By directly solving the Boltzmann equation in the path integral form, the position and time dependent velocity distribution of electrons f(x, v, t) is accurately calculated perhaps for the first time. In this method, the position and time resolved transport quantities z(x, t) which give clear insight for the inner structure of an electron swarm are easily calculated. The calculation of the transport coefficients in definitions for each type of e xperiments such as PT, SST, and of arrival time spectra are also possible. The theory and procedures of this analysis and the preliminary results calculated in the ramp model gas of Reid within bounded space are presented with discussion.

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An exact expression of the mean arrival time drift velocity W_m of electrons in swarms in gases is deduced by taking into account the third and higher order gradient terms in the continuity equation. Here, W_m is defined as the ratio of the difference between the two positions in the field direction to the difference between the mean arrival times of electrons at the positions. The deduced expression is:
W_m=W_r-2α_TD_L+3α_T²D₃-4α_T³D₄+…,
where W_r is the center-of-mass drift velocity, D_L is the longitudinal diffusion coefficient and D_n (n_??_3) are the higher order coefficients. α_T is the Townsend first ionization coefficient. The importance of the present expression lies in that despite that W_m is the most commonly measured drift velocity by shutter techniques, there has been no exact expression for it, and also in that recent exact treatment of electron and ion swarms has started to consider the higher order coefficients.

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A numerical calculation shows that the mean arrival time drift velocity W_m and the average velocity W_v of the electrons in isolated swarms assume very close values with common gases such as Ar, N₂, CH₄ and SiH₄. If W_m=W_v is proved, there should be considerable influences on theoretical and experimental studies of electron swarms. The purpose of the present paper is to clarify if W_m=W_v. By a study using a Monte Carlo simulation technique and deliberately arranged model cross sections, it is found that W_m≠W_v in general. A reason why W_m_??_W_v in real gases is given.

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Transport coefficients defined as quantities to understand quantitative characteristics of swarm behaviors of charged particles have often been used for any weakly ionized gas medium as clear concepts. However, when positive ions are generated only by elecctrons for example, the positive ion swarm is influenced by the electron swarm. Therefore, transport coefficients for the positive ions should be distinguished from those obtained theoretically and experimentally only in some fundamental process of the positive ion swarm. This means that suitable expressions of the transport coefficients are given for a balanced mechanism between the generation and the loss of charged particles to maintain the steady state of the media. In the present paper, the mobility and diffusion coefficient are treated especially for positive ions under the abovepoint of view. In addition, the problem in the cylindrical positive column of a glow discharge is discussed as an example.

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The electron swarm parameter in a spatially uniform RF field has been investigated in Ar and in the model gas with the Ramsauer-Townsend minimum. Second-order analysis of the time dependent energy distribution has been executed over the range of angular frequency of the driving field between 10⁵ and 10⁸ s^-1 at an R. M. S. reduced-field of 50 Td and 1 Torr. Periodic nonlinear time behavior of the electron swarm has been exhibited and discussed from the viewpoint of the collisional relaxation time and the period of the driving field.

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The present paper reports the effective ionization coefficient α/p(=α/p-η/p) and the total secondary ionization γT for Ar and C₃F₈ mixtures measured by the steady-state Townsend method for 70<E/p<150V•cm^-1 Torr^-1, where α/p is the Townsend first ionization coefficient, η/p is the electron attachment coefficient, E is the electric field and p is the gas pressure reduced to 20°C. These gas mixtures are important for competent application in diffuse discharge opening switches. The results show that while α/p increases with E/p, the curve of α/p against ractional C₃F₈ partial pressure k monotonically decreases with k. It is also found that γT rapidly decreases with k.

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The electron impact ionization coefficient and excitation coefficient for Xe (1s₄) in He-Xe (1, 2, 5, 10, 20, 50%) gas mixtures have been measured as functions of E/N by using a Steady State Townsend (SST) method. The ionization coefficient becomes larger than that of pure He and Xe when the amount of Xe is less than 10%, while the excitation coefficient of the 1s4 level of Xe increases as the Xe concentration increases. These experimental values have been compared with the results of Boltzmann equation analysis, and the contributions of individual atomic processes to the effective values have been discussed. The determined coefficients would be useful for a simulation of the gas discharge in a plasma display panel.

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The electrons released from the cathode are controlled by the shutter pulse and they can move into the drift space while the shutter pulse is open. The electron swarm arrives at the collector after some drifting period. Electrons on the collector are introduced to a high-vacuum region through the orifice and detected with an electron detecting element as pulse signals. The detected electrons show some scattering on the arrival time. We get the arrival time spectra after a number of repetitions.
The drift velocity of electrons is obtained from the time interval between the time when the shutter is open and the time at which the arrival time spectrum shows the peak.
By this experimental apparatus using pulse-counting method, the drift velocities of electrons in N₂ and the mixed gas for a carbon-dioxide gas laser was measured over the range 15 Td_??_+E/N_??_60Td Td and 5Td_??_E/N_??_80Td, respectively. The present data for N₂ were in good agreement with those of J. J. Lowke [Aust. J. Phys., 16, 115(1963)], who used the ordinary time of flight method, over the E/N range. The result for CO₂ laser gas was compared with the calculated one using a twoterm Boltzmann equation and published sets of cross-sections.

