A numerically efficient framework that takes into account the effect of the Coulomb collision operator at arbitrary collisionalities is introduced. Such model is based on the expansion of the distribution function on a Hermite-Laguerre polynomial basis, to study the effects of collisions on magnetized plasma instabilities at arbitrary mean-free path. Focusing on the drift-wave instability, we show that our framework allows retrieving established collisional and collisionless limits. At the intermediate collisionalities relevant for present and future magnetic nuclear fusion devices, deviations with respect to collision operators used in state-of-the-art turbulence simulation codes show the need for retaining the full Coulomb operator in order to obtain both the correct instability growth rate and eigenmode spectrum, which, for example, may significantly impact quantitative predictions of transport. The exponential convergence of the spectral representation that we propose makes the representation of the velocity space dependence, including the full collision operator, more efficient than standard finite difference methods.

中文翻译：

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任意碰撞下的漂移波不稳定性理论

引入了一个数值有效的框架，该框架考虑了库仑碰撞算子在任意碰撞情况下的影响。这种模型基于Hermite-Laguerre多项式的分布函数的展开，以研究碰撞对任意均值自由路径上磁化等离子体不稳定性的影响。着眼于漂移波不稳定性，我们证明了我们的框架允许检索已建立的碰撞和无碰撞极限。在与当前和未来的磁核聚变设备有关的中间碰撞中，在最新的湍流模拟代码中使用的碰撞算子存在偏差，这表明需要保留完整的库仑算子，以便获得正确的不稳定性增长速率和本征模频谱，例如 可能会严重影响运输的定量预测。我们提出的频谱表示的指数收敛使速度空间相关性（包括完整的碰撞算子）的表示比标准有限差分方法更有效。