Non-equilibrium Electron Energy Distribution Research Articles

Gas Discharge Properties of Inverse-Brush-Electrodes Driven by Alternating Current

The inverse-brush-electrodes (IBE) structure with a large area is designed to investigate the discharge mechanism driven by alternating current (ac). It is found that the IBE structure increases the number of secondary electrons and reduces the breakdown voltage by comparing the discharge processes of IBE and plate electrodes. Meanwhile, the breakdown mechanism of gas discharge driven by ac is analyzed in detail. Additionally, the designed IBE structure has a negative differential conductivity enhancement effect than that of plate electrodes when plasmas are generated in the heavy noble gas. Finally, the negative differential conductivity enhancement phenomenon of the IBE structure is analyzed by experiments and simulations. This effect originates from the non-equilibrium electron energy distribution function (EEDF), which is due to the more suprathermal electrons generated by the IBE structure.

Effect of Nonequilibrium Electron-Energy Distributions on Efficiency of Rydberg State Population via Resonant Recombination

Effect of Nonequilibrium Electron-Energy Distributions on Efficiency of Rydberg State Population via Resonant Recombination

Influence of Electronic Non-Equilibrium on Energy Distribution and Dissipation in Aluminum Studied with an Extended Two-Temperature Model.

When an ultrashort laser pulse excites a metal surface, only a few of all the free electrons absorb a photon. The resulting non-equilibrium electron energy distribution thermalizes quickly to a hot Fermi distribution. The further energy dissipation is usually described in the framework of a two-temperature model, considering the phonons of the crystal lattice as a second subsystem. Here, we present an extension of the two-temperature model including the non-equilibrium electrons as a third subsystem. The model was proposed initially by E. Carpene and later improved by G.D. Tsibidis. We introduce further refinements, in particular, a temperature-dependent electron–electron thermalization time and an extended energy interval for the excitation function. We show results comparing the transient energy densities as well as the energy-transfer rates of the original equilibrium two-temperature description and the improved extended two-temperature model, respectively. Looking at the energy distribution of all electrons, we find good agreement in the non-equilibrium distribution of the extended two-temperature model with results from a kinetic description solving full Boltzmann collision integrals. The model provides a convenient tool to trace non-equilibrium electrons at small computational effort. As an example, we determine the dynamics of high-energy electrons observable in photo-electron spectroscopy. The comparison of the calculated spectral densities with experimental results demonstrates the necessity of considering electronic non-equilibrium distributions and electron–electron thermalization processes in time- and energy-resolved analyses.

Vibrational excitation cross sections for non-equilibrium nitric oxide-containing plasma

A full set of vibrationally-resolved cross sections for electron impact excitation of NO(X2Π, v) molecules is calculated from ab initio molecular dynamics, in the framework of the local-complex-potential approach. Electron–vibration energy exchanges in non-equilibrium thermodynamic conditions are studied from a state-to-state model accounting for all electron impact excitation and de-excitation processes of the nitric oxide vibration manifold, and it is shown that the calculated vibration relaxation times are in good agreement with the experimental data. The new vibrational excitation cross sections are used in a complete electron impact cross section set in order to obtain non-equilibrium electron energy distributions functions and to calculate electron transport parameters in NO. It is verified that the new cross sections bring a significant improvement between simulations and experimental swarm data, providing an additional validation of the calculations, when used within the complete set of cross sections investigated in this work.

Ionization and Electronic State Excitation of CO2 in Radio-frequency Electric Field

The rate coefficients for the electron impact ionization and electronic state excitation of the CO2 molecule are calculated in non-equilibrium conditions in the presence of time-dependent electric field. A Monte Carlo simulation has been employed in order to determine non-equilibrium electron energy distribution functions in the CO2 gas, within one period of time-dependent radio-frequency (RF) electric field. By using the distribution functions, ionization rate coefficients for the CO2 molecule have been obtained within one period in RF frequency range at effective reduced electric field up to 500 Td. All obtained rate coefficients have been period averaged, as they can be of use in practical applications in the modeling of RF discharges in CO2.

Magneto-Oscillations of the Charge of a Field-Effect Transistor That Are due to a Microwave-Induced Nonequilibrium Electron Energy Distribution

The observation of microwave-induced changes in the charge of a field effect transistor with a channel formed by a bilayer electron system has confirmed that microwave radiation induces a nonequilibrium electron energy distribution function, which generates magneto-oscillations of the resistance of two-dimensional electron systems. The observed periodicity and beating of magneto-oscillations of the charge have been explained by the redistribution of electrons between the layers, which occurs because of the corresponding nonequilibrium occupation of electronic states.

