[1] Streamers are thin filamentary plasmas that can initiate spark discharges in relatively short (several centimeters) gaps at near ground pressures and are also known to act as the building blocks of streamer zones of lightning leaders. These streamers at ground pressure, after 1/N scaling with atmospheric air density N, appear to be fully analogous to those documented using telescopic imagers in transient luminous events (TLEs) termed sprites, which occur in the altitude range 40–90 km in the Earth's atmosphere above thunderstorms. It is also believed that the filamentary plasma structures observed in some other types of TLEs, which emanate from the tops of thunderclouds and are termed blue jets and gigantic jets, are directly linked to the processes in streamer zones of lightning leaders. Acceleration, expansion, and branching of streamers are commonly observed for a wide range of applied electric fields. Recent analysis of photoionization effects on the propagation of streamers indicates that very high electric field magnitudes ∼10 Ek, where Ek is the conventional breakdown threshold field defined by the equality of the ionization and dissociative attachment coefficients in air, are generated around the tips of streamers at the stage immediately preceding their branching. This paper describes the formulation of a Monte Carlo model, which is capable of describing electron dynamics in air, including the thermal runaway phenomena, under the influence of an external electric field of an arbitrary strength. Monte Carlo modeling results indicate that the ∼10 Ek fields are able to accelerate a fraction of low-energy (several eV) streamer tip electrons to energies of ∼2–8 keV. With total potential differences on the order of tens of MV available in streamer zones of lightning leaders, it is proposed that during a highly transient negative corona flash stage of the development of negative stepped leader, electrons with energies 2–8 keV ejected from streamer tips near the leader head can be further accelerated to energies of hundreds of keV and possibly to several tens of MeV, depending on the particular magnitude of the leader head potential. It is proposed that these energetic electrons may be responsible (through the “bremsstrahlung” process) for the generation of hard X rays observed from ground and satellites preceding lightning discharges or with no association with lightning discharges in cases when the leader process does not culminate in a return stroke. For a lightning leader carrying a current of 100 A, an initial flux of ∼2–8 keV thermal runaway electrons integrated over the cross-sectional area of the leader is estimated to be ∼1018 s−1, with the number of electrons accelerated to relativistic energies depending on the particular field magnitude and configuration in the leader streamer zone during the negative corona flash stage of the leader development. These thermal runaway electrons could provide an alternate source of relativistic seed electrons which were previously thought to require galactic cosmic rays. The duration of the negative corona flash and associated energetic radiation is estimated to be in the range from ∼1 μs to ∼1 ms depending mostly on the pressure-dependent size of the leader streamer zone.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2005JA011350

Monte Carlo model for analysis of thermal runaway electrons in streamer tips in transient luminous events and streamer zones of lightning leaders

The widespread use of SF/sub 6/ by the electric power and other industries has led to increased concentrations of SF/sub 6/ in the atmosphere. This causes concern as to possible effects on global warming, because SF/sub 6/ is a potent greenhouse gas. This paper first touches on this issue and then documents the behavior of high pressure gases such as N/sub 2/ and SF/sub 6//N/sub 2/ mixtures that can be realistically considered as acceptable intermediate or long-term replacements for pure SF/sub 6/ in some HV applications. The possible use of dilute SF/sub 6//N/sub 2/ mixtures as an alternative to pure SF/sub 6/ for some of industry's insulation needs (albeit at higher pressure) is documented, and existing knowledge on these mixtures and on the individual components (N/sub 2/ and SF/sub 6/), both basic and applied, is compiled. A guide to existing literature is provided. >

SF/sub 6//N/sub 2/ mixtures: basic and HV insulation properties

Electron transport in crossed electric and magnetic dc fields in CF4 is considered by employing an exact Monte Carlo simulation technique. Emphasis is placed on explicit and implicit effects of the combination of both the shape of cross-sections and magnetic field on relaxation processes and steady-state transport data. It has been shown that the application of a magnetic field changes the relaxation processes by increasing the relaxation times as well as, by introducing the oscillatory behaviour of some transport quantities during the relaxation process itself. The electron transport parameters studied here are collision frequency, mean energy, drift velocity, diffusion tensor and collisional rates for 1 E/N 1000 Td and 0 B/N 1000 Hx (1 Td = 10 −21 Vm 2 ,1 Hx= 10 −27 Tm 3 ). Special attention is paid to the study of sensitivity of transport data in E × B fields on the energy dependence and nature of the cross-sections. The validity of the effective reduced electric field concept through Tonks’ theorem is also investigated for CF4 in the evaluated range of mean energies.

https://iopscience.iop.org/article/10.1088/0022-3727/38/16/032/pdf

Monte Carlo studies of electron transport in crossed electric and magnetic fields in CF4

Ion energy distribution functions (IEDFs) at the electrodes in single frequency (SF) and dual frequency (DF) radio-frequency discharges in Ar at pressures of 20 and 45 mtorr are measured and calculated. A numerical simulation of the IEDF on the base of a self-consistent particle-in-cell model with Monte Carlo collisions was performed. In addition, a semianalytical model was developed to calculate the IEDF in collisionless and collisional SF and DF plasmas. The IEDF width for the intermediate frequency case was determined from both experimental and theoretical results. The possibility of frequency decoupling is discussed.

