As part of a systematic study of approximations commonly made in solutions of the Boltzmann equation for electrons in molecular gases, we have investigated the effects of anisotropic scattering on electron transport coefficients in ${\mathrm{N}}_{2}$ and have extended our study of the multiterm expansion technique to higher E/n. A critical survey of published data yields a set of differential and integral cross sections for electron energies from 0.003 to ${10}^{4}$ eV. For electric-field--to--gas-density ratios E/n between 10 and 500 Td (1 Td${=10}^{\mathrm{\ensuremath{-}}21}$ V ${\mathrm{m}}^{2}$), the changes in the commonly measured transport and reaction coefficients resulting from the introduction of anisotropic elastic and inelastic scattering, while keeping the elastic momentum-transfer cross section constant, are less than 1%.These calculations were made with use of the multiterm spherical-harmonic expansion solution of the Boltzmann equation. For 500lE/nl1500 Td the changes in scattering anisotropy cause changes in transport and reaction coefficients which increase with E/n to about 10%. The errors in drift velocity, mean energy, and the reaction coefficients resulting from the use of the two-term spherical-harmonic expansion rather than a six-term expansion are less than 3% at 1500 Td.However, the errors in the diffusion coefficients become large (g25%) at our highest E/n. The calculated transport coefficients are in generally good agreement with experiment for E/n less than 300 Td, but the differences increase at higher E/n. The importance of proper interpretation of ionization and excitation experiments at high E/n is illustrated by calculations which model either an exponential growth of density in time or an exponential growth with position. The calculated ionization coefficients are low compared to most experiments for E/n less than 200 Td. At E/ng600 Td the agreement is good for the spatial growth experiments, but the calculated values are below experiment from the temporal growth experiments. The calculated excitation coefficients are generally higher than experiment at low and high E/n but in agreement with experiment at E/n near 150 Td.

Anisotropic scattering of electrons by N2 and its effect on electron transport.

Electron–molecule collision calculations using the R-matrix method

A new apparatus has been constructed for the measurement of absolute partial electron-impact-ionization cross sections of neutral atoms, molecules, and free radicals. A fast neutral beam is prepared by charge-transfer neutralization of a mass-selected ion beam and is ionized as it crosses an electron beam. From careful analysis of the apparatus, the absolute accuracy of measured cross sections is calculated to be \ifmmode\pm\else\textpm\fi{}12%. Combined with statistical errors, this gives about \ifmmode\pm\else\textpm\fi{}15% for the overall accuracy. Measurements of ionization cross sections for the four rare gases He, Ne, Ar, and Kr from 0 to 200 eV agree with the most reliable previous values within \ifmmode\pm\else\textpm\fi{}6%. The measured Xe ionization cross section is 12% greater than the previous best value. Ratios of double- and triple-ionization to single-ionization cross sections for Ar, Kr, and Xe confirm the recent measurements of Stephan, Helm, and M\"ark [J. Chem. Phys. 73, 3763 (1980)].

Absolute cross sections for electron-impact ionization of the rare-gas atoms by the fast-neutral-beam method

Electron scattering by molecules II. Experimental methods and data

[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

Total scattering cross sections have been measured in the same apparatus for positrons and electrons colliding with ${\mathrm{H}}_{2}$, ${\mathrm{N}}_{2}$, and C${\mathrm{O}}_{2}$ using a beam transmission technique. The projectile impact energies range from 1 - 500 eV for ${e}^{+}\ensuremath{-}{\mathrm{H}}_{2},2\ensuremath{-}500$ eV for ${e}^{\ensuremath{-}}\ensuremath{-}{\mathrm{H}}_{2},0.5\ensuremath{-}750$ eV for ${e}^{+}\ensuremath{-}{\mathrm{N}}_{2},2.2\ensuremath{-}700$ eV for ${e}^{\ensuremath{-}}\ensuremath{-}{\mathrm{N}}_{2},0.5\ensuremath{-}60$ eV for ${e}^{+}\ensuremath{-}{\mathrm{CO}}_{2}$, and $2\ensuremath{-}50$ eV for ${e}^{\ensuremath{-}}\ensuremath{-}{\mathrm{CO}}_{2}$. The onset of positronium formation is clearly seen by an abrupt rise in the total cross sections for positrons colliding with each of the molecules at the respective positronium-formation thresholds. The positron measurements are compared with the electron measurements at intermediate energies for ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$. This comparison reveals a merging of the cross sections for ${\mathrm{H}}_{2}$ at energies above 200 eV, while for ${\mathrm{N}}_{2}$ the electron results remain higher than the positron results at all energies. Estimates are made of potential experimental errors, as well as the experimental resolution for discrimination against projectiles scattered at small forward angles.

