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This paper is the first from a set of two companion papers on radio-frequency (RF) discharges. These two papers are in turn part of a larger series on the foundations of plasma and discharge physics. In this part we cover the basics of non-magnetized capacitive and inductive RF discharges, introduce the main concepts related to them and provide reference literature for further reading. In the second part we concentrate on RF discharges in the presence of external magnetic field. These types of RF discharges find a wide range of applications in various industries. Among the most prominent examples are the microelectronics industry for etching and deposition of thin films, the medical and food industry for the application of various coatings and changing the wettability of surfaces, the space industry to power ion-gridded thrusters for satellites, the fusion and elementary particle research for the production of beams of energetic ions or atoms. The paper introduces the basic concepts of RF power deposition and describes in more detail the operating conditions of the plasma reactors. The most important physical phenomena encountered in these discharges are outlined through the use of simplified models. The paper is intended as an entry point for newcomers to the field and provides ample of references (including textbooks) for further reading on the more specific and/or subtle aspects of the operation of these types of RF discharges.

The inductively coupled array (INCA) discharge is a plasma source with a tailored electric field configuration that allows efficient stochastic heating of the electrons. The desired field configuration is realized by an array of small planar coils. This discharge configuration offers dense plasma production at pressures as low as 0.1 Pa and option for upscaling to square meter sizes. The theoretical works, which led to the development of the INCA discharge, propose two different electric field configurations—the ortho- and the para-configuration. The initial experimental work (P. Ahr et al 2018 Plasma Sources Sci. Technol. 27 105010) studied the ortho-configuration. Here we investigate the performance of the alternative configuration, the para-array, and compare it to the ortho-configuration. The results show similar behaviour of the electrical and of the plasma parameters. However, on first sight the ortho-array appears to perform better. The differences disappear when the power actually coupled to the plasma is considered. For both configurations the electron density follows the same linear trend with the power coupled into the plasma and the electron temperature remains nearly constant as prescribed by the energy balance equation of the electrons. The power coupling efficiency for both configurations increases with the plasma density, approaching 60% at a plasma density of 1 × 1017 m−3. No signs of saturation are observed. The variation of the electron distribution functions with the pressure shows that in the para-configuration the transition into the stochastic heating mode occurs at a pressure twice lower than that for the ortho-array in a very good agreement with the theoretical expectations. Based on the comparison of the discharge parameters and its performance, the advantages and the shortcomings of using one or the other configuration are outlined.

Retarding field energy analyzers are commonly used for the experimental determination of the distribution of ions. Measurements require taking the first derivative of the measured current with respect to the retarding voltage, which limits the accuracy of the results. Here a commercial energy analyzer is combined with a lock-in detection and AC modulation technique to obtain ion distribution functions with an improved dynamic range. The technical realization of the method together with its theoretical motivation are presented. The various challenges for implementing the technique and ways to address them are given. The energy resolution of the method is discussed based on the concept of transfer functions, and the influence of the various adjustable parameters (grid bias voltages, frequency and amplitude of the modulation signal) on the obtained results are studied. The application of the method to an inductive discharge readily shows a dynamic range of more than three orders of magnitude. This dynamic range provides information on additional plasma parameters, such as the potential and the plasma density at the sheath edge and in the center of the discharge. Possibilities for further improvement of the technique are discussed.

Tunable diode laser absorption spectroscopy (TDLAS) is a commonly used technique to measure the temperature and density of atoms or molecules in a gas. In this work, we demonstrate that the TDLAS diagnostics could be effectively applied to measure the magnetic field in a low-density weakly magnetized plasma using the Zeeman splitting of the absorption spectrum of lines from noble gases. The laser wavelength is tailored to fit the 1 s 5 &rarr, 2 p 6 transition of atomic Ar with the wavelength &lambda, = 763.51 nm . Two mechanisms of line broadening and splitting are observed: Doppler broadening and Zeeman effect. The latter is especially pronounced by applying polarization-selective observation of the absorption to the TDLAS measurements. By fitting the &sigma, and &pi, components of the absorption spectrum, the line-integrated magnetic field on the order of 30&ndash, 50 mT is determined. The agreement between the measured values and the vacuum field (neglecting the impact of the plasma) calculations on the axis of the PSI-2 is found to be about 15&ndash, 20%.

