Universität Stuttgart
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Item Open Access Ion-acoustic solitons : analytical, experimental and numerical studies(2011) Aziz, Farah; Stroth, Ulrich (Prof. Dr. rer. nat.)Plasma is a nonlinear and dispersive medium that supports the propagation of several types of electrostatic and electromagnetic waves. Ion-acoustic waves are very simple kind of waves that take the form of solitary waves, if the effects of nonlinearity and dispersion are balanced with each other in the plasma. A solitary wave is called a soliton if it retains its shape during propagation and after collision with another solitary wave. In the present thesis, the research work is mainly focused on the theoretical, experimental and numerical analyses of ion-acoustic solitons. The analytical part deals with the soliton propagation, reflection and transmission in an inhomogeneous plasma having electrons being trapped in the soliton potential. The experimental and simulation parts emphasize on the soliton evolution mechanisms and their propagation in a Double-Plasma (DP) device. One-dimensional propagation of the solitons is analyzed under the effects of ion temperature, density inhomogeneity and temperature and concentration of trapped electrons. Here, the usual KdV equation is found to be modified by variable coefficients and an additional term appearing due to the density gradient present in the plasma. This modified KdV (mKdV) equation is solved by using a novel technique, called sine-cosine method. The linear and nonlinear analyses lead us to infer that the soliton propagation characteristics are significantly modified in the presence of even a small population electrons trapped by the wave potential and hence interact strongly with the wave during its propagation. Apart from the one dimensional propagation of mKdV solitons, oblique reflection of the solitons from a density gradient is investigated in the plasma. In relation to the transmission and reflection of the solitons from a semi-transparent grid, conditions are obtained for the obliqueness of the propagation and maximum drift velocity of ions. Also, a transmission-reflection conservation law is derived, based on which the mechanism of soliton reflection and transmission is explored in detail. The contribution of trapped electrons to the solitons’ propagation, reflection and transmission is examined through energy, amplitude and width of the solitons, in addition to the effects of temperature and drift of the ions. As mentioned, the experimental and simulation studies are conducted in a DP device. This device consists of two plasma regions, the source chamber and a target chamber, both housed in a common vacuum chamber. Here, the excitation of linear and nonlinear ion-acoustic waves is carried out by applying bursts of sinusoidal signals on the grid that separates the source and the target chambers. The soliton generation mechanism in the target chamber is explored by carrying out diagnostic measurements using a Langmuir probe. It is observed that the soliton profiles are accompanied by a burst of fast ions and a depression of ions, when electron temperature Te remains much larger than the ion temperature Ti, i.e. Te >> Ti. Soliton profiles are investigated for different peak-to-peak amplitudes, durations and frequencies of the applied grid signal. Particle-In-Cell (PIC) simulations are carried out in order to study in detail the evolution and propagation mechanism of the solitons. The simulation results show similar features as observed in the experiment for Te/Ti > 10. A detailed insight into the soliton evolution mechanism is obtained based on the ion phase- space distributions obtained from the simulations. Also, the effect of the amplitude, duration and frequency of the excitation signal on the soliton evolution is simulated. The simulated soliton is found to behave in a consistent manner under the effect of the parameters and it acquires a saturation in its amplitude after undergoing an initial enhancement. However, the simulations with Te/Ti < 10 having higher concentrations of resonant ions show strong interaction of the waves with the ions, producing another soliton through energy exchange mechanism. Finally, the generation mechanism of this second soliton is discussed based on the simulation studies.