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Particle and heat transport in fusion devices often exceed the neoclassical prediction. This anomalous transport is thought to be produced by turbulence caused by microinstabilities such as ion and electron-temperature-gradient (ITG/ETG) and trapped-electron-mode (TEM) instabilities, the latter ones known for being strongly influenced by collisions. Additionally, in stellarators, the neoclassical transport can be important in the core, and therefore investigation of the effects of collisions is an important field of study. Prior to this thesis, however, no gyrokinetic simulations retaining collisions had been performed in stellarator geometry. In this work, collisional effects were added to EUTERPE, a previously collisionless gyrokinetic code which utilizes the δ f method. To simulate the collisions, a pitch-angle scattering operator was employed, and its implementation was carried out following the methods proposed in [Takizuka & Abe 1977, Vernay Master's thesis 2008]. To test this implementation, the evolution of the distribution function in a homogeneous plasma was first simulated, where Legendre polynomials constitute eigenfunctions of the collision operator. Also, the solution of the Spitzer problem was reproduced for a cylinder and a tokamak. Both these tests showed that collisions were correctly implemented and that the code is suited for more complex simulations. As a next step, the code was used to calculate the neoclassical radial particle flux by neglecting any turbulent fluctuations in the distribution function and the electric field. Particle fluxes in the neoclassical analytical regimes were simulated for tokamak and stellarator (LHD) configurations. In addition to the comparison with analytical fluxes, a successful benchmark with the DKES code was presented for the tokamak case, which further validates the code for neoclassical simulations. In the final part of the work, the effects of collisions were investigated for slab and toroidal ITGs and TEMs in a tokamak configuration. The results show that collisions reduce the growth rate of slab ITGs in cylinder geometry, whereas they do not affect ITGs in a tokamak, which are mainly curvature-driven. However it is important to note that the pitch-angle scattering operator does not conserve momentum, which is most critical in the parallel direction. Therefore, the damping found in a cylinder could be the consequence of this missing feature and not a physical result [Dimits & Cohen 1994]. Nonetheless, the results are useful to determine whether the instability is mainly being driven by a slab or toroidal ITG mode. EUTERPE also has the feature of including kinetic electrons, which made simulations of TEMs with collisions possible. The combination of collisions and kinetic electrons made the numerical calculations extremely time-consuming, since the time step had to be small enough to resolve the fast electron motion. In contrast to the ITG results, it was observed that collisions are extremely important for TEMs in a tokamak, and in some special cases, depending on whether they were mainly driven by density or temperature gradients, collisions could even suppress the mode (in agreement with [Angioni et al. 2005, Connor et al. 2006]). In the case of stellarators it was found that ITGs are highly dependent on the device configuration. For LHD it was shown that collisions slightly reduce the growth rate of the instability, but for Wendelstein 7-X they do not affect it and the growth rate showed a similar trend with collisionality to that of the tokamak case. Collisions also tend to make the ballooning structure of the modes less pronounced.
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.