52.65.Rr Particle-in-cell method
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Institute
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.
This thesis constitutes a computational study of charge and ion drag force on micron-sized dust particles immersed in rf discharges. Knowledge of dust parameters like dust charge, floating potential, shielding and ion drag force is very crucial for explaining complex laboratory dusty plasma phenomena, such as void formation in microgravity experiments and wakefield formation in the sheaths. Existing theoretical models assume standard distribution functions for plasma species and are applicable over a limited range of flow velocities and collisionality. Kinetic simulations are suitable tools for studying dust charging and drag force computation. The main aim of this thesis is to perform three dimensional simulations using a Particle-Particle-Particle-Mesh ($P^3M$) model to understand how the dust parameters vary for different positions of dust in rf discharges and how these parameters on a dust evolve in the presence of neighboring dust particles. At first, rf discharges in argon have been modelled using a three-dimensional PIC-MCC code for the discharge conditions relevant to the dusty plasma experiments. All necessary elastic and inelastic collisions have been considered. The plasma background is found collisional, charge-exchange collisions between ions and neutrals being dominant. Electron and ion distributions are non-Maxwellian. The dominant heating mechanism is Ohmic. Then, simulations have been done to compute the dust parameters for various sizes of dust located at different positions in the rf discharges. Dust charge and floating potential in the presheath are slightly larger than the values in the bulk due to the higher electron flux to the dust particle in the presheath. From presheath to the sheath the charge and floating potential values decrease due to the decrease of the electron current to the dust. A linear dependence of dust potential on dust size has been found, which results in a nonlinear dependence of the dust charge with the dust size when the particle is assumed to be a spherical capacitor. This has been verified by independently counting the charges collected by the dust. %where indeed it has been noted that the dust charge %scales nonlinearly with the dust size. The computed dust parameters are also compared with theoretical models. Simulated dust floating potentials are comparable to values obtained from Allen-Boyd-Reynolds (ABR) and Khrapak models, but much smaller than the values obtained from Orbit Motion Limited (OML) model. The dust potential distribution behaves Debye-H\"{u}ckel-like. The shielding lengths are in between ion and electron Debye lengths. % indicating shielding by both ions and electrons. Further, the orbital drag force is typically larger than the collection drag force. The total drag force for the collisional case is larger than for the collisionless case and it scales nonlinearly with the dust size. The collection drag values and size-scaling agrees with Zobnin's model. The charging and drag force computation is then extended to two and multiple static dust particles in the rf discharge to study the influence of neighboring dust particles on the dust parameters. Initially, the dust parameters on two dust particles are computed for various interparticle separation distances and for dust particles placed at different locations in the rf discharge. It is observed that for dust separations larger than the shielding length the dust parameters for the two dust particles match with the single dust particle values. As the dust separation is equal to or less than the shielding length the ion drag force increases due to the buildup of a parallel drag force component. However, the main dust properties like charge, potential, vertical component of ion drag are not affected considerably. This is attributed to the smaller collection impact parameter values compared to the dust separation. %This is because the %collection impact parameter values in the sheath and the presheath are smaller %than the smallest dust separation and in case of the dust in the bulk, the %collection impact parameter is comparable with the dust separation. Then the dust charges on multiple dust particles located at different positions in the discharge and arranged along the discharge axis are also computed. It is found that the charges of the multiple dust particles in the bulk or presheath do not differ much from the single particle values at that location. But the dust charges of multiple dust particles located in the sheath drastically differ from the single dust parameter values. Due to ion focusing from dust particles in the upper layers, the ion current increases to dust particles in the lower layers resulting in smaller charge values. This is as well the case where dust particles are vertically aligned as in the standard experiments of dusty plasmas. In conclusion, this work used a fully kinetic (PIC and MD or $P^3M$) model to study the physics of dust charging in rf plasmas. Our simulations revealed that the dust parameters vary considerably from the bulk to the sheath. The CX collisions increase flux to the dust thereby affecting the dust parameters and their scaling with dust size. Also, a dust particle affects the charging dynamics of its neighbor only when their separation is within the shielding length. In the plasma sheath, ion focussing can cause great reduction in dust charges.