Total-cross-section measurements for positrons and electrons colliding with H 2 , N 2 , and C O 2

Total scattering cross sections have been measured in the same apparatus for positrons and electrons colliding with helium, neon, and argon atoms in the energy range from 15 to 800 eV using a beam-transmission technique. These measurements reveal a merging of the positron and electron cross-section curves for helium at energies above 200 eV while the available theories predict this merging to occur at considerably higher energies. For neon and argon the positron and electron total-cross-section curves are slowly approaching each other at the highest energies. The present experimental approach is analyzed with regard to the discrimination against small-angle forward elastic scattering, and estimates are made of other potential errors in the measured total cross sections. The present results are used to test the zero-energy sum rule, obtained from forward dispersion relations, and it is found that these data are consistent with prior measurements in that the sum rule is found to fail for electron scattering and to be valid for positron scattering.

Measurements of total scattering cross sections for intermediate-energy positrons and electrons colliding with helium, neon, and argon

Total scattering cross sections have been measured for 0.3--31 eV positrons colliding with helium atoms and for 0.25--24 eV positrons colliding with neon atoms using a beam-transmission technique. These measurements have resulted in the first direct observations of Ramsauer-Townsend effects for positrons colliding wih helium and neon, and also provide clear indications of the onset of positronium formation in each of these gases. As an over all check of the reliability of the experimental approach for measuring total scattering cross sections for positrons, electron-atom scattering cross sections have been measured in the identical apparatus, using the same target gases, and the same technique as was used for the positron measurements.

Measurements of total scattering cross sections for low-energy positrons and electrons colliding with helium and neon atoms

We have measured total (${\mathrm{Q}}_{\mathrm{T}}$ ) and positronium formation (${\mathrm{Q}}_{\mathrm{Ps}}$ ) cross sections for 1--302-eV positrons (${\mathrm{e}}^{+}$ 's) and ${\mathrm{Q}}_{\mathrm{T}}$ 's for electrons (${\mathrm{e}}^{\mathrm{\ensuremath{-}}}$ 's) scattered by hydrogen atoms and molecules. A beam transmission technique is used to measure ${\mathrm{Q}}_{\mathrm{T}}$ 's where the projectile beam passes through a low-temperature scattering cell containing a mixture of hydrogen atoms and molecules generated in an adjacent radio-frequency discharge region. ${\mathrm{Q}}_{\mathrm{Ps}}$ 's are measured using the same scattering cell by detecting coincidences of 511-keV annihilation \ensuremath{\gamma} rays produced by the decay of para-Ps and by the interaction of ortho-Ps with the walls of the scattering cell in which the Ps is formed. The present ${\mathrm{e}}^{+}$ -H ${\mathrm{Q}}_{\mathrm{T}}$ 's and ${\mathrm{Q}}_{\mathrm{Ps}}$ 's agree very well with theoretical calculations. Comparisons of the present ${\mathrm{e}}^{+}$ and ${\mathrm{e}}^{\mathrm{\ensuremath{-}}}$ -H ${\mathrm{Q}}_{\mathrm{T}}$ 's show a merging to within 20% for energies above 12 eV.

Measurements of total and positronium formation cross sections for positrons and electrons scattered by hydrogen atoms and molecules

Total cross sections (${Q}_{T}$'s) have been measured for 1--500-eV positrons and electrons scattered by ${\mathrm{O}}_{2}$, ${\mathrm{CH}}_{4}$, and ${\mathrm{SF}}_{6}$ using a beam-transmission technique. The positron ${Q}_{T}$'s are compared with the corresponding electron ${Q}_{T}$'s for each target gas. It is found that the positron ${Q}_{T}$'s are, in general, lower than the electron results. There are no prominent structures observed for positron scattering at low energies that would be comparable to the narrow shape resonances observed for electrons scattering from various molecules, such as ${\mathrm{SF}}_{6}$. The positron ${Q}_{T}$ curve for ${\mathrm{CH}}_{4}$ reveals a significant increase in the vicinity of its positronium formation threshold, while the ${\mathrm{O}}_{2}$ and ${\mathrm{SF}}_{6}$ curves are monotonically increasing in this vicinity. At the highest energies investigated, there are indications of a tendency toward merging of the positron and electron ${Q}_{T}$'s for these gases. Interesting similarities are found in a comparison of the present positron and electron ${Q}_{T}$ curves for ${\mathrm{CH}}_{4}$ with prior comparison measurements for argon.

W. E. Kauppila

Papers

Total-cross-section measurements for positrons and electrons colliding with H 2 , N 2 , and C O 2

Measurements of total scattering cross sections for intermediate-energy positrons and electrons colliding with helium, neon, and argon

Measurements of total scattering cross sections for low-energy positrons and electrons colliding with helium and neon atoms

Measurements of total and positronium formation cross sections for positrons and electrons scattered by hydrogen atoms and molecules

Total-cross-section measurements for positron and electron scattering by O 2 , CH 4 , and SF 6