Steady-state Townsend Experiment Research Articles

Transport of electrons and propagation of the negative ionisation fronts in indium vapour

We study the transport of electrons and propagation of the negative ionisation fronts in indium vapour. Electron swarm transport properties are calculated using a Monte Carlo simulation technique over a wide range of reduced electric fields E/N (where E is the electric field and N is the gas number density) and indium vapour temperatures in hydrodynamic conditions, and under non-hydrodynamic conditions in an idealised steady-state Townsend (SST) setup. As many indium atoms are in the first metastable state at vapour temperatures of a few thousand Kelvin, the initial Monte Carlo code was extended and generalized to consider the spatial relaxation and the transport of electrons in an idealised SST experiment, in the presence of thermal motion of the host-gas atoms and superelastic collisions. We observe a significant sensitivity of the spatial relaxation of the electrons on the indium vapour temperature and the initial conditions used to release electrons from the cathode into the space between the electrodes. The calculated electron transport coefficients are used as input for the classical fluid model, to investigate the inception and propagation of negative ionisation fronts in indium vapour at various E/N and vapour temperatures. We calculate the electron density, electric field, and velocity of ionisation fronts as a function of E/N and indium vapour temperature. The presence of indium atoms in the first metastable state significantly affects the characteristics of the negative ionisation fronts. The transition from an avalanche into a negative ionisation front occurs faster with increasing indium vapour temperature, due to enhanced ionisation and more efficient production of electrons at higher vapour temperatures. For lower values of E/N, the electron density behind the streamer front, where the electric field is screened, does not decay as one might expect for atomic gases, but it could be increased due to the accumulation of low-energy electrons that are capable of initiating ionisation in the streamer interior.

Measurement of the electron attachment properties of SF5CF3 and comparison to SF6

The electron attachment properties of are experimentally investigated using a pulsed Townsend setup. Different / and / mixtures, with mole fractions ranging from to 1, are characterized. The effective ionization rate coefficient, electron drift velocity and reduced longitudinal electron diffusion coefficient in these mixtures are obtained. For low mole fractions of , the effective ionization rate coefficient is compared to calculations from available electron scattering cross sections, and is also used for estimating the electron attachment cross section of . For pure , the present data is compared to early data from a steady-state Townsend experiment. The presentation of the measurement results is followed by a discussion on the properties of and and their significance for gaseous electrical insulation.

Electron Swarm Parameters in $\hbox{c-C}_{4} \hbox{F}_{8}$ and $\hbox{CO}_{2}$ Gas Mixtures From Boltzmann Equation Analysis

The electron swarm parameters in c-C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> /CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gas mixtures, including the density-normalized effective ionization coefficient (α-η)/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> and the drift velocity <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> , are calculated for the overall density-reduced electric-field strength <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> values from 150 to 600 Td (1 Td = 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-17</sup> V · cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ). These calculations have been performed through solving the Boltzmann equation under the two-term approximation in the condition of steady-state Townsend experiment. The c-C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> content <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> in the gas mixtures can be varied over the range of 0%-100 %. From the variation curve of (α-η)/ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> with the c-C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> mixture ratio <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> , the limiting field strength ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> ) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">lim</sub> for each c-C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> concentration is determined for the analysis of the insulation characteristics of the c-C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> /CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> mixture. Additionally, the global-warming potential and the liquefaction temperature of c-C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">8</sub> /CO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> gas mixtures are also taken into account to evaluate the possibility of applying in gas insulation of power equipment.

Periodic structures in the Franck-Hertz experiment with neon: Boltzmann equation and Monte-Carlo analysis

The Franck-Hertz experiment with neon gas is modelled as an idealised steady-state Townsend experiment and analysed theoretically using (a) multi-term solution of Boltzmann equation and (b) Monte-Carlo simulation. Theoretical electron periodic electron structures, together with the ‘window’ of reduced fields in which they occur, are compared with experiment, and it is explained why it is necessary to account for all competing scattering processes in order to explain the observed experimental ‘wavelength’. The study highlights the fundamental flaws in trying to explain the observations in terms of a single, assumed dominant electronic excitation process, as is the case in text books and the myriad of misleading web sites.

