Transverse Drift Velocity Research Articles

Townsend's first ionization coefficients in crossed electric and magnetic fields in nitrogen

Townsend's first ionization coefficient (αT) in crossed electric and magnetic fields has been measured in nitrogen over the range of 140 ≤ E/p ≤ 360 volts cm−1 torr-1 and E/p ≤ 650 Oe torr−1. A coaxial cylinder geometry has been employed to avoid diffusion losses in the Ē.× H¯ direction. The initial photoelectric current is obtained by making the ultra-violet radiation obtained in an auxiliary glow discharge fall on the cathode of the coaxial cylinder geometry. Prebreakdown currents in the range of 10−12 − 10−9 amps are measured using the pressure variation technique of Townsend's experiment. The results of Bagnall and Haydon (1965), and Heylen and Bunting (1969) overlap with the present results over a relatively small range of E/p and E/p. Using the equivalent pressure concept the electron molecule collision frequency γ has been derived for the above range of E/p and E/p. It has been observed that γ changes with E/p at a constant E/p and also that γ changes as a function of E/p at a constant E/p. The transverse drift velocity for electrons in crossed fields has been derived from the measured Townsend first ionization coefficient.

Effect of a transverse drift velocity of the electrons on helicon waves in InSb

Helicon waves are excited from an evanescent microwave at 1 to 2 GHz above an InSb rod subjected to crossed static electric and magnetic fields. The recorded variations of microwave power against static magnetic field B, sample temperature, and sample current are explained by invoking the existence of “modified” helicon waves. From theoretical calculations, the electronic drift velocity involves a longitudinal component of the microwave electric field. This one is proportional to the drift velocity, the phase velocity of the helicon wave remaining unaffected. This model is able to explain the measurements. The main parameters of the semiconductor (mobility, carrier concentration, and drift velocity) are deduced from the experimental results. Dans notre experience, une sonde excitatrice cree une onde evanescente a une frequence de l'ordre de 1 GHz, au-dessus d'un barreau d'InSb type p. On applique un champ magnetique statique perpendiculaire a l'axe du barreau qui est parcouru longitudinalement par un courant. La variation de la puissance microonde detectee quand l'on fait varier la valeur du champ B, la temperature de l'echantillon (c'est-a-dire la densite des porteurs) ou la vitesse de derive des electrons, est expliquee par l'excitation d'une onde Helicon „modifiee” le long de B. D'apres les calculs theoriques, la presence d'une vitesse de derive provoque l'apparition d'une composante longitudinale du champ electrique proportionnelle a cette vitesse alors que la vitesse de phase n'est pratiquement pas modifiee. Ce modele nous permet d'interpreter correctement nos mesures. Nous sommes donc en mesure de determiner, d'apres les releves experimentaux effectues, la mobilite, la concentration des porteurs et la vitesse de derive des electrons aux differentes temperatures realisees.

Moderate and strong magnetic field electron drift velocities in nitrogen, oxygen and air†

Abstract By means of the equivalent reduced electric field concept, calculation of the electron transverse and perpendicular drift velocity and their ratio, tan θ, is extended to a moderate and a strong crossed magnetic field for nitrogen, oxygen and air, for average electron energies, from 0-1 to 10 ev. Data are presented on a constant electron energy rather than constant E/p basis. It is shown numerically that the prior assumed constant electron collision frequency values, derived from the various transport coefficients, inherently vary widely (by about a factor of 2(. Even for a given transport coefficient and constant electron energy, the collision frequency changes with applied magnetic field ( also by a factor of 2). The advantage of carrying out experiments at constant electron energy in the presence of a crossed magnetic field is discussed.

Trajectory of Charged Particles in Weakly Inhomogeneous Magnetic Fields

The detailed time dependence of the trajectory, and particularly of the acceleration, of a charged particle moving nonrelativistically in a weakly inhomogeneous, slowly varying electromagnetic field is calculated by a method that involves superimposing a conventional perturbation expansion in the weak field on the expansion of Berkowitz and Gardner and of Kruskal, the latter expansion being asymptotically valid in the limit of small Larmor radius and slowly varying fields. Fourier transforms are introduced to facilitate isolation of rapidly varying terms from the most general solutions for the coefficients in the expansion. The calculations are carried to first order in the weak inhomogeneity and (at least formally) to all orders in Larmor radius. The resulting velocity reproduces the familiar transverse drift velocities of first-order orbit theory, emphasizes that in the presence of fields varying slowly in time the polarization and curvature drifts are to be calculated from the time derivative of the fields as seen from a frame of reference fixed with respect to the guiding center of the particle's orbit, and permits calculation of higher-order contributions to the drift velocities, contributions of second order in Larmor radius being explicitly evaluated; the resulting acceleration prepares the way for a study of the effect of weak inhomogeneities on the radiative output of single particles.

