Transverse Diffusion Coefficient Research Articles

Comparison of Monte Carlo and Boltzmann calculation of electron diffusion to absorbing electrodes

Calculations have been made of the effect of absorbing electrodes on a continuous stream of electrons travelling in a gas in a uniform electric field. The effective electron drift and diffusion coefficients become a complex function of position, so that the electron density distribution is no longer given by the solution of the electron continuity equation using the usual equilibrium drift velocity and either the transverse or the longitudinal diffusion coefficients appropriate to the applied electric field and gas pressure. Calculations for a momentum transfer cross-section proportional to electron speed indicate an increase of the average electron energy of about a factor of two at the anode. Predictions using Monte Carlo methods and solutions of the Boltzmann transport equation are in good agreement. Monte Carlo calculations are also applied to predict the influence of absorbing boundaries on the Townsend-Huxley experiment (1974). Predicted current ratios compared with ratios obtained from a solution of the continuity equation lie between ratios obtained using both isotropic and conventional transverse and longitudinal diffusion coefficients.

Diffusion and the power spectral density of velocity fluctuations for electrons in InP by Monte Carlo methods

The low-frequency parallel and transverse diffusion coefficients for electrons in InP are calculated using Monte Carlo methods for lattice temperatures of 200, 300, and 500 K. The sensitivity of the computed values to the duration of the flight sampling time is investigated, and this is shown to be a consequence of the frequency dependence of the diffusion coefficient. To test this hypothesis the variation of the parallel diffusion coefficient with both frequency and field at 300 K is determined. For fields above threshold the parallel diffusion coefficient first rises from its low-frequency value to a maximum and thereafter decreases with increasing frequency; for fields substantially below threshold a slow monotonic decrease is observed.

Measurement of the transverse diffusion and Townsend's first ionisation coefficients from the observation of the photon flux produced in a Townsend discharge in molecular hydrogen

The method used to obtain the transport parameters of a Townsend discharge reported by Blevin et al. in 1976 from the observation of the photon flux produced in the discharge has been extended to enable measurements of the transverse diffusion coefficient and Townsend's first ionisation to be made. The results obtained in molecular hydrogen are now reported.

Diffusion coefficient of hot electrons in GaAs

The longitudinal and transverse diffusion coefficient of hot electrons in GaAs at a lattice temperature of 300 K has been calculated by the Monte Carlo technique. The calculations showed that drift velocity and diffusion coefficient of hot electrons in GaAs can be fitted to available experimental data if the three-valley Γ- L- X model is used. The estimates of some parameter values of GaAs conduction band have been made.

Anisotropy of the differential conductivity and of the transverse diffusion coefficient in n-type silicon

Measurements of the transverse differential conductivity of hot carriers in semiconductors are performed, for the first time, using an experimental setup described in the present paper. This allows the determination of the transverse diffusion coefficients.

TURBULENT DIFFUSION IN CHANNELS WITH A SURFACE COVER

The effect of a surface cover (ice-cover) on transverse spreading of a tracer released at a constant and steady rate into a turbulent channel flow is investigated. Velocity, depth and transverse profiles of tracer concentration were obtained at four cross-sections downstream of the tracer source. It is shown that the transverse diffusion coefficient for ice-cover conditions, in a straight rectangular channel, is approximately 50% smaller than the corresponding coefficients for open water conditions. However, when these coefficients are normalised with the product of shear velocity, u *, and hydraulic radius, R, they do not differ significantly. An expression is derived for evaluating the average transverse diffusion coefficient over a channel reach by using concentration measurements at one station downstream of tracer source. This expression is found to give good results.

Self-diffusion and undulation modes in a Smectic A liquid crystal

High-resolution neutron quasi-elastic scattering measurements on an aligned smectic A sample of terephthal-bis-butyl-aniline are presented and analysed in terms of self-diffusion and undulation mode motions. (1) We find good agreement with the longitudinal and transverse diffusion coefficients D measured by Krüger et al. [5] using spin-echo techniques. (2) We conclude that self-diffusion alone is sufficient to explain both our line widths and line shapes. The undulation mode contribution to the broadening, if present, is too small to be seen in our range of wave vectors.

