bi-Maxwellian Electron Energy Distribution Research Articles

Plasma properties in the vicinity of the last closed flux surface in hydrogen and helium fusion plasma discharges

The origin of the bi-Maxwellian electron energy distribution function (EEDF) observed in the scrape-off layer (SOL) of tokamak plasmas by means of Langmuir probes is still under discussion. It has been assumed that the ionization of hydrogen and deuterium neutrals by thermal electrons penetrating the SOL from the bulk plasma is the main reason for the appearance of a second Maxwellian. To validate this assumption, radial measurements of the electron temperatures and densities, or the plasma properties in helium plasmas in the GOLEM tokamak and the TJ-II stellarator were performed. The radial profiles of the low-temperature electron group densities follow the trend of the calculated radial profiles of the electron sources arising from the ionization of neutrals in both deuterium and helium plasmas in TJ-II. The difference in the radial location where the bi-Maxwellian EEDF appears can be explained by the difference in the rate coefficients for ionization of deuterium and helium. The results of probe measurements in GOLEM and the WEST tokamak divertor, at one radial location in the SOL, are compatible with the hypothesis concerning the ionization of neutral atoms and the type of the EEDF.

Influence of electron energy distribution on fluid models of a low-pressure inductively coupled plasma discharge

The aim of the present paper is to examine the influence of assumption on the electron energy distribution function on the relation between the plasma potential and the electron temperature for both electropositive (argon) and electronegative (chlorine) plasmas. A one-dimensional fluid model is used for simplicity although similar results were obtained using a self-consistent two-dimensional fluid model coupled with the Maxwell's equations for inductively coupled plasmas. We find that for electropositive plasma only a bi-Maxwellian electron energy distribution function provides reasonable results compared to measurements in low-pressure inductively coupled plasmas, namely, the increasing plasma potential for increasing electron temperature. For electronegative plasma, the plasma potential is an increasing function of the electron temperature for all electron distributions considered in the model. However, the scaling factors do not agree with the conventional plasma theory. We explain these results by the deviation of electrons from a Boltzmann distribution, which is due to non-equilibrium and non-local nature of plasma at the low-pressure conditions.

Experimental observations of local plasma parameters in the COMPASS divertor in NBI-assisted L-mode plasmas

This paper presents an experimental characterization of the local plasma parameters in the COMPASS open divertor in deuterium, L-mode plasmas by means of Langmuir probes during neutral beam injection (NBI) heating. The effect of NBI heating of the core plasma on the local divertor plasma parameters is investigated under different plasma configurations and different directions of the magnetic field and plasma current for different line-averaged electron densities. At low line-averaged densities below 6 × 1019 m-3, a low NBI heating power level does not lead to any significant changes in the plasma parameters in the divertor region. It is also found that for a reversed magnetic field the influence of NBI in the divertor is stronger at higher line-averaged electron density and plasma current. In the divertor, the impact of the NBI heating is more pronounced at high delivered powers (above P NBI = 320 kW) and line-averaged densities (above 7 × 1019 m-3). The electron temperature and the floating potential at the outer target increases respectively with 10–50% and 100%, while the plasma potential in the inner divertor increases twofold. At a higher line-averaged density, the NBI heating affects the edge plasma, namely, the electron temperature in the midplane scrape-off layer and the heating moves toward the divertor. Thus, a twice as high electron temperature is observed in the divertor and a bi-Maxwellian electron energy distribution function arises.

On the electron energy distribution function in the high power impulse magnetron sputtering discharge

We apply the ionization region model (IRM) and the Orsay Boltzmann equation for electrons coupled with ionization and excited states kinetics (OBELIX) model to study the electron kinetics of a high power impulse magnetron sputtering (HiPIMS) discharge. In the IRM the bulk (cold) electrons are assumed to exhibit a Maxwellian energy distribution and the secondary (hot) electrons, emitted from the target surface upon ion bombardment, are treated as a high energy tail, while in the OBELIX the electron energy distribution is calculated self-consistently using an isotropic Boltzmann equation. The two models are merged in the sense that the output from the IRM is used as an input for OBELIX. The temporal evolutions of the particle densities are found to agree very well between the two models. Furthermore, a very good agreement is demonstrated between the bi-Maxwellian electron energy distribution assumed by the IRM and the electron energy distribution calculated by the OBELIX model. It can therefore be concluded that assuming a bi-Maxwellian electron energy distribution, constituting a cold bulk electron group and a hot secondary electron group, is a good approximation for modeling the HiPIMS discharge.