Electric propulsion devices of using xenon propellant are nowadays widely adopted for the space missions. A collisional-radiative (CR) model of xenon needs to be developed to understand the kinetic mechanisms of the excited and energetic species in these devices and also to support their optical diagnostics. Previously, due to limitations in the fundamental cross section data, Xe CR models focused on the atomic species; the ionic species, which also play important roles for the thrusters, were not studied in detail. In our previous paper, a fully relativistic Dirac B-spline R-matrix method was applied to calculate the relevant cross sections for electron collisions with the Xe+ ion. Based on these data, a comprehensive CR model—with the kinetics of metastable and excited levels of both Xe and Xe+ included—could be built. The calculated density distributions of atomic and ionic levels are examined by optical measurements in Hall thrusters in all of the four typical regions (near-anode-, ionization-, acceleration-, and plume-region). The special kinetic behaviors of the excited species are analyzed, and a set of rate coefficient data used for the Xe CR model is also provided.

Recently a novel concept for collisionless electron heating and plasma generation at low pressures was theoretically proposed (Czarnetzki and Tarnev 2014, Phys. Plasmas 21 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 (Czarnetzki 2018, Plasma Sources Sci. Technol. 27 105011). Here, a new concept is experimentally realized for the first time by the inductively coupled array (INCA) 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 behavior 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 of the presence of superenergetic 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.

In this paper, the novel technique of THz time domain spectroscopy has been applied to obtain time-resolved measurements of the plasma density in the active zone of a HiPIMS discharge with a titanium target. The obtained peak values are in the range of 1012–1013 cm−3 for discharge current densities of 1–4 A cm−2 at 0.5 and 2 Pa argon pressure. The measured densities show good correlation with the discharge current and voltage and the intensity of various atomic and ionic lines. The well known phases of the discharge have been identified and related to the variation of the electron density. The measurement results show that the plasma density remains nearly constant during the runaway/self-sputtering phase. Based on that, it is conjectured that singly charged titanium ions are the dominant ion species during this phase.

Surfaces exposed to a plasma experience a certain pressure that pushes them away from the volume. This effect has been investigated experimentally in a recent article by Thomas Trottenberg, Thomas Richter, and Holger Kersten from Kiel University/Germany [Eur. Phys. J. D 69, 91 (2015)]. The experimental results are impressive and have actually drawn the attention of the community to an interesting question which so far has been largely ignored. In addition to their experimental results the Kiel group proposes also a rough concept in order to explain their findings which provides certainly a basic qualitative understanding of the physical processes involved. However, on a closer inspection the picture developed so far is not entirely satisfying and the problem seems to require a more fundamental approach. This comment shows that the effect of the wall pressure can be described exactly using only analytical methods. The physical situation is analyzed by three different approaches. First, the simple case of only one spatial dimension is presented in detail. Second, the case of spherical symmetry is analyzed by some simplifying assumptions in order to investigate the effect of higher dimensionality. Third, a formal derivation for arbitrary geometry is given. This general result includes the one-dimensional case but does not allow a convenient connection between the pressures at the wall and in the center. Finally, the results are summarized and some conclusions are drawn.

Electron energy distribution functions (EEDF) are obtained from probe measurement data along the axis of the metallic chamber of an inductively driven tandem plasma source. The numerical procedure for calculating the second derivative of the' probe current combines Savitzky-Golay smoothing filter and the three-point differentiator with a varying step. The EEDF is obtained through the Druyvesteyn formula from the calculated second derivative. The shape of the EEDFs in argon gas at low pressures is investigated for the case of a tandem plasma source. Experimental EEDFs are compared with Maxwellian distributions, and deviations in the tail are observed at higher pressures, which are explained in terms of the ratio between the electron-electron collision frequency and the excitation frequency. Axial variations of the slope and of the area below the EEDF curve result in electron temperature and concentration decrease along the axis.

