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In this paper, the electron-cyclotron resonance (ECR) mechanism of electrons heating by electromagnetic wave in ECR microwave low-pressure plasma reactors is considered. In such reactors, ionization is mainly provided by fast electrons trapped by multipolar magnetic system. A particle simulation is carried out for statistical ensemble of electrons in magnetic systems of different configurations with taking into account previous experimental results. The escape of fast electrons from the magnetic traps to the walls is identified as the major factor behind the loss of electrons in the limit of a collisionless plasma. A comparative evaluation of different multipolar magnetic systems is made. Basic requirements are set out concerning the optimal design of multipolar ECR plasma reactors. Several approaches for providing the efficient ECR heating of electrons are proposed.