Spin-Orbit Effects in Crossed Electric and Magnetic Fields;Γ7Band of Wurtzite-Type Crystals

The ${\ensuremath{\Gamma}}_{7}$ conduction band of the wurtzite-type II-VI compounds has a spin-orbit term linear in k. Effects of this spin-orbit term in crossed electric and magnetic fields are investigated on the basis of a one-band formalism. The effective Hamiltonian is solved for four different cases, according to the strength of the crossed electric and magnetic fields: (A) Strong magnetic field and weak electric field---this is essentially the simple band case; (B) weak magnetic field and weak electric field (the coupling between cyclotron motion and spin states via the spin-orbit term plays a dominant role in determining the energy spectrum); (C) strong magnetic field and strong electric field. (The major contribution to the spin-orbit interaction comes from a term representing the influence of transverse drift motion upon spin states. As a result, the spin splitting exhibits a nearly linear dependence on the electric field, and the direction of the spin axis tends toward that of the electric field with increasing electric field); (D) weak magnetic field and strong electric field [both of the spin-orbit effects, which are predominant either in the case (B) or in the case (C), are equally important, and perturbation theory is not applicable. Variational solutions have amplitudes distributed over many Landau and spin states, so that the selection rule for the intraband transitions is relaxed.] The conditions for observing these spin-orbit effects by means of intraband transitions are discussed for the actual II-VI compounds. It is found that spin-orbit effects may possibly be observed in magnetic dipole transitions under the condition of case C for CdS and ZnS, as well as in electric and magnetic dipole transitions under the condition of case A or C for CdSe. In the strong electric field of case C, the transverse drift velocity is one or two orders of magnitude larger than the velocity of sound in the crystal. Hence, phonon clouds build up around an electron to cause broadening of the resonance line. This can be avoided by carrying out the resonance experiment before the phonon clouds build up, i.e., by employing a pulsed transverse electric field.

Electron drift velocities in a moderate and in a strong crossed magnetic field†

From energy balance considerations in the presence and absence of a crossed magnetic field and without assuming an a priori constant electron collision frequency, an equivalent reduced electric Held concept is evolved which reduces to the more familiar equivalent pressure one when the electric field is kept constant. Using the concept and assuming a Maxwellian electron energy distribution, calculation of the electron transverse and perpendicular drift velocity and their ratio tan θ is extended to a moderate and strong magnetic field for hydrogen gas. The results are in good agreement with experimental data in the electron energy range where ionization by collision occurs. It is shown numerically that average electron collision frequency values, derived from the various transport coefficients, inherently vary widely. If the average electron collision frequency is derived from a given transport coefficient, then its value still depends on the magnitude of the reduced magnetic field even when the average ele...

Calculated magnetic electron drift velocities in H2, N2, O2, air and C2H6for 10

The influence of the ratio of magnetic field to gas pressure on the perpendicular and transverse drift velocity of an electron swarm is examined quantitatively for H2, N2, O2, air and C2H6 for mean energies from 0?1 to 10 ev. Whereas the perpendicular drift velocity reaches a peak value when the electron collision frequency is approximately equal to the cyclotron frequency, the transverse velocity starts to decline when this equality is reached. In contrast, the ratio of the perpendicular to transverse velocity, which is shown to be an important quantity governing gaseous discharge movement, continues to increase with B/p; the increase is almost linear throughout except for gases exhibiting the Townsend-Ramsauer effect. Expressions are derived for the low and high magnetic field case and values in the intermediate region, which lies in the range 10-3 B/p 10-1 Wb m-2 torr-1, are obtained numerically. The mobility values for the different gases at a fixed value of mean energy and B/p differ by up to a factor of 10, and this should allow discharge propagation velocities to be identified with particular movement mechanisms unless obscured by feedback processes. At low magnetic fields the perpendicular drift velocity is derived as a function only of B/p and E/p. If the equivalent pressure concept were used in the derivation of Amp?re's law, the magnitude of the force on a conductor in a crossed magnetic field would be higher than hitherto accepted. The relevance and application of the calculated magnetic transport data to practical discharges are mentioned briefly.

The influence of a crossed magnetic field on a gaseous Townsend discharge

The early treatment by Townsend of the influence of a crossed magnetic field on the movement of an electron swarm in a uniform electric field is extended to high electric fields when ionization occurs and secondary processes can no longer be neglected. It is shown that the discharge moves bodily in the ev×B direction with a velocity, when secondary electron emission by positive ion bombardment of the cathode takes place, given by v = vT+ (tan θ− + tan θ+)(τ+/τs + τ+) in which νT+ is the transverse ion drift velocity, θ− and θ+ are the electron and ion deflection angles and τ+ and τs are the ion transit and site times. The site time is the delay which occurs between the impact of a positive ion on to a surface and the subsequent emission of an electron; the transit time is the time it takes for the ion to cross the gap. When secondary electron emission by photon bombardment takes place, the propagation velocity of the gaseous discharge is given by v = vperp(v*/vT− + v*) in which ν* is the photon velocity and νperp- and νT- are the electron perpendicular and transverse drift velocity respectively. Because of the importance of θ-, the dependence of the perpendicular and transverse electron drift velocity on collision cross section, mean energy, E/p and B/p is examined in detail over a wide range and quantitative results obtained for hydrogen. Whereas νperp− reaches a maximum with increase in B/p when v0 approximately equals eB/mp, tan θ− continues to increase linearly with B/p from low to high magnetic fields. Good agreement is obtained with some but not all of the experimental data reported in the literature. The need for similar data on positive ions is pointed out.

Transverse Fields, Hall Currents, and Electron Drift Velocities in a θ-Pinch

Transverse Fields, Hall Currents, and Electron Drift Velocities in a θ-Pinch