QUANTUM-MECHANICAL INTERPRETATION OF PLASMA TURBULENCE

The matrix elements describing nonlinear effects in a weakly unstable plasma are interpreted by means of Feynman diagrams involving the shielded Coulomb potential, given by V8(q, ω) = 4πe 2/q2ε(q, ω), where ε(q, ω) is the dielectric response function. The quasiparticles or plasmons are obtained from the poles of V8, but effects of the nonresonant parts of V 8 are also retained. All the matrix elements describing interactions of Langmuir oscillations in a strong magnetic field through second order in the quasiparticle numbers are found explicitly and shown to yield the correct classical results in the limit ℏ → 0. In particular, the equations of Walters and Harris for three-wave scattering in a cold plasma are extended to finite temperatures, and the shielding or dressing of the electrons is included in the equations for the nonlinear Landau damping. The self-energy of a plasmon is also represented by diagrams and the optical theorem is used to compare the self-energy with the scattering matrices. It is found that the quantum method provides a relatively simple way of deriving and interpreting equations for the time development of the wave spectrum and particle diffusion.