A simple method for theoretical determination of the radius- and time-dependent electron temperatures in nanosecond pulsed longitudinal discharges in helium and neon assuming a bi-Maxwellian electron energy distribution function

Assuming a bi-Maxwellian electron energy distribution function, the temporal and radial distribution of the electron temperature is determined in nanosecond pulsed longitudinal discharges used for excitation of two prospective high-power gas-discharge lasers, namely, a deep ultraviolet Cu+ Ne-H2-CuBr laser and a He-Sr+ recombination laser. For this purpose, the parameters of the set of nonstationary heat-conduction equations for the two groups of electrons, namely, the electrical power density and the specific heat capacity, are determined for each group. A 2D(r,t) numerical model is also developed in order to solve the set of the equations.

Plasma potential and electron temperature evaluated by ball-pen and Langmuir probes in the COMPASS tokamak

The radial distributions of the main plasma parameters in the scrape-off-layer of the COMPASS tokamak are measured during L-mode and H-mode regimes by using both Langmuir and ball-pen probes mounted on a horizontal reciprocating manipulator. The radial profile of the plasma potential derived previously from Langmuir probes data by using the first derivative probe technique is compared with data derived using ball-pen probes. A good agreement can be seen between the data acquired by the two techniques during the L-mode discharge and during the H-mode regime within the inter-ELM periods. In contrast with the first derivative probe technique, the ball-pen probe technique does not require a swept voltage and, therefore, the temporal resolution is only limited by the data acquisition system. In the electron temperature evaluation, in the far scrape-off layer and in the limiter shadow, where the electron energy distribution is Maxwellian, the results from both techniques match well. In the vicinity of the last closed flux surface, where the electron energy distribution function is bi-Maxwellian, the ball-pen probe technique results are in agreement with the high-temperature components of the electron distribution only. We also discuss the application of relatively large Langmuir probes placed in parallel and perpendicularly to the magnetic field lines to studying the main plasma parameters. The results obtained by the two types of the large probes agree well. They are compared with Thomson scattering data for electron temperatures and densities. The results for the electron densities are compared also with the results from ASTRA code calculation of the electron source due to the ionization of the neutrals by fast electrons and the origin of the bi-Maxwellian electron energy distribution function is briefly discussed.

The role of plasma chemistry on functional silicon nitride film properties deposited at low-temperature by mixing two frequency powers using PECVD.

Control of the plasma densities and energies of the principal plasma species is crucial to induce modification of the plasma reactivity, chemistry, and film properties. This work presents a systematic and integrated approach to the low-temperature deposition of hydrogenated amorphous silicon nitride films looking into optimization and control of the plasma processes. Radiofrequency (RF) and ultrahigh frequency (UHF) power are combined to enhance significantly the nitrogen plasma and atomic-radical density to enforce their effect on film properties. This study presents an extensive investigation of the influence of combining radiofrequency (RF) and ultrahigh frequency (UHF) power as a power ratio (PR = RF : UHF), ranging from 4 : 0 to 0 : 4, on the compositional, structural, and optical properties of the synthesized films. The data reveal that DF power with a characteristic bi-Maxwellian electron energy distribution function (EEDF) is effectively useful for enhancing the ionization and dissociation of neutrals, which in turn helps in enabling high rate deposition with better film properties than that of SF operations. Utilizing DF PECVD, a wide-bandgap of ∼3.5 eV with strong photoluminescence features can be achieved only by using a high-density plasma and high nitrogen atom density at room temperature. The present work also proposes the suitability of the DF PECVD approach for industrial applications.

