## 52.35.-g Waves, oscillations, and instabilities in plasmas and intense beams (see also 94.20.wf Plasma waves and instabilities in physics of the ionosphere; 94.30.cq MHD waves, plasma waves, and instabilities in physics of the magnetosphere; 96.50.Tf MHD waves, pl

### Refine

#### Keywords

- Plasma (3)
- Plasmaphysik (2)
- Beam (1)
- Cluster (1)
- Dusty Plasma (1)
- Dynamik (1)
- Finite Systeme (1)
- Fusion (1)
- Kaltes Plasma (1)
- Komplexes Plasma (1)

This thesis is devoted to experiments on three-dimensional dust clouds which are confined in low temperature plasmas. Such ensembles of highly electrically charged micrometer-sized particles reveal fascinating physics, such as self-excited density waves and vortices. At the same time, these systems are challenging for experimental approaches due to their three-dimensional character. In this thesis, new optical diagnostics for dusty plasmas have been developed and, in combination with existing techniques, have been used to study these 3D dusty plasmas on different size and time scales.

The collisionless tearing mode is investigated by means of the delta-f PIC code EUTERPE solving the gyrokinetic equation. In this thesis the first simulations of electromagnetic non-ideal MHD modes in a slab geometry with EUTERPE are presented. Linear simulations are carried out in the cases of vanishing and finite temperature gradients. Both cases are benchmarked using a shooting method showing that EUTERPE simulates the linearly unstable tearing mode to a very high accuracy. In the case of finite diamagnetic effects and values of the linear stability parameter Delta of order unity analytic predictions of the linear dispersion relation are compared with simulation results. The comparison validates the analytic results in this parameter range. Nonlinear single-mode simulations are performed in the small- to medium-Delta range measuring the dependency of the saturated island half width on the equilibrium current width. The results are compared with an analytic prediction obtained with a kinetic electromagnetic model. In this thesis the first simulation results in the regime of fast nonlinear reconnection~(medium- to high-Delta range) are presented using the standard gyrokinetic equation. In this regime a nonlinear critical threshold has been found dividing the saturated mode from the super-exponential phase for medium-Delta values. This critical threshold has been proven to occur in two slab equilibria frequently used for reconnection scenarios. Either changing the width of the equilibrium current or the wave number of the most unstable mode makes the threshold apparent. Extensive parameter studies including the variation of the domain extensions as well as the equilibrium current width are dedicated to a comprehensive overview of the critical threshold in a wide range of parameters. Additionally, a second critical threshold for high-Delta equilibria has been observed. A detailed comparison between a compressible gyrofluid code and EUTERPE is carried out. The two models are compared with each other in the linear regime by measuring growth rates over wave numbers of the most unstable mode for two setups of parameters. Analytical scaling predictions of the dispersion relation relevant to the low-Delta regime are discussed. Employing nonlinear simulations of both codes the saturated island half width and oscillation frequency of the magnetic islands are compared in the small-Delta range. Both models agree very well in the limit of marginal instability and differ slightly with decreasing wave vector. Recently, the full polarisation response in the quasi-neutrality equation was implemented in EUTERPE using the PadÃ© approximation of the full gyrokinetic polarisation term. Linear simulation results including finite ratios of ion to electron temperature are benchmarked with the dispersion relation obtained from a hybrid model. Finite temperature effects influence the saturated island width slightly with increasing ion to electron temperature ratio which has been verified by both models.

