Scaling laws for plasma confinement

Scaling laws for plasma energy confinement must be invariant under any transformation which leaves the basic plasma equations themselves invariant. Hence, constraints can be placed on the scaling laws even though the calculation of energy loss may be quite intractable. These constraints are derived for several plasma models and shown to be characteristic of the model. Hence, in addition to reducing the number of parameters which have to be obtained empirically, these results could delineate which plasma models are appropriate for the calculation of losses. They show that the empirical scaling laws at present proposed for tokamaks are incompatible with many conventional plasma models.