Nonlinear mixing as a plasma density probe

Nonlinear mixing of two electromagnetic waves, ω± and k±, in an inhomogeneous isotropic and collisionless plasma in the parameter range β2/3(KL)1/3 ≪ 1 is studied. Here β is the ratio of electron thermal velocity to speed of light, K = Ω/c, Ω = ω+ − ω−, and L is a local characteristic length for electron density variation. Langmuir waves, Ω and kL, are found to be excited in two different ways. When (Δk/ K)β2/3(KL)1/3 ≫ 1, where Δk = k+ − k−, resonant wave mixing occurs in which the generated Langmuir waves satisfy kL ≈ Δk. When (Δk/K)β2/3(KL)1/3 ≪ 1, nonlinear conversion takes place at the critical surface where Ω equals the local plasma frequency, the Langmuir waves propagating antiparallel to the density gradient and not along Δk. Coherent scattering of electromagnetic waves off the density perturbations associated with the excited Langmuir waves is studied.