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Developing large-area inductively coupled plasma sources requires deviation from the standard coil concepts and the development of advanced antenna designs. First steps in this direction employ periodic array structures. A recent example is the Inductively Coupled Array (INCA) discharge, where use is made of the collisionless electron heating in the electric field of a periodic array of vortex fields. Naturally, the efficiency of such discharges depends on the how well the experimental array realizes the theoretically prescribed field design. In this work two diagnostic methods are employed to measure the field structure of the INCA discharge. Ex situ B-dot probe measurements are compared to in situ radio-frequency modulation spectroscopy (RFMOS) and good agreement be tween their results is observed. Both diagnostics show systematic deviations of the experimentally generated field structure from the one employed in the theoretical description of the INCA discharge. The subtleties in applying both diagnostic methods together with an analysis of the possible consequences of the non-ideal electric field configuration and ways to improve it are discussed.

We report first ns-resolved absorption measurements of the ro-vibrational excitation of CO$_2$. The high temporal resolution of 8 ns is made possible by a fast detector (rise-time 5 ns), sensitive in the mid-infrared region. The resolution is achieved by a slow temperature scan of a quantum cascade laser and a segmented data capturing scheme. A repetitively pulsed ns discharge in 10% CO$_2$ + 90% He at 150 mbar and a repetition rate of 2 kHz is investigated. The evolution of the population densities of the different vibration modes as well as the associated vibrational and rotational temperatures within the discharge pulse of only 150 ns length are simultaneously determined and provide valuable insight into the CO$_2$ excitation dynamics. A preferential excitation in the asymmetric vibrational mode is observed in the discharge phase shortly after the breakdown., Comment: 6 pages with 7 figures

The understanding of the ro-vibrational dynamics in molecular (near)-atmospheric pressure plasmas is essential to investigate the influence of vibrational excited molecules on the discharge properties. In a companion paper, results of ro-vibrational coherent anti-Stokes Raman scattering (CARS) measurements for a nanosecond pulsed plasma jet consisting of two conducting molybdenum electrodes with a gap of 1 mm in nitrogen at 200 mbar are presented. Here, those results are discussed and compared to theoretical predictions based on rate coefficients for the relevant processes found in the literature. It is found, that during the discharge the measured vibrational excitation agrees well with predictions obtained from the rates for resonant electron collisions calculated by Laporta et al [PlasmaSources Science and Technology 23 065002 (2014)]. The predictions are based on the electric field during the discharge, measured by EFISH and the electron density which is deduced from the field and mobility data calculated with Bolsig+. In the afterglow a simple kinetic simulation for the vibrational subsystem of nitrogen is performed and it is found, that the populations of vibrational excited states develop according to vibrational-vibrational transfer on timescales of a few $\mu$s, while the development on timescales of some hundred $\mu$s is determined by the losses at the walls. No significant influence of electronically excited states on the populations of the vibrational states visible in the CARS measurements ($v \lesssim 7$) was observed.

CO$_2$ dissociation stimulated by vibrational excitation in non-equilibrium discharges has drawn lots of attention. Ns-discharges are known for their highly non-equilibrium conditions. It is therefore of interest to investigate the CO$_2$ excitation in such discharges. In this paper, we demonstrate the ability for monitoring the time evolution of CO$_2$ ro-vibrational excitation with a well-selected wavelength window around 2289.0 cm$^{-1}$ and a single CW quantum cascade laser (QCL) with both high accuracy and temporal resolution. The rotational and vibrational temperatures for both the symmetric and the asymmetric modes of CO$_2$ in the afterglow of CO$_2$ + He ns-discharge were measured with a temporal resolution of 1.5 $\mu$s. The non-thermal feature and the preferential excitation of the asymmetric stretch mode of CO$_2$ were experimentally observed, with a peak temperature of $T_{v3, max}$ = 966 $\pm$ 1.5 K, $T_{v12, max}$ = 438.4 $\pm$ 1.2 K and $T_{rot}$ = 334.6 $\pm$ 0.6 K reached at 3 $\mu$s after the nanosecond pulse. In the following relaxation process, an exponential decay with a time constant of 69 $\mu$s was observed for the asymmetric stretch (001) state, consistent with the dominant deexcitation mechanism due to VT transfer with He and deexcitation on the wall. Furthermore, a synchronous oscillation of the gas temperature and the total pressure was also observed and can be explained by a two-line thermometry and adiabatic process. The period of the oscillation and its dependence on the gas components is consistent with a standing acoustic wave excited by the ns-discharge.

