Verification of Theory on Weak Turbulence Relating to the Sequence of Diffuse Plasma Resonances in Space

Abstract

An interpretation of the sequence of diffuse plasma resonances observed by space probes (Alouette 2 and ISIS‐1 satellites) is developed in terms of wave‐particle nonlinear interaction in a weakly turbulent plasma including the electrostatic electron cyclotron harmonic wave instability. Observations and theory indicate that the center frequency $f_{\mathrm{Dn}}$ of the diffuse plasma resonance ${\mathrm{[nf}}_H{\mathrm{<f}}_{\mathrm{Dn}}{\text{<(n+1)f}}_H\hspace{0.17em}\mathrm{and}{\mathrm{\hspace{0.17em}f}}_{\mathrm{Dn}}{\mathrm{<f}}_T]$ and the center frequency of the electrostatic wave resonance ${\mathrm{[nf}}_H{\mathrm{<f}}_{\mathrm{Qn}}{\text{<(n+1)f}}_H\hspace{0.17em}\mathrm{and}{\mathrm{\hspace{0.17em}f}}_T{\mathrm{<f}}_{\mathrm{Qn}}]$ satisfy the condition of the wave‐particle nonlinear interaction with the ${\text{2f}}_H$ resonance according to the condition ${\text{2π[f}}_H{\mathrm{-\hspace{0.17em}(\hspace{0.17em}f}}_{\text{Qn+2}}{\mathrm{-f}}_{\mathrm{Dn}}{\mathrm{)]=[K(f}}_{\text{Qn+2}}{\mathrm{)-\hspace{0.17em}k\hspace{0.17em}(f}}_{\mathrm{Dn}}\mathrm{)]·v}$ , where ${\mathrm{nf}}_H{\mathrm{,\hspace{0.17em}f}}_T$ and v are the cyclotron harmonic frequency, the upper hybrid frequency, and the thermal velocity of the plasma, respectively; and $\mathrm{k}\mathrm{(f)}$ is a wave vector as a function of a frequency $f$ . The weaker diffuse plasma resonance branch observed at $f_{\text{Dn1}}$ (where $f_{\text{Dn1}}{\mathrm{>f}}_{\mathrm{Dn}}$ ) satisfies the condition ${\text{2π[f}}_H{\mathrm{-\hspace{0.17em}(f}}_{\text{Qn+1}}{\mathrm{-f}}_{\text{Dn1}}{\mathrm{)]\hspace{0.17em}=\hspace{0.17em}[k(f}}_{\text{Qn+1}}{\mathrm{)-k(f}}_{\mathrm{Dn}}\mathrm{)]·V}$ . The longest time duration of the $f_{\mathrm{Dn}}$ resonance coincides with the most favorable condition for the electrostatic electron cyclotron harmonic wave instability which is obtained by solving the dispersion equation obtained for a linear approximation of the kinetic wave equation for the warm magnetoactive plasma. The electrostatic field due to the transmission of the intense rf pulse produces plasma turbulence involving nonlinear wave‐wave interaction and temperature anisotropy which leads to the instability; this instability supplies energy to the turbulence. The $f_H$ and ${\text{2f}}_H$ nonlinear wave‐particle interactions in the turbulence heat the plasma to maintain the temperature anisotropy which lengthens the time over which the cyclotron harmonic wave instability conditions prevail; this process can be thought of as a feedback system. The results also indicate that the $f_H{\text{,\hspace{0.17em}2f}}_H$ and $f_{\mathrm{Qn}}$ waves are dependent on the $f_{\mathrm{Dn}}$ resonance generation.