Electron actual drift velocities

When the discharge has been set up, there is a movement of electrons from cathode to anode and a corresponding movement of positive ions from the anode to cathode. These transfers of electrons and ions to each electrode must balance to maintain electrical neutrality in the circuit. Thus, the number of positive ions discharging at the cathode must equal the number of electrons discharging at the anode. This occurs, but the actual drift velocities of electrons and ions toward the respective electrodes are not equal. 

Two other attempts, without the use of a distribution function, are worth mentioning, as these are operationally related to experiments and serve to give a rough estimate of the thermalization time. Christophorou et al. (1975) note that in the presence of a relatively weak external field E, the rate of energy input to an electron by that field is (0 = eEvd, where vd is the drift velocity in the stationary state. Under equilibrium, it must be equal to the difference between the energy loss and gain rates by an electron s interaction with the medium. The mean electron energy is now approximated as (E) = (3eD )/(2p), where fl = vd /E is the drift mobility and D is the perpendicular diffusion coefficient (this approximation is actually valid for a Maxwellian distribution). Thus, from measurements of fl and D the thermalization time is estimated to be... 

In order to obtain reliable rate data at elevated pressures in sources employing continuous ion extraction, it is necessary to know the time that the reactant ion remains in the ion source. At conditions above about 0.1 Torr, it is no longer permissible to assume the time to be the free-fall time in the empty source. At higher pressures, it becomes necessary to compute the retention time from the mobility ft = Ho d lp) T/2Ti). The drift velocity is t) = pE, where E is the field strength. The time in the source is l/v, where I is the distance from the center of the electron beam to the ion exit slit. At elevated pressures, the time will thus increase with pressure. Consequently, the reaction order will appear greater than it actually is. For example, Chong and Franklin found that the reaction... 

Up until the early 1960 s the electron transport coefficients w (electron drift velocity) and (transverse electron diffusion coefficient) were considered to be independent of N. This is probably because the experimental studies were traditionally conducted at low N (gas pressures < 1 atm). The transport coefficients w and [actually D /y where ]i is the electron mobility (w=yE)] are functions of the gas, T, and E/N (e.g., see Hunter and Christophorou, 1984). 

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