Rotation catalyzed chiral magnetovortical instability

TL;DR

The paper analyzes how global rotation in a co-rotating frame profoundly enhances the chiral magnetovortical instability (CMVI) in chiral MHD. By deriving the MC-wave spectrum and a CVE/CME–augmented dispersion relation, it shows that rotation splits the Alfvén mode into magneto-Coriolis waves with frequencies $\omega_f$ and $\omega_s$, and that CMVI is catalyzed when the chiral Alfvén frequency $\omega_{CA}=\xi'_\omega\omega_A$ exceeds these MC-wave frequencies. The key finding is that rotation enables CMVI for any finite $\xi'_\omega$, creating unstable windows whose extent scales with the rotation rate $\Omega$ and that CVE-driven growth can rapidly amplify magnetic/kinetic energies and helicities, potentially driving a dynamo in rotating chiral plasmas. The results have potential implications for rotating astrophysical plasmas and the rotating quark-gluon plasma in heavy-ion collisions, and motivate future studies of nonlinear saturation and dynamo efficiency under rotation.

Abstract

We demonstrate that a background rotation significantly catalyzes the chiral magnetovortical instability in chiral magnetohydrodynamics. The rotation splits the linearly polarized Alfven wave into two circularly polarized magneto-Coriolis waves, one of which exhibits a lower frequency than the original Alfven wave. We find that this low-frequency magneto-Coriolis wave is always unstable in the presence of even a weak chiral vortical effect. This instability may enable new dynamo mechanism applicable to various rotating chiral plasmas.

Figures (5)

• Figure 1: Left:$\mathrm{Im}^{*}(\omega^{+}_{-})\equiv \mathrm{Im}(\omega^{+}_{-})/(\gamma_\eta/2)$ as a function of $k$ (in unit of $1/\eta$). Different colors correspond to different CVE coefficients. When $\xi'_\omega>1$, $\mathrm{Im}^{*}(\omega^{+}_{-})$ has a zero point (indicated by the magenta points) located at $2\Omega\xi_{\omega}^{\prime}/B_{0}^{\prime} (\xi_{\omega}^{\prime 2}-1)$, which separates the stable and unstable $k$ regimes. Right:$\mathrm{Im}^{*}(\omega^{-}_{-})\equiv \mathrm{Im}(\omega^{-}_{-})/(\gamma_\eta/2)$ as a function of $k$. Different colors correspond to different CVE coefficients. When $\xi'_\omega\geq1$, $\mathrm{Im}^{*}(\omega^{-}_{-})$ is always positive. When $\xi'_\omega<1$, $\mathrm{Im}^{*}(\omega^{-}_{-})$ has a zero point (indicated by the magenta points) located at $2\Omega\xi_{\omega}^{\prime}/B_{0}^{\prime} (1-\xi_{\omega}^{\prime 2})$, which separates the stable and unstable $k$ regimes. The parameters are $\eta\Omega=1, B_{0}^{\prime}=4$, and $\theta=\pi/3$.
• Figure 2: The numerical results of the normalized CVE coefficient, magnetic energy, kinetic energy, cross helicity, magnetic helicity, and kinetic helicity as a function of time $t$. Different colors correspond to different rotations. The initial value for CVE coefficient is $\xi'_\omega(0)=2$.
• Figure 3: Square of the right-handed velocity component, $|v_+(t,{\boldsymbol k})|^2$, in units of $\eta^6$ for different initial values of $\xi'_\omega=0.2, 0.4, 0.8,$ and $1.2$ (from top left to bottom right). The other parameters are $\Gamma=0$, $\Omega=5/\eta$, and $B'_0=5$. Different colors correspond to different times.
• Figure 4: The numerical results of the normalized CVE coefficient, magnetic energy, kinetic energy, cross helicity, magnetic helicity, and kinetic helicity as a function of time $t$. Different colors correspond to different rotations. The initial value for CVE coefficient is $\xi'_\omega(0)=0.8$ and the chirality flipping rate is $\Gamma=0.01/\eta$.
• Figure 5: Left: Curves $\mathrm{C}_{1,2}$ in the $(\omega^{*}_{a}, \omega^{*}_{b})$ plane for Case 1, where $\omega^{*}_{a,b}\equiv \eta\,\omega_{a,b}$. The curves $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ have two intersection points that shift with $\xi_{\omega}^{\prime}$. When $\xi_{\omega}^{\prime}\le 1$, both the two intersection points have negative $\omega_{b}^{*}$, corresponding to stable damped modes. Only when the zero point condition $\omega_{C_{2}}< \omega_{C_{1}-}$ is satisfied and $\xi_{\omega}^{\prime}>1$, one of intersection points becomes positive for $\omega_{b}^{*}$, indicating instability. Right: Curves $\mathrm{C}{1,2}$ in the $(\omega^{*}_{a},\omega^{*}_{b})$ plane for Case 3. One of the intersection points become positive for $\omega_{b}^{*}$ when the zero point condition $\omega_{C_{2}}< \omega_{C_{1}-}$ is satisfied, which allows for $\xi_{\omega}^{\prime}\le1$. The parameters are $\eta k= 0.5, \eta \Omega=1, B_{0}^{\prime} =4,\theta=\pi/3$.