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- Electrostatic Trapping as a Self-Consistent Phenomenon in Plasmas and other Collective Systems (2004)
- This thesis investigates self-consistent electrostatic structures in plasmas and related collective systems. They are coherent structures in which particles become trapped in the wave potential. These phenomena require a kinetic description i.e. a description in which the velocity distribution of the particles is taken into account. Trapping structures extend the areas in configuration space in which a plasma is unstable. The main argument and result of this work is that there exist certain kinds of perturbations of an equilibrium that can destabilize the plasma, even if linear theory predicts stability. The usual procedure in plasma theory of analyzing the stability of a plasma by means of a linearization of the equations is therefore questioned. Particle trapping is an essentially nonlinear phenomenon, still present for infinitesimally small wave amplitudes. The effect of the particle trapping is therefore not linked only with the treatment of finite amplitudes, as often assumed, but has also to be taken into account from the very beginning if one wants to arrive at generally valid predictions about stability and the associated anomalous transport. Thus it is not surprising that the problem of transport represents a not yet closed chapter in the theory of plasmas, a fact which is shown in many examples from fusion and space research, where almost collisionless plasmas are present. Particle trapping is however not confined to classic plasmas. Another result of this work is to show that the applied formalism can also be extended to other systems that present a collective behavior. Namely, a quantum extension is possible, which allow us to investigate quantum-like systems and also to draw a connection between electrostatic trapping in plasmas and envelope solitons in nonlinear optical media like e.g. optical fibers. The longitudinal dynamics of charged particle beams in accelerators and storage rings provides a further example of a collective system in which the phenomenon of particle trapping plays an essential role of the dynamics.