proportional to n2T 2. The triple product scales as The triple product is only weakly dependent on temperature as T -1/3. This makes the triple product an adequate measure of the efficiency of the confinement scheme. Inertial confinement The Lawson criterion applies to inertial confinement fusion (ICF) as well as to magnetic confinement fusion (MCF) but in the inertial case it is more usefully expressed in a different form. A good approximation for the inertial confinement time is the time that it takes an ion to travel over a distance R at its thermal speed where mi denotes mean ionic mass. The inertial confinement time can thus be approximated as By substitution of the above expression into relationship (), we obtain This product must be greater than a value related to the minimum of T 3/2/<σv>. The same requirement is traditionally expressed in terms of mass density ρ = <nmi>: Satisfaction of this criterion at the density of solid D-T (0.2 g/cm3) would require a laser pulse of implausibly large energy. Assuming the energy required scales with the mass of the fusion plasma (Elaser ~ ρR3 ~ ρ−2), compressing the fuel to 103 or 104 times solid density would reduce the energy required by a factor of 106 or 108, bringing it into a realistic range. With a compression by 103, the compressed density will be 200 g/cm3, and the compressed radius can be as small as 0.05 mm. The radius of the fuel before compression would be 0.5 mm. The initial pellet will be perhaps twice as large since most of the mass will be ablated during the compression. The fusion power times density is a good figure of merit to determine the optimum temperature for magnetic confinement, but for inertial confinement the fractional burn-up of the fuel is probably more useful. The burn-up should be proportional to the specific reaction rate (n2<σv>) times the confinement time (which scales as T -1/2) divided by the particle density n: Thus the optimum temperature for inertial confinement fusion maximises <σv>/T3/2, which is slightly higher than the optimum temperature for magnetic confinement. Non-thermal systems Lawson's analysis is based on the rate of fusion and loss of energy in a thermalized plasma. There is a class of fusion machines that do not use thermalized plasmas but instead directly accelerate individual ions to the required energies. The best-known examples are the migma, fusor and