Simulating Axion Electrodynamics in Magnetized Plasmas: Energy transfer in the inhomogeneous and strongly varying limit

Abstract

In this work we study the electromagnetic response induced by axions in a magnetized plasma, focusing specifically on characterizing energy transfer and energy losses from the ambient axion field in highly inhomogeneous and strongly varying backgrounds. Using a suite of both frequency-domain and time-domain simulations, we solve for: the efficiency of photon excitation in a rapidly varying background, the indirect excitation of Alfvén modes, occurring when a Langmuir-Ordinary (LO) mode is resonantly excited near a combined cutoff-resonance of the dispersion relations of the LO and Alfvén modes, and the excitation of electric fields in small localized plasma under-densities. We identify a particularly interesting regime in which energy can be transferred into sub-luminal plasma modes ($ω< k$) with an efficiency greater than that of super-luminal modes ($ω> k$). Our results highlight a variety of less conventional ways in which axions (and other light degrees of freedom that mix with electromagnetism, such as dark photons or gravitons) can interact in extreme astrophysical environments.

Figures (22)

• Figure 1: Illustration of how axions can lead to the indirect excitation of Alfvén modes. Incoming axion wave (dark blue) travels from a low density background into a high density background (plasma density profile shown with light blue shaded region). At $k_\mu^{\rm axion} = k_\mu^{\rm LO}$ the axion resonantly excites an LO mode (red cross); the LO modes travels a small distance before being reflected at the cut-off (yellow). Note that Alfvén mode only exists for plasma densities above the resonance point. For sufficiently large gradients, the excited LO mode can tunnel through the barrier and excite the Alfvén mode (green). For non-relativistic/semi-relativistic axions and large gradients, the WKB approximation is strongly violated across all processes. Numerical simulations are developed in this work in order to understand the efficiency of this process.
• Figure 2: Schematic representation of the rotation of the unmixed basis, inside (in blue) and outside (in green) the plasma barrier, compared to the original (mixed) one (shown in black). The mixing angles on the background, $\theta_{\rm{bkg}}$, and at the top of the barrier, $\theta_{\rm{max}}$, have positive and negative sign, respectively, due to the fact that the plasma frequencies satisfy $\omega_{p, \rm{bkg}} < m_a < \omega_{p, \rm{max}}$.
• Figure 3: Comparison of the LO (bottom right quadrant) and Alfvén (top left quadrant) modes, plotted as the ratio of $k/\omega$ vs the ratio of $\omega / \omega_p$, for various values of $\theta_B$ (relevant values, in radians, are written next to each curve). For reference, we also provide an illustrative example for the axion in red, highlighting the level crossings with the LO mode using small red points. Despite one mode being super-luminal (LO) and the other sub-luminal (Alfvén), one can see the cut-off (occurring for the LO mode at $\omega/\omega_p = 1$) in the dispersion relation become increasingly degenerate with the resonance of the Alfvén mode (occurring at $\omega = \omega_p |\cos\theta_B|$) in the limit that $\theta_B \rightarrow 0$. Should the background vary sufficiently quickly near the cut-off and resonance, one will expect a non-zero tunneling probability of any incident wave (see sections below).
• Figure 4: Snapshots of the evolution for the simulation with $n_{\rm{max}} = 15 \, \mathop{\mathrm{cm}}\nolimits^{-3}$, and $W = 1.3 \, \mathop{\mathrm{km}}\nolimits^{-1}$ in the region close to the boundary of the barrier. The upper panel shows the profile of the axion, while the lower panel the profile of the component of the electric field that is parallel to the background magnetic field, $E^y$. Different colors refer to different snapshots. The horizontal dashed line indicates the value $m_a$, while the gray dotted line denotes the profile of the plasma frequency, extracted at the beginning of the simulation. The simulation starts with a wave packet of the axion in the unmixed basis outside the barrier. When it enters the plasma it undergoes a conversion process. A photon wave packet is produced, which propagates towards the right together with the axion. Since they posses different group velocities, they gradually separate, with the photon traveling slower. An additional wave packet of the electromagnetic field propagating toward the left is also produced in the conversion, but its amplitude is substantially smaller, and it is barely visible in the bottom panel.
• Figure 5: Normalized conversion probability for an axion traversing a magnetized medium as a function of the inverse spatial gradient scale of the background plasma $W$, normalized in units of the axion de Broglie wavelength, for the time-domain (left) and frequency-domain (right) simulations. In the time-domain simulations, we adopt an axion mass $m_a = 10^{-10} \, \mathop{\mathrm{eV}}\nolimits$, a group velocity $v_g \approx 0.9$, a coupling constant is $g_{a\gamma \gamma} = 4 \times 10^{-12} \, \mathop{\mathrm{eV}}\nolimits^{-1}$ and a background magnetic field $B_0 = 10^{-5} \, T$, and we run the simulations for three values of the maximum height of the plasma boundary $\omega_{p, {\rm max}}$. In the frequency domain simulation, we instead show results for an axion mass $m_a = 10^{-5} \, \mathop{\mathrm{eV}}\nolimits$, an axion velocity of $v = 0.7$ and a background magnetic field strength $B_0 = 10 \, T$. In both cases, we compare the simulation results (dots) with the analytic expression for the resonant conversion probability given in Eq. \ref{['eq:pa_resonant']}, and with the non-resonant conversion probability (neglecting the sharp boundaries). Both figures show excellent agreement with the limiting cases, with deviations from these asymptotic results occurring near $W \lambda_a \sim \mathcal{O}(1)$ values. This result provides confidence that both time-domain and frequency-domain simulations are capable of accurately resolving resonant and non-resonant dynamics in a regime where the WKB approximation is strongly violated.