On the so-called first-order magnetic pumping by sawtooth-waveform magnetic variations

Summary form only given, as follows. The heating of plasmas by sawtooth-waveform magnetic-induction variations has been examined. Analytic solutions to the magnetic-pumping problem, numerical solutions to a pair of coupled partial differential equations that describe magnetic pumping, and computer simulations of magnetically pumped plasmas were used. The sawtooth variations are divided into adiabatic-drop sawtooths in which the first adiabatic invariants of the plasma particles are conserved during the drops and ultrafast-drop sawtooths in which the first adiabatic invariants are not conserved during the drops. For the adiabatic drop sawtooths, the magnetic pumping is found to be only half as efficient at heating plasmas as Alfven´s (1950) original square-wave magnetic pumping. For small-amplitude magnetic variations, this pumping is a second-order process. For the ultrafast-drop sawtooths, the plasma heating rate is found to depend on the location within the plasma device, even for devices with uniform magnetic fields and uniform magnetic-field variations. This means that a proper calculation of plasma heating by ultrafast-drop sawtooths is a difficult task. Either form of sawtooth magnetic pumping is thus impractical for heating magnetically confined fusion plasmas.<>