Electron Energy Distribution In Plasma Research Articles

Modeling the energetic tail of a dusty plasma's electron energy distribution and its effect on dust grain charge and behavior

A model for a weakly ionized dusty plasma is proposed in which UV or x-ray radiation continuously creates free electrons at high energy, which then cool through collisions with a cold neutral gas before recombining. The transition of a free electron from high energy at birth to low energy at demise implies that the electron energy distribution is not the simple Maxwellian of an isolated system in thermal equilibrium, but instead has a high-energy tail that depends on the recombination time. This tail can have a major effect on dust grain charging because the flux of tail electrons can be substantial even if the density of tail electrons is small. Detailed analytic and numerical calculations of dust grain charging show that situations exist in which a small high-energy tail dominates charge behavior. This implies that dust grain charge in terrestrial and space dusty plasmas may be significantly underestimated if a Maxwellian distribution is assumed and the non-thermal dynamics are neglected.

Methane detection to 1 ppm using machine learning analysis of atmospheric pressure plasma optical emission spectra

Optical emission spectroscopy from a small-volume, 5 μl, atmospheric pressure RF-driven helium plasma was used in conjunction with partial least squares-discriminant analysis for the detection of trace concentrations of methane gas. A limit of detection of 1 ppm was obtained and sample concentrations up to 100 ppm CH4 were classified using a nine-category model. A range of algorithm enhancements were investigated including regularization, simple data segmentation and subset selection, feature selection via Variable Importance in Projection and wavelength variable compression in order to address the high dimensionality and collinearity of spectral emission data. These approaches showed the potential for significant reduction in the number of wavelength variables and the spectral resolution/bandwidth. Wavelength variable compression exhibited reliable predictive performance, with accuracy values >97%, under more challenging multi-session train—test scenarios. Simple modelling of plasma electron energy distribution functions highlights the complex cross-sensitivities between the target methane, its dissociation products and atmospheric impurities and their impact on excitation and emission.

Plasma-Profile Control in an ICP Reactor

ICP is widely used in electromagnetic scattering due to its high electron density and simple structure. The distribution of plasma parameters can affect the electromagnetic scattering, so the control of plasma parameter distribution is very important for aircraft stealth. Firstly, the effect of the number of coil turns on the plasma parameter distribution is analyzed. With the increase of the number of coil turns, the peak value of induced magnetic field decrease, the width of magnetic field increase and the homogeneity of plasma increase. Then, the Boltzmann solver is used to calculate the plasma electron energy distribution function at different positions under the four-turn coil. Finally, the influence of external circuit capacitance on plasma parameter distribution is analyzed. In this cavity structure, the electron density first increases and then decreases with the external circuit capacitance increase, and the peak value is on 75 pF. In this study, we propose a method to further regulate the plasma parameter distribution by using terminal capacitance to control the induced magnetic field.

Elevating the Precision of Plasma Probe Diagnostics by Elimination of Bare Probe Protective Shields’ Influence

Probe diagnostics of the low pressure inductive xenon plasma were conducted using classic cylindrical Langmuir probes with conventional protection of their circuits against radio frequency interferences by bare metal shields. The dimensions of their probetips were determined in the special experiment that provided negligible local plasma distortions. Accurate probe measurements were used to determine the spatial plasma parameter distributions in a gas discharge unit of an ion thruster model which helped to develop its ion-extracting grate. The subsequent analysis of probe measurements showed that in these experiments, the plasma electron energy distribution function (EEDF) was quite noticeably deviated from the Maxwell function depending on the main probe shield length that varied from maximum to zero. Use of an additional probe in the special position where its shield was rather long with zero shield length of the main probe showed that the additional shield lowered all plasma parameters. Comparison of both probes’ data identified the principled relationship between measurement errors and EEDF distortions caused by bare probe shield and this dependence was used to correct the initial probe measurements. Therefore plasma probe diagnostics became more precise due to the lowered influence of the bare probe protective shields. Its physical analysis based on previous authors’ works showed that this effect was caused by a shortcircuited double-probe phenomenon in the bare metal shields.

