Fundamental Emission of Type III Bursts Produced in Non-Maxwellian Coronal Plasmas with Kappa-Distributed Background Particles

Abstract

Detailed simulations based on quasi-linear theory are presented for fundamental ($f_{\rm p}$) emission of type III bursts produced in non-Maxwellian, suprathermal, background coronal plasma by injection of energetic electrons during flares with a power-law or Maxwellian velocity distribution, where $f_{\rm p}$ is the electron plasma frequency. The background plasma is assumed to have a kappa (κ) distribution, as inferred from solar wind data and proposed by theories for the corona and solar wind. The predicted type III beam speeds, Langmuir wave levels, and the drift rate and flux of $f_{\rm p}$ emission are strongly sensitive to the presence of suprathermal background electrons in the corona. The simulations show the following results. i) Fast beams with speeds $v_{\rm b}>0.5c$ are produced for coronal background electrons with small κ (κ≲5) by injected electrons with power-law spectra. ii) Moderately fast beams with $v_{\rm b} \approx0.3\,\mbox{--}\,0.5c$ are generated in coronal plasma with κ≲8 by injections of power-law or Maxwellian electrons. iii) Slow beams with $v_{\rm b}<0.3c$ are produced for coronal background electrons with large κ (κ>8), including the asymptotic limit κ→∞ where the electrons are Maxwellian, for both power-law and Maxwellian injections. The observation of fast type III beams (with $v_{\rm b}>0.5c$) thus suggests that these beams are produced in coronal regions where the background electron distribution has small κ by injected electrons with power-law spectra, at least when such beams are observed. The simulations, from the viewpoint of type III bursts, thus support: i) the presence, at least sometimes, of suprathermal background electrons in the corona and the associated mechanisms for coronal heating and solar wind acceleration; ii) power-law spectra for injected energetic electrons, consistent with observations of such electrons in situ and of X-ray emission.

Appendix: Spontaneous Emission of Langmuir and Ion Sound Waves

The spontaneous emission coefficient $\alpha_{\rm M}$ for wave mode M is related to the three-dimensional particle distribution function $f({\bf p})$ via (Melrose 1986)

$$ \alpha_{\rm M}({\bf k})=\int \mathrm{d}^3{\bf p} w_{\rm M}({ \bf k,p})f({\bf p}) , $$

(18)

where ${\bf p}=m{\bf v}$ is the particle momentum, and

$$ w_{\rm M}({\bf k,p})=\frac{2\pi e^2 R_{\rm M}({\bf k})}{\epsilon_0 \hbar|\omega_{\rm M}({\bf k})|} \bigl|{\bf e}_{\rm M}^{\ast}({ \bf k})\cdot{\bf v}\bigr|^2 \delta\bigl\{\omega_{\rm M}({\bf k})-{\bf k}\cdot{\bf v}\bigr\} . $$

(19)

Here ${\bf e}_{\rm M} ({\bf k})$ is the unit electric vector of the wave mode M, and $R_{\rm M}({\bf k})$ represents the ratio of electric to total energy in the M mode, with (Melrose 1986)

$$\begin{aligned} R_{\rm L}({\bf k}) =&\frac{1}{2} \biggl[\frac{\omega_{\rm L}({\bf k})}{\omega_{\rm p}} \biggr]^2 , \end{aligned}$$

(20)

$$\begin{aligned} R_{\rm S}({\bf k}) =&\frac{1}{2} \biggl[\frac{\omega_{\rm S}({\bf k})}{\omega_{\rm pi}} \biggr]^2 , \end{aligned}$$

(21)

for Langmuir and ion sound waves, respectively, where $\omega_{\rm pi}=(n_{\rm e} e^{2}/m_{\rm i}\varepsilon_{0})^{1/2}$ is the ion plasma frequency. Applying the isotropic three-dimensional κ distributions corresponding to Equation (1) to Equations (18) – (21) and using the dispersion relations [Equations (4) and (5)], we obtain the spontaneous emission rates given by Equations (6) and (7).