Hydrodynamic modes in a magnetized chiral plasma with vorticity

By making use of a covariant formulation of the chiral kinetic theory in the relaxation-time approximation, we derive the first-order dissipative hydrodynamics equations for a charged chiral plasma with background electromagnetic fields. We identify the global equilibrium state for a rotating chiral plasma confined to a cylindrical region with realistic boundary conditions. Then, by using linearized hydrodynamic equations, supplemented by the Maxwell equations, we study hydrodynamic modes of magnetized rotating chiral plasma in the regimes of high temperature and high density. We find that, in both regimes, dynamical electromagnetism has profound effects on the spectrum of propagating modes. In particular, there are only the sound and Alfvén waves in the regime of high temperature, and the plasmons and helicons at high density. We also show that the chiral magnetic wave is universally overdamped because of high electrical conductivity in plasma that causes an efficient screening of charge fluctuations. The physics implications of the main results are briefly discussed.

Figure 1

A charged element in a rotating plasma and the local electromagnetic fields. Note that the electric and Lorentz forces on a local element of plasma are equal in magnitude and opposite in direction.

Figure 2

The comparison of the approximate analytical results (solid lines) for the real (red lines and points) and imaginary (blue lines and points) parts of the energy for the Alfvén waves with the corresponding numerical results (points) at $\mathrm{\Omega }=0$ for three fixed values of the magnetic field: $\hslash eB/T^2=0.5\times {10}^{-3}$ (left panel), $\hslash eB/T^2={10}^{-3}$ (middle panel), and $\hslash eB/T^2=1.5\times {10}^{-3}$ (right panel). The real and imaginary parts of the energy are shown in red and blue, respectively. The other model parameters are $\tau T/\hslash ={10}^2$, $\mu /T={10}^{-4}$, and $\hslash k_{\perp }/T={10}^{-4}$.

Figure 3

The real parts of the energies of the Alfvén waves with different values of the angular momentum: $m=0$ (left panel), $m=\pm 3$ (middle panel), and $m=\pm 6$ (right panel). The other model parameters are $\tau T/\hslash ={10}^2$, $\mu /T={10}^{-4}$, $\hslash \mathrm{\Omega }/T={10}^{-6}$, $\hslash eB/T^2={10}^{-3}$, $RT/\hslash ={10}^4{\alpha }_{0,1}\approx 2.4\times {10}^4$, and $k_{\perp }={\alpha }_{m,1}/R$.

Figure 4

The positive branches of the real part of helicon energies for several values of the angular momentum, i.e., $m=-4$ (red line), $m=-2$ (orange line), $m=0$ (olive line), $m=2$ (green line), and $m=4$ (blue line). The other model parameters are $\hslash eB/{\mu }^2\approx 2\times {10}^{-3}$, $\tau \mu /\hslash =100$, $\hslash \mathrm{\Omega }/\mu ={10}^{-7}$, and $k_{\perp }={\alpha }_{m,1}/R$.

Figure 5

The ranges of angular momenta $m$ for which helicon modes can have negative group velocity. The colored bands correspond to three smallest values of the transverse momenta $k_{\perp }^{(i)}$ with $i=1$, 2, 3 (from red to blue, respectively).