Scattering of Electrons in Ionized Gases

Abstract

Velocity distribution of electrons in low pressure discharges from hot cathodes.---Analysis of the current received by a collector placed opposite a hot cathode indicates that there are three groups of electrons present; (1) primary electrons which retain practically all the momentum they acquired in passing through the positive ion sheath around the cathode; (2) secondary electrons moving in random directions with a Maxwellian velocity distribution corresponding to a temperature roughly proportional to the energy of the primaries (200,000\ifmmode^\circ\else\textdegree\fi{} for 100 volt primaries) and approximately independent of the nature or pressure of the gas or the current density; (3) ultimate electrons having a Maxwellian distribution of velocities corresponding to a much lower temperature than that of the secondaries, a temperature which is independent of the current density or the voltage of the primary electrons and which varies with the gas used and decreases slowly as the pressure is raised. The number of ultimate electrons is roughly 1000 times that of the primaries and secondaries for mercury vapor, although relatively less numerous in the case of hydrogen. In the uniform positive column of arcs only ultimate electrons are present.The velocity distribution of the primary electrons may be resolved into a drift velocity normal to the cathode surface and a random motion with a Maxwellian distribution corresponding to a temperature which varies approximately with the square of the current and is a maximum at a mercury vapor pressure of about 0.6 bar, falling to a low value at 8 bars, and is considerably higher with 35 volts accelerating potential than with 80 volts. Under favorable conditions with 40 mil-amp. this temperature may rise to 80000\ifmmode^\circ\else\textdegree\fi{} and there are then appreciable numbers of these primaries which can reach a collector charged to a potential as much as 40 volts below that of the cathode. Experiments with two crossed electron beams prove that the secondary and ultimate electrons, directly or indirectly, are responsible for very little if any of the scattering.A study of the ultimate electrons in the positive column of a low voltage mercury arc shows that the Maxwellian velocity distribution corresponding to a high temperature (30000\ifmmode^\circ\else\textdegree\fi{}) is maintained in a small tube in spite of the fact that the negatively charged walls of the tube constantly tend to disturb this distribution by selective removal of the faster electrons. The number of collisions of the electrons with each other and with atoms were far too few to maintain the observed distribution. Measurements of the mobilities of electrons in arcs and of the electron concentration differences produced by a transverse magnetic field gave values for the mean free path only 1/10 as great as the values determined by a direct method. These results all indicate that the electrons in low pressure arcs suffer many changes of momentum during the time intervals between successive collisions between atoms, ions or electrons.Mechanism of electron scattering.---After analyzing the effects to be expected when a beam of primary electrons encounters a cloud of stationary electrons or a cloud of particles of small mass but of high temperature, it appears that the experimental results for the ratio of the scattering to the average retardation of the beam was best accounted for by collisions with a cloud of radiation quanta, a kind of Compton effect. The observed scattering is, however, about ${10}^{16}$ times greater than a normal Compton effect would give It is suggested that the joint action of excited atoms and radiation may multiply the Compton effect sufficiently, or it may be that the presence of a free electron within a distance of a wave-length from an excited atom may greatly increase the probability of a quantum jump and that momentum is delivered to the electron in the process. In arcs the ultimate electrons may be in a kind of thermal equilibrium with radiation and excited atoms.Scattered electrons in high vacuum.---In connection with a study of the Barkhausen-Kurz effect and in a magnetron with negatively charged end plates, exidence of the presence of electrons with abnormally high speeds has also been obtained. These have been explained as due to electric oscillations, but the effects have also been obtained when oscillations are not present. This seems to indicate that electron scattering similar to that observed in low pressure gases can also occur in high vacuum.