The non-equilibrium ro-vibrational distribution functions of molecules in a plasma can heavily influence the discharge operation and the plasma-chemistry. A convenient method for measuring the distribution function is by means of coherent anti-Stokes Raman scattering (CARS). CARS spectra are measured in a ns-pulsed plasma between two parallel, 1 mm spaced molybdenum electrodes in nitrogen at 200 mbar with pulse durations of 200 ns / 250 ns and a repetition rate of 1 kHz. The CARS spectra are analyzed by a fitting routine to extract information about the vibrational excitation of the nitrogen molecules in the plasma. It is found that during the discharge the vibrational distribution for $v \lesssim 7$ can be described by a vibrational two-temperature distribution function. Additionally, the electric field is measured by the E-FISH method during the discharge pulse. It is found to be constant in time after the initial ionization wave with values close to 81 Td for the investigated conditions. During the afterglow between two discharge pulses a more general fitting approach is used to obtain the population differences of two neighboring vibrational states. This allows to capture the more complex vibrational dynamics in that time period. The measurement results are discussed in more detail and compared to simple models in a companion paper.

Under low-collisionality conditions the isotropic part of the electron velocity distribution function in a plasma becomes non-local and the electrons can be described by a single global distribution function . This is also the regime required for non-local collisonless (stochastic) heating in oscillating and spatially inhomogeneous electric fields. Solution of the Boltzmann equation under these conditions requires usually computationally involving multi-dimensional PIC/MC simulations. The necessity of multi-dimensional simulation arises mainly from the complicated time and space dependence of the collisionless electron heating process. Here it is shown that a time, volume, und solid angle averaged Fokker-Planck operator for the interaction of electrons with an external field can replace the local Ohmic heating operator resulting from a two-term approximation of the Boltzmann equation. This allows consistent treatment of collisional as well as collisonless heating. This operator combined with the dissipative operators for interaction with neutrals, as resulting from the two-term approximation, plus an additional operator for surface losses provide altogether a kinetic description for the determination of the global static and isotropic distribution function of the system. The new operators are relatively easy to integrate in classical local Boltzmann solvers and allow for a fast calculation of the distribution function. As an example, an operator describing non-local collisionless as well as collisional heating in inductively coupled plasmas (ICPs) is derived. The resulting distribution function can then be used to calculate rates and moments in a fluid model of the plasma, similarly to the common practice in the local and highly collisional case. A certain limitation of the above concept is the necessity of using pre-defined field structures., Comment: 41 pages, 5 figures, 46 references

Recently a novel concept for collisionless electron heating and plasma generation at low pressures was proposed theoretically (U Czarnetzki and Kh Tarnev, Phys. Plasmas 21 (2014) 123508). It is based on periodically structured vortex fields which produce certain electron resonances in velocity space. A more detailed investigation of the underlying theory is presented in a companion paper (U Czarnetzki, submitted to PSST (2018), arXiv:1806.00505). Here, the new concept is experimentally realized for the first time by the INCA (INductively Coupled Array) discharge. The periodic vortex fields are produced by an array of small planar coils. It is shown that the array can be scaled up to arbitrary dimensions while keeping its electrical characteristics. Stable operation at pressures around and below 1 Pa is demonstrated. The power coupling efficiency is characterized and an increase in the efficiency is observed with decreasing pressure. The spatial homogeneity of the discharge is investigated and the behaviour of the plasma parameters with power and pressure are presented. Linear scaling of the plasma density with power and pressure, typical for conventional inductive discharges, is observed. Most notably, the plasma potential and the corresponding mean ion energy show clear evidence for the presence of super energetic electrons, attributed to stochastic heating. In the stochastic heating mode, the electron distribution function becomes approximately Maxwellian but with increasing pressure it turns to the characteristic local distribution function known from classical inductive discharges. Large area processing or thrusters are possible applications for this new plasma source., Comment: There is an accompanying theoretical paper by Czarnetztki (see abstract)

