Measuring the growth of Alfven wave parametric decay instability using counter-propagating waves in a linear device: theory and simulations

The parametric decay instability (PDI) of Alfven waves---where a pump Alfven wave decays into a backward-propagating child Alfven wave and a forward ion acoustic wave---is a fundamental nonlinear wave-wave interaction and holds significant implications for space and laboratory plasmas. However, to date there has been no direct experimental measurement of PDI. Here, we propose a novel and experimentally viable scheme to quantify the growth of Alfven wave PDI on a linear device using a large pump Alfven wave and a small counter-propagating seed Alfven wave, with the seed wave frequency tuned to match the backward Alfven wave generated by standard PDI. Using hybrid simulations, we show that energy transfer from the pump to the seed reduces the latter's spatial damping. By comparing seed wave amplitudes with and without the pump wave, this damping reduction can be used as a direct and reliable proxy for PDI growth. The method is validated in our simulations across a range of plasma and wave parameters and agrees well with theoretical predictions. Notably, the scheme exhibits no threshold for PDI excitation and is, in principle, readily implementable under current laboratory conditions. This scheme is a critical step toward solving the challenge of experimentally accessing Alfven wave PDI and provides an elegant method that may be used to validate fundamental theories of parametric instabilities in controlled laboratory settings.