Invariance principles and plasma confinement

If the equations that describe the observed anomalous transport in magnetic confinement systems are invariant under a scale transformation then any confinement time calculated from them must exhibit the same invariance, no matter how intractable the calculation. This principle places constraints on the form of the confinement time scaling which are characteristic of the plasma model represented by the equations. These constraints reduce the number of parameters which have to be investigated empirically and can serve to indicate which plasma models could describe the observed losses. By extending this argument to specific models of turbulent transport in which the magnetic configuration and the physical mechanism for transport are identified, one can closely define the form of local transport coefficients-in certain cases completely determining them. The paper provides a review of these ideas, shows how they provide a theoretical framework for discussing existing empirical confinement scalings and illustrates their use in classifying and determining the form of local transport coefficients.