Results from tandem-type probe diagnostics of a plasma source based on an inductive discharge are presented in this study. The driver region is in the classical form of a cylindrically shaped inductive discharge, with a coil positioned over a gas discharge tube, whereas a bigger metal chamber provides volume for plasma expansion. Low pressure argon discharges were studied. The axial profiles of the plasma parameters were measured in the discharge in the metal chamber. The results obtained show that decreasing electron temperature and plasma density with increasing distance from the driver characterizes the behavior of the expanding plasmas. Moreover, two regions with different rates of variation of the plasma parameters complete the plasma expansion volume: a faster drop close to the driver and slow axial changes away from it. The gas pressure and power applied for the discharge maintenance were the external parameters varied.

A paper by El Saghir and Shannon (2012 Plasma Sources Sci. Technol. 21 025003) raises the question about the validity of the widely-used Druyvesteyn formula for obtaining the electron energy distribution function by cylindrical probes. They conclude that there are deviations between the Druyvesteyn formula for cylindrical and for spherical probes. In this comment this conclusion is questioned and the correct expressions are derived. It is shown that no such difference exists when all three velocity components are correctly accounted for. Furthermore, the disturbance to the plasma introduced by the probe is estimated.

The power-off phase of pulsed low-pressure plasmas (the so-called afterglow) in noble gases is a rich field for both fundamental and application oriented research. The physics of these plasmas is complex and involves various processes: Initially, electrons cool rapidly to temperatures close to the gas temperature by evaporative cooling. At sufficiently high plasma densities the low kinetic electron energy strongly enhances three-body recombination into Rydberg states. Finally, subsequent collisional-radiative decay leads to emission of radiation and populates the metastable states of the atoms. The various steps are investigated experimentally and are compared to analytical models. This allows us to follow all steps throughout in a single experiment involving diagnostics of electron density, metastable density, and emission. Excellent agreement with the models is achieved. The mechanisms included are: (i) for electrons, balance between evaporative cooling and Coulomb collisions with ions leading to thermalization; (ii) consistent combination of re-ionization and microfield reduction of the ionization energy in the recombination rate; (iii) adiabatic balance of recombination and collisional and radiative de-excitation; and (iv) radiative population and diffusional and pooling collisional loss of metastable levels. Although the experiment is carried out in argon, the underlying physics is generally applicable for the afterglow of high-density low-pressure discharges in atomic gases.

At low pressures and sufficiently high initial plasma densities (>10 17 m -3 ), the afterglow is governed by three-body recombination. A characteristic for this process is the formation of highly excited states followed by emission of photons and the appearance of spectral lines not present in the power-on phase. Here, this process has been illustrated using a fast streak camera to record the afterglow spectrum.

The study presents results from a 2D model of hydrogen discharges in a tandem type of a plasma source. Analysis of the particle and electron‐energy balance outlines the pattern of the source operation: (i) discharge production in the driver governed by the mechanisms ensuring self‐consistency of hydrogen discharges in regions with rf power deposition, however, here influenced by the fluxes going to the second chamber of the source, and (ii) plasma existence in the expansion volume of the source completely determined by the particle fluxes from the first chamber. The influence of varying applied power and gas pressure is discussed.

In this work a time-dependent collisional-radiative model for recombining plasmas is developed. It tracks the collisional and radiative capture of electrons into highly-excited (Rydberg) states and their consecutive deexcitation through collisions and radiation to the ground or the metastable state. The model allows the calculation of the net recombination rate and the electron energy gain by recombination. It is coupled to the volume-averaged balance equations for the electron density and temperature. The numerical solution of these equations includes a model for the diffusion cooling of the electrons (Celik et al 2012 Phys. Rev. E 85 046407) and a simplified model for the gas cooling. Using as only input the experimentally determined initial values of the electron density and temperature, gas temperature and metastable density, the temporal evolution of all parameters in the afterglow is calculated and compared with measurements. The results reproduce very well the measured quantities (electron density, light emission and metastable density) without the need to invoke adjustable parameters. This gives confidence in the validity of the model that allows it to be used not only to deepen the understanding of afterglow plasmas but also to tailor their properties as required for applications. The analysis of the model results further shows that gas heating and cooling must be explicitly taken into account to reproduce experimental observations. The electron heating by recombination is another process that is important for the good agreement. Both of these effects were largely ignored in previous works on afterglows.

