Applications Aspects of the Diffusion of Slow Electrons in the Ionospheric Gases

The paper presents the results of precise of the calculations of the diffusion of slow electrons in ionospheric gases, such as, (Argon – Hydrogen mixture, pure Nitrogen and Argon – Helium – Nitrogen) in the presence of a uniform electric field and temperature 300 Kelvin. Such calculations lead to the value Townsend's energy coefficient (KT) as a function of E/P (electric field strength/gas pressure), electric field (E), electric drift velocity (Vd), momentum transfer collision frequency ( ), energy exchange collision frequency ( ) and characteristic energy (D/?). The following physical quantities are deduced as function s E/P: mean free path of the electrons at unit pressure, mean energy lost by an electron per collision, mean velocity of agitation and the collisional cross-section of the molecules. The results are presented graphically and in tabular form. This results appeared a good agreement with the experimental data.

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Suppression of runaway of electrons in a Lorentz plasma. II. crossed electric and magnetic fields

Journal of Plasma Physics ◽

10.1017/s0022377800005146 ◽

1970 ◽

Vol 4 (3) ◽

pp. 441-450 ◽

Cited By ~ 1

Author(s):

Barbara Abraham-Shrauner

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Electric Field ◽

Electric Fields ◽

Cyclotron Frequency ◽

Collision Frequency ◽

Uniform Electric Field ◽

Drift Motion ◽

Electric And Magnetic Fields ◽

The Magnetic Field

Suppression of runaway of electrons in a weak, uniform electric field in a fully ionized Lorentz plasma by crossed magnetic and electric fields is analysed. A uniform, constant magnetic field parallel to a constant or harmonically time varying electric field does not alter runaway from that in the absence of the magnetic field. For crossed, constant fields the passage to runaway or to free motion as described by constant drift motion and spiral motion about the magnetic field is lengthened in time for strong magnetic fields. The new ‘runaway’ time scale is roughly the ratio of the cyclotron frequency to the collision frequency squared for cyclotron frequencies much greater than the collision frequency. All ‘runaway’ time scales may be given approximately by t2E Teff where tE is the characteristic time of the electric field and Teff is the ffective collision time as estimated from the appropriate component of the electrical conductivity.

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Структура призондового слоя в газоразрядной плазме при произвольной ориентации плоского зонда относительно электрического поля в плазме

Журнал технической физики ◽

10.21883/jtf.2019.10.48170.54-19 ◽

2019 ◽

Vol 89 (10) ◽

pp. 1545

Author(s):

O. Мурильо ◽

А.С. Мустафаев ◽

В.С. Сухомлинов

Keyword(s):

Electric Field ◽

Electron Energy ◽

Exchange Process ◽

Mean Free Path ◽

Ionization Rate ◽

Inert Gases ◽

Mutual Orientation ◽

Mean Velocity ◽

Charge Exchange Process ◽

The Mean

AbstractWe investigate the structure of the wall sheath of a gas discharge near a flat surface at a negative potential for high mean electron energy. It is shown that in the conditions where the mean energy of ions in the plasma is much lower than the mean electron energy, the parameters of the wall sheath weakly depend on the mutual orientation of the normal to the surface and the electric field in the plasma for an arbitrary ratio of the Debye radius to the ion mean free path relative to the resonant charge exchange process. It is found that for inert gases (He, Ar) for ratio E / P of the electric field to pressure exceeding 10 V/(cm Torr) in the plasma, the disregard of ionization in the perturbed wall sheath can lead to substantial errors in the calculation of its parameters. It is shown that the ionization leads to an increase in the electric field in the wall sheath and, as a consequence, to an increase in the mean velocity of ions at the boundary between the quasi-neutral presheath and the part of the perturbed wall sheath in which quasi-neutrality is substantially violated. The parameters of the wall sheath where quasi-neutrality is significantly violated depend on the ionization rate much less strongly than the corresponding parameters of the quasi-neutral presheath. We have determined the relation for concentration of charged particles in the unperturbed plasma from the ion saturation current considering the actual ion energy distribution function in the plasma as well as ionization in the presheath and the part of the perturbed wall sheath in which quasi-neutrality is violated significantly.

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The motion of electrons in gases

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

10.1098/rspa.1923.0039 ◽

1923 ◽

Vol 103 (720) ◽

pp. 53-57 ◽

Cited By ~ 4

Keyword(s):

Kinetic Theory ◽

Electric Field ◽

Free Path ◽

Mean Free Path ◽

Theoretical Formula ◽

Kinetic Theory Of Gases ◽

Thermal Agitation ◽

Mean Velocity ◽

Gas Molecules

The velocity ( v ) of an electron in a gas, due to an electric field of strength X, is given approximately by theoretical formula v = 0·815 X e λ/ m V. where e denotes the charge on the electron, λ its mean free path, m its mass, and V its mean velocity of thermal agitation. Townsend has made many determinations of this velocity v , and also of V, in several gases at different pressures ( p ) and finds that v is a function of X/ p , and that the values of λ given by the above equation are of the same order, in most cases, as those deduced from the viscosity by means of the kinetic theory of gases. The equation v = 0·815X e λ/ m V is obtained by assuming that there is no persistence of velocities when electrons collide with gas molecules.

