Oscillations in Ionized Gases

A simple theory of electronic and ionic oscillations in an ionized gas has been developed. The electronic oscillations are so rapid (ca. ${10}^9$ cycles) that the heavier positive ions are unaffected. They have a natural frequency ${\nu }_e={\left(\frac{n{e}^2}{\pi m}\right)}^{\frac{1}{2}}$ and, except for secondary factors, do not transmit energy. The ionic oscillations are so slow that the electron density has its equilibrium value at all times. They vary in type according to their wave-length. The oscillations of shorter wave-length are similar to the electron vibrations, approaching the natural frequency ${\nu }_p={\nu }_e{\left(\frac{m_e}{m_p}\right)}^{\frac{1}{2}}$ as upper limit. The oscillations of longer wave-length are similar to sound waves, the velocity approaching the value $v={\left(\frac{k{T}_e}{m_p}\right)}^{\frac{1}{2}}$. The transition occurs roughly (i.e. to 5% of limiting values) within a 10-fold wave-length range centering around $2{\mathrm{}\left(2\right)\mathrm{}}^{\frac{1}{2}}\pi {\lambda }_D$, ${\lambda }_D$ being the "Debye distance." While the theory offers no explanation of the cause of the observed oscillations, the frequency range of the most rapid oscillations, namely from 300 to 1000 megacycles agrees with that predicted for the oscillations of the ultimate electrons. Another observed frequency of 50 to 60 megacycles may correspond to oscillations of the beam electrons. Frequencies from 1.5 megacycles down can be attributed to positive ion oscillations. The correlation between theory and observed oscillations is to be considered tentative until simpler experimental conditions can be attained.