The measurement of high gas temperatures using colliding shock waves

The attenuation of a shock wave travelling through an arc discharge is a major problem for the technique of gas temperature measurement evolved by Edels and Whittaker in 1957. Their method of dealing with shock attenuation is subject to uncertain errors. In this paper we describe a new technique employing colliding shock waves which avoids this difficulty. The problem of the collision of plane opposing shock waves is solved graphically for values of the parameter γ which are constant at 1·4, 1·5 and 1·6. These solutions indicate that any three of the four shock velocities involved completely determine the entire collision. It is argued that this plane wave theory can be applied to the leading edges of convex shock waves involved in the collision within an arc discharge so that the gas temperature at the point of collision can be determined. Thus attenuation problems do not arise. Shock collisions have been recorded on a suitably designed streak camera. Typical examples are given from which the procedure for calculating temperatures is illustrated. By obtaining many such collisions throughout repetitive discharges temperature distributions have been built up. These distributions have been compared directly with distributions obtained with the method of Edels and Whittaker for arcs of 11·3, 7·7 and 20 A. The agreement between the two techniques is to within the experimental errors, but there are systematic differences. In particular, the older technique yields asymmetrical distributions of temperature with an axial value ½ to 1% lower than the new. The new technique, however, demands greater experimental control of shock synchronization and of the quality of the photographic record for example. The measured temperature distributions are compared with those derived theoretically from two arc models, one of cylindrical symmetry, the other of spheroidal symmetry. Assuming a heat loss by conduction only and a linearized σ - S relationship, the distributions are calculated for both models for a 10 A arc. As expected, the model of spheroidal symmetry shows the closer agreement with our measurements.