Time-resolved curling-probe measurements of electron density in high frequency pulsed DC discharges

A plasma-induced shift in the resonance frequency of a curling probe measured by using a network analyzer (NWA) yields the electron density. This technique was applied here for measuring time-varying electron density in pulsed DC glow discharges. Using the NWA in an on-sweep synchronization mode with the discharge pulse allows measuring at pulse frequencies below 0.5 kHz. For higher pulse frequencies, an on-point mode was introduced which enabled time-resolved measurements of electron density at pulse frequencies reaching 25 kHz, with the minimal time interval of 2 µs, typically for nitrogen discharge at 10 Pa. In the afterglow regime, the decay time constant of electron density was measured for nitrogen and argon discharges at 40 Pa. In the case of argon, the electron density was observed to decrease in three steps. This characteristic behavior was tentatively attributed to a bi-Maxwellian electron energy distribution and Ramsauer effect, supported by Langmuir probe measurements.

Bi-Maxwellian electron energy distribution function in the vicinity of the last closed flux surface in fusion plasma

The first-derivative probe technique was applied to derive data for plasma parameters from the IV Langmuir probe characteristics measured in the plasma boundary region in the COMPASS tokamak and in the TJ-II stellarator. It is shown that in the COMPASS tokamak in the vicinity of the last closed flux surface (LCFS) the electron energy distribution function (EEDF) is bi-Maxwellian with the low-temperature electron fraction predominating over the higher temperature one, whereas in the far scrape-off layer (SOL) the EEDF is Maxwellian. In the TJ-II stellarator during NBI heated plasma the EEDF in the confined plasma and close to the LCFS is bi-Maxwellian while in the far SOL the EEDF is Maxwellian. In contrast, during the ECR heating phase of the discharge both in the confined plasma and in the SOL the EEDF is bi-Maxwellian. The mechanism for the appearance of a bi-Maxwellian EEDF in the vicinity of the LCFS is discussed. The comparison of the results from probe measurements with ASTRA package and EIRENE code calculations suggests that the main reason of the appearance of a bi-Maxwellian EEDF in the vicinity of the LCFS is the ionization of the neutral atoms. Results for the electron temperatures and densities obtained by the first-derivative probe technique in the COMPASS tokamak and in the TJ-II stellarator were used to evaluate the radial distribution of the parallel power flux density. It is shown that in the SOL the radial distribution of the parallel power flux density is a double exponential. It is pointed out that in the calculations of the parallel power flux density at the LCFS the energy losses from ionization mechanisms must be taken into account.

Global model analysis of negative ion generation in low-pressure inductively coupled hydrogen plasmas with bi-Maxwellian electron energy distributions

A global model was developed to investigate the densities of negative ions and the other species in a low-pressure inductively coupled hydrogen plasma with a bi-Maxwellian electron energy distribution. Compared to a Maxwellian plasma, bi-Maxwellian plasmas have higher populations of low-energy electrons and highly vibrationally excited hydrogen molecules that are generated efficiently by high-energy electrons. This leads to a higher reaction rate of the dissociative electron attachment responsible for negative ion production. The model indicated that the bi-Maxwellian electron energy distribution at low pressures is favorable for the creation of negative ions. In addition, the electron temperature, electron density, and negative ion density calculated using the model were compared with the experimental data. In the low-pressure regime, the model results of the bi-Maxwellian electron energy distributions agreed well quantitatively with the experimental measurements, unlike those of the assumed Maxwellian electron energy distributions that had discrepancies.

Observation of inverse hysteresis in the E to H mode transitions in inductively coupled plasmas

An inverse hysteresis is observed during the E mode to H mode transition in low pressure argon inductively coupled plasmas. The transition is accompanied by an evolution of electron energy distribution from the bi-Maxwellian to the Maxwellian distribution. The mechanism of this inversion is not clear. However, we think that the bi-Maxwellian electron energy distribution in E mode, where the proportion of high energy electron is much higher than the Maxwellian distribution, would be one of the reasons for the observed inverse hysteresis. As the gas pressure increases, the inverse hysteresis disappears and the E to H mode transition follows the scenario of usual hysteresis.

