Linear Mode Conversion in Ultramagnetized Pair Plasmas: Single-Parameter Scaling

Abstract

In neutron star (NS) magnetospheres, plasma waves propagate as normal modes with distinct propagation dynamics that strongly influence observable signals. This letter presents a unified theory of linear mode conversion between Alfv'en (A), superluminal ordinary (O), and extraordinary (X) modes, incorporating the effect of magnetic-field geometry and local plasma response. Magnetic field-line curvature induces A-X conversion for low frequencies and O-X conversion at high frequencies, whereas plasma gradients alone do not drive X-mode coupling. We show that a single dimensionless parameter controls both conversion channels. The conversion efficiency follows the universal nonadiabatic transition probability of a multilevel quantum system. Efficient conversion occurs within a narrow angular window between the wave vector and magnetic field, localizing potential conversion sites in the NS magnetosphere. This linear mechanism naturally accounts for complex polarization features observed in pulsars and some fast radio bursts.

Figures (5)

• Figure 1: Cold plasma dispersion curves of A- (red), O- (blue) and X-modes (black) for $\gamma_0=1$. Solid lines are dispersion curves with $k_{\perp}/\omega_\mathrm{p}=0.05$, dashed lines with $k_{\perp}/\omega_\mathrm{p}=0.1$. The red shaded region corresponds to A--X conversion, the blue shaded region to O--X coupling, the gray shaded region to A--O--X conversion.
• Figure 2: Illustration of the coordinate system adjusting to field line bending. Shaded surfaces highlight the $\boldsymbol{k}-\boldsymbol{B}$ plane before (grey) and after (blue) the rotation. As the wave propagates from $z_0$ to $z$, the magnetic field vector rotates by angles $\theta$ with the $\boldsymbol{z_0}$-axis, and $\varphi$ in the $\boldsymbol{x_0}-\boldsymbol{y_0}$ plane. The local coordinate system $(\boldsymbol{x},\boldsymbol{y},\boldsymbol{z})$ has $\boldsymbol{z}\|\boldsymbol{B}$, and $\boldsymbol{x}$ in the $\boldsymbol{x_0}-\boldsymbol{y_0}$ plane.
• Figure 3: Mode energy evolution during O--X conversion ($\varepsilon=20$, left panels) and A--X conversion ($\varepsilon=0.1$, right panels). Cases with $k_{\rm res}=1$, $\tilde{k}_x=0.05$, $\rho=10R$ ($R=10\rm{km}$), and $\varphi=\pi/2$ are shown in the top row. In the bottom row, one parameter varies as indicated while the others remain fixed. Normal modes can only be defined and distinguished outside the conversion region. Nevertheless, for illustration we track the mode electric fields and energy in this figure and Equation (\ref{['basis']}).
• Figure 4: A--X and O--X conversion efficiencies $\eta$ as a function of $\Delta$. We compare numerically obtained efficiencies (black line) with the formula proposed by nakamura2012nonadiabatic and davis1975nonadiabatic, and the fit formulae (dashed red line, Equation \ref{['fit']}). Our analysis scans a wide parameter range of azimuthal field line bending $\varphi\in[0,2\pi]$, field line curvature $\rho/R\in[1,100]$, frequency parameter $\varepsilon\in[0.01,100]$, and normalized wave vector in the $\boldsymbol{x_0}$-direction $\tilde{k}_x\in[0.005,0.5]$.
• Figure 5: Mode energy evolution during conversion at the mode-resonance point. Three mode conversion is shown on the left panel considering longitudinal plasma gradient and field line bending effect. A--O conversion is shown on the right panel when field line bending is neglected. Both cases are with parameters $\omega_{\mathrm{p}}=10^8\mathrm{Hz},\ \gamma_0=10,\ L_{\mathrm{p}}=R,\ \varphi=\pi/2$ except different choice of $\tilde{k}_x$ and $\rho$.