The Mean-Field Dynamo Equations with Discontinuous Coefficients and Parker’s Slab Model

The paper discusses the properties of dynamo models with discontinuous distribution of the induction coefficients, showing that no additional source terms appear due to the discontinuities. The apparent contradiction between Parker’s (1971) result for his !-dynamo model and later results, which gave rise to the introduction of additional terms by Ruzmaikin et al (1979), is shown to be due to misinterpretation. Parker’s fields agree well with both, the exact solution and numerical results obtained with a finite-difference scheme. It is shown that the !-approximation is justified even for a discontinuous -coefficient, provided that the magnetic Reynolds numbers R! and R are large and small enough, respectively.