Radar detection of interplanetary shocks: Scattering by anisotropic Langmuir turbulence

Earth-directed interplanetary shocks associated with coronal mass ejections (CMEs) are known to have a severe impact on the magnetosphere, causing strong geomagnetic storms and substorms. Hence, early detection of such shocks is important. Here we study the feasibility of radar detection of interplanetary shocks. We consider a scattering mechanism, which is based on the induced scattering t+l⇄tt+l⇄t of a radar wave by anisotropic Langmuir turbulence, being generated by the shock-accelerated electrons. The problem is studied for an arbitrary angle between the electron beam and the incident radar wave, vb∧ktvb∧kt, and special emphasis is put on the study of a dependence of the scattering process on this angle. We obtain and analyze analytical expressions for the frequency shift, scattering cross-section of the turbulence, coefficient of absorption (due to scattering), and the optical depth. We show that the detection of such shocks is possible if the turbulence energy density exceeds W=10-5nT (nT   is the thermal energy density of a plasma), which is quite realistic according to our estimations. The altitudes in the solar corona where reflections may occur depend on the angle vb∧ktvb∧kt. If expressed in local plasma frequencies, ωpωp, the altitudes span is ωt/8≲ωp⩽ωtωt/8≲ωp⩽ωt for vb∧kt=πandωt/120≲ωp⩽ωt for vb∧kt=π/2vb∧kt=π/2, where ωtωt is a frequency of the transmitted radar wave. Thus the scattering occurs much closer to the radar in the second case than in the first. Detection of the scattered signal, in the general case, requires a remote receiver, since the radar wave backscatters only for vb∧kt=πvb∧kt=π.