Equivalence of weak turbulence and quasi-normal Markovian closure theories for plasmas

The present paper demonstrates that the weak turbulence closure theory of kinetic plasma turbulence is equivalent to the quasi-normal Markovian (QNM) closure theory developed in the fluid turbulence context. While the plasma weak turbulence theory, largely formulated in the former Soviet plasma physics community, adopted the description “weak” to mark the distinction from a phenomenological theory of Langmuir wave collapse, which is known as the “strong” turbulence theory, it was nevertheless recognized in the fluid turbulence literature that the plasma weak turbulence theory and the QNM closure theory are conceptually equivalent. In spite of this, however, the actual demonstration of the equivalence between the two approaches has not been carried out in the literature. The present paper achieves such a concrete demonstration on the basis of a framework in which the plasma is considered unmagnetized and primarily interacting through the electrostatic force. This is done for the sake of simplicity, but the general methodology is applicable to more general situations, such as electromagnetic plasma turbulence or turbulence in magnetized plasmas.