In order to study instabilities caused by inhomogeneities of the electric field and plasma density in the auroral zone, numerical algorithms are developed and numerical simulations are performed for different conditions in the background plasma. To this end, a nonlocal dispersion relation for a given type of wave is analyzed. It is shown that the dispersion relation has unstable solutions in a wide range of frequencies and wavenumbers. These solutions manifest themselves in satellite observations as a broadband spectrum of electrostatic perturbations. Two mechanisms of broadband noise generation related to the gradients of the density and electric field are compared.