bi-Maxwellian Electron Energy Distribution Function 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.

Instability enhanced thermalization of bi-Maxwellian EEDF in multi-dipole confined hot cathode discharge: an experimental observation

In multi-dipole confined hot cathode discharges, the presence of up to three distinct electron species has been observed by performing linear fitting of the Langmuir probe I–V traces. Nevertheless, the fundamental mechanism underlying the generation of hot electrons remains ambiguous. This work presents experimental observations to comprehensively investigate the impact of the instability-enhanced thermalization effect on the thermal equilibrium of both hot and cold electrons. Temperature composition of the electron energy distribution function (EEDF) was measured via a Langmuir probe, while instabilities was measured using a spectrum analyzer. The experimental results confirm the existence of a transition from a three-temperature Maxwellian EEDF composition to a two-temperature Maxwellian EEDF composition as the population of high-energy electrons increases. Furthermore, the process of thermalization between hot and cold electrons is found to be correlated to the effect of instability-enhanced collisions. The intensity of collisional instability also decreases with increased neutral collisionality.

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.

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.

Effect of the resonant magnetic perturbation on the plasma parameters in COMPASS tokamak’s divertor region

The resonant magnetic perturbation (RMP) has proven to be a useful way to suppress edge-localized modes that under certain conditions can damage the device by the large power fluxes carried from the bulk plasma to the wall. The effect of RMP on the L-mode plasma parameters in the divertor region of the COMPASS tokamak was studied using the array of 39 Langmuir probes embedded into the divertor target. The current-voltage (IV) probe characteristics were processed by the first-derivative probe technique to obtain the plasma potential and the electron energy distribution function (EEDF) which was approximated by a bi-Maxwellian EEDF with a low-energy (4-6 eV) fraction and a high-energy (11-35 eV) one, the both factions having similar electron density. Clear splitting was observed during the RMP pulse in the low-field-side scrape-off-layer profiles of the floating potential Ufl and the ion saturation current density Jsat; these two quantities were obtained both by direct continuous measurement and by evaluation of the IV characteristics of probes with swept bias. The negative peaks of Ufl induced by RMP spatially overlaps with the local minima of Jsat (and ne) rather than with its local maxima which is partly caused by the spatial variation of the plasma potential and partly by the changed shape of the EEDF. The effective temperature of the whole EEDF is not correlated with the negative peaks of Ufl, and the profile of the parallel power flux density shows secondary maxima due to RMP which mimic those of Jsat.

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.

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.

Experimental observation of the plasma potential with the screening temperature

An experimental investigation of the Boltzmann relation in the plasma bulk region and the presheath region was performed at low pressure inductively coupled plasma with bi-Maxwellian distribution. The spatial profiles of the electron energy distribution function (EEDF) were measured from the discharge center to the plasma boundary with an ion mean free path scale. The screening temperature was derived from the Einstein relation and the bi-Maxwellian EEDFs, and it has the same expression as the electron temperature in the ion directed velocity to the sheath edge in plasmas with the bi-Maxwellian EEDFs. Radial variations of the ambipolar potential and the presheath potential were calculated with the screening temperature and compared with the obtained value from the spatially measured EEDFs. It was shown that the ambipolar potential and the presheath potential are governed by the screening temperature.

The New Langmuir Probe Analysis Algorithm Based on Wavelet Transforms to Obtain Electron Energy Distribution Function of Bi-Maxwellian Plasma

A new algorithm to analyze digitized Langmuir probe (LP) data was developed with wavelet transforms to provide the electron energy distribution function (EEDF) for bi-Maxwellian plasmas. Because most algorithms to analyze probe data have been developed with the Druyvesteyn formula, which is based on the second derivative of the current with respect to the probe voltage, the accuracy of the analysis is very sensitive to the noise level during the acquisition of the data’s derivative. Especially, the number of hot electrons in the bi-Maxwellian plasma is small enough to compare the noise level, and the noise-filtering method is the kernel in the development of the algorithm to analyze the bi-Maxwellian EEDF. Here, a bi-orthogonal wavelet and continuous wavelet transforms are chosen for the de-noising and the dierentiation processes, respectively. This provides the filtered data with minimum loss of important information. Artificial LP data sets composed of electrons were generated with various bulk and hot temperatures, and the developed algorithm was evaluated for various white noise levels. For the case of noise levels 10 times ion saturation current, the plasma parameters, such as the population of hot electrons and the temperatures of hot and bulk electrons, were accurately analyzed with only a few percent deviations from the input.

