Gyrokinetic simulations are fundamental to understanding and predicting turbulent transport in magnetically confined fusion plasmas. Previous simulations have used model collision operators with approximate field-particle terms of unknown accuracy and/or have neglected collisional finite Larmor radius (FLR) effects. We have implemented the linearized Fokker–Planck collision operator with exact field-particle terms and full FLR effects in a gyrokinetic code (GENE). The new operator, referred to as “exact” in this paper, allows the accuracy of model collision operators to be assessed. The conservative Landau form is implemented because its symmetry underlies the conservation laws and the H-theorem, and enables numerical methods to preserve this conservation, independent of resolution. The implementation utilizes the finite-volume method recently employed to discretize the Sugama collision model in GENE, allowing direct comparison between the two operators. Results show that the Sugama model appears accurate for the growth rates of trapped electron modes (TEMs) driven only by density gradients, but appreciably underestimates the growth rates as the collisionality and electron temperature gradient increase. The TEM turbulent fluxes near the nonlinear threshold using the exact operator are similar to the Sugama model for the η e = d ln T e / d ln n e = 0 case, but substantially larger than the Sugama model for the η e = 1 case. The FLR effects reduce the growth rates increasingly with wavenumber, deepening a “valley” at the intermediate binormal wavenumber as the unstable mode extends from the TEM regime to the electron temperature gradient instability regime. Application to the Hinton–Rosenbluth problem shows that zonal flows decay faster as the radial wavenumber increases and the exact operator yields weaker decay rates.

中文翻译：

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陀螺精确线性化朗道碰撞算子的首次实现与模型对比

陀螺动力学模拟是理解和预测磁约束聚变等离子体中湍流传输的基础。以前的模拟使用了具有未知精度的近似场粒子项的模型碰撞算子和/或忽略了碰撞有限拉莫尔半径 (FLR) 效应。我们已经在陀螺动力学代码 (GENE) 中实现了具有精确场粒子项和完整 FLR 效应的线性 Fokker-Planck 碰撞算子。在本文中称为“精确”的新算子允许评估模型碰撞算子的准确性。之所以采用保守的朗道形式，是因为它的对称性是守恒定律和 H 定理的基础，并使数值方法能够保持这种守恒，而与分辨率无关。该实现利用最近用于离散化 GENE 中的 Sugama 碰撞模型的有限体积方法，允许在两个算子之间进行直接比较。结果表明，Sugama 模型对于仅由密度梯度驱动的俘获电子模式 (TEM) 的增长率似乎是准确的，但随着碰撞性和电子温度梯度的增加，该模型明显低估了增长率。使用精确算子在非线性阈值附近的 TEM 湍流通量类似于 η e = d ln T e / d ln ne = 0 情况下的 Sugama 模型，但明显大于 η e = 1 情况下的 Sugama 模型。FLR 效应随着波数的增加而逐渐降低增长率，随着不稳定模式从 TEM 状态扩展到电子温度梯度不稳定状态，在中间副法向波数处加深“谷”。对 Hinton-Rosenbluth 问题的应用表明，随着径向波数的增加，纬向流衰减得更快，精确算子产生更弱的衰减率。