The Effective Sampling Method of Electron Energy Distributions using the Higher Order Sampling and Spline Function

A novel method for sampling electron energy distribution with good statistics in Monte Carlo simulation(MCS) using the Higher Order Sampling and spline function is developed. Electron energy distributions f(e) obtained by the developed method, are in excellent agreement with those obtained by conventional sampling method in equilibrium and non-equilibrium regions. The sampling method is extended to two dimensional, and applied to the sampling of spatial variation of energy distribution f(e, x) of Steady State Townsend experiment. The obtained energy distributions are good agreement with those by conventional method. It is found that traced electron number in MCS can be reduced to 1/10 of the conventional method by using the developed sampling method.

Monte Carlo studies of non-conservative electron transport in the steady-state Townsend experiment

An investigation of the spatial relaxation of the electrons and benchmark calculations of spatially resolved non-conservative electron transport in model gases has been carried out using a Monte Carlo simulation technique. The Monte Carlo code has been specifically developed to study the spatial relaxation of electrons in an idealized steady-state Townsend (SST) experiment in the presence of non-conservative collisions. Calculations have been performed for electron transport properties with the aim of providing the benchmark required to verify the codes used in plasma modelling. Both the spatially uniform values and the relaxation profiles of the electron transport properties may serve as an accurate test for such codes. The explicit effects of ionization and attachment on the spatial relaxation profiles are considered using physical arguments. We identify the relations for the conversion of hydrodynamic transport properties to those found in the SST experiment. Our Monte Carlo simulation code and sampling techniques appropriate to these experiments have provided us with a way to test these conversion formulae and their convergence.

Magnetic field effects on spatial relaxation of swarm particles in the idealized steady-state Townsend experiment

The effect of a magnetic field at right angles to an electric field on spatial relaxation of a swarm of charged particles emitted by a plane source into a gas-the idealized steady-state Townsend experiment-is examined. The Boltzmann equation is solved using an adaptation of the "two-temperature" moment method, involving a Burnett function representation of the velocity distribution function, a technique which is valid for charged particles of arbitrary mass and is intrinsically of a "multiterm" nature. Results are presented for electrons in model and real gases, and are benchmarked against an exact analytical solution of the Boltzmann equation for a particular collision model. The application of a magnetic field significantly alters the relaxation profiles: in general, it can both enhance or retard spatial relaxation of transport properties. For methane gas, a multiterm analysis is essential to correctly account for the relaxation near the source, even though a two-term approximation may be sufficient when the magnetic field is sufficiently strong and hydrodynamic conditions dominate.

Measurement of electron transport coefficients in tetramethylsilane vapour

This paper reports four electron transport coefficients in tetramethylsilane (TMS, Si(CH3)4) vapour which is utilized in plasma-enhanced chemical vapour deposition (PECVD) of thin films such as SiC and SiN. The coefficients, namely the density-normalized effective ionization coefficient (αeff/N), the mean-arrival-time drift velocity (Wm) and the product of the longitudinal electron diffusion coefficient and the gas density (NDL) have been experimentally determined using a double-shutter drift tube method based on an arrival-time spectra theory over a reduced electric field (E/N) range of 30–5000 Td (1 Td = 10−21 V m2). The result shows that the coefficient αeff/N increases rapidly at an E/N value of about 200 Td and then reaches a value of 9.84 × 10−16 cm2 at an E/N value of 5000 Td. It is revealed that the values of the coefficient αeff/N are practically equal to those in SiH4 gas which is a representative gas used in PECVD. The reliability of the αeff/N values is checked by a steady-state Townsend experiment. The drift velocity (Wm) monotonically increases with E/N except at 50 Td < E/N < 200 Td, where a slight negative differential conductivity is observed. The longitudinal diffusion coefficient (NDL) has a minimum value at an E/N value of about 100 Td in the present measurement. Its variation profile against E/N is similar to that in SiH4 although its profile shifts to higher E/N. The ratio of the longitudinal diffusion coefficient to the mobility (DL/μ) is deduced from the Wm and the NDL values, which monotonically increases from 0.1 to about 10 eV with E/N in the present E/N range.

Measurement of electron-transport coefficients in O by a double-shutter drift-tube method

A double-shutter drift-tube technique based on an analysis of arrival-time spectra has been applied to experimentally determine three electron-transport coefficients in , namely the ratio of the effective ionization coefficient to the gas density , the mean-arrival-time drift velocity and the product of the longitudinal electron-diffusion coefficient and the gas density over a wide range of 7-5000 Td . The result shows that the obtained is in excellent agreement with that of the steady-state Townsend experiment at of 500-5000 Td. In a lower range, however, some difference is observed. As a result of examination, it is revealed that the difference approximately gives the true attachment coefficient under the present experimental conditions. The determined takes an almost constant value at Td and, in the other ranges, monotonically increases with . Its profile differs from available experimental data at Td but is rather close to theoretically derived data. The ratio of the longitudinal diffusion coefficient to the electron mobility is also deduced. Furthermore, the result analysed by the conventional time-of-flight method is presented for comparison.

