Sara Gallian

Ion energy distribution functions behind the sheaths of magnetized and non-magnetized radio frequency discharges

The effect of a magnetic field on the characteristics of capacitively coupled radio frequency discharges is investigated and found to be substantial. A one-dimensional particle-in-cell simulation shows that geometrically symmetric discharges can be asymmetrized by applying a spatially inhomogeneous magnetic field. This effect is similar to the recently discovered electrical asymmetry effect. Both effects act independently, they can work in the same direction or compensate each other. Also the ion energy distribution functions at the electrodes are strongly affected by the magnetic field, although only indirectly. The field influences not the dynamics of the sheath itself but rather its operating conditions, i.e., the ion flux through it and voltage drop across it. To support this interpretation, the particle-in-cell results are compared with the outcome of the recently proposed ensemble-in-spacetime algorithm. Although that scheme resolves only the sheath and neglects magnetization, it is able to reproduce the ion energy distribution functions with very good accuracy, regardless of whether the discharge is magnetized or not.

Full-wave modeling of the O–X mode conversion in the Pegasus toroidal experiment

The ordinary-extraordinary (O-X) mode conversion is modeled with the aid of a 2D full-wave code in the Pegasus Toroidal Experiment as a function of the launch angles. It is shown how the shape of the plasma density profile in front of the antenna can significantly influence the mode conversion efficiency and, thus, the generation of electron Bernstein waves (EBW). It is therefore desirable to control the density profile in front of the antenna for successful operation of an EBW heating and current drive system. On the other hand, the conversion efficiency is shown to be resilient to vertical displacements of the plasma as large as \pm 10 cm.

Analytic model of the energy distribution function for highly energetic electrons in magnetron plasmas

This paper analyzes a situation which is common for magnetized technical plasmas such as dc magnetron discharges and HiPIMS systems, where secondary electrons enter the plasma after being accelerated in the cathode fall and encounter a nearly uniform bulk. An analytic calculation of the distribution function of hot electrons is presented; these are described as an initially monoenergetic beam that slows down by Coulomb collisions with a Maxwellian distribution of bulk (cold) electrons, and by inelastic collisions with neutrals. Although this analytical solution is based on a steady-state assumption, a comparison of the characteristic time-scales suggests that it may be applicable to a variety of practical time-dependent discharges, and it may be used to introduce kinetic effects into models based on the hypothesis of Maxwellian electrons. The results are verified for parameters appropriate to HiPIMS discharges, by means of time-dependent and fully-kinetic numerical calculations.

Reconstruction of the static magnetic field of a magnetron

The simulation of magnetron discharges requires a quantitatively correct mathematical model of the magnetic field structure. This study presents a method to construct such a model on the basis of a spatially restricted set of experimental data and a plausible a priori assumption on the magnetic field configuration. The example in focus is that of a planar circular magnetron. The experimental data are Hall probe measurements of the magnetic flux density in an accessible region above the magnetron plane [P. D. Machura et al., Plasma Sources Sci. Technol. 23, 065043 (2014)]. The a priori assumption reflects the actual design of the device, and it takes the magnetic field emerging from a center magnet of strength m C and vertical position d C and a ring magnet of strength m R, vertical position d R, and radius R. An analytical representation of the assumed field configuration can be formulated in terms of generalized hypergeometric functions. Fitting the ansatz to the experimental data with a least square met...

Ion energy distribution functions in magnetized capacitively coupled RF discharges

Summary form only given. The influence of a spatially inhomogeneous static magnetic field on the characteristics of capacitively coupled radio frequency discharges is investigated. In particular, the focus is placed on the sheath dynamics and the ion energy distribution functions (IEDFs) of ions impinging the electrodes. For this study we employ two different kinetic models. The first is the Particle-in-Cell (PIC) code yapic [1], which takes into account the entire discharge; the second code is the Ensemble-in-Spacetime (EST) model [2] which resolves the plasma boundary sheath only. We make a comparison of the two models by using the sheath voltage and the ion flux through the sheath calculated with PIC as input for EST. [3] We find excellent agreement of the IEDFs calculated with both methods. In addition, good qualitative agreement of the sheath dynamics is observed. However, a quantitative discrepancy between the models can be identified, caused by different collision processes implemented in both models. While it is found that electrons are strongly affected by the applied magnetic field, ions are only indirectly influenced in terms of the asymmetry of the discharge. In addition, we find that EST may be used as an efficient postprocessing tool to obtain the IEDFs even in magnetized cases, in particular if only simplified (i.e., global or fluid-dynamic) models are available.