Strategy for tuning the average charge state of metal ions incident at the growing film during HIPIMS deposition

Energy and time-dependent mass spectrometry is used to determine the relative number density of singly- and multiply-charged metal-ion fluxes incident at the substrate during high-power pulsed magnetron sputtering (HIPIMS) as a function of the average noble–gas ionization potential. Ti is selected as the sputtering target since the microstructure, phase composition, properties, and stress-state of Ti-based ceramic thin films grown by HIPIMS are known to be strongly dependent on the charge state of Tin+ (n = 1, 2, …) ions incident at the film growth surface. We find that the flux of Tin+ with n > 2 is insignificant; thus, we measure the Ti2+/Ti+ integrated flux ratio JTi2+/JTi+ at the substrate position as a function of the choice of noble gas–Ne, Ar, Kr, Xe, as well as Ne/Ar, Kr/Ar, and Xe/Ar mixtures -- supporting the plasma. We demonstrate that by changing noble–gas mixtures, JTi2+ varies by more than two orders of magnitude with only a small change in JTi+. This allows the ratio JTi2+/JTi+ to be continuously tuned from less than 0.01 with Xe, which has a low first-ionization potential IP1, to 0.62 with Ne which has a high IP1. The value for Xe, IPXe1=12.16eV, is larger than the first ionization potential of Ti, IPTi1=6.85eV, but less than the second Ti ionization potential, IPTi2=13.62eV. For Ne, however, IPNe1=21.63eV is greater than both IPTi1 and IPTi2. Therefore, the high-energy tail of the plasma-electron energy distribution can be systematically adjusted, allowing JTi2+/JTi+ to be controllably varied over a very wide range.

Note: Enhanced production of He⁺ from the Versatile Ion Source (VIS) in off-resonance configuration.

The Versatile Ion Source (VIS) is a microwave discharge ion source installed at INFN-LNS and here used as test-bench for the production of high intensity low emittance proton beams and for studies on plasma physics. A series of measurements have been carried out with VIS in order to test the source with light ions. In particular a He(+) beam has been characterized in terms of plasma discharge parameters. The experiment has been triggered by the observation of X-radiation emission from the plasma for some configuration of the magnetic field profile. The plasma electron energy distribution function is in fact modified when in some regions of the plasma chamber under-resonance discharge takes place, fulfilling the condition that allows the electromagnetic wave to electrostatic wave conversion. These tests allowed obtaining more than 50 mA of He(+) beams.

Made-to-order nanocarbons through deterministic plasma nanotechnology

Through a combinatorial approach involving experimental measurement and plasma modelling, it is shown that a high degree of control over diamond-like nanocarbon film sp3/sp2 ratio (and hence film properties) may be exercised, starting at the level of electrons (through modification of the plasma electron energy distribution function). Hydrogenated amorphous carbon nanoparticle films with high percentages of diamond-like bonds are grown using a middle-frequency (2 MHz) inductively coupled Ar+CH4 plasma. The sp3 fractions measured by X-ray photoelectron spectroscopy (XPS) and Raman spectroscopy in the thin films are explained qualitatively using sp3/sp2 ratios 1) derived from calculated sp3 and sp2 hybridized precursor species densities in a global plasma discharge model and 2) measured experimentally. It is shown that at high discharge power and lower CH4 concentrations, the sp3/sp2 fraction is higher. Our results suggest that a combination of predictive modeling and experimental studies is instrumental to achieve deterministically grown made-to-order diamond-like nanocarbons suitable for a variety of applications spanning from nano-magnetic resonance imaging to spin-flip quantum information devices. This deterministic approach can be extended to graphene, carbon nanotips, nanodiamond and other nanocarbon materials for a variety of applications.

Studies of electron energy distribution in plasma produced by a resonant laser pulse

Using the Langmuir probe method we evaluated the electron energy distribution (EED) in plasma produced in a Na+He mixture by a laser pulse tuned to the 3S–3P transition. We proposed a new method of retrieving the EED from the probe characteristics at high gas pressures, when the free path of the electrons is less than the probe radius, i.e. in the range of 2–100 Torr. The method consists of using a combination of the first and second derivatives of the electron current. The systematic error that usually occurs when the EED is treated by means of traditional Langmuir and diffusion probes was reduced by two to three times when treated this way. Two phase temporal evolution of the electron distribution was observed. Initially the shape of the EED was close to the Maxwellian function. Its temperature corresponded to the effective excitation temperature, which can characterize the total population of excited sodium atoms. When the concentration of excited atoms decreased, one observed a transformation of the EED function. At the second phase it became well Maxwellized only in the low energy region. The high energy part of the EED had a non-equilibrium shape. This was caused by relaxation of fast electrons produced by super-elastic collisions with residual excited atoms.

Comparison of particle-in-cell simulations and a wave-population model of electron-beam-plasma interactions

A spatially independent beam stability model [W. K. Rose et al., Astrophys. J. 280, 550 (1984)] is compared with one-dimensional particle-in-cell (PIC) simulations. The model uses rate equations to evaluate the coupling of longitudinal waves created by beam-plasma instabilities. Equilibrium solutions of the stability model are examined and wave energies from the model are compared with PIC simulations. The PIC simulations enable the stability model to be benchmarked and to explore the temporal evolution of the background plasma electron energy distribution, a capability not presently treated in the stability model. The generation of hot plasma electron tails is examined in the PIC simulations. The scalable, spatially independent model can be used in laboratory and astrophysical parameter regimes while numerical constraints limit the parameter regimes treatable in the PIC simulations.