Usually the self-absorption method is adopted to determine the metastable species density in a large number of low-temperature plasmas. In the previous works this method only gives an average metastable density from the line-integrated emission out of the plasma, assuming a uniform density profile. Instead, this work uses an optical probe immersed in the plasma. From the emission spectra measured at different positions, it is possible to obtain the actual metastable density profile. As an example, this technique is used to investigate an inductive Ar plasma at pressures 0.1–1 Pa. The spatial densities of Ar(1s5) and Ar(1s3) (in Paschen's notation) are experimentally determined, being in agreement with those predicted by a self-consistent collisional–radiative model published previously. Based on these results, application of the same method to the other kinds of rare-gas discharges is discussed.

Collisional-radiative models for excited rare-gas atoms in low-temperature plasmas are a widely investigated topic. When these plasmas are optically thick, an ‘escape factor’ is introduced into the models to account for the reabsorption of photons (so-called radiation trapping process). This factor is usually obtained assuming a uniform density profile of the excited species; however, such an assumption is often not satisfied in a bounded plasma. This article reports for the first time a self-consistent collisional-radiative model without using an ad hoc ‘escape factor’ for excited Ar atoms in the 2p states (in Paschen’s notation). Rather, the rate balance equations—i.e. the radiation transfer equations—of the 2p states are numerically solved to yield the actual density profiles. The predictions of this self-consistent model and a model based on the escape factor concept are compared with spatially-resolved emission measurements in a low-pressure inductive Ar plasma. The self-consistent model agrees well with the experiment but the ‘escape factor’ model shows considerable deviations. By the comparative analysis the limitations and shortcomings of the escape factor concept as adopted in a significant number of works are revealed.

The electron density evolution is investigated in a pulsed 60 MHz capacitively coupled low pressure oxygen discharge. A 77 GHz microwave interferometer is used for the time-resolved measurement of the electron density. It is found that, as the duration of the power-off period varies in the range of 0.01–2 ms, the electron density evolution pattern changes significantly. This change is more pronounced at the power-on front, due to the competition between the dissociative-attachment and the ionization processes. A global model is developed to explain the behaviour of electron density evolution under different conditions. The model predicted results agree well with the measured ones. Moreover, it is proposed that, using the measured electron density and a simple global model in the afterglow, the electronegativity and the negative ion lifetime during the power-on phase can be estimated. The value of the electronegativity at various electron densities obtained by this method is found to be consistent with the results measured by the photo-detachment technique in a previous work (Stoffels 1995 Phys. Rev. E 51 2425) under similar discharge conditions.

Discharges in hydrogen are actively investigated not only in connection with materials processing and surface treatment but also as sources of negative hydrogen ions for fusion applications. Current sources for H- production rely on surface reactions enhanced by cesium which can cause substantial problems in operation. Here, we present a novel design concept intended for negative hydrogen ion production. First, results on the discharge performance are shown.

Optical emission spectroscopy is used to investigate capacitively coupled argon and argon–hydrogen–silane plasmas. The argon collisional–radiative model (CRM) used to extract the electron density and temperature from the spectra is presented. The electron energy distribution function, which is an input parameter to the model, is discussed in detail. Its strong variation with pressure is found to significantly influence the results for the (effective) temperature. For the analysis of the spectra the common line-ratio technique is applied. Special attention is paid to the choice of lines and a pair of line-ratios for optimum accuracy is suggested. For the argon gas mixture at high partial pressure of the admixed molecular gases the CRM reduces to a corona-like model, extended by a quenching term. The line-ratio method is found to fail under these conditions due to the strong depopulation of the argon 1s states. As a consequence, individual line intensities have to be used and an absolute calibration is required. An easy calibration method, which relies on the results obtained by the line-ratio method in pure argon, is proposed and applied.

