Parametric decay of oblique Alfvén waves in two-dimensional hybrid simulations

Certain types of plasma waves are known to become parametrically unstable under specific plasma conditions, in which the pump wave will decay into several daughter waves with different wavenumbers and frequencies. In the past, the related plasma instabilities have been treated analytically for various parameter regimes and by use of various numerical methods, yet the oblique propagation with respect to the background magnetic field has rarely been dealt with in two dimensions, mainly because of the high computational demand. Here we present a hybrid-simulation study of the parametric decay of a moderately oblique Alfvén wave having elliptical polarization. It is found that such a compressive wave can decay into waves with higher and lower wavenumbers than the pump.

Figure 1

Two-dimensional power spectral density of the magnetic field fluctuations at $t=500$. The straight line starting at the origin (red) indicates the initial propagation direction with $\vartheta ={10}^{\circ }$. The color coding represents the power spectral density in arbitrary units.

Figure 2

Two-dimensional power spectral density of the density fluctuations at $t=500$. The straight line starting at the origin (red) indicates the initial propagation direction with $\vartheta ={10}^{\circ }$. The color coding represents the power spectral density in arbitrary units.

Figure 3

One-dimensional power spectral density for the magnetic field fluctuations at $t=500$ along the initial direction of propagation. Additionally, the initial spectrum is shown (green dashed line).

Figure 4

One-dimensional power spectral density for the density fluctuations at $t=500$ along the initial direction of propagation. Additionally, the initial spectrum is shown (green dashed line).

Figure 5

One-dimensional dispersion analysis of the magnetic field fluctuations along the direction $\vartheta ={10}^{\circ }$ at $t=500$. The color coding represents the power spectral density. The enhancement in power corresponds to A/IC waves propagating obliquely to the background magnetic field. The curved solid line starting at the origin (red) shows the cold-plasma dispersion relation for oblique A/IC waves with $\vartheta ={10}^{\circ }$.