This dissertation was motivated by the Variable Specific Impulse Magnetoplasma Rocket (VASIMR) project. The VASIMR device has a magnetic mirror configuration and consists of three main components: a low energy helicon plasma source, which creates cold plasma via rf-discharge; an ion cyclotron-resonance heating (ICRH) section, which is used to deposit rf-power into the plasma; and a magnetic nozzle, which forms highly directed superalfvenic outgoing plasma flow. The dissertation is focused on fundamental physics issues of the helicon source operation and ICRH. A first-principle theory for helicon sources with a self-consistent treatment of the particle balance, power balance, and rf-field structure has been developed. The problem of particle balance reduces to kinetic ion transport under the effect of the ambipolar electric field and ion-neutral collisions. Power balance involves electron heating by rf-field, heat conduction, and radiation. The rf-power deposition is associated with the excitation of radially localized helicon modes by an external antenna. The radial density gradient in a plasma forms a potential well for the modes, with the resulting mode frequency being significantly lower than that for a uniform plasma. This explains the high efficiency of the source at low frequencies. The three key physics ingredients have been combined into a 1D numerical model for a source with predominantly radial flow. The code calculates the evolution of the plasma density, electron temperature, and the rf-fields. These calculations specify the parameter range for a stable steady-state operation of the helicon discharge. The ICRH concept in VASIMR has two distinct features: 1) each ion passes the resonance only once and 2) the ion motion is collisionless. The ion response to the rf-field during single-pass ICRH can be essentially nonlinear. A self-consistent nonlinear model for the deposition of rf-power in the ion cyclotron frequency range into a steady-state plasma flow has been developed. The one-dimensional fluid-type simulations confirm the theoretical picture of the near-resonance behavior and wave energy conversion into the energy of the directed ion flow. The regimes relevant to the VASIMR experiment are discussed and issues such as the transition of plasma profiles and the increase in gas pressure due to plasma production observed in the experiment are addressed.