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Experimental investigation of the diffusion of slow electrons in nitrogen and hydrogen

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1952.0225 ◽

1952 ◽

Vol 215 (1123) ◽

pp. 467-480 ◽

Cited By ~ 69

Keyword(s):

Experimental Investigation ◽

Cross Sections ◽

Mean Free Path ◽

Uniform Electric Field ◽

Tabular Form ◽

Energy Coefficient ◽

Slow Electrons ◽

Physical Quantities ◽

Unit Pressure ◽

Gas Pressures

This paper presents the results of precise measurements of the diffusion of slow electrons in hydrogen and nitrogen in the presence of a uniform electric field. Such measurements lead directly to the value of Townsend’s energy coefficient ( k T ) as a function of Z/p (field strength/gas pressure). Since the drift velocity ( W ) of the electrons is also known (Nielsen & Bradbury 1936), the following physical quantities are deduced as functions of Z/p : mean free path of the electrons at unit pressure, mean energy lost by an electron per collision and the collisional cross-sections of the molecules. Measurements of the diffusion were obtained from two apparatuses which differed in dimensions and metal of the electrodes. The range of gas pressures employed was 3 to 14 mm of mercury. A table shows that the values of k T as a function of Z/p derived from these measurements agree (with one exception) to within 3%, and it is therefore considered that the measurements are trustworthy. The results are presented graphically and in tabular form.

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Suppression of runaway of electrons in a Lorentz plasma.: I. Harmonically time varying electric field

Journal of Plasma Physics ◽

10.1017/s0022377800005079 ◽

1970 ◽

Vol 4 (2) ◽

pp. 387-402 ◽

Cited By ~ 4

Author(s):

Barbara Abraham-Shrauner

Keyword(s):

Electric Field ◽

High Frequency ◽

Particle Distribution ◽

Collision Frequency ◽

Uniform Electric Field ◽

Perturbation Scheme ◽

Time Varying ◽

Runaway Electrons ◽

Two Component ◽

Zero Frequency

The suppression of runaway electrons in a Lorentz plasma is demonstrated for a two-component, fully ionized plasma in the presence of a high frequency, weak, uniform electric field. The time for runaway to occur for electric field frequencies high compared to the collision frequency is longer than the runaway time for low electric field frequencies or zero frequency, by the ratio of the frequency of the electric field to the collision frequency squared. Both the resolvant method developed by Prigogine and co-workers and the double perturbation scheme of the Poincaré—Lighthill method are employed to derive the diffusion equation for the modified one-particle distribution function in the collision-dominated region of velocity space.

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Ionization, excitation, and chemical reaction in uniform electric fields II-The energy balance and energy efficiencies for the principal electron processes in hydrogen

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1936.0185 ◽

1936 ◽

Vol 157 (890) ◽

pp. 146-166 ◽

Cited By ~ 17

Keyword(s):

Electric Field ◽

Random Motion ◽

Electron Collision ◽

Uniform Electric Field ◽

Uniform Field ◽

Mean Velocity ◽

Electron Collisions ◽

Average Electron Energy ◽

Stationary Concentration ◽

Gas Molecules

In a previous communication, Part I, Emeléus, Lunt, and Meek* have discussed the rate of an electron collision process, ionization, in a uniform electrical field. In this paper we elaborate their analysis and extend it to five other types of electron collision processes. The discharge conditions now postulated are those of a swarm of electrons moving through a gas under the influence of a uniform electric field so that the system is in a steady state, the current density being sufficiently low so that the stationary concentration of all products of electron collisions (ions and excited particles) is negligible compared with that of the gas molecules in the ground state. Such conditions are realized with considerable exactitude in the uniform positive column. This is of particular importance because in such a discharge the rates of the various types of electron collisions contemplated in the present theory are sufficiently large to enable comparisons to be made between experiment and the predictions of the theory. There are many experiments, notably those of Townsend* and Langmuir, relating to the conditions now postulated which show the velocities of the electrons in the swarm are distributed at random about a mean, and that the mean velocity greatly exceeds that of the gas molecules (or atoms) in which the swarm moves; in a given gas the average electron energy, V electron-volts, has been shown by Townsend and his collaborators to be a function of X p -1, the ratio of the electric field to the gas pressure. In addition to this random motion, there is a relatively small drift motion of the swarm in the direction of the uniform field X ; the drift velocity, W cm. sec.-1, in a given gas is also a function of X p -1, and its magnitude determines the rate at which electrons gain energy from the field, and also the magnitude of the (drift) current carried by the ionized gas.

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The Diffusion of Slow Electrons in Deuterium

Australian Journal of Physics ◽

10.1071/ph550468 ◽

1955 ◽

Vol 8 (4) ◽

pp. 468 ◽

Cited By ~ 9

Author(s):

Barbara IH Hall

Keyword(s):

Cross Section ◽

Mean Free Path ◽

Lateral Spread ◽

Electron Stream ◽

Collisional Cross Section ◽

The Mean ◽

Energy Coefficient ◽

Slow Electrons ◽

Deuterium Molecule ◽

Unit Pressure

The agitational energies and drift velocities of slow electrons diffusing in deuterium are measured as a function of the ratio Z/p of the electric field strength Z to the gas pressure p. The lateral spread of the diffusing electron stream is measured, which enables Townsend's energy coefficient to be calculated. Drift velocities are measured using a magnetic deflection method. On the basis of the kinetic theory of gases these measurements are used to calculate values for the mean free path L of the electrons at unit pressure, the mean proportion η of the energy lost by an electron in a collision with a deuterium molecule, and the collisional cross section A of the molecules in collisions with the electrons. The values obtained are compared with those of Crompton and Sutton (1952) for hydrogen.

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