New Thermodynamical Force in Plasma Phase Space that Controls Turbulence and Turbulent Transport

Abstract

Physics of turbulence and turbulent transport has been developed on the central dogma that spatial gradients constitute the controlling parameters, such as Reynolds number and Rayleigh number. Recent experiments with the nonequilibrium plasmas in magnetic confinement devices, however, have shown that the turbulence and transport change much faster than global parameters, after an abrupt change of heating power. Here we propose a theory of turbulence in inhomogeneous magnetized plasmas, showing that the heating power directly influences the turbulence. New mechanism, that an external source couples with plasma fluctuations in phase space so as to affect turbulence, is investigated. A new thermodynamical force in phase-space, i.e., the derivative of heating power by plasma pressure, plays the role of new control parameter, in addition to spatial gradients. Following the change of turbulence, turbulent transport is modified accordingly. The condition under which this new effect can be observed is also evaluated.

A Parameter that Denotes Non-Equilibrium Property for Turbulent Plasmas

“…The first term in RHS of Eq. (3a) indicates the driving by the spatial inhomogeneity of mean parameters, and the second term shows a new mechanism [9]. The second term in the RHS represents the change rate of distribution function by heating process, and it directly affects the fluctuations without the change in f 0 .…”

“…This crude estimate of the impact of operator by a scalar coefficient is introduced for an analytic insight of the problem. An analysis was developed by taking an example of trapped particle mode [9]. Combining Eqs.…”

“…While such a similarity between ξ and Γ heat exists, the main difference is that the parameter Γ heat denotes the direct impact of heating (sources) on turbulence, so that the turbulent transport can vary immediately after the source changes in time. The term (9) indicates that the direct influence of heating on turbulence is more effective for perturbations with longer correlation time. Based on this consideration, the response of long-range fluctuations (which are linearly stable and driven by nonlinear processes) was studied in [10].…”

“…a new thermodynamic force, defined in the parameters of velocity space, was introduced, and its relation to the inhomogeneities in real space was also discussed [9]. This new idea has given an explanation of transport hysteresis [4][5][6][7][8] as was discussed in [10,11].…”

“…It is usually assumed that the micro-and macrotimescales are discriminated. The cross-scale dynamics in multi-scale turbulence leads the mixing of timescales [9,10]. Here we discuss the timescale mixing, which is introduced by the new thermodynamic force in the plasma turbulence.…”