Dispersion Models in Coastline Waters with Predominant Transverse Shear

SYNOPSISMixing problems in a shallow coastline water with horizontal velocity distribution are cosidered. The maximum scale within which mixing phenomena are classified into diffusion in coastline waters is first inferred from existing data. Law of similitude in a reasonably straight channel is reconsidered for a distorted Froude similarity model focusing our attention on the three-dimensional velocity distribution. An analysis of the dispersion in the flow field which has the deviation of flow velocity in transverse direction due to meso-scale turbulence of topographical origin has been performed through a circulation model.The circulation model permits the estimation of the longitudinal dispersion coefficient from the geometry and the flow velocity of the system, making use of the experimental relationship between the transverse diffusion coefficient and the intensity of the circulation in wake regions obtained in a simple hydraulic model. Agreement of the predicted value of the longitudinal dispersion ...

Ratio of transverse to longitudinal resistivities of isolated cardiac muscle fiber bundles

The ratio of transverse to longitudinal resistivities (рt/р1) of isolated cat cardiac muscle bundles (papillary muscles and ventricular trabeculae) composed of parallel fibers was measured and compared with frog sartorius muscles. Similar measurements made on a physical model representing such bundles of parallel fibers, consisting of layers of glass rods orderly packed with Ringer solution filling the interstices, gave a рt/р1 of 7. This ratio averaged 11 for cardiac muscle and 21 for skeletal muscle, indicating that in both muscles the transverse conductivity and effective diffusion coefficient are much less than the longitudinal values. Equilibration of cardiac muscle in ten-fold diluted Ringer (sucrose to isotonicity) to raise the resistance of the interstitial fluid (ISF) 8.5-fold raised р1 6.3-fold, but hardly affected р1, so that рt/р1 was markedly reduced to 2.0. In sartorius, the high-resistance solution had much less of an effect on р1 or on рt/р1. Equilibration in hypertonic Ringer (2 X isotonicity with sucrose) raised р1 and lowered рt slightly in both types of muscles, resulting in a small decrease in рt/р1. Calculations of the ratio of the resistance of the cellular pathway to that of the extracellular pathway averaged 20 for cardiac muscle compared to only 0.82 for skeletal muscle. The data indicate that the longitudinal current path through the myocardial cells is high in resistance compared to that through the ISF, suggesting that the intercalated disks are high-resistance membranes. The resistivity of the disk membranes averages 576 Ω-cm2, assuming a 6.4-fold increase in surface area due to convolutions; this value approaches that of the sarcolemma, and is much higher than the maximum (2 Ω-cm2) allowable for significant DC electrical coupling to occur between contiguous cells. The fact that the extracellular fluid of a parallel-fibered muscle bundle itself acts as a cable could account for the observation that measurements of the tissue length constant by extracellular application of current give large values; thus, such measurements cannot be used to determine the resistance of the cell junctions in muscles composed of short cells.

Transport coefficlents of gaseous ions in an electric field

The linear Boltzmann equation for the motion of ions or electrons in neutral gases is solved by a moment-expansion method to obtain mobilities and diffusion coefficients in both pure gases and multicomponent mixtures as functions of electric field strength and temperature. The results are valid for all mass ratios and all forms of ion-neutral scattering, the only limitation being the assumption of elastic collisions. The transport coefficients are found as series in ( E N ) 2 , but this explicit field dependence is eliminated to produce relations among experimental quantities. Among these are relations giving the longitudinal and transverse diffusion coefficients in terms of the mobility, and the composition dependences of the diffusion coefficients and the mobility at different electric field strengths in terms of the mobilities in the pure components. Some numerical examples and comparisons with experiment indicate that these relations are useful to high values of the electric field. Deviations from Fick's law of diffusion are shown to involve only higher derivatives of ion density; the first two higher-order transport coefficients are calculated to a first approximation and their effects on ion diffusion discussed.