A planar-type surface-wave plasma source with a subwavelength diffraction grating inclusion for large-area plasma applications

The electromagnetic wave through the subwavelength diffraction grating can be largely absorbed by surface-wave plasmas (SWPs). A SWP source is built with two slot-array antennas element. Due to the dissipation of surface waves in overdense plasmas, this source can provide remarkable discharge efficiency of 4.4 cm2/W experimentally and 96% of incident power numerically. When the applied power as low as 200 W is supplied to the SWP source, a homogeneous plasma with the uniform area up to 14×36 cm2 and the plasma density up to 1.04×1018 m−3 is generated under the quartz slab. By varying the incident power and gas pressure, the parameter of plasmas can be easily controlled without density jumping. Moreover, the characters of bi-Maxwellian electron energy distribution prove that our SWP source yield plasmas by surface heating actually. These excellent performances make the proposed source meet the requirements in large-area plasma processing and also give its advices for plasmas heating in next meter-size SWP sources.

A Langmuir probe system for high power RF-driven negative ion sources on high potential

A fully automated Langmuir probe system capable of operating simultaneously with beam extraction has been developed and commissioned for the negative hydrogen ion source testbeds at IPP Garching. It allows the measurement of temporal and spatial distributions of the plasma parameters within a single plasma pulse (<5 s). This system can operate even in the presence of multi-harmonic RF interference due to a novel transformer-based RF compensation system. Analysis methods of the probe data are described in the paper along with a discussion of errors. Measurements of the plasma parameters for RF powers (30–80 kW) and source pressures (0.3–0.8 Pa) both in plasma generation region and near the plasma grid have been carried out. The plasma generation region has both a high density (>1018 m−3) and hot (Te > 10 eV) plasma with bi-Maxwellian electron energy distribution at low pressures. The plasma found near the plasma grid is very different being of low density (⩽1017 m−3) and very cold (Te < 2 eV). This plasma is also strongly influenced by the presence of caesium, the potential of the plasma grid, and if an ion beam is extracted from the source. Caesium strongly reduces the plasma potential of the source and enhances the negative ion density near the plasma grid. Extracting an ion beam is observed to reduce the electron density and increase the potential near the plasma grid. Applying a potential greater than the plasma potential to the plasma grid is found to significantly decrease the electron density near the plasma grid.

Control of Energetic Electron Component in a Magnetically Confined Diffusion Ar Plasma

The possibility of variation of the fraction of the energetic electron component in a magnetically confined diffusion argon plasma with a bi-Maxwellian electron energy distribution function (EEDF) created in the target part of a double plasma device by changing the anode voltage is demonstrated. The growth of fraction of the energetic electrons with a decrease of the anode voltage while the separation grid potential is kept constant is observed. An analysis of the loss rates of cold and hot electrons is given. Mechanisms of the formation of the bi-Maxwellian EEDF in the magnetically confined diffusion plasma are discussed.

プラズマ応用技術におけるシミュレーション研究 3. Kinetic Computer Modeling of Microwave Surface-Wave Plasma Production

Kinetic computer plasma modeling occupies an intermediate position between the time consuming rigorous particle dynamic simulation and the fast but rather rough cold- or warm-plasma fluid models. The present paper reviews the kinetic modeling of microwave surface-wave discharges with accent on recent kinetic self-consistent models, where the external input parameters are reduced to the necessary minimum (frequency and intensity of the applied microwave field and pressure and geometry of the discharge vessel). The presentation is limited to low pressures, so that Boltzman equation is solved in non-local approximation and collisional electron heating is neglected. The numerical results reproduce correctly the bi-Maxwellian electron energy distribution functions observed experimentally.

Measurement of the electron energy distribution function in an argon radio-frequency discharge in the γ mode

The α–γ transition in an argon radio-frequency discharge has been measured using Langmuir probes and a current–voltage monitor. At two pressures, bi-Maxwellian electron energy distribution functions were measured in the γ mode. Increasing the gas pressure results in a decrease in the high-energy component of the electron energy distribution function. A transition region in the current–voltage characteristic is also observed.

