Conditions for the validity of unmagnetized-plasma theory in describing weakly magnetized plasmas

An investigation is made of the conditions under which the expression for the dielectric tensor from magnetized-plasma theory may be approximated by that from unmagnetized-plasma theory. Surprisingly, the conditions usually quoted are shown to be inaccurate chiefly because they make no reference to the form of the plasma distribution function. Corrected conditions depend strongly on the distribution function and their application is thus highly problem-dependent. For completely arbitrary distributions these conditions are generally stronger than the commonly quoted ones for weakly damped waves. By contrast, the conditions applicable to axisymmetric distributions can be weaker than some of those commonly quoted. A geometric interpretation of the revised conditions for axisymmetric distributions is given in terms of the resonance ellipses of cyclotron maser theory and is illustrated with reference to dispersion and instability of Langmuir and Bernstein waves in weakly magnetized plasmas. These results apply to all weakly magnetized plasmas that can be described by the linearized Vlasov equations and imply that some investigations which have used the commonly quoted conditions to justify use of unmagnetized-plasma theory may be in error on this point.