Experimental investigation of plasma dynamics in dc and short-pulse magnetron discharges

The spatiotemporal evolution of the electron energy distribution function (EEDF) and of plasma parameters such as the electron density, the electron temperature and the plasma and floating potentials has been investigated using spatially and temporally resolved single Langmuir probe measurements in dc and mid-frequency, short-pulse magnetron discharges with a repetition frequency of 10 kHz and a duty cycle of 10%. In the pulsed discharge of the short duty cycle, a peak electron temperature higher than 10 eV was observed near the cathode fall region during the early phase of the pulse-on, which is about three times higher than the steady-state value of the electron temperature in the dc discharge. The temporal evolution of the measured EEDFs showed the initial efficient electron heating during the early phase of the pulse-on and the subsequent relaxation of electron energy by the inelastic collisions and the diffusive loss. The high-energy electrons generated during the pulse-on phase diffused the downstream region toward the grounded substrate, resulting in a bi-Maxwellian EEDF consisting of the background low-energy electrons and the high-energy electrons. The results of the spatially and temporally resolved probe measurements will be presented and the enhanced efficiency of the electron heating in the short-pulse discharge will be explained on the basis of the global model of a pulsed discharge.

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.

Heating-mode transition in the capacitive mode of inductively coupled plasmas

The evolution of the electron energy distribution function (EEDF) against pressure is investigated in the capacitive mode of inductively coupled plasma (ICP). A significant change in the EEDFs is observed: a bi-Maxwellian EEDF at low pressure (⩽10 mTorr) evolves into a Druyvestein-like EEDF at high pressure (⩾50 mTorr) in the capacitive mode (low-density mode) while the EEDFs in the inductive mode (high-density mode) does not evolve like in the capacitive mode due to high electron–electron collisions. This EEDF transition in the capacitive mode of ICP is similar to that in the capacitive coupled plasma (CCP) reported in literature [V. A. Godyak and R. B. Piejak, Phys. Rev. Lett. 65, 996(1990)] as pressure increases. This observation directly shows that the electron heating mechanism of the capacitive mode in the ICP is the same as that in the CCP, as expected.

Dependence of Fluorocarbon Plasma Chemistry on the Electron Energy Distribution Function

Recent diagnostics of high-density plasmas suggest a difference in the electron energy distribution function (EEDF) between a surface wave plasma and an inductively coupled plasma, which may be a main reason for the difference between the radical compositions of the two types of fluorocarbon plasmas at the same electron density. In order to account for the experimental result, a simple model is described based on a bi-Maxwellian EEDF with a bulk-electron temperature Tb and a tail-electron temperature Tt (>Tb). For simplicity, the conventional C4F8 etching gas is replaced by feeding CF3, CF2 and CF radicals into a vessel. A set of particle-balance equations is formulated with wall reactions (radical sticking, charge neutralization) and inelastic electron collisions are taken into account. Numerical solutions for the discharge in 2 mTorr C4F8/18 mTorr Ar show that the plasma becomes less dissociative and CFx radical rich (F radical poor) with increasing Tt and decreasing Tb. For example, the radical density ratio of CFx/F at the electron density of 3×1011 cm-3 is two times larger in the bi-Maxwellian EEDF of Tb=1.5 eV and Tt=5.0 eV than in the `single' Maxwellian EEDF of Tb=2.75 eV.

Electron energy distribution function and plasma potential in a planar inductive argon discharge without electrostatic screen

Studies on electron heating are done during the power coupling change in the discharge mode transition (E–H mode transition) in a planar inductive argon discharge without electrostatic screen (Faraday shield). The electron energy distribution function (EEDF) evolution is measured by the alternating current superposition method with a radio frequency (rf) compensated Langmuir probe. The trend of its integrals, electron density and effective electron temperature, and especially the plasma potential against rf power are presented. It is demonstrated that the plasma potential is governed primarily by the high-energy electron tail in a plasma with bi-Maxwellian EEDF. The interdependence of the EEDF and the plasma potential is discussed. The experimental results show that the plasma potential against rf power reflects a change in the relative contribution of capacitive power coupling to electron heating.

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>

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.