Tonks-Langmuir problem for a bi-Maxwellian plasma

An analytical solution of the Tonks-Langmuir (TL) problem with a bi-Maxwellian electron energy distribution function (EEDF) is obtained for a plasma slab. The solution shows that the ambipolar potential, the plasma density distribution, and the ion flux to the wall are mainly governed by the cold electrons, while the ionization rate and voltage drop across the wall sheath are governed by the hot electrons. The ionization rate by direct electron impact is found to be spatially rather uniform, contrary to the T-L solution where it is proportional to the plasma density distribution. The temperature of hot electrons defined by the ionization balance is found to be close to that of the T-L solution for a mono-Maxwellian EEDF, and is in reasonable agreement with experiments carried out in a low pressure capacitance RF discharge. The energy balance for cold electrons in this discharge shows that their heating by hot electrons via Coulomb interaction is equalized by the cold electrons' escape to the RF electrodes during collapse of the RF sheath. >

A self-consistent model for the discharge kinetics in a high-repetition-rate copper-vapor laser

A self-consistent computer model has been developed to simulate the discharge kinetics and lasing characteristics of a copper-vapor laser (CVL) for typical operating conditions. Using a detailed rate-equation analysis, the model calculates the spatio-temporal evolution of the population densities of 11 atomic and ionic copper levels, four neon levels, and includes 70 collisional and radiative processes, in addition to radial particle transport. The long-term evolution of the plasma is taken into account by integrating the set of coupled rate equations describing the discharge and electrical circuit through multiple excitation-afterglow cycles. A time-dependent two-electron group model, based on a bi-Maxwellian electron energy distribution function, has been used to evaluate the energy partitioning between the copper vapor and the neon-buffer gas. The behavior of the plasma in the cooler end regions of the discharge tube near the electrodes, where the plasma kinetics are dominated by the buffer gas, has also been modeled. Results from the model have been compared to experimental data for a narrow-bore (/spl phi/=1.8 cm) CVL operating under optimum conditions. Close agreement is obtained between the results from the model and experimental data when comparing electrical I-V characteristics of the discharge tube and circuit, and spatio-temporal evolution of the population densities of the laser levels and other excited Cu I and Ne I states, and lasing characteristics. During the period of lasing action, the populations of the laser levels are perturbed by 10-20 percent due to stimulated emission.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Capacitive RF discharges modelled by particle-in-cell Monte Carlo simulation. II. Comparisons with laboratory measurements of electron energy distribution functions

For pt.I see ibid., vol.2, no.4, p.261-72 (1993). Bi-Maxwellian electron energy distribution functions (EEDFS) have been measured experimentally in argon RF discharges at 13.56 MHz by Godyak et al. (Plasma Sources Sci. Technol. 1 36 (1992)). The observed EEDFS at low pressures had very-low-energy and high-energy components. We show particle-in-cell Monte-Carlo (PIC-MCC) simulations, which produce the same EEDFS. Excellent agreement is obtained between the effective low and high electron temperatures in simulations and those measured in the laboratory. Our simulations, with the same physical parameters as in the laboratory, obtain the same transition point in the electron heating mode, from stochastically dominated heating at low pressures to ohmically dominated heating at high pressures.

A time-dependent two electron group model for a discharge excited He-Sr recombination laser

A time-dependent two electron group model 2EGM, based on a bi-Maxwellian electron energy distribution function (EEDF), has been developed to simulate the discharge kinetics in a high-current, high-repetition frequency, pulsed He-Sr recombination laser. A comparison is made between the results predicted by 2EGM and 1EGM (Maxwellian) simulations and experimental data corresponding to typical operating conditions of the laser. Results from the 2EGM indicate that during the current pulse, the high-energy tail region of the EEDF is severely depleted due to both inelastic collisions between electrons and ground state helium atoms and incomplete thermalization via Coulomb collisions. This leads to a highly non-Maxwellian EEDF, a feature which cannot be accommodated in the 1EGM simulation. In addition, the He*(23S), Sr, and Sr+ population densities predicted by the 2EGM are shown to be in close agreement with the experimental data, whereas the 1EGM predicts a partitioning of energy between helium and strontium states which is inconsistent with the observed population densities.