Quasi-Stationary Process

Quasi-Stationary Process


a process in a limited system that spreads within the system so quickly that in the time required for it to expand to the limits of the system its state does not have time to change.

In examining a quasi-stationary process it is possible therefore to disregard the time required for it to spread through the system. For example, if a variable external electromotive force is at work in some section of a closed electric circuit but the time required for the electro-magnetic field to spread to the remotest points of the circuit is so short that the amplitude of the electromotive force does not have a chance to change appreciably, then the changes in voltages and currents in the circuit may be considered a quasi-stationary process. The variable electric and magnetic fields generated by the electric charges (whose distribution and velocities change with time) moving in the circuit prove to be the same at each instant as for stationary electric and magnetic fields (the fields of stationary charges and currents), whose distribution and velocities (which do not change in time) coincide with those of the charges present in the system at the instant under consideration.

However, in the case of nonstationary currents, eddy fields induced by changes in the magnetic fields arise in addition to the electric fields of the charges. The effect of these fields can be taken into account by introducing the induced electromotive force (in addition to the electromotive force of nonelectromag-netic origin from the sources). The introduction of the induced electromotive force does not violate the main feature of stationary currents—the equality of current intensities in all sections of a nonbranching circuit. For this reason, Kirchhoffs laws are valid for electric circuits satisfying the conditions of the quasi-stationary (quasi-stationary currents).

The conditions defining quasi-stationary processes can be formulated most simply for the case of periodic processes. Processes may be considered quasi-stationary if the propagation time between the points of the system under consideration that are most remote from each other is short in comparison to the duration of the process or if the distance between these points is small in comparison to the corresponding wavelength (which amounts to the same thing).

The concept of quasi-stationary processes may also be applied to other systems (for example, mechanical and thermodynamic). If, for example, one end of an elastic rod is acted on by a variable external force directed along the rod, and if the process is quasi-stationary, that is, if the magnitude of the force does not have time to change during the period required for a longitudinal elastic wave to spread from one end of the rod to the other, then the accelerations of all points in the rod at each instant are determined by the value of the force at the same instant. The process of thermal conductivity may be considered quasi-stationary if equalization of the temperature in the heat-conducting rod takes place much more rapidly than does the change in external conditions—the temperatures T1 and T2 of the ends of the rod.