Transport properties of the three-dimensional guiding-centre plasma

Equilibrium and non-equilibrium properties of the three-dimensional guiding-centre plasma (in which the particles move with the guiding-centre drift across constant magnetic field lines, and according to Newton's laws along the field lines) are investigated. In equilibrium, the transverse spatial diffusion and conductivity coefficients are calculated, and are shown to be related via a generalized Einstein relation. The diffusion coefficient consists of a Bohm-like 1/B contribution which tends to zero as the plasma volume tends to infinity, as well as a classical 1/B2 contribution, which is independent of the size of the system. The Gibbs ensemble is constructed, and it is seen that thermal equilibrium results for the pair correlation, fluctuation spectra etc. are exactly the same as for the three-dimensional unmagnetized plasma. In the non-equilibrium case the appropriate Liouville equation and BBGKY hierarchy are considered. It is shown that to first order there is no tendency for the system (assumed spatially uniform) to relax towards thermal equilibrium.

Computer Simulation of an Electron Swarm at low E/p in Helium

A computer simulated electron swarm at E/P293 = 1�0 V cm -1 tore 1 in a model gas has been used to examine the validity of a recent theory of electron drift and diffusion. The computed results are in agreement with well-established theories for the electron energy distribution function, drift velocity and transverse diffusion coefficient, and confirm that, for a constant momentum transfer cross section, the longitudinal diffusion coefficient is approximately half the transverse coefficient. However, significant differences have been found between the computed swarm and the predictions of the theory of Huxley (1972). In particular, over the time scale considered, the electron swarm is not symmetric about its centroid but is spatially anisotropic in such a way that it could appropriately be described as 'pear shaped'.

Field Tests of Transverse Mixing in Rivers

Five tests were made on transverse mixing in rivers. The transverse turbulent diffusion coefficient, averaged over long flow distances, was as much as three times larger than the value for an equivalent straight rectangular flume. This increase is due to the additional mixing associated with the protective groins which were present and with the helical motion resulting from channel bends. Net transverse velocities exist in rivers and can cause the local rates of transverse spreading to be significantly different from the rate associated with the average diffusion coefficient. Recommendations are given for conditions to be met in order to obtain meaningful data from field tests on rates of transverse diffusion in rivers.

Predicted electron transport coefficients and operating characteristics of CO2–N2–He laser mixtures

Calculations have been made of transport coefficients of electrons in gas mixtures for ratios CO2:N2:He of 1:1:8, 1:2:3, 1:7:30, and 1:0.25:3. New cross sections for CO2 derived from swarm experiments are used together with previously published cross sections for N2 and He. Curves are presented of the predicted electron drift velocity, transverse and longitudinal diffusion coefficients, and ionization and attachment coefficients for E/N values ranging from 10−18 to 1 × 10−15 V cm2; E is the electric field strength and N the gas number density. Examples are given of derived distribution functions and comparisons are made with a Maxwellian distribution function. The percentage of the input electrical power which excites vibrational processes coupled to the 001 upper laser level of CO2 is given as a function of E/N. The maximum efficiency from these calculations increases for increasing ratios of N2:CO2, because the proportion of energy used to excite the bending and stretching modes of CO2 is then reduced. By assuming a recombination coefficient of 10−7 cm3 sec−1, the operating E/N for self-sustained glow discharges is predicted as a function of current density for various laser mixtures by equating the ionization rate to the attachment and recombination rate.

Ansiotropy of the Diffusion Coefficient in Nematic Liquid Solutions Measured by NMR Techniques

A gradient coil has been constructed for exact relative measurements of the longitudinal (Dʟ) and transverse (Dᴛ) diffusion coefficients of nematic liquid crystals and of small molecules dissolved therein. Some small molecules dissolved in the nematic phase of Licristal IV showed a Dʟ/Dᴛ ratio varying from about 1.1 to 1.25, depending on the concentration. In contrast, tetramethylsilane dis­solved in p-methoxy-benzylidene-p'-n-butyl-aniline showed no anisotropy in the nematic phase.