The measurement of electron transport coefficients in methane by a double-shutter drift tube method combined with ATS analysis

Three important transport coefficients, namely the ratio of the Townsend first ionization coefficient to the gas number density , the mean-arrival-time drift velocity and the product of the longitudinal diffusion coefficient and the gas number density , in methane have been experimentally determined over a wide range of E/N, E being the electric field and N the gas number density, from 0.2 to 2000 Td by a double-shutter drift tube method analysed by an arrival-time-spectrum (ATS) technique. Equilibrium of the electron energy at high values of E/N in the present experiment is confirmed by a Monte Carlo simulation for the same gas. The present values of and as a function of E/N agree well with those in the literature which were obtained by using techniques such as the steady-state Townsend experiment, time-of-flight analysis and a pulse experiment. This demonstrates the validity of the present drift tube method and ATS analysis. The present result for , however, agrees with that in the literature in the rough shape of variation with E/N only; it is found that there are differences of a few tens of percentage in the present values against the values in an earlier paper and that a local maximum and minimum found in the previous article do not exist.

Properties of electron swarms in gases in the upstream region of an electron source

Exponential spatial growth of electron swarms in gases under steady-state Townsend conditions may be observed not only in the downstream region of an electron source but also in the upstream region due to backward diffusion. Relations among swarm parameters in the upstream region were deduced and found to have peculiar characteristics. For example, the sign of the average electron velocity Vd for steady-state Townsend conditions depends on whether the gas is electropositive or electronegative. This property is confirmed quantitatively by calculating the electron energy distribution using a propagator method modified for analysis in the upstream region. As an example of the effect of backward diffusion, the decay in the electron number density in front of the anode in a steady-state Townsend experiment between parallel plane electrodes was studied. The decay is caused by the missing electrons absorbed at the anode. The energy distribution of the missing electrons has a non-equilibrium relaxation region and the equilibrium region lies towards the cathode direction. The number density of the missing electrons showed an exponential spatial dependence in the equilibrium region. The relative gradient of the decrease agreed well with the relative density gradient alpha obtained in the upstream region. It was also found that the electron energy distribution in the decaying region tends to that in the upstream equilibrium region.

Transverse electron swarm parameters by a Fourier-transformed Boltzmann equation analysis

A method for calculating the electron swarm parameters in the transverse direction to the electric field by employing a Fourier-transformed Boltzmann equation is presented. In the method, the typical transverse swarm parameter, the transverse diffusion coefficient DT, is derived from the dispersion relation of the eigenvalue of the equation. The method is applied to methane (CH4) and sulphur hexafluoride (SF6). The results are compared with those from the conventional methods and it is shown that the present method is a reliable means to deduce the transverse coefficient DT. The lateral development of the electron swarms for the model of the steady-state Townsend experiment is also discussed.

A Boltzmann equation analysis of electron swarm parameters in CO2 laser mixtures

Electron swarm parameters in CO2 laser gas mixtures have been analysed for a range of the ratio of electric field to gas number density E/N from 2.83 to 283 Td (E/p0=1-100 V cm-1 Torr-1 at 0 degrees C) by a Boltzmann equation method in which the effect of electron impact ionisation and attachment can be considered properly (Thomas 1969, Tagashira et al. 1977, Taniguchi et al. 1977). Gas mixtures of CO2, N2 and He with concentration ratios of the respective gases of 1:1:8, 1:7:30, 1:1:3 and 1:2:3 are studied. The dissociation and dissociative ionisation processes for CO2 have been taken into account in addition to the electron collision processes considered in a previous study of Lowke et al. (1973). The results show that the present values of the ionisation coefficient and of the ratio of electron diffusion coefficient to mobility for the steady-state Townsend experiment are by about a few tens of percent lower than the previous theoretical values of Lowke et al. at high E/N values, but are in good agreement with recent experimental values of Lakhsminarasimha et al. (1976) for the whole E/N range studied. The excitation coefficient for the vibrational levels, important for the CO2 laser action, and the electron attachment coefficient are also calculated and discussed.