In this paper, a self-consistent model for the average radial turbulent transport of heat and particles in 2D anisothermal interchange-dominated electrostatic ExB drift turbulence in sheath-limited scrape-off layers is presented. Diffusion models are used for the turbulent particle and heat fluxes, in which the transport coefficients scale with the square root of the turbulent kinetic energy ($k_{\perp }$). The interchange drive proves to be the main source of turbulent kinetic energy, while the sheath term provides the main sink. These observations are qualitatively the same as for the isothermal case studied earlier. An analytical relation for the interchange term is derived, showing that the turbulent ExB thermal energy flux is the direct driver for $k_{\perp }$ through the interchange source. A series decomposition of the sheath term in the $k_{\perp }$ equation shows it includes a sink contribution that was also present in the isothermal case, but also a new source due to the sheath-driven conducting-wall (SCW) instability caused by electron temperature fluctuations. Using a simple regression model to close the total sheath term, a closed model for the turbulent transport is obtained. The interchange drive due to the ExB energy flux leads to a self-saturation mechanism in the model, where the gradients and turbulence intensity increase until a sufficient transport level is reached to carry the power and particles across the field lines to find a balance with the sheath sink. An implementation of this model in a 1D mean-field code approximates the profiles of the turbulence simulations with remarkable accuracy in part of the parameter space, while the error increases in parameter regimes where the relative importance of the SCW term is varied.

中文翻译：

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鞘层限制刮除层中二维交换主导的静电 ExB 湍流中湍流粒子和热传输的自洽平均场模型

在本文中，提出了一种自洽模型，用于在鞘限制刮除层中二维非等温交换主导的静电 ExB 漂移湍流中热量和粒子的平均径向湍流传输。扩散模型用于湍流粒子和热通量，其中传输系数与湍流动能的平方根成比例（${ķ}_{\perp }$）。交换驱动被证明是湍流动能的主要来源，而鞘项提供了主要的汇。这些观察结果在质量上与之前研究的等温情况相同。导出了交换项的解析关系，表明湍流 ExB 热能通量是${ķ}_{\perp }$通过交换源。鞘项的一系列分解${ķ}_{\perp }$方程表明它包括在等温情况下也存在的汇贡献，但由于电子温度波动引起的鞘层驱动导电壁（SCW）不稳定性，它还包括一个新源。使用简单回归模型对总鞘项进行封闭，得到湍流输运的封闭模型。由于 ExB 能量通量导致的交换驱动导致模型中的自饱和机制，其中梯度和湍流强度增加，直到达到足够的传输水平以携带能量和粒子穿过场线以找到平衡鞘水槽。该模型在一维平均场代码中的实现近似于湍流模拟的轮廓，在部分参数空间中具有显着的准确性，