Mean Magnetic Field in Renovating Random Flow

Abstract

Abstract An integral equation is derived for a mean magnetic field in a random velocity field that renovates after a characteristic time τ. It is shown that in two cases, i.e. when (a) the correlation time is short, τ < l/v 0 (where l and v 0 are the characteristic scale and velocity), and (b) for long wave components of the field, k −1 ≫ v 0 τ, the equation is reduced to the differential one, whose form has first been given by S TEENBECK , K RAUSE and R ÄDLER . Expressions for the equation coefficients are obtained in the two above cases. In a general case the integral equation cannot be reduced to the differential one although its spectral properties are close in a certain sense to those of the SKR‐equation. There are differences, however (specifically, the integral equation yields a higher rate for the field growth), that are shown on the example of the Gaussian distribution (at time renewal) of particles moving along random paths.