The Van Kampen normal-mode method is applied in a comprehensive study of the linear wave perturbations of a homogeneous, magnetized and finite-temperature plasma, described by the collisionless Vlasov–Maxwell system in its non-relativistic version. The analysis considers a stable, Maxwellian background, but is otherwise completely general in that it allows for arbitrary wave propagation direction relative to the equilibrium magnetic field, multiple plasma species and general polarization states of the perturbed electromagnetic fields. A convenient formulation is introduced whereby the generator of the time advance is a Hermitian operator, analogous to the Hamiltonian in the Schrödinger equation of quantum mechanics. This guarantees a real frequency spectrum and complete bases of normal modes. Expansions in these normal-mode bases yield immediately the solutions of initial-value problems for general initial conditions. With standard initial conditions and propagation direction parallel to the equilibrium magnetic field, all the familiar results obtained following Landau’s Laplace transform approach are recovered. Considering such parallel propagation, the present work shows also explicitly and provides an example of how to construct special initial conditions that result in different, damped but otherwise arbitrarily prescribed time variations of the macroscopic variables. The known dispersion relations for perpendicular propagation are also recovered.

Van Kampen正模方法用于对均匀，磁化和有限温度等离子体的线性波扰动的综合研究，无碰撞Vlasov-Maxwell系统在其非相对论版本中对此进行了描述。该分析考虑了稳定的麦克斯韦背景，但由于它允许相对于平衡磁场，多种等离子体物质和扰动电磁场的一般极化状态的任意波传播方向，因此是完全通用的。引入了一种方便的公式，其中时间提前量的生成器是Hermitian算符，类似于量子力学的Schrödinger方程中的哈密顿量。这保证了真实的频谱和正常模式的完整基础。这些普通模式基数的展开立即产生了一般初始条件下初始值问题的解。在标准的初始条件和平行于平衡磁场的传播方向的情况下，可以恢复使用Landau Laplace变换方法获得的所有熟悉的结果。考虑到这种并行传播，本工作还明确显示并提供了一个示例，说明如何构建特殊的初始条件，这些条件会导致宏观变量的不同的，阻尼的但以其他方式任意规定的时间变化。还恢复了垂直传播的已知色散关系。可以恢复使用Landau的Laplace变换方法获得的所有熟悉的结果。考虑到这种并行传播，本工作也明确显示并提供了一个示例，说明如何构建特殊的初始条件，这些条件会导致宏观变量的不同，衰减但任意规定的时间变化。还恢复了垂直传播的已知色散关系。可以恢复使用Landau的Laplace变换方法获得的所有熟悉的结果。考虑到这种并行传播，本工作也明确显示并提供了一个示例，说明如何构建特殊的初始条件，这些条件会导致宏观变量的不同，衰减但任意规定的时间变化。还恢复了垂直传播的已知色散关系。