A Wien displacement law for impact radiation

A flash of radiation is produced when a hypervelocity projectile strikes a target, By the term hypervelocity, we mean a collision in which the sound s peeds characterizing the materials in the target and the projectile are les s than the impact velocity, When the temperature and pressure ahead of the shock are low, it can be shown that the temperature, T-o, behind the shock varies quadratically with impact velocity, v. If the shocked material and t he radiation it emits are in thermodynamic equilibrium, the initial intensi ty of the radiation varies according to T-o(4), so that we obtain, finally, I similar to V-8. Because I is the total radiated power per unit area of t he source, integrated over all wavelengths, it can be accurately measured o nly by a detector with a very wide spectral response, If a detector having a limited spectral response is used instead, one observes I similar to V-Z, where the value of z depends on the detector, Although such a detector wil l not, in general, be able to confirm the V-8 rule, it may be able to confi rm that the wavelength of maximum emission satisfies lambda(max) similar to 1/V-2, a result which can be derived from the Wien displacement law under the same assumptions used to obtain the velocity dependence of the source i ntensity, To confirm the Wien law, the response time of the detector must b e less than 1 ns for a shock release temperature of 188 kK and less than 1 mu s for shock release temperature of 18 kK, Between these limits, the requ ired response time decreases as the release temperature increases, (C) 1999 Elsevier Science Ltd. All rights reserved.