Electron-induced vibrational excitation of CO2 in dc electric and magnetic fields

In the present study rate coefficients for vibrational excitation of CO_{2} gas molecules by electrons in the presence of uniform electric and magnetic fields are investigated. Calculations are performed for transition from the ground state to each of the symmetric, asymmetric, and bending vibrational states. A Monte Carlo simulation is used to produce nonequilibrium electron energy distribution functions. Results are obtained for the electric field over gas number density ratio, E/N, ranging from 20 to 1000 Td, and for the magnetic field over gas number density ratio, B/N, with values of 0, 1000, 2000, and 3000 Hx.

Dissociative Electron Attachment From Vibrationally Excited Molecules in Nanosecond Repetitively Pulsed CO Discharges and Afterglows.

Non-equilibrium vibrational distributions and electron energy distributions of CO in nanosecond repetitively pulsed (NRP) discharges and afterglows have been determined from a coupled solution of the time dependent Boltzmann equation for the electron energy distribution function (eedf) of free electrons and the master equations for the vibrational distribution function (vdf) of CO and the electronic excited states of CO and O and C atoms. Emphasis is given to the role of dissociative electron attachment (DEA) from vibrationally excited states in affecting the eedf and vdf under extreme conditions, i.e., an optically thick plasma with quenching processes involving the electronic excited states, populated by a sequence of discharge pulses and corresponding afterglows. In particular, the quenching process of the a3Π electronic state of CO determines a pumping of vibrational quanta in the ground state, which in turn largely modifies the CO vdf promoting the activation of DEA process. DEA rate coefficients have been obtained by using a complete set of vibrational (v) dependent cross sections through the CO−(X2Π) channel and by using the experimental v = 0 cross section of Rapp and Briglia, which should include the contribution of other CO− resonant states. The importance of the last contribution has been also estimated by using a scaling law to extend the v = 0 cross section over all the vibrational ladder of CO. In particular, this mechanism becomes competitive with the other reactive channels for very short inter-pulse delay times, i.e., the tid = 1 μs, being less important for longer inter-pulse delay times, i.e., the tid = 25 μs.

Non-equilibrium electron and vibrational distributions under nanosecond repetitively pulsed CO discharges and afterglows: II. the role of radiative and quenching processes

The non-equilibrium vibrational distributions and electron energy distributions of CO in nanosecond repetitively pulsed discharges and afterglows have been determined from a coupled solution of the time-dependent Boltzmann equation for the electron energy distribution function (eedf) of free electrons, the master equations for vibrational levels of CO and the electronic excited states of CO, O and C atoms. The optically thick plasma conditions have been investigated in a companion paper (part I), while in the present paper we also show the results obtained by allowing radiative emission processes (optically thin plasma) as well as electronic excited state collisional quenching processes. Two case studies, which differ for the duration of the afterglow following each pulse (1 μs and 25 μs case studies) are discussed, and each pulse is characterized by a time-dependent electric field profile in the range 0–20 ns. The results, which depend on the number of pulses considered in the discharge and the corresponding afterglow duration, show several peaks in the eedf due to super-elastic electronic collisions. On the other hand, the quenching process of the a3Π electronic state of CO determines the pumping of vibrational quanta in the v = 27 level, which in turn largely modifies the vibrational distribution function (vdf) of CO. As a consequence, the quenching of the a3Π state increases the reactivity of CO through the Boudouard reaction, and under given conditions, this channel can become more important than the dissociation rates by electron impact collisions.

Modeling and experimental characterization of the plasma produced by a velvet cathode in a linear induction accelerator