Reaction pathways in remote plasma nitridation of ultrathin SiO2 films

Low-temperature nitridation of 3 nm SiO2 films using He/N2 and N2 remote radio frequency (rf) plasmas was investigated. On-line Auger electron spectroscopy and angle-resolved x-ray photoelectron spectroscopy (ARXPS) were employed to determine the concentration, spatial distribution, and local chemical bonding of nitrogen in the resultant films. Experiments were performed using a substrate temperature of 300 °C and 30 W rf power. Nitridation using an upstream He/N2 remote plasma at 0.1 Torr incorporates nitrogen at the top surface of the SiO2 film. In contrast, a lower concentration of nitrogen distributed throughout the film is obtained when the process pressure is increased to 0.3 Torr. ARXPS indicates a N–Si3 local bonding configuration, irrespective of the spatial distribution of N atoms. Slightly more nitrogen is incorporated using a downstream He/N2 plasma at each process pressure. By comparison, nitridation of SiO2 films using a N2 remote plasma at 0.1 Torr is very slow. Optical emission spectroscopy indicates that He dilution enhances the generation of N2+(B 2Σu+) species by altering the plasma electron energy distribution and by providing an additional kinetic pathway (Penning ionization). Changing the He/N2 remote plasma configuration from upstream to downstream (at 0.1 and 0.3 Torr) also enhances N2+(B 2Σu+) generation. For upstream He/N2 remote plasmas, the intensity of N2 first positive emission from N2(B 3Πg) states increases with pressure, whereas the N2+ first negative emission from N2+(B 2Σu+) states decreases. We infer from these observations that N2+ species are primarily responsible for top surface nitridation at 0.1 Torr, and that neutral species [N2(A 3Σu+) metastables and N atoms] are associated with sub-surface nitrogen incorporation.

Time- and space-resolved radio-frequency plasma electron energy distributions from a displacement-current-based electric probe diagnostic

A displacement-current-based, Langmuir probe technique was developed to measure time-resolved and spatially dependent electron energy distribution functions (EEDF) in a 100 mTorr argon plasma. This diagnostic was designed to take consideration of the changes in displacement current collected at the probe due to changes in the probe tip sheath potential. The EEDFs collected displayed evidence of a time-dependent as well as spatially dependent electron beam component. The beam energy was seen to increase with the instantaneous plasma potential. The electron density was found to be 3.2±1.1×109, 1.0±1.5×1010, and 2.7±1.0×109 cm−3 at locations 0.6, 1.8, and 2.8 cm from the grounded electrode, respectively. Mean electron energies were also spatially dependent, measuring 8.7±0.8, 11.3±1.0, and 6.9±0.7 eV at locations 0.6, 1.8, and 2.8 cm from the grounded electrode, respectively.

Plasma heating by a strong laser field with statistically distributed parameters

The energy absorption rate by a classical homogeneous plasma irradiated by a strong fluctuating laser field via inverse bremsstrahlung is considered. A chaotic-field model is used and comparison is made with the fundamental model of a purely coherent field. In the present analysis, the emphasis is put on the interplay between the laser field statistics and the plasma electron energy distribution. Numerical calculations are concerned with the dependence of the energy absorption rates on laser intensity and frequency. Laser intensity values up to 4.6\1015 W/cm2 are considered. The multiphoton structure of the energy absorption is analysed as well. Concerning the joint influence of the radiation and particle statistics on the absorption rate, the basic result may be stated as follows. For situations where the particle thermal velocityv T is larger than the oscillatory velocityv 0 imparted by the field (v T ≥v 0, relatively weak field), the absorption rate is only weakly dependent on the field statistics. For situations, instead, whenv 0≫v T , which occurs for very high intensities, the reverse becomes true: now the initial particle velocity distribution plays the modest role of a velocity spread of an electron beam oscillating atv 0. In general, for very high intensities (v 0≫v T ), the energy absorption via bremsstrahlung becomes less effective because the high oscillatory velocityv 0 reduces the time available to electrons for the interaction with the ions, the third body which makes possible the exchange for energy between electrons and a radiation field. We report also, for the first time, results on the Marcuse effect for the case of a chaotic laser field, along with calculations of the absorption rate for a directed electron beam.