During the past decade, various physical properties of the Yukawa ball, like structure and energy states, were unraveled using experiments. However, the dynamical features served further attention. Therefore, the main aim of my thesis was to investigate and understand how a finite system-represented by Yukawa clusters-evolves from a solid, crystalline structure to a liquid-like system, how it behaves in this phase and in what manner the reordering back into the solid state can be described. As a method of choice to reach this goal, laser heating has been proven successful. Moreover, the special importance of wakefields for dust clusters confined at low neutral gas pressure was addressed. Melting of finite dust clouds can be induced in two ways, either by altering the properties of the ambient plasma or by laser heating. The latter was shown to be a generic melting scenario, allowing to estimate a critical coupling parameter at the melting point. Moreover, the melting transition of finite 3D dust systems was found to be a two-step process where angular order is lost before the radial order starts to diminish at higher energies. Next, the mode dynamics of finite 3D dust ensembles in the solid and the liquid phase was studied. Crystal and fluid modes revealed the main spectral properties of the system. The normal modes are mainly suited to describe crystalline states. Fluid modes were excited naturally and via laser heating, with excitation frequencies almost independent of the coupling parameter in the solid and the liquid-like regime. Tuning the plasma parameters can be used to vary the particle-particle interaction via the ion focus. Both methods, even though assuming equilibrium situations, allowed to hint at these wakefields. The corresponding peaks in the fluid and normal mode spectra were no eigenmodes, confirming the nonequilibrium character of the ion focusing effect. First steps to extend the normal mode theory to achieve the dynamics of wake-affected nonequilibrium dust clusters were presented. Statistical quantities were obtained evaluating long-run experiments and transport coeffcients for finite dust systems were calculated via the instantaneous normal mode technique. Diffusion was found considerably higher for 3D than for 2D dust clusters. Using the configurational entropy, we have shown that in 2D and 3D disorder increases with increasing size of the system, in agreement with simulations. The temperature dependence of the configurational entropy differs for 2D and 3D dust clouds, with a threshold behavior found for finite 2D ensembles only. Finally, using instantaneous normal modes to reveal the total fraction of unstable modes, the predictive connection of Keyes (Phys Rev E 62, p7905, 2000), between transport and disorder was tested and verified for 2D, but not for 3D clusters. The reason for this has to be left open. Finally, laser-mediated recrystallization processes of finite 3D dust clouds were investigated. First, the temporal evolution of the Coulomb coupling parameter was traced during heating and recrystallization. A cooling rate has been determined from the initial phase of recrystallization. This cooling rate is lower than damping by the neutral gas, in agreement with simulations. We have observed a large fraction of metastable states for the final cluster configurations. Further, we have revealed that the time scale for the correlation buildup in the finite 3D ensemble was on even slower scales than cooling. Thus, different time scales can be attributed to the fast emergence of the shells and to the slower individual ordering within the shells.

Beams of ions and electrons are a source of free energy which can be transferred to waves via an instability. Beams exist in almost all plasma environments, but their instabilities are particularly important for the dynamics of space plasmas. In the absence of collisions, the instability drives waves to large amplitudes and forms nonlinear structures such as solitary waves. The electric fields in these waves can scatter particles in the background plasma, or disrupt currents. Both of these effects are important for the overall dynamics of the plasma. In this thesis, both electron and ion beam plasma instabilities have been investigated in the linear plasma device VINETA and using a Particle-in-Cell simulation. The electron beam instability has been demonstrated by previous authors to be a useful diagnostic for the plasma density. The spatial resolution of previous results was confirmed at a few millimetres, and a temporal resolution of 1ms was shown for the first time. An ion beam was generated with a double plasma discharge. Compared to space, this environment and indeed most laboratory plasmas have considerably higher collisionality and a limited spatial extent which introduces gradients in the plasma. Gradients perpendicular to the beam propagation direction are linked to a decrease of both the wavelength and amplitude of the instability. It was observed in both experiment and simulation that gradients in sheaths at the boundaries of the plasma not only affect the time averaged plasma parameters, but also excite instabilities. Fluctuations within the sheath spread the beam in velocity space, effectively increasing its temperature. Warmer beams require a higher drift velocity to excite an instability. This was also confirmed by experimental and numerical results. Collisions are shown to be the dominant damping force for the electron beam instability. For ions, collisions play an important role in the simulation, but appear to be overshadowed by Landau damping from impurities in the experiment. When boundary conditions are removed from the simulation, wave amplitudes increase and nonlinear effects become important. Saturation by particle trapping and coalescence of phase space holes is observed, which could eventually lead to the solitary waves as they are observed in space plasmas.