Kappa-Distributed Electrons in Solar Outflows: Beam-Plasma Instabilities and Radio Emissions

Abstract

Electrostatic (ES) wave instabilities are assumed to be at the origin of radio emissions from interplanetary shocks, and solar coronal sources are most likely induced by electron beams, more energetic but less dense than electron strahls in the solar wind. In this paper, we present the results of a new dispersion and stability analysis for electron populations with Kappa velocity distributions, as often indicated by in situ observations. We investigate, both theoretically and numerically, three electron plasma beam configurations with different implications in the generation of radio emissions. The same three cases, but for Maxwellian distributed electrons, were considered in numerical simulations by Thurgood and Tsiklauri (Astronomy and Astrophysics 584:A83, 2015). Our kinetic plasma approach clarifies the nature of the unstable mode as being an electron beam ES instability (and not a Langmuir instability) in all cases, and for both Kappa and Maxwellian approaches. Electron beam waves are Landau resonant and with frequencies of the fastest growing modes close to but below the plasma frequency (i.e., $\omega \lesssim \omega _{pe}$). Suprathermal Kappa tails tend to inhibit the instability by reducing the growth rates, but these effects become minor if the drift speed of the beam is sufficiently high compared to the thermal speed of the electrons. The frequency downshift, also revealed by the observations, clearly tends to increase in the presence of a Kappa-distributed beam. Particle-in-cell (PIC) simulations confirm the inhibiting effects of (initially) Kappa-distributed electrons, but these minor effects in the linear and quasi-linear phases unexpectedly lead to significant decreases in the wave energy levels of the (primary) ES fluctuations near the plasma frequency and higher harmonics. As a result, EM radio (secondary) emissions generated nonlinearly after saturation are even more drastically reduced and can even be completely suppressed. However, the EM emissions around the second harmonic ($\omega \lesssim 2 \, \omega _{pe}$) are markedly powered by two symmetric countermoving beams, even in the presence of Kappa electrons. These results offer real promise for a realistic interpretation and modeling of radio emissions observed in heliosphere, arguing in favor of a rigorous spectral analysis of the wave instabilities at their origin.

Appendix: 2D Spectra of EM Fields

In Figure 11, we display the 2D spatial FFTs of the out-of-plane EM fields (color coded on the right side) as functions of both wave-numbers $k_{x}$ and $k_{y}$ in the simulation plane. By dashed contours we plot the fundamental (F) and second harmonic (H) emissions expected at $\omega _{pe}$ and $2\, \omega _{pe}$. Only the emissions obtained in case 1 approach these dashed lines, e.g., for $k_{y} > 0$, whereas in case 3 the spectra show a significant down-shift in wave numbers and frequencies. These spectra can help to quantify the properties of radio emissions and to understand the nonlinear wave–wave interactions from which they originate.

We chose later snapshots, at $\omega _{pe}t \simeq 450$ after the saturation of the ES instabilities, to differentiate between various fluctuating EM fields resulting from the nonlinear decay of the enhanced ES fluctuations. We can thus distinguish between radio emissions with a more or less isotropic distribution ($k_{x,y} \ne 0$), e.g., in cases 1 and 3, and the highly anisotropic EM waves with perpendicular propagation ($k \simeq k_{y}$), e.g., in cases 2 and 3. These late spectra appear dominated by the perpendicular emissions with very high intensities, especially for the case where the electrons are (initially) Kappa distributed. Thurgood and Tsiklauri (2015) discussed Weibel-like fluctuations with a major contribution to the energy density of nonlinear EM emissions. In our case, in the presence of the background magnetic field, we can associate these emissions with the ordinary mode (O-mode), which can be excited and powered by the filamentation (Weibel-like) instability of the electron beams.