  We consider the damped/driven cubic NLS equation on the torus of a large
period $L$ with a small nonlinearity of size $\lambda$, a properly scaled
random forcing and dissipation. We examine its solutions under the subsequent
limit when first $\lambda\to 0$ and then $L\to \infty$. The first limit, called
the limit of discrete turbulence, is known to exist, and in this work we study
the second limit $L\to\infty$ for solutions to the equations of discrete
turbulence. Namely, we decompose the solutions to formal series in amplitude
and study the second order truncation of this series. We prove that the energy
spectrum of the truncated solutions becomes close to solutions of a
damped/driven nonlinear wave kinetic equation. Kinetic nonlinearity of the
latter is similar to that which usually appears in works on wave turbulence,
but is different from it (in particular, it is non-autonomous). Apart from
tools from analysis and stochastic analysis, our work uses two powerful results
from the number theory.
