Quantum field renormalization group in~the theory of~stochastic Langmuir turbulence

L. Ts. Adzhemyan ; A. N. Vasil'ev ; M. Gnatich ; Yu. M. Pis'mak

Teoretičeskaâ i matematičeskaâ fizika, Tome 78 (1989) no. 3, pp. 368-383

Résumé

Quantum field theory renormalization group is used for analysing the Langmuir stochastic turbulence of plasma described by the Zakharov equations [1] with random noises. Existence of the dissipative scaling critical regime is proved, for which all the critical exponents are nontrivial and are calculated in the framework of the $4-\varepsilon$ expansion up to $\varepsilon^2$. An explicit expression is obtained for the scaling asymptotics of the longitudinal dielectric permeability $\varepsilon_\parallel(\omega,k)$ in the neighbourhood of a “critical point” $\varepsilon_\parallel(\omega_e,0)=0$ ($\omega_e$ is the Langmuir frequency). The expression implies, in particular, that the usual dispersion law of the Langmuir waves $\omega-\omega_l\sim k^2$ is substitutted for small $k$ by the law $\omega-\omega_l\sim k^{2-\gamma_a}$ in which the exponent $\gamma_a$ is known up to $\varepsilon^2$.