A novel electron heating mechanism based on periodically structured vortex fields induced in a plane was first proposed in 2014 [U. Czarnetzki and Kh. Tarnev, Physics of Plasmas 21, 123508 (2014)]. This theoretical concept has now been realized in an experiment which confirms efficient collisionless heating in such array structures [Ph. Ahr, T.V. Tsankov, J. Kuhfeld, U. Czarnetzki, submitted to Plasma Sources Science and Technology, arXiv:1806.02043v1 (2018)]. The new concept is called "Inductively Coupled Array": INCA. Here, the physical mechanism behind the collisionless (stochastic) heating is investigated by two analytical models. Firstly, the electron heating rate in an array field structure with an exponential spatial decay of the field in the direction perpendicular to the plane is investigated by stochastically averaging single electron trajectories. The approach is similar to the Lieberman model for the classical stochastic heating in standard inductively coupled plasmas. This analysis shows that classical stochastic heating by thermal motion along the vertical direction makes a negligible contribution. However, there is a strong collisonless non-local heating effect in the plane. In conclusion, heating is non-local in the plane but local in the vertical direction. This insight allows a straightforward solution of the collisionless Boltzmann equation which not only confirms the results of the Lieberman model but provides also explicit expressions for the complex conductivity. Based on the conductivity an effective stochastic collision frequency, the complex damping coefficient and the related field penetration of the field into the plasma is calculated. Finally, elastic collisions with neutral background atoms are included in the model and a condition for dominance of stochastic heating over Ohmic heating is derived., Comment: Updated version with arXiv reference for the experimental paper included, section 2.3 and appendix C have been updated and a minor error corrected

A long-standing debate in the literature about the kinetic form of the Bohm criterion is resolved for plasmas with single positive ion species when transport is dominated by charge exchange collisions. The solution of the Boltzmann equation for the ions gives the exact form free of any divergence and contains an additional term that is not included in the classical result. This term includes collisional and geometric effects and leads to a noticeable correction. Further, the question is addressed whether the space charge argument at the bottom of the Bohm criterion can actually lead to a meaningful definition of the transition point between bulk and sheath. The analysis is supported by a numerical model and experiments, showing excellent agreement throughout. As a novelty in diagnostics, the theoretical results allow from the ion velocity distribution function (IVDF), measured at the wall, a reconstruction of the IVDF and the electric field at any point in the plasma. This property is used to reconstruct non-intrusively also the ion density, flow velocity, mean energy and effective temperature and the electron density and temperature as functions of the spatial coordinate and potential. Finally, the fluid equation for ion momentum balance is verified., Comment: First version

The control of the spatial distribution of micrometer-sized dust particles in capacitively coupled radio frequency discharges is relevant for research and applications. Typically, dust particles in plasmas form a layer located at the sheath edge adjacent to the bottom electrode. Here, a method of manipulating this distribution by the application of a specific excitation waveform, i.e. two consecutive harmonics, is discussed. Tuning the phase angle \theta between the two harmonics allows to adjust the discharge symmetry via the Electrical Asymmetry Effect (EAE). An adiabatic (continuous) phase shift leaves the dust particles at an equilibrium position close to the lower sheath edge. Their levitation can be correlated with the electric field profile. By applying an abrupt phase shift the dust particles are transported between both sheaths through the plasma bulk and partially reside at an equilibium position close to the upper sheath edge. Hence, the potential profile in the bulk region is probed by the dust particles providing indirect information on plasma properties. The respective motion is understood by an analytical model, showing both the limitations and possible ways of optimizing this sheath-to-sheath transport. A classification of the transport depending on the change in the dc self bias is provided, and the pressure dependence is discussed., Comment: 25 pages, 16 figures