Gyrokinetic modeling of magnetized technical plasmas

Summary form only given. Many technical plasma processes, like magnetically enhanced reactive ion etching (MERIE), plasma ion assisted deposition (PIAD), and conventional and high-power impulse magnetron sputtering (dcMS/HiPIMS) employ (partially) magnetized high density plasmas at relatively low pressures. (Typical values are p~0.01-1 Pa, B~10-100 mT, ne ~1015-1020 m-3.) These plasmas are, at least in their active regions, characterized by a peculiar ordering of the dynamic length and corresponding time scales: λD ≪ s ≪ L~λ ≪ λ*, with λD Debye length, s sheath thickness, rL Larmor radius, L system length, and λ and λ* elastic and inelastic electron mean free path, respectively. Such plasmas are very difficult to analyze. Fluid models do not apply and numerical kinetic approaches like particle-in-cell are rather expensive. An alternative may be “gyrokinetics”. This theory - actually more a class of theories - was designed and successfully employed in the field of fusion plasmas1. It relies on the insight that the fast gyro motion of magnetized particles can be mathematically separated from the slower drift motion and be “integrated out”, leaving only the dynamics on slower time scales and longer length scales. Unfortunately, however, magnetized technical plasmas are considerably different from fusion plasmas. (Differences concern the magnetic field topology, the presence of material walls and of collisions with neutrals, the fact that only electrons are magnetized, etc.). Direct application of theories developed for fusion is thus not possible. This paper will present a gyrokinetic theory for magnetized technical plasmas that is based on first principles. The outset is a general kinetic description of the electron component which incorporates the scaling mentioned above. A multi-time scale formalism is employed which results in four separate levels. Explicitly solving the first three levels and substituting into the last gives the desired self-consistent transport theory on the slowest time scale. The approach shares features both with “bounced averaged gyrokinetics”2 (of fusion theory) and with “nonlocal theory”3 (of low temperature plasma physics).

Parametric studyoflow frequency rotating structures in high power impulse magnetron sputtering (HIPIMS) discharges

Summary form only given. HiPIMS discharges are able to produce a high density plasma (peak electron density 1018 - 1020 m-3) by applying large voltages to a target. Electrons are effectively magnetized by a strong magnetic field (100 mT), and exhibit an E x B drift in the azimuthal direction in the plane of the target. Magnetically confined highly ionized plasmas are known to show a vast range of instabilities ranging from MHz (i.e. modified two stream instability1) to 10 - 100 kHz range 2,3,4. We focus here on the low frequency structure rotating in the same direction, at about 10% of the speed of the E x B electron drift. Understanding of the formation and behavior of these spoke like structures is fundamental in determining the overall plasma density, discharge current and cross field transport. In an Argon/Aluminum discharge it has been observed that only a single structure rotating with constant angular speed remains when the power density reaches 4 kW/cm2 5. We theorize that this configuration is one of ”periodic equilibrium”, and we apply a kinetic global model approach to the structure region and evolve the system through a pseudo-transit 6. The species densities ne(t), nAr(t) and nAl(t) reach a steady state after only a few periods T = 1/Ω. We present here an improved chemistry model, and an extensive sensitivity analysis of the resulting steady state on the initial conditions of the simulation.

Phenomenological description of a symmetry breaking rotating instability in HPPMS discharges

Summary form only given. High Power Pulsed Magnetron Sputtering (HPPMS) is a recently developed Ionized Physical Vapor Deposition (IPVD) technique. A bias voltage is applied to the target for a few hundred microseconds with a frequency of a few hundreds of Hertz, delivering several kW cm−2 of power to the target. This results in the production of an ultra dense plasma with a high ionization degree, showing some peculiar behaviors.

Influence of non-confined electrons at the boundaries in a HPPMS discharge - limit to gyro-average validity

Summary form only given. High Power Pulsed Magnetron Sputtering (HPPMS) is a novel Ionized Physical Vapor Deposition (IPVD) technique, able to achieve an ultra dense plasma with a high ionization degree of sputtered atoms.

Full‐wave modeling of the O‐X mode conversion in the Pegasus Toroidal Experiment

The potential of an EBW heating scheme via the O—X—B mode conversion scenarios has been investigated for the PEGASUS toroidal experiment. With the 2D full‐wave code IPF‐FDMC the O—X conversion has been modeled as a function of the poloidal and toroidal injection angles for a microwave frequency of 2.45 GHz. Based on preliminary Langmuir probe measurements in the mode conversion layer, different density profiles have been also included in the simulations. A maximum mode conversion efficiency of approximately 80 % has been found, making EBW heating an attractive heating scheme for PEGASUS.