Abstract
The parametric decay instability of Alfvén waves has been widely studied, but few investigations have examined wave packets of finite size and the effect of different boundary conditions on the growth rate. In this paper, we perform a linear analysis of circular and arc-polarized wave trains and wave packets in periodic and open boundary systems in a low-β plasma. We find that both types of wave are 3–5 times more stable in open boundary conditions compared to periodic. Additionally, once the wave packet width ℓ becomes smaller than the system size L, the growth rate decreases nearly with a power law γ ∝ ℓ/L. This study demonstrates that the stability of a pump wave cannot be separated from the laboratory settings, and that the growth rate of daughter waves depends on the conditions downstream and upstream of the pump wave and on the fraction of volume it fills. Our results can explain simulations and experiments of localized Alfvén waves. They also suggest that Alfvénic fluctuations in the solar wind, including sharp impulses known as switchbacks, can be more stable than traditional theory suggests depending on wind conditions.
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