Asymmetrical capacitively coupled RF discharges in oxygen, argon and hydrogen have been experimentally investigated with the innovative technique of the phase resolved optical emission spectroscopy. This diagnostic tool allows to measure spatio-temporally resolved emission intensities of electronically excited species with a high resolution. The spatial (axial) resolution was better than 1 mm and a temporal resolution of about 1.5 ns has been achieved. Therefore the plasma induced optical emission within the RF cycle (TRF = 73.75 ns) from the RF sheath region with a typical mean sheath thickness of about 5mm has been studied. Spatio-temporally resolved optical emission patterns of the following optical transitions have been measured for a total gas pressure in the range of 20 to 100 Pa and self-bias voltages between -50 and -550 V: Oxygen plasma Emission at 777.4 nm and 844.6 nm (atomic oxygen) Argon plasma Emission at about 751 nm and 841 nm (argon) Hydrogen plasma Emission at 656.3nm (atomic hydrogen, H alpha-line) These transitions are the most prominent ones of the investigated excited species in these plasmas as could be shown from overview spectra of the plasma induced optical emission in the range from 350 to 850 nm. For the first time such extensive PROES measurements in oxygen CCRF plasmas are presented in this work. The additional investigations of argon and hydrogen plasmas serve as a reference and for a direct comparison with results from the literature. The temporal behavior of the emission intensity is influenced by the effective lifetime of the emitting states which is on the order of the nanosecond time scale of the RF cycle. Therefore, it does not represent the real temporal behavior of the excitation. A simple method has been applied to calculate relative excitation rates from the measured emission intensities to distinguish different excitation mechanisms and their correct relative temporal behavior. In a close collaboration within the framework of the Sonderforschungsbereich Transregio 24 'Fundamentals of Complex Plasmas' a newly 1d3v PIC-MCC code for simulations of capacitive RF discharges in oxygen has been developed by Matyash et al. The very close coupling of experiment and modeling allowed a really detailed and microscopic understanding of the processes and dynamics from the sheath to the bulk plasma in CCRF discharges. The spatio-temporally resolved excitation rate profiles show four different excitation structures (I-IV). Excitation processes due to the following mechanisms in CCPs could be identified and characterized: I Electrons expelled from growing sheath II Electrons detached from negative ions (collisions with neutrals) + secondary electrons from the electrode surface (ion bombardment) III Field-reversal effect, reduced mobility of electrons (electron-neutral collisions) IV Heavy-particle collisions These excitation mechanisms are characterized by different temporal and spatial behaviors of the excitation rate within the RF cycle. Additionally it has been shown that the excitation by electron impact in the investigated oxygen plasmas results mainly from dissociative electron impact excitation (O2 + e -> O + O* + e) and not from direct electron impact excitation (O + e -> O* + e). Actinometry measurements show that the results are not really credible. Thus actinometry is not applicable on the investigated oxygen RF plasma. A challenge in interpretation is the observed excitation pattern IV. Pattern IV has to be caused in connection with heavy particle collisions nearby the electrode surface and could be observed in all the three plasmas oxygen, argon and hydrogen. It is located directly in front of the powered electrode and appears during almost the whole RF cycle. The temporal modulation is nearly sinusoidal and weak in comparison to the first three patterns. This is due to the weak RF modulation of the ion flux towards the electrode surface which has been proven by a PIC simulation. It could be shown that the modulation degree of pattern IV depends on the transition time of the corresponding positive ions through the RF sheath which is influenced by the ion mass. In oxygen as well as in argon CCRF plasmas pattern IV is less modulated than in hydrogen CCRF plasmas due to the heavier ions in oxygen and argon. Additionally the modulation degree increases with increasing pressure due to the more confined plasma at higher pressures which is yielding in a stronger modulated ion current towards the powered electrode.