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Over the last few years, the interest of the international scientific community for high power accelerators in the megawatt range has been increasing. For such machines, the ion source has to deliver a beam intensity that ranges from several tens up to a hundred of mA. One of the major challenges is to extract and transport the beam while minimizing the emittance growth and optimizing its injection into the radio frequency quadrupole. Consequently, it is crucial to perform precise simulations and cautious design of the low energy beam transport (LEBT) line. In particular, the beam dynamics calculations have to take into account not only the space charge effects but also the space charge compensation of the beam induced by ionization of the residual gas. The physical phenomena occurring in a high intensity LEBT and their possible effects on the beam are presented, with a particular emphasis on space charge compensation. Then, beam transport issues in different kind of LEBTs are briefly reviewed. The SOLMAXP particle-in-cell code dedicated to the modeling of the transport of charge particles under a space charge compensation regime is described. Finally, beam dynamics simulations results obtained with SOLMAXP are presented in the case of international fusion materials irradiation facility injector.