  We consider the numerical modeling of the Farley-Buneman instability
development in the earth's ionosphere plasma. The ion behavior is governed by
the kinetic Landau equation in the four-dimensional phase space, and since the
finite difference discretization on a tensor product grid is used, this
equation becomes the most computationally challenging part of the scheme. To
relax the complexity and memory consumption, an adaptive model reduction using
the low-rank separation of variables, namely the Tensor Train format, is
employed.
  The approach was verified via the prototype MATLAB implementation. Numerical
experiments demonstrate the possibility of efficient separation of space and
velocity variables, resulting in the solution storage reduction by a factor of
order tens.