International audience; The self-absorption technique is a simple method to determine the line integrated density of metastable atoms in low-pressure plasmas. In order to employ this technique, it is necessary to make an assumption on the spatial profiles of both the emission intensity and the absorbing species, which usually are unknown and can be highly nonuniform. Taking Ar*(1s5) atoms in a capacitively coupled plasma as an example, the influence of nonuniformity on the measurement of the line integrated density of the absorbing species is investigated analytically. It is proved that when the two spatial profiles are the same, the obtained line integrated density is independent of the functional form of this profile. This is also true if the density of the absorbing species is small (weak absorption), even though the emission profile is different from that of the absorbing species. However, if the density is high (strong absorption), the choice of the profiles has a significant influence on the deduced line integrated density. In the experiment, it is found that in argon-oxygen mixture discharges, in which Ar*(1s5) density is low (weak absorption), the measured densities by self-absorption are in very good agreement with the results obtained from laser absorption. However, in pure argon discharge, when the density is high (strong absorption), the measured densities by self-absorption are significantly smaller than that by laser absorption. Both phenomena have been predicted by the model results. The smaller densities obtained by self-absorption in the pure argon discharge are attributed to the assumption of the same spatial profile used in the model.

A novel plasma source with a magnetic X-point has been developed to probe an alternative for cesium-free negative hydrogen ion production. This study presents first results for the gas and vibrational temperatures in the source at 1 Pa and various RF powers. The temperatures are obtained from analysis of the intensity distribution of the molecular Fulcher-α bands. The gas temperature increases with the RF power, while the vibrational temperature remains constant in the studied range of RF powers. Both quantities show no appreciable spatial dependence. The obtained high values of the vibrational temperatures indicate a high population of the vibrational levels, favourable for the volume negative ion production. A theoretical concept indicates the presence of an optimum value for the vibrational temperature at which the negative hydrogen ion yield by volume processes has a maximum. Coincidently, the measured value is close to this optimum. This indicates that the novel concept can provide certain advantages compared to other sources based on volume production.

The study presents results from measurements of the negative hydrogen ion density b y laser photo-detachment in the expanding plasma region of an inductively-driven tandem plasma source. The results obtained show that the negative ion density and the plasma electronegativity increase with increasing the high-frequency power absorbed in the discharge. An optimum gas pressure range ((1-3) Pa) for negative ion production in the expansion chamber is observed.

A small‐size inductively‐driven tandem (two‐chamber) plasma source, with a magnetic filter for electron cooling located in the second chamber of the source, is studied experimentally. The results are for the concentration of the negative hydrogen ions in the expanding plasma region of the source and its correlation with the axial variation of the electron density and temperature. The position of the magnetic filter has been varied in the measurements. The obtained spatial distribution of the electron temperature and density is in agreement with theoretical predictions for the operation of the filter. The results suggest that although the detected negative ions are locally produced, the locations of the regions of their effective production in the source—positions of the lowest electron temperature and/or of the highest electron density–are nonlocally formed, not only by the plasma expansion through the magnetic filter but also by plasma expansion from the driver into the second bigger‐size chamber of the source.

A 2D fluid‐plasma model of a tandem two‐chamber plasma source operating in hydrogen gas is presented in the study. The configuration of the source is of the type of the inductively‐driven sources developed for neutral beam injection heating of fusion plasmas: the rf power deposition is in the first smaller‐radius chamber of the source and the second bigger‐radius chamber is a volume for plasma expansion from the driver. Plasma maintenance in the source governed by transport processes—charged‐particle and electron‐energy fluxes—is the main conclusion stemming from the results. Moreover, the metal walls of the source and its different dimensions in the longitudinal and transverse directions determine a regime of a rf discharge characterized by a dc current in the source: electrons and ions flowing in different directions determine a solenoidal current in the discharge. This is accompanied by a strong drop of electron temperature, charged‐particle and hydrogen‐atom densities and plasma potential at the trans...