Comments on 'Thermonuclear Power Plants'

Abstract

I the July issue of J E T PROPULSION (vol. 26, 1956,pp. 559564) a paper by Hsue-shen Tsien, 'Thermonuc lea r Power P lan t s , appeared. A paper by us on a similar subject (On the Possibility of Applying Thermonuclear Reactions to Rocket Propulsion) appeared in Studii si Cercetdri de Fizica (Studies and Researches in Physics), no. 2, 1956. As our paper arrives a t conclusions quite contrary to those of Dr . Tsien. we would like to draw at tent ion to certain s ta tements and methods of calculation used by Dr . Tsien, which, in our opinion, are not correct and lead to these differences: 1 The most impor tan t parameter of the motor is its diameter. Dr . Tsien calculates it by evaluating the reaction quenching on the basis of similitude considerations. The value he finds is of the order of tens of meters. He justifies this method by affirming t h a t it is not possible to use methods from astrophysics a t such temperatures and densities, the mean free-path being of the same order of magni tude as the dimensions of the system. Affirming this, Dr . Tsien nevertheless applies Maxwell 's distribution function to the calculation of the reaction rate, this being obviously in contradiction to the affirmation mentioned above. A rigorous calculation, based on the physical properties of mat ter , leads to values many orders of magni tude greater. Even under a pressure of 10 a t in (Dr. Tsien works with a pressure of only 100 a tm) and a tempera ture of 10 K, the tempera ture gradient near the center is only ^ 1 0 ~ 1 2 • r K / c m , r being the distance from the center. This result shows also t h a t Dr . Tsien's afore-mentioned claim, t h a t the mean free pa th is of the same order of magnitude as the dimensions of the system, is not valid. 2 Dr . Tsien chose for the reaction in the central zone a tempera ture of 1.6 X 10 K and a pressure of 100 a tm. Under the condition of a thermodynamic equilibrium, this temperature and pressure cannot exist together, the radiat ion pressure alone amount ing to 1.68 X 10 a tm . Even if this is not taken into account, a tempera ture of 1.6 X 10 K is not the best choice. As was shown in our paper, a t a pressure of 100 a t m the maximum rate of the t r i t ium-deuter ium reaction (Dr. Tsien works with the deuter ium-deuter ium reaction, which, in the absence of resonance, is slower and less energetic than the first) takes place a t a much lower temperature , namely, a t about 400,000 K and has the value of 10 ~ ca l /cm 3 sec, while Dr . Tsien finds the value of 0.87 cal /cm 3 sec. To get the Tsien figure, a pressure of approximately 50,000 a t m is needed, the temperature a t which the reaction rate is optimal being then 1.85 X 10 K. These differences are due to the fact t h a t Dr . Tsien does not take into consideration the radiation pressure. I t was shown in our paper t ha t the tempera ture gradient being extremely small, the tempera ture in the central zone should be chosen on considerations of maximum tempera ture