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Investigation of the Dynamics of Radiation Fronts

by

William W. Zuzak

B.E. (Eng. Sc. Phys.) University of Saskatchewan, 1963
M.Sc. University of Saskatchewan, 1965

A thesis submitted in partial fulfilment of the requirements for the degree of

Doctor of Philosophy

in the Department of Physics,

University of British Columbia
August, 1968


ABSTRACT

A theoretical investigation of steady radiation fronts was carried out for the experimentally realistic situation in which ionizing or dissociating radiation passes through a transparent window into an absorbing gas. It was shown that five different types of radiation fronts may occur depending on the ratio of photon flux to absorber density. It was possible to calculate the flow in each case provided the final temperature behind the radiation front was assumed. This final temperature may be calculated if the structure and all reactions within the radiation front are taken into account.

An analytic expression can be obtained if particle motion and recombination are neglected, and the radiation is assumed to be monochromatic. This ideal case corresponds closely to a weak R-type radiation front. A first order relativistic correction indicates that the width of the front decreases as the velocity of the front approaches the speed of light.

In an associated experiment, radiation fronts in oxygen and iodine were produced by an intense light pulse from a constricted arc. The experiment in iodine demonstrated the beginning of the formation of a radiation front during the 10 μsec light pulse. Radiation induced shock waves were observed in oxygen after the decay of the light pulse. These Mach 1.1 shocks were considered theoretically as unsteady one-dimensional flow and were treated by the method of characteristics, which was modified to include energy input. The agreement betrween the theoretical and experimental results was satisfactory.

7.1 Method of Characteristics
7.2 Method of Finite Differences

SUMMARY AND CONCLUSIONS

The object of this thesis was to investigate both theoretically and experimentally phenomena associated with radiation fronts for the experimentally realistic situation of ionizing and dissociating radiation, passing through a transparent window into a tube containing the absorbing gas.

Five different types of steady radiation fronts may occur for the experimental situation under consideration. At one extreme of high radiation intensity and low particle density there is little particle motion associated with the front; at the other extreme of relatively low intensities and high particle densities the particle motion is dominant and a shock front propagates ahead of the radiation front. The speed of the various discontinuities and all thermodynamic quantities may be calculated either if the detailed structure of the radiation front and mechanisms occuring within it are known or if the temperature behind the radiation front is assumed. Conversely, a measurement of this temperature would yield important information about these mechanisms.

It was shown that for the case of no recombination or collisional dissociation, the structure of a steady radiation front produced by monochromatic radiation could be described by a simple analytical expression in terms of Lagrangian co-ordinates. This expression depends only on the absorber density and on the absorption coefficient, α. A simple relativistic correction must be made if the velocity of the radiation front is near that of light; this causes an apparent steepening of the front.

A treatment of the structure of a dissociation front in oxygen for a simplified reaction scheme was outlined. It was pointed out that, in general, it is necessary to consider all the reactions within the radiation front. A numerical solution was attempted for a weak D-type front preceded by a Mach 3 shock but was unsuccessful.

For an experimental investigation of radiation fronts an intense pulsed light source, which consists of an arc discharge through a narrow channel in polyethylene, was constructed. The average intensity of this "Bogen" light source (in a solid angle of 0.1 steradians at 500 nm and operated at a discharge voltage of 3.0 kV) was measured to be (1.9 +/- 0.2) x 103 times as bright as a standard carbon arc. Along the axis the intensity is about three times larger than this value. This indicates that the effective black body temperature of the source is from 60,000 oK and 150,000 oK.

Experiments were carried out at low and high absorber densities, No. An experiment in iodine at a low density, No, illustrated the beginning of the formation of a radiation front. Although the measurements were quite crude, the agreement with theory was quite reasonable. The author suggests a similar type of experiment be attempted with a strong d.c. light source.

Shock fronts in oxygen at a high density, No, were detected by means of piezoelectric pressure probes. At high pressures (1 atm) the shocks formed very near the lithium flouride window, while at low pressures (0.03 atm) the point of formation was about one cm from the window. The speed of propagation of the shocks was 364 +/- 8 m/sec for all pressures, at least at distances far from the LiF window.

Attempts to detect photoionization in the test chamber showed only that photons in the wavelength region 120 nm to 200 nm were especially efficient in knocking out electrons from brass or dielectric material. Attempts to detect ionization fronts proved fruitless.

It was shown how the development of a radiation front may be considered as unsteady one-dimensional flow with energy input and treated by the method of characteristics at constant time intervals or by the method of finite differences. These theories were appled to calculate the evolution of the shocks which were observed in oxygen. The theoretical results agreed well with the experimental results. It was also pointed out that if sufficient computer time were available and a constant energy input were used, these methods could be used to obtain steady state solutions (complete with thermodynamic quantities, velocities and the front structure) which we had attempted to calculate previously. It had been hoped that it would be possible to compare the results of such a calculation with the structure obtained by the method outlined in Chapter 4 (an attempt which proved unsuccessful). Since this was not practicable the author hopes that he has at least pointed out a possible mode of attack for future work in this field.

In conclusion, the author would like to point out that future work in this field depends upon the development of extremely intense sources of radiation both d.c. and pulsed. The author can only dream in anticipation of a gigawatt laser, radiating for tens of microseconds and adjustable to any frequency desired.


W.Z., 2014.01.04 Addendum:  The publications associated with the research in my Ph.D. thesis at UBC are listed below.

(1)  Pressure Pulse Detection by Frustrated Internal Reflection, B. Ahlborn and W.W. Zuzak, Rev. Sc. Inst., 38, 194 (1967)
(2)  Experimental Investigation of Radiation Fronts, W.W. Zuzak and B. Ahlborn, Physica, 41, 193 (1969)
(3)  Steady Radiation Fronts Behind Windows, B. Ahlborn and W.W. Zuzak, Can. J. Phys., 47, 1709 (1969)
(4)  Radiation-Induced Shocks in Oxygen, W.W. Zuzak and B. Ahlborn, Can. J. Phys., 47, 2667 (1969)
(5)  Application of Radiation Fronts in Chemical Lasers, W.W. Zuzak (Unpublished draft, 2.0 MB pdf file)