Theory of Nonlinear Waves in Hot Space Plasmas

物质的等离子体状态在宇宙中非常丰富。等离子体动力学在近地空间环境、太阳、太阳系以及超新星遗迹、空间喷气和脉冲星等遥远天体附近的许多过程中发挥着基本作用。通常情况下，等离子体在其自然环境中是无碰撞的。在这样的等离子体中，普通气体中粒子碰撞的作用被具有电磁结构和波的粒子相互作用所取代。因此，波的研究对于理解等离子体过程是至关重要的。热等离子体或高β等离子体是热等离子体压力与磁场压力相当或超过磁场压力的等离子体。与冷等离子体相比，热等离子体的理论描述复杂得多。尽管宇宙中有大量的无碰撞等离子体，但目前唯一可以在自然条件下对等离子体进行全面实验研究的地方就是地球空间环境。从地球附近的实验研究可知，热等离子体(如磁鞘、环电流)区域富含大振幅、非线性、低频波。对这种波的严格描述，即使使用线性近似(这只适用于振幅极小的波)也是一个相当复杂的问题。本提案的主要目标是在先前在PPA/G/S/2002/000094号项目的框架内发展的热等离子体中低频波的线性理论的成功的基础上，发展热、均匀和非均匀等离子体中的非线性波的一般理论。基于这一理论，就有可能生产出一套工具，简化在卫星实验中观察到的低频波的识别。这些工具将包括计算实际条件下的波参数，这些参数与在空间等离子体中实验观察到的参数相对应。然后，这一工具可用于识别目前或未来的卫星飞行任务所观测到的波，如星系团或金星快车。此外，我们还将研究发展的理论对超新星遗迹等遥远天体附近的粒子加速过程的影响。

The plasma state of matter is highly abundant in the universe. Plasma dynamics play a fundamental role in many of the processes in the near geo-space environment, at the sun, in the solar system and in the vicinity of remote astrophysical objects such as supernova remnants, space jets, and pulsars. Often plasma in its natural environment is collisionless. In such plasmas the role of particle collisions in an ordinary gas is replaced by particle interactions with electric and magnetic structures and waves. Therefore a study of waves is vital for understanding of plasma processes. Hot or high beta plasma is the plasma in which thermal plasma pressure is comparable to or exceeds the magnetic field pressure. The theoretical description of hot plasmas is much more complicated in comparison to cold plasma. In spite of the profusion of collisionless plasmas in the universe the only place where comprehensive experimental studies of plasma under natural conditions can be conducted at present is the geo-space environment. It is known from experimental studies in the vicinity of Earth that regions with hot plasma (e.g. magnetosheath, ring current) are rich with large amplitude, nonlinear, low frequency waves. The rigorous description of such waves even using a linear approximation (which is only valid for cases of waves with infinitesimally small amplitude) represents a quite complicated problem. The main goal of the present proposal is to develop a general theory of nonlinear waves in hot, uniform and non-uniform plasmas, building on the success of the linear theory of low frequency waves in hot plasma previously developed in the framework of the PPARC grant PPA/G/S/2002/000094. Based on this theory, it is then possible to produce a set of tools that will simplify the identification of low frequency waves observed in satellite experiments. These tools will include calculations of wave parameters in realistic conditions that correspond to those observed experimentally in space plasma. This tool may then be applied to the identification of waves observed by current or future satellite missions such as Cluster or Venus Express. In addition, we will study the implications of the developed theory to processes involved in the acceleration of particles in the vicinity of remote astrophysical objects such a supernova remnants.