Parametric Excitation of Alfvén and Ion Acoustic Waves

The threshold is derived for parametric excitation of Alfv\'en waves in a uniform plasma in which the background magnetic field is modulated sinusoidally in time. Including the plasma pressure we show that ion acoustic waves can also be excited directly. Both cases are absolutely unstable for any interaction length. Finally, we analyze the subsequent decay of the excited Alfv\'en wave into an ion acoustic and another Alfv\'en wave.