Ergodic mixing for turbulent drift motion in an inhomogeneous magnetic field

The turbulent E×B drift of a test particle in an inhomogeneous magnetic field is not reducible to a simple diffusion, but rather leads to a biased diffusion producing an inhomogeneous density distribution (pinch effect). The statistical properties of the long‐time chaotic two‐dimensional drift motion of a charged particle in the magnetic field B(x,y) and the time‐dependent electrostatic potential φ(x,y,t) are studied by numerical symplectic integration. For a conditionally periodic potential with two or more incommensurate frequencies, an ergodic behavior is demonstrated in which the probability density of the particle position is proportional to the magnetic field B. The accuracy of this prediction is found to be independent of the number N ω of the incommensurate frequencies for N ω≥2. The relation of this result with the Kolmogorov‐Arnold‐Moser theory is discussed.