In article is discussed the electrodeless plasma acceleration in electric propulsion with high-frequency ionization of working body – helicon low power plasma thruster. Design, configuration of the external magnetic field and results of thruster laboratory model testing are presented. Questions of thruster discharge chamber geometry influence on its efficiency and preliminary investigations are described. Basic mechanisms of plasma acceleration in helicon engines are discussed. Assessment calculations of different acceleration mechanisms contributions, such as electromagnetic acceleration and acceleration under the influence of electron pressure, in the engine thrust were conducted. It is shown that for a given configuration of helicon plasma thruster laboratory model the main mechanism of plasma acceleration is electromagnetic.