This paper proposes a metric bracket for representing Coulomb collisions in the so-called guiding-centre Vlasov–Maxwell–Landau model. The bracket is manufactured to preserve the same energy and momentum functionals as does the Vlasov–Maxwell part and to simultaneously satisfy a revised version of the H-theorem, where the equilibrium distributions with respect to collisional dynamics are identified as Maxwellians. This is achieved by exploiting the special projective nature of the Landau collision operator and the simple form of the system's momentum functional. A discussion regarding a possible extension of the results to electromagnetic drift-kinetic and gyrokinetic systems is included. We anticipate that energy conservation and entropy dissipation can always be manufactured whereas guaranteeing momentum conservation is a delicate matter yet to be resolved.

中文翻译：

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导向中心 Vlasov-Maxwell-Landau 模型的能量和动量守恒碰撞支架

本文提出了一个度量括号，用于表示所谓的引导中心 Vlasov-Maxwell-Landau 模型中的库仑碰撞。制造支架以保持与 Vlasov-Maxwell 部分相同的能量和动量泛函，并同时满足 H 定理的修订版本，其中关于碰撞动力学的平衡分布被确定为麦克斯韦分布。这是通过利用朗道碰撞算子的特殊射影性质和系统动量泛函的简单形式来实现的。包括关于可能将结果扩展到电磁漂移动力学和陀螺动力学系统的讨论。