| Charged particles, with the energy range from around 1 keV to several MeV, are called energetic particles by convention. Since five decades ago, when Dr. Van Allen discovered the radiation belt, the energetic particles in the near-earth space has attracted a lot of attention. Despite the relatively insignificant number density of the energetic particles, if compared with the plasma density, they are well believed to be a key factor in the energy and flux couplings between the solar wind, magnetosphere and the ionosphere, and to be able to produce a lot of phenomena in the earth's magnetosphere, e.g., the aurora, the magnetospheric storms and substorms.In the study of the energetic particles in the magnetosphere, the most important issues are their sources, sinks and the acceleration mechanisms. Recently, there are a series of controversies regarding to these mechanisms, including: the controversy between the ULF and the VLF waves in their role for accelerating particles in the inner magnetosphere, the one regarding to the special role of cusp for energetic particles, and the explanation of the plasma sheet features depending on the IMF orientations, etc.In Chapter 1, after an introduction to the Earth's magnetosphere and the energetic particles contained in the magnetosphere, we briefly introduce the adiabatic theory and review the previous observations and theories in the study of energetic particles, to highlight the series of controversies.In Chapter 2, based on the Cluster data, we provide the first direct observational evidence of the resonance between the ULF waves and the energetic particles. As we know, the electric field carried by the ULF waves can accelerate or decelerate the energetic particles during their drift motion, depending on the phase difference between them. In the special cases when the phase difference does not vary, the particles can be stably energized. The so-called resonance effect can alter the third adiabatic invariant of the energetic particles, and therefore shift their radial positions. Here we make use of the multi-point observational advantages of the Cluster mission, observe the interactions between the ULF waves and the energetic particles, and relate the observational data with the resonance theory in a quantitative manner. We further point out that the poloidal mode and the toroidal mode of the ULF waves corresponds to different resonance energy range, which provides a new effective way to understand the source and acceleration mechanism of the energetic particles in the radiation belt. This part of our work, after its publication, was reported by the European Space Agency (http://sci.esa.int) as a top story [Masson, 2007], and selected by DISCOVER magazine (http://discovermagazine.com) as one (No. 37) of the top 100 science stories of 2007.In Chapter 3, we apply the adiabatic theory to the cusp region, and firstly present the concept of the cusp magnetic minimum plane to explore the dynamic process of particle exchanging in the cusp region. The motions of energetic particles in the cusp are discussed analogous to those in the inner magnetosphere, as a combination of the gyro, bounce and drift motions. A particle would also follow a closed orbit around the cusp region if the three adiabatic invariants were constants, however, this is seldom the case because of the highly disturbed nature of the cusp region. The violation of the adiabatic condition results in the particle motion of diffusion, acceleration, cusp injection and departure, which are also reproduced by test particle simulations. It is of importance to note the coexistence of open field lines and closed ones within the same drift path in the cusp region, which allows the particles in the magnetosheath to enter the magnetosphere via the cusp region, and vise versa. Our work highlight the role of the cusp as a window for particle exchange between the solar wind and the magnetosphere, and improve the present understanding of the energetic particles in the cusp region.In Chapter 4, we suggest a new mechanism for solar wind particles to directly penetrate the magnetopause to the plasma sheet. Because the magnetic field varies in a spatial scale comparative to the particle gyro-radius, all of the traditional adiabatic invariants are no longer constants. However, we make use of a nontrivial adiabatic invariant that remain valid in the current sheet to describe the motion of energetic particles in the equatorial magnetopause. It is found that the conditions for magnetosheath particles to penetrate the magnetopause depend on IMF: during southward IMF, there is an energy filter effect, only those particles with energies higher than a critical criteria can enter the magnetosphere; for northward IMF, the energy filter effect disappears, which allows more particles to the plasma sheet. This mechanism has never been discussed before, and is important because of the observational fact that the particle characteristics in the plasma sheet also depend on IMF. Although there are several processes suggested, e.g., the high-latitude reconnection and the Kelvin-Helmholtz instability at the flank region, they can not explain the phenomenon satisfactorily. Our work, on the other hand, provide a new view in the explanation of this pending controversy. In Chapter 5, a new method in the determination of the orientation and velocity of flux rope is presented, based on the multi-point observations of the Cluster constellation. During southward IMF, the transient magnetic reconnection at the magnetopause would produce flux ropes connecting the magnetosphere and the magnetosheath, and allows the magnetosheath particles to enter the magnetosphere. The so-called Flux Transfer Events (FTEs) is widely believed to be a most important source of particles in the magnetosphere. Therefore, Therefore, it is important to correctly determine the orientation and velocity of an observed flux rope, in describing the motion and source mechanisms of energetic particles in the magnetosphere. Since the discovery of the FTEs, the PAA method based on minimum variance principal is used to determine the orientation of flux ropes, however, the method has a strong ambiguity because all of the three eigenvectors obtained can be the right orientations based on different models. Here we develop a new method called Multiple Triangulation Analysis (MTA), to overcome the ambiguity in the traditional PAA technique, and provide a new way to better obtain the orientation and velocity of the flux ropes and therefore allow us to better understand the flux rope's role in transporting energetic particles into the magnetosphere.In summary, the complicated motions of the energetic particles in the magnetosphere are described, with several controversies being discussed and explained. It should be noted, however, that there are many other candidate mechanisms beyond our scope, and we did not exclude their effects. Future studies are required to analyze the respective roles of all these mechanisms in more detail, to discover the relationship between the particle dynamics and the space weather, and to establish a integrated model of the energetic particles in the magnetosphere.
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