Abstract In this paper we investigate charged particle transport and acceleration in a two-dimensional system with an uniform electric field and stationary magnetic field fluctuations. The main idea of this study is to consider dependencies of transport and acceleration rates on properties of distributions of magnetic field fluctuations. We develop a simplified model of magnetic fluctuations with a regulated distribution and apply the test particle approach. System parameters are chosen to simulate conditions typical for ion dynamics in the deep Earth magnetotail. We show that for a fixed power density of magnetic field fluctuations the particle acceleration is more effective in the system where particles interact with small-amplitude (but frequent) fluctuations. In systems with large-amplitude rare fluctuations the particle scattering is less effective and the particle acceleration is weaker.