Ambipolar Drift, Deformation, and Diffusion of a Plasma in a Magnetic Field

The theoretical problem of a weakly ionized, constant temperature, three particle plasma in an externally generated magnetic field is reformulated by transforming the set of 14 macroscopic plasma equations (continuity and momentum equations for ions and electrons plus Maxwell's equations) in 14 unknowns (ion and electron number densities and velocities plus the effective electric and magnetic fields) into an equivalent set of 4 integral equations in 4 unknowns. In the course of this transformation, it is shown that the plasma behavior can be interpreted in terms of three ambipolar processes : drift, deformation, and diffusion. Plasma diffusion is characterized by two diffusion coefficients : the usual Schottky formula applying in the direction parallel to the effective magnetic field and a new expression for the ambipolar transverse diffusion coefficient applying in directions perpendicular to the effective magnetic field. The new ambipolar coefficient differs markedly from the familiar ambipolar coefficient associated with the names of Bickerton, Lehnert, Holway, Allis, and Buchsbaum; and, in general, it gives values for the transverse diffusion coefficient which are two orders of magnitude larger than those given by the latter. It is concluded that ambipolar diffusion can produce a transverse diffusion coefficient large enough to account for the diffusion rates measured by Bohm, Burhop, Massey, and Williams in argon arc discharges.

Collisional Diffusion in a Toroidal Pinch

Transverse diffusion coefficients in a toroidal pinch are investigated for three regions of collision frequencies. The configuration of a toroidal pinch is characterized by a large poloidal magnetic field B P comparable to a toroidal magnetic field B T . We calculated diffusion coefficients following the scheme of Galeev and Sagdeev. In a toroidal pinch particles can be trapped in a local magnetic mirror formed by both a toroidal magnetic field and a poloidal magnetic field. Furthermore B P ≃ B T reduces the connection length of a toroidal pinch. Transverse diffusion coefficients including these effects are shown to be smaller than D GS which is given by Galeev and Sagdeev. in the banana region \(D_{\bot}{\simeq}D_{\text{GS}}\sqrt{\delta/\varepsilon}\) is obtained and in the plateau region D ⊥ ≃ D GS (δ 2 / ε 2 ), where ε denotes an aspect ratio and a small parameter δ denotes the inhomogeneity of the toroidal magnetic field in the toroidal pinch. Here it is noted that a safety factor included in D ⊥ may be smaller than or comparable to unity. In the MHD region D ⊥ also includes a factor δ/ ε .

The Transverse Diffusion Coefficient in a Square Lattice

The transverse diffusion coefficient is calculated by integrating the current derived from heterogeneous multigroup dipole theory in a finite, square system, along two opposite sides of the square cell. Use of response coefficients allows the result to be presented in relatively simple form, regardless of fuel element complexity. Subsequently, the buckling dependence is eliminated from the diffusion coefficient, or reduced to lowest order, making it consistent with the low order approximation represented by dipole theory. Results are compared with other methods and a numerical example is given.

Transport phenomena in neutral and ionized gases

Transport processes in gases are examined from both the point of view of non-equilibrium thermodynamics and kinetic theory. Thermodynamics is used to establish concise representations of the general properties of transport coefficients, and in particular, it is shown how the redundancy of Onsager relations in systems with geometrical symmetries can be removed by using the theory of irreducible tensorial sets. The Boltzmann equation for fully and partially ionized gases is solved by a polynomial expansion of the distribution function, and expressions for transport coefficients are obtained in terms of the inverse of certain infinite-dimensional matrices. In the case of fully-ionized gases, it is shown that the approximations associated with the Fokker-Planck equation are accurate as long as the deviation from equilibrium is not substantial. Partially-ionized gases are considered under significantly nonequilibrium conditions brought about by application of an electric field. A new expression is obtained for ion mobility, and comparison is made with the earlier theories of Wannier and Kihara. For electrons, it is shown by way of direct numerical calculations that approximation of the distribution function by the first two terms of an expansion in Legendre polynomials is satisfactory even when the deviation from Maxwellian is substantial. Anisotropic diffusion of ions and electrons in an electric field is also examined, and expressions are derived for longitudinal and transverse diffusion coefficients both via solution of the Boltzmann equation and through thermodynamic analysis.

Transverse Diffusion and Conductivity Coefficients for a Three-Dimensional Magnetized Equilibrium Plasma

Equilibrium transport coefficients are calculated for a three-dimensional magnetized plasma. It is shown that the transverse spatial diffusion and conductivity coefficients are related via a generalized Einstein relation. These coefficients have both a $\frac{1}{B}$ (volume dependent) term (with $B$ a uniform magnetic field) as well as a $\frac{1}{{B}^{2}}$ (volume independent) term for a finite plasma. For an infinite plasma, the coefficients have a "classical" $\frac{1}{{B}^{2}}$ dependence.