Plasma Electron Energy Distribution of a Beam-Plasma Type Ion Source

The plasma electron energy distributions of a beam-plasma type ion source are experimentally investigated in relation to the ion source operational parameters. These parameters are the primary electron beam current (beam-plasma discharge current) and the pressure of the working gas. Using the experimental results, we show that the beam-plasma discharge is an effective method of heating a plasma, with the plasma electrons being distributed in the range of a few eV to a few tens eV. As a result, a plasma is produced with a density of more than 1011 particles/cm3. Beam-plasma type ion sources using the beam-plasma discharge are highly stable and controllable, and can be operated over a wide range of gas pressures and primary electron beam currents.

The temperature of thermal X-ray and gamma-ray sources

The temperature of a source can be accurately measured, assuming that it is optically thin and exhibits a bremsstrahlung, on the basis of the shape of its spectral distribution. An explicit relation is derived for the temperature in terms of this slope, and as a sum of correction terms to the limiting form of the bremsstrahlung formula. The corrections can be evaluated easily in terms of simple, accurate asymptotic formulae. For the case where there is a distribution of temperatures in the plasma, an additional correction is derived in terms of the rms variation in the plasma temperature. Corrections due to a modified Bessel function, the Born approximation, plasma electron energy distribution and electron-electron bremsstrahlung are discussed

Electron reflection and secondary emission in probe analysis of plasmas

Abstract The integral equation which occurs in the theory of the determination of the plasma electron energy distribution function ƒ( V) from the second derivative of the probe current versus retarding potential curve, when reflection and secondary emission are taken into account, cannot, in general, be solved for lack of quantitative reflection and secondary emission data. By consideration of some special cases it is shown that relatively little error is likely to result from neglect of reflection and secondary emission in many instances if ƒ( V) is broad on a V/≤ V≥ scale. If ƒ( V) is narrow, spurious groups and negative values may appear to the low energy side of the peak. Possible advantages of a rough or porous probe surface in minimizing errors in ƒ( V) and in the measurement of the plasma electron number density are indicated.

Determination of electron energy distribution in a plasma

A simple method of direct display of electron energy distribution in a gaseous plasma is presented. The apparatus is an analog computer used on line with a Langmuir probe. The new features of this work are (1) an analysis of the time response of a filter input differentiating operational amplifier, (2) a procedure for noise eliminating differentiation that is also capable of taking account of the higher derivatives of the input signal, and (3) a simple determination of the plasma potential with a phase comparator. The method is being used in the analysis of electron energies in a positive column plasma. The results so far found show that the distribution has a single peak sharper than the Maxwellian at pressures of about 0.1 Torr and it changes into a two-peak distribution at lower pressures (∼0.01 Torr). The second peak also found in similar studies by other investigators (Alexeff and Howell, Rezacova et al.) is possibly due to the presence of accelerated electrons from the hot cathode of the discharge.

Direct display of the electron energy distribution in plasma by means of analog correlator

Direct display of the electron energy distribution in plasma by means of analog correlator

A new method for time-resolved measurements of plasma electron energy distributions

Abstract A method using difference quotient circuits is described for measuring the second derivative of a prove characteristic in time varying plasmas.

Electron energy distributions in plasmas V. A search for evidence of a high anomalous rate of energy exchange between the electrons of a low-pressure discharge

Since earlier measurements of electron energy distributions obtained with the Druyvesteyn probe method showed no evidence of the scattering observed in mercury by Langmuir (1925) and Merrill & Webb (1939), the method has now been used to examine discharges in hydrogen, neon, krypton and mercury in a search for evidence of such a high rate of energy exchange between the electrons. This was, in fact, observed in neon when, as the discharge current was increased, the well-defined group of primary electrons from the filament disappeared, giving rise to a uniform distribution. In krypton and mercury, the distribution near the filament was usually uniform, although frequently there was evidence of a strongly broadened primary group and electrons were often observed with energies greater than the potential difference between the filament and the measuring probe. This behaviour is almost certainly to be explained in terms of Langmuir scattering near the filament, but the scattering was always restricted to regions very close to the filament and was never observed in the positive column. Indeed, after the initial scattering the distribution is influenced by the applied field in a similar manner to that observed in earlier measurements and thus, in these gases, although the distribution is quite uniform near the filament there are very marked departures from uniformity further from the cathode as the distribution is accelerated in either a uniform field or through a step of potential, giving rise to well defined primary and secondary groups of electrons. These newly created primaries are not scattered. Measurements in high-field regions in krypton show a high ratio of primary to secondary electrons. This is due to the pronounced Ramsauer effect in this gas and was observed earlier in argon. The change of energy distribution resulting from the contamination of a discharge in neon by argon and mercury has been investigated.