A Reduced Transport Model for Ion Heat Diffusivity by Gyro-Kinetic Analysis with Kinetic Electrons in Helical Plasmas

Abstract

A high ion temperature plasma in the Large Helical Device is examined in the case in which the ion temperature gradient mode is unstable. The nonlinear gyro-kinetic simulation is performed to evaluate the turbulent ion heat diffusivity with the kinetic electron response. It is clarified that the decay time of zonal flows [S. FerrandoMargalet et al., Phys. Plasmas 14, 122505 (2007)] decreases radially outward due to the trapped electron and the ion energy transport increases outward. To reduce the computational cost for applying to the dynamical transport simulation, an extended transport model for the ion heat diffusivity in terms of the mixing length estimate and the characteristic quantity for the linear response of zonal flows is proposed. Turbulent transport is one of the most critical issues for plasma confinement in magnetic fusion devices. Theoretical expressions for the turbulent transport due to the various instabilities were reviewed [1]. Recently, a large number of the gyro-kinetic simulations which are applied to the turbulent transport have been performed in toroidal plasmas, e.g. [2][3][4][5][6][7][8]. The gyro-kinetic analysis results in tokamak [9][10][11] and helical [12][13][14] plasmas have been studied with the experimental observations. Gyro-kinetic simulations of helical plasmas require a large number of mesh points along the field line in order to capture the helical ripple structure. Therefore, the gyro-kinetic analysis in helical plasmas consumes the larger computer resources than for tokamaks. In helical plasmas, it is not practical to perform the nonlinear gyro-kinetic simulation at each time step of the dynamical transport code. The reduced model, which reproduces the nonlinear gyro-kinetic analysis results, is needed for the dynamical transport simulation in helical plasmas.The GKV code [15] has been used to examine the ion temperature gradient (ITG) mode and zonal flows in the Large Helical Device (LHD) for studying the turbulent transport [13]. The gyro-kinetic simulation with the adiabatic electron is performed for the high ion temperature LHD discharge (shot number 88343 [16]). The ion energy flux by the ITG mode instability agrees with the experimental results [13,14]. The reduced model for the ion heat diffusivity is proposed [14] by the simulation with the adiabatic electron. This reduced model is the function of the author's e-mail: toda@nifs.ac.jp linear growth rate for the ITG mode and the zonal flow decay time [17,18]. In tokamak plasmas, the gyro-kinetic analysis at each time step is globally performed in the dynamical transport simulation [19,20]. How to apply the reduced model of the turbulent ion heat diffusivity from the gyro-kinetic simulation with the adiabatic electron to the transport code has been shown in helical plasmas [21]. The simulation with the kinetic electron shows the larger ion energy flux than the experimental results in the high-T i LHD discharge [22]. On the other hand, the electron and ion energy fluxes of the simulation results with the kinetic el...

Reduced models of turbulent transport in helical plasmas including effects of zonal flows and trapped electrons

“…The residual level of zonal flows for the case of the KE response is smaller than that for the MAE response in the SD at ρ = 0.65. This tendency is the same in the SD at ρ = 0.80 (Toda et al 2017). However, it is clarified that the residual level for the KE condition is found to be closer to that for the MAE condition at ρ = 0.65 in the IW in figure 4(b) than in the SD.…”

Transport Simulation for Helical Plasmas by use of Gyrokinetic Transport Model

“…The exponents are shown by B 1e = 0.30, B 2e = 0.62, B 3e = 0.63, B 1i = 0.66, B 2i = 3.1, and B 3i = 0.26. The coefficients in the ion heat diffusivity model (2) are different from those in [22], because the simulations are performed in the high-T i and low-T i plasmas for the discharge #88343 in this article and only in the high-T i plasmas for [22]. With the much lower computational cost, the heat diffusivity models enable us to reproduce the nonlinear simulation results by use of linear simulation results.…”

“…This reduced model is the function of the linear growth rate for the ITG mode and the zonal flow decay time [20,21]. The ion heat diffusivity model for the kinetic electron response was shown in helical plasmas [22]. The heat diffusivity models for the electron and ion heat transport, and the quasilinear flux models for the particle and heat transport have been proposed, where the larger number of the wavelength in the wider wavelength region than those in [22] is taken [23].…”

“…The ion heat diffusivity model for the kinetic electron response was shown in helical plasmas [22]. The heat diffusivity models for the electron and ion heat transport, and the quasilinear flux models for the particle and heat transport have been proposed, where the larger number of the wavelength in the wider wavelength region than those in [22] is taken [23]. How to apply the reduced model of the turbulent ion heat diffusivity in the adiabatic electron condition to the transport code has been shown in helical plasmas [24].…”

Recent Progress in the Numerical Simulation Reactor Research Project

“…(2) can well predict the nonlinear GKV simulation results, and it is applied to the integrated transport code (TASK3D) [60] which is found to successfully simulate the T i profile in the high-T i LHD experiment [61]. Extension of the χ i model is also done to include effects of trapped electrons on the ITG turbulent transport in the LHD plasmas [62]. In addition, quasilinear models for the ion energy flux, the electron energy flux, and the particle flux are newly constructed for the case of the ITG turbulence including effects of trapped electrons, for which reasonable agreements between the quasilinear flux models and the nonlinear GK simulations are verified [63].…”