Theory of first-order plasma heating by collisional magnetic pumping

Plasma heating by collisional magnetic pumping is investigated theoretically. This treatment yields solutions to the energy transfer equations in the form of an energy increase rate, which gives quantitatively the amount of energy increase per rf driving cycle. The energy increase rates (or heating rates) proportional to the first and second powers of the field modulation factor δ (defined as the ratio of the change in the magnitude of the magnetic field to its background dc value) are derived for an arbitrary rf waveform of the pumping magnetic field. Special cases are examined, including the sinusoidal and sawtooth pumping waveforms. The energy increase rate in the case of a sawtooth waveform was found to be proportional to the first power of δ (first-order heating). This heating rate is many orders of magnitude larger than heating for the sinusoidal case: The latter is proportional to the square of δ and is strongly dependent on the collisionality of the plasma. The use of a sawtooth pumping waveform improves the efficiency of collisional magnetic pumping and heating rates comparable to those possible with ion or electron cyclotron resonance heating methods may be achieved