lawson criterion. For the deuterium–tritium reaction, the physical value is at least The minimum of the product occurs near . Extension into the "triple product" A still more useful figure of merit is the "triple product" of density, temperature, and confinement time, nTτE. For most confinement concepts, whether inertial, mirror, or toroidal confinement, the density and temperature can be varied over a fairly wide range, but the maximum attainable pressure p is a constant. When such is the case, the fusion power density is proportional to p2<σv>/T 2. The maximum fusion power available from a given machine is therefore reached at the temperature T where <σv>/T 2 is a maximum. By continuation of the above derivation, the following inequality is readily obtained: The quantity is also a function of temperature with an absolute minimum at a slightly lower temperature than . For the D-T reaction, the minimum occurs at T = 14 keV. The average <σv> in this temperature region can be approximated as so the minimum value of the triple product value at T = 14 keV is about This number has not yet been achieved in any reactor, although the latest generations of machines have come close. JT-60 reported 1.53x1021 keV.s.m−3. For instance, the TFTR has achieved the densities and energy lifetimes needed to achieve Lawson at the temperatures it can create, but it cannot create those temperatures at the same time. ITER aims to do both. As for tokamaks, there is a special motivation for using the triple product. Empirically, the energy confinement time τE is found to be nearly proportional to n1/3/P 2/3. In an ignited plasma near the optimum temperature, the heating power P equals fusion power and therefore is