  The small-scale kinematic dynamo in a two-dimensional chaotic flow is
studied. The analytic approach is developed in framework of the
Kraichnan-Kazantsev model. It is shown that the growth of magnetic field
$\bm{B}$ fluctuations stops at large times in accordance with so-called
anti-dynamo theorems. The value of $\bm{B}^2$ increased therewith in square of
the magnetic Prandtl number times. The spatial structure of the correlation
tensor of the magnetic field is found.