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Electron drift velocities obtained by simulation of Schlumbohm's and Frommhold's experiments using a Monte Carlo method are compared with theoretical electron drift velocities such as the diffusion modified drift velocity V_d, the average drift velocity of electrons W_v, the center of mass drift velocity W_r and the mean arrival time drift velocity W_m, when electron impact ionisation is present. The calculation is carried out using a constant collision frequency model gas for reducing the computational time. It is found that the electron drift velocities calculated by simulating Schlumbohm's and Frommhold's experiments do not agree with any of the theoretical electron drift velocities described above, but coincide with a drift velocity represented as (W_r+W_m)/2.

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It is well known that the dielectric strength of ternary gas mixtures comprised of N₂, SF₆, and small amount of c-C₄F₈ is much higher than that of binary gas mixtures of N₂ and SF₆ under both of uniform and non-uniform DC fields. Electron swarm parameters of the binary and ternary gas mixtures are calculated by a Boltzmann equation. Especially, the authors focus ionization coefficients and electron attachment coefficients of the gases, and analyze and discuss the dielectric characteristics to investigate basic physical processes with respect to the mixing of gases from a point of ionization and electron attachment phenomena. Consequently, it is shown that the improvement in breakdown strength of gases results from the fact that more electrons attach to SF₆ due to the effects of c-C₄F₈ which acts as increasing the number of electrons in low electron energy range under low mixture ratios of c-C₄F₈.

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The Boltzmann equation used in a theoretical analysis of an excimer laser is discussed for finding an electron-energy distribution function in low reduced electric field strength below 0.5Td and clarifying the dependence of the electron attachment coefficient on the laser gas mixtures. Based on both numerical and experimental results, the generation of the discharge instability of a KrF laser is also discussed. Electron-energy distribution function as the solution of the Boltzmann equation can be obtained by transforming electron energy of a variable in the equation to the logarithm of electron energy. An electron attachment coefficient becomes large at the end of the first half cycle of the current through the laser gap. At the same time, the discharge instability of the excimer laser is generated. It is shown that the large change of the electron density owing to the attachment is possible to be one of the factors bringing the discharge instability. The electron-energy distribution function is largely varied with krypton and fluorine concentrations and affects strongly the attachment coefficient.

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One of the most important aspects of the glow discharge is the description of the cathode region. The cathode regions of N₂ glow discharge have been investigated using a spectroscopic technique in the current range 2-7mA, in pressure range 5 to 60 Torr. These glow discharges have a constricted positive column, while voltage-current characteristics are negative.
The cathode region extending from the cathode surface to about 2mm under the present experimental condition can be separated into three regims of cathode fall, negative glow and Farady dark space.
For comparisons between the present constricted glow discharges in N₂ and the diffused glow discharges in Ar, He and Ne at low pressures, the discharge luminescences are measured as functions of discharge current and gas pressure, and the axial distributions of rotational and vibrational temperatures are also estimated using the emission spectrum of the second positive bands of N₂ radiated from the glow discharge.
As a results, it can be seen that the electric and luminous charactristics of the constricted glow discharge was very different to those of the diffused glow discharge and also the discharge produced in the vicinity of the cathode was heated up to the rotational temperature of 400-800K and the vibrational temperature of 800-60, 000K.

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The time interval from voltage application to the arc occurrence in the impulse discharge process of a positive point to plane configuration having a protrusion on the plane was measured in air at low pressure. The time was compared with one in the configuration without protrusion under the same conditions. Simultaneously with the measurements of the time, the luminous phenomena of the discharge processes were examined by an image converter camera and a still camera.
Furthermore, before and after the frequent discharges, the surface condition of the protrusion exposed to the impulse discharges was observed by an electron probe microanalyser, and the binding energy of Cu-2p3/2 at the protrusion surface was investigated by means of a x-ray photoelectron spectroscope.
The main results are as follows: (1) The time till arc occurrence in the configuration with protrusion as compared with one in the configuration without protrusion is larger for low applied voltages and smaller for high applied voltages. (2) As the number of times of the discharge is increased, the time till arc occurrence is later and finally both of the time and the length of the discharge channel become roughly constant. (3) The surfaces of protrusion and plane are oxidized by frequent impulse discharges. Consequently, the change of cathode spot position occurs.

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The induced toroidal electric field is measured optically by using a Pockels device. The electric field induced by the conventional transformer method is generally smaller than 100V/cm and, in this works, a transformer with the multiple primary coils has been used for the field induction. On the measurement the electric field is much smaller in the Pockels device than in air due to the large permittivity (ε_s_??_56). In order to avoid the decrease in the sensitivity the measurement system has been put in water (ε_s_??_82). The retardation by Pockels effect is of the order of 10^-2 and the measurement values of the induced electric field are 40-200V/cm which are agreed with those calculated from one turn voltage within about 20%.

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