Alfvén Instability in a Compressible Flow

A new ideal magnetohydrodynamic instability is presented. It is shown that linear incompressible Alfvénic disturbances can get over-reflected and exponentially amplified in compressible plasma flows. A simple and transparent stability criterion for a two-layer model is derived. The instability does not require a shear in the flow and may arise for rather moderate sub-Alfvénic flow speeds. It is therefore important to be aware of the Alfvén instability when dealing with laboratory or astrophysical plasma flows.

Figure 1

A semi-infinite two-layer model in which the flow speed $u_0$, the Alfvén speed $c_A$ and the density ${\rho }_0$ are step functions of $z$. The $-$ and $+$ superscripts denote the constant values of these equilibrium quantities in the intervals $0<z<L$ and $z>L$. Small-amplitude arbitrary Alfvénic disturbances are launched from the left boundary at $z=0$.

Figure 2

Evolution of the field perturbation $b(t,z)$ at $z=L$ for two different flow speed profiles which satisfy the instability criterion: the solid and dashed lines represent the cases $u_0^{-}=0.08c_A^{-}$ and $u_0^{-}=0.1c_A^{-}$, respectively. In both cases, the following parameter values have been chosen: $\alpha =5$, $c_A^{+}=0.01c_A^{-}$. Time is normalized with respect to $c_A^{-}/L$.

Figure 3

Time-distance plot for the field perturbation $b(t,z)$ between $0<z<L$. The flow speed $u_0^{-}=0.1c_A^{-}$. Other parameters are the same as in Fig. 2. Dark and bright regions represent positive and negative values of $b(t,z)$, respectively.