  In this paper spatial correlations of parallel edge dislocations are studied.
After closing a hierarchy of equations for the many-particle density functions
by the Kirkwood superposition approximation, we derive evolution equations for
the correlation functions. It is found that these resulting equations and those
governing the evolution of density fields of total as well as geometrically
necessary dislocations around a single edge dislocation are formally the same.
The second case corresponds to the already described phenomenon of Debye
screening of an individual dislocation. This equivalence of the correlation
functions and screened densities is demonstrated also by discrete dislocation
dynamics simulation results, which confirm the physical correctness of the
applied Kirkwood superposition approximation. Relation of this finding and the
linear response theory in thermal systems is also discussed.
