Finite Correlation Time Effects in Kinematic Dynamo Problem
Authors: A.A. Schekochihin and R.M. Kulsrud
Date of PPPL Report: February 2000
Presented at: Sherwood International Fusion Theory Conference held in Los Angeles, CA March 27-29, 2000.
One-point statistics of the magnetic fluctuations in kinematic régime with large Prandtl number and non delta-correlated in time advecting velocity field are studied. A perturbation expansion in the ratio of the velocity correlation time to the dynamo growth time is constructed in the spirit of the Kliatskin-Tatarskii functional method and carried out to first order. The convergence properties are improved compared to the commonly used van Kampen-Terwiel method. The zeroth-order growth rate of the magnetic energy is estimated to be reduced (in three dimensions) by approximately 40%. This reduction is quite close to existing numerical results.