Experimental and Theoretical Study of Ion Energy Distribution Function in Single and Dual Frequency RF Discharges

[1] Detailed Boltzmann kinetic calculations of the electron distribution functions resulting from thermal runaway in a constant electric field are presented. Thermal runaway is considered to occur when an initially thermal electron is accelerated above the 150 eV peak in the dynamical friction force in air and becomes a runaway electron. We investigate the role of runaway breakdown in situations where thermal runaway, as well as conventional breakdown, is occurring. The electric field strengths studied span the range from the threshold for runaway breakdown in air (∼0.3 MV/m at sea level) through conventional breakdown (2.4–3.2 MV/m at sea level) and exceeding the Dreicer field (25 MV/m at sea level), above which all electrons are runaways. We initiate our simulations with a population of pseudothermal electrons or with a combination of thermal and runaway (∼1 MeV) electrons. We find that when thermal runaway occurs the self-similar electron distribution function is identical in the presence or absence of a seed runaway population. We show that attempts to obtain the electric field from remote measurements of optical line ratios are ambiguous both in the context of the absolute field and in the underlying kinetics. By considering the runaway electrons as a separate population we conclude that the avalanche rate of low-energy electrons is equivalent to that of runaway electrons at a reduced field of 140 Td (3.8 MV/m at standard temperature and pressure). Above that field the conventional avalanche rate will control the avalanche rate of the entire population. Below that field the runaway avalanche rate will control the avalanche rate of the entire population.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2009JA014509

Temporally self‐similar electron distribution functions in atmospheric breakdown: The thermal runaway regime

The motion of electrons in mercury vapour is traced using the Monte Carlo simulation for 10<or=E/N<or=2000 Td (1 Td=10-17 V cm2) by adopting a null collision technique. The momentum transfer cross sections for electron energy 0.05<or= epsilon <or=50 eV obtained from the literature, and the excitation cross sections are derived as a function of electron energy to produce good agreement between the measured and calculated values of Townsend's first ionization coefficient. Electron swarm parameters, namely the drift velocity, ionization coefficient and mean energy have been calculated, and good agreement is obtained with published results over a wide range of E/N.

Monte Carlo simulation of electron motion in mercury vapour

The electron swarm parameters, namely, the drift velocity, mean energy, attachment coefficient, and ionization coefficients are obtained in oxygen by solving the Boltzmann equation over a wider range of E/N values . Previous investigations have used either a space-time independent energy distribution or have adopted a rigorous approach for only a narrow range of E/N. The present analysis overcomes these restrictions and shows that the Fourier method of solving the Boltzmann equation yields very good results over the entire range of E/N.

Calculation of electron swarm parameters in oxygen using a rigorous Boltzmann equation analysis

The drift velocity, mean energy and ionization coefficients in nitrogen are re-evaluated using the Monte Carlo technique over the range of 50 ⩽ E/N ⩽ 560 Td Recently published data on cross-sections, including ten vibrational levels and eighteen excitation levels, are used in the simulation for the first time The theoretical swarm parameters agree very well with experimental and other theoretical results with only a slight modification of the cross-sections New data on collision frequencies for ionization, dissociation and various excitation states are reported

Evaluation of transport coefficients in nitrogen by the monte carlo method

The influence of a magnetic field on electron transport coefficients in mercury vapour has been studied using a Monte-Carlo simulation technique. The ranges of parameters studied are 10<or=E/N<or=1000 Td and O<or=B/N<or=20*10-19T cm3 (where E is the electric field, B the magnetic field and N the gas number density). Data on ionization coefficients, transverse and perpendicular drift velocities and mean energy are evaluated at various magnetic field strengths. The results are examined in the light of the effective reduced electric field (EREF) concept. It is found that the EREF is a good approximation for the mean energy, collision frequency and ionization coefficient if the appropriate collision frequency which is dependent on E/N and B/N (instead of a constant collision frequency) is used in EREF calculations. As a result, the application of a magnetic field perpendicular to the electric field decreases the transverse drift velocity, mean energy and ionization coefficient. The influence of the magnetic field on the energy distribution function is also studied.

Electron transport coefficients in mercury vapour in E*B fields

The electron swarm parameters in mercury vapour are studied for high values of E/N from 300 to 1400 Td (1 Td = 10−17 V cm2) by a rigorous Boltzmann-equation analysis. Three kinds of electron swarm parameters defined according to the time of flight (TOF), the pulsed Townsend, (PT) and the steady state Townsend (SST), conditions are calculated. The results for TOF agree very well with those obtained in a Monte-Carlo simulation.

Jianfen Liu

Papers

Monte Carlo simulation of electron motion in mercury vapour

Calculation of electron swarm parameters in oxygen using a rigorous Boltzmann equation analysis

Evaluation of transport coefficients in nitrogen by the monte carlo method

Electron transport coefficients in mercury vapour in E*B fields

Boltzmann-equation analysis of electron swarm parameters in mercury vapour at high values of E/N