Theory of 2ωpe radiation induced by the bow shock

A new radiation emission mechanism is proposed to explain electromagnetic radiation observed at twice the electron plasma frequency, 2ωpe, in the upstream region of the Earth's bow shock. This radiation has its origin at the electron foreshock boundary where energetic electron beams and intense narrow‐band Langmuir waves are observed. The proposed emission mechanism results from the interaction of the electron beam and Langmuir waves that are backscattered off thermal ions. This interaction is described by a nonlinear dispersion equation which incorporates an effect owing to electron trajectory modulation by the backscattered Langmuir waves. Subsequent analysis of the dispersion equation reveals two important consequences. First, a long‐wavelength electrostatic quasi‐mode with frequency at 2ωpe is excited, and second, the quasi‐mode and the electromagnetic mode are nonlinearly coupled. The implication is that, when the excited 2ωpe quasi‐mode propagates in an inhomogeneous medium with slightly decreasing density, the quasi‐mode can be converted directly into an electromagnetic mode. Hence the electromagnetic radiation at twice the plasma frequency is generated. Numerical solutions of the dispersion equation with the choice of parameters that describe physical characteristics of the electron foreshock are presented, which illustrates the viability of the new mechanism.