A high power electron diode is used to generate an intense high quality pulsed electron beam (2.6 kA, 4 MeV) in order to produce a bremsstrahlung radiation pulse for the first axis of the flash radiography facility named Epure. The plasma created by surface flashover of the velvet cathode provides a zero work function emitter used to produce the space-charge-limited electron beam. In order to optimize the design of diodes and to better understand the plasma dynamics, we have developed a 0D Collisional-Radiative Model (CRM) which describes the time-dependent evolution of the density of the plasma species in three plasma compositions: 100% H, 95% H + 5% C, and 64% H + 31% O + 5% C. The non-equilibrium electron energy distribution functions (EEDFs) are pre-calculated for a large range of electron mean energies for each mixture. EEDFs and cross sections of electron impact processes are then used to tabulate the electron rate coefficients needed to simulate the time-dependent plasma species densities. The evolution of the electron mean energy is estimated through the electron beam current density itself inferred from particle-in-cell calculations experimentally validated. Visible emission spectroscopy measurements were performed in order to investigate the plasma composition, to measure the Hα/Hβ intensity ratio, and to estimate the electron density. It was shown that the electron density in our setup is between 1014 and 1016 cm−3. Experimental results were compared to the 0D CRM. Results from the time-dependent CRM show that for the three studied plasma compositions, maximum electron densities range from 0.9 × 1014 cm−3 to 1.7 × 1014 cm−3 and that the electron energy averaged over the time interval of the electronic beam pulse is about 3.5 eV. An estimate of the electron energy inside the plasma during the relaxation provides values ranging from 0.10 eV to 0.12 eV based on comparison between the calculated and measured Hα/Hβ intensity ratio averaged over 5 μs. Moreover, main reactions involved in the evolution of the electron density were pointed out.

Vibrational kinetics of electronically excited states in H2 discharges

The evolution of atmospheric pressure hydrogen plasma under the action of repetitively ns electrical pulse has been investigated using a 0D state-to-state kinetic model that self-consistently couples the master equation of heavy particles and the Boltzmann equation for free electrons. The kinetic model includes, together with atomic hydrogen states and the vibrational kinetics of H2 ground state, vibrational levels of singlet states, accounting for the collisional quenching, having a relevant role because of the high pressure. The mechanisms of excitations, radiative decay and collisional quenching involving the excited H2 states and the corresponding cross sections, integrated over the non-equilibrium electron energy distribution function (EEDF) to obtain kinetic rates, are discussed in the light of the kinetic simulation results, i.e. the time evolution during the pulse of the plasma composition, of the EEDF and of the vibrational distributions of ground and singlet excited states.

Excitation of Electronic States of N2 in Radio-Frequency Electric Field by Electron Impact

Electron impact excitation rate coefficients for singlet and triplet electronic states of the carbon monoxide molecule have been calculated under non-equilibrium conditions in the presence of radio-frequency electric field. A Monte Carlo simulation of electron transport has been performed in order to determine non-equilibrium electron energy distribution functions within one period of applied electric field. By using these distribution functions and corresponding cross sections, the excitation rate coefficients have been calculated for all electronic states of CO in the frequency range from 13.56 up to 500 MHz, at reduced root mean square electric field values ranging from 200 to 700 Td. We expect these rates to be valuable for modeling radio-frequency CO plasmas since excited neutrals exhibit greater chemical reactivity than neutrals in ground electronic state, hence altering many properties of plasma.

Non-equilibrium vibrational and electron energy distribution functions in mtorr, high-electron-density nitrogen discharges and afterglows

Non-equilibrium vibrational distributions (vdf) and non-equilibrium electron energy distribution functions (eedf) in a nitrogen plasma at low pressure (mtorr) have been calculated by using a time-dependent plasma physics model coupled to the Boltzmann equation and heavy particle kinetics. Different case studies have been selected showing the non-equilibrium character of both vdf and eedf under discharge and post-discharge conditions in the presence of large concentrations of electrons. Particular attention is devoted to the electron-molecule resonant vibrational excitation cross sections acting in the whole vibrational ladder. The results in the post-discharge conditions show the interplay of superelastic vibrational and electronic collisions in forming structures in the eedf. The link between the present results in the mtorr afterglow regime with the existing eedf in the torr and atmospheric regimes is discussed.

Ionization of CO in radio-frequency electric field

The rate coefficients for the electron impact ionization of the CO molecule have been calculated in the presence of the radio-frequency (RF) electric field. The non-equilibrium electron energy distribution functions, used for the rate coefficient calculations, were generated by using a Monte Carlo simulation. The rate coefficients were obtained, time resolved within one period, in the frequency range from 13.56 up to 500 MHz, at effective reduced electric field values up to 700 Td. A temporal behavior of the rate coefficients under the influence of magnitude and frequency of the fields has been studied. The total ionization rate coefficients and the rate coefficients for the production of different ion fragments have been period averaged and presented in the order to be of use for practical implementation in the RF discharges in CO. Also, the temporal characteristics of the electron energy distribution functions and the diffusion coefficients have been studied separately revealing some interesting features in their time dependence within the period of electric field oscillations.

