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One of the main processes in space plasma is the interaction of charged particles with a turbulent electromagnetic field. This process is responsible for the acceleration of charged particles and the heating of plasma in planetary magnetospheres, the solar corona, and other astrophysical plasma systems. At the same time, according to numerous studies of electromagnetic turbulence in the Earth’s magnetotail, electromagnetic turbulence is non-Gaussian in nature: there are wider “tails” in the distribution of the electromagnetic field compared to the Gaussian distribution. This is due to the presence of rare but strong bursts in the behavior of the electromagnetic field. Such bursts are usually associated with localized structures such as magnetic clouds or plasmoids and can significantly affect the acceleration of particles in the solar wind. To describe the processes of acceleration and transport of charged particles in turbulent magnetospheric and solar plasmas, a model of a turbulent electromagnetic field with a controlled intermittency level is proposed. It is shown that the larger the parameter characterizing the level of intermittency, the higher the energy values charged particles can achieve. This work is supported by the grant MK-5053.2022.6 of the Ministry of Science and Higher Education of the Russian Federation.