The Vlasov equation describes collisionless plasmas in the continuum limit and applies to many fundamental plasma energization phenomena. Because this equation governs the evolution of plasma in six-dimensional phase space, studies of its structure have mostly been limited to numerical or analytical methods. Here terms of the Vlasov equation are determined from observations of electron phase-space density gradients measured by the four Magnetospheric Multiscale spacecraft in the vicinity of magnetic reconnection at Earth’s magnetopause. We identify which electrons in velocity space substantially support the electron pressure divergence within electron-scale current layers. Furthermore, we isolate and characterize the effects of density, velocity and temperature gradients on the velocity-space structure and dynamics of these electrons. Unipolar, bipolar and ring structures in the electron phase-space density gradients are compared to a simplified Maxwellian model and correspond to localized gradients in density, velocity and temperature, respectively. These structures have implications for the ability of collisionless plasmas to maintain kinetic Vlasov equilibrium. The results provide a kinetic perspective relevant to how the electron pressure divergence may develop to violate the electron frozen-in condition and sustain electron-scale energy conversion processes, such as the reconnection electric field, in collisionless space plasma environments.

Vlasov 方程描述了连续极限中的无碰撞等离子体，并适用于许多基本的等离子体激发现象。因为这个方程控制着等离​​子体在六维相空间中的演化，所以对其结构的研究大多局限于数值或分析方法。这里 Vlasov 方程的项是根据对地球磁层顶磁重联附近的四个磁层多尺度航天器测量的电子相空间密度梯度的观察确定的。我们确定了速度空间中的哪些电子基本上支持电子尺度电流层内的电子压力发散。此外，我们分离并描述了密度、速度和温度梯度对这些电子的速度-空间结构和动力学的影响。单极，将电子相空间密度梯度中的双极和环状结构与简化的麦克斯韦模型进行比较，并分别对应于密度、速度和温度的局部梯度。这些结构对无碰撞等离子体维持动力学 Vlasov 平衡的能力有影响。该结果提供了一个动力学观点，与电子压力发散如何发展以违反电子冻结条件和维持电子尺度能量转换过程有关，例如在无碰撞空间等离子体环境中的重新连接电场。这些结构对无碰撞等离子体维持动力学 Vlasov 平衡的能力有影响。该结果提供了一个动力学观点，与电子压力发散如何发展以违反电子冻结条件和维持电子尺度能量转换过程有关，例如在无碰撞空间等离子体环境中的重新连接电场。这些结构对无碰撞等离子体维持动力学 Vlasov 平衡的能力有影响。该结果提供了一个动力学观点，与电子压力发散如何发展以违反电子冻结条件和维持电子尺度能量转换过程有关，例如在无碰撞空间等离子体环境中的重新连接电场。