Ionization of N2 in radio-frequent electric field

Rate coefficients for the electron impact ionization of the N2 molecule are calculated in non-equilibrium conditions in the presence of time-dependent electric field. A Monte Carlo simulation has been developed in order to determine non-equilibrium electron energy distribution functions within one period of the radio-frequent (RF) electric field. By using these distribution functions, rate coefficients for ionization of the N2 molecule have been obtained time resolved within one period in the frequency range from 13.56 up to 500 MHz, at effective reduced electric field values up to 700 Td. This work presents an insight into the temporal characteristics of ionizing process and provides the ionization rate coefficients that can be of great use for correct implementation in modeling RF plasma discharges. A behavior of rate coefficients under the influence of magnitude and frequency of the fields was studied separately revealing some interesting features in time dependence.

Numerical Study of the H<sup>0 </sup>Atomic Density and the Balmer Line Intensity Profiles in a Hydrogen Negative Ion Source with the Effect of Non-Equilibrium Electron Energy Distribution Function

Numerical Study of the H<sup>0 </sup>Atomic Density and the Balmer Line Intensity Profiles in a Hydrogen Negative Ion Source with the Effect of Non-Equilibrium Electron Energy Distribution Function

Time-dependent quantum tunneling and nonequilibrium heating model for the generalized Einstein photoelectric effect

By combining the time-dependent Schr\"odinger equation with microscopic kinetic equations, a model for femtosecond-laser-induced electron emission from a metallic surface is developed to capture the physics of nonequilibrium heating and also the multiple-energy time-dependent tunneling. Using this model, we observe an enhanced electron emission due to the tranmission resonance at a particular energy level with a barrier height that produces a resonant frequency near to the laser frequency. Contrary to both pure optical tunneling and pure multiphoton emission models, the model provides better agreement with experiments. The generalized Einstein photoelectric effect is found to be inaccurate in this regime because of the nonequilibrium electron energy distribution, the resonant enhancement, and the ultrashort laser pulse width. The role of photons in the multiphoton electron emission regime is studied in detail. A smooth transition from the multiphoton regime to the optical tunneling regime is demonstrated.

Numerical study of atomic production rate in hydrogen negative ion sources with the effect of non-equilibrium electron energy distribution function

Spatial non-uniformity of the dissociative hydrogen atom (H0) production has been investigated in a large negative ion source (JAEA 10 A source) with the electron energy distribution function (EEDF) obtained by a Monte-Carlo simulation code for electron transport in 3D3V (three dimensional real and velocity) space. It has been shown that the H0 production rate becomes larger in the upper region (one side in the longitudinal direction) of the source chamber. This spatial non-uniformity of the H0 production profile is mainly explained by the non-equilibrium features of the EEDF in the upper region, i.e., the EEDF consists of thermal electron component with kinetic energy ε < 25 eV and fast electron component with energy ε > 25 eV in the upper region, while the EEDF mainly consists of only thermal electrons in the bottom region. These characteristics for the EEDF and the energy dependence of cross-sections for dissociation and dissociative ionization processes lead to the non-uniform profile of the H0 production. The above numerical results of the spatial H0 non-uniformity are validated and confirmed by comparisons with those by spectroscopic measurement. It has been clarified that the non-equilibrium (fast electron) component of the EEDF has a large contribution to the non-uniformity of the H0 production rate.

EFFECTS OF MICROWAVE FREQUENCY ON ELECTRON ENERGY DISTRIBUTION FUNCTION AND AIR BREAKDOWN USING THE FLUID MODEL

The non-equilibrium electron energy distribution function (EEDF) obtained via solving the Boltzmann equation is introduced into the ∞uid model,and the efiects of the microwave frequency on the EEDF and air breakdown are investigated. Numerical simulations show that the breakdown threshold of the ∞uid model with the non- equilibrium EEDF agrees well with that of the reported experiments. The microwave frequency plays an important role on the shape of the non-equilibrium EEDF at low pressures. The breakdown time at the low pressures predicted by the Maxwellian EEDF is shorter than that from the non-equilibrium EEDF in low-frequency oscillating flelds, while matches the latter in high-frequency oscillating flelds.

Nonequilibrium Tunneling Spectroscopy in Carbon Nanotubes

We report measurements of the nonequilibrium electron energy distribution in carbon nanotubes. Using tunneling spectroscopy via a superconducting probe, we study the shape of the local electron distribution functions, and hence energy relaxation rates, in nanotubes that have bias voltages applied between their ends. At low temperatures, electrons interact weakly in nanotubes of a few microns channel length, independent of end-to-end-conductance values. Surprisingly, the energy relaxation rate can increase substantially when the temperature is raised to only 1.5 K.