Electron velocity distributions, fractional energy transfer, and collision rates for potential Na, NaHe, and NaXe electrically excited laser discharges

Abstract

The Boltzmann transport equation including elastic, inelastic, ionization, electron-electron, and electron-ion interactions has been numerically solved to determine the electron velocity distribution, the fractional electron energy transfer, and the collision rates for potential Na, NaHe, and NaXe electrically excited laser discharges. Previously reported theoretical and experimental cross-section data from the literature were used in the calculations. Na, like all of the alkali atoms, has a very large cross section (∼4×10−15 cm2) for electronic excitation of the first level (an allowed optical resonant ns→np transition). This value greatly exceeds all other low-energy inelastic cross sections for both the Na and the He and/or Xe buffer gases. Such a combination of cross sections enables the input electron energy to be very efficiently transferred to the potential upper laser level, Na(3 P). The computed distribution functions are shown to be strongly non-Maxwellian and exhibit an energy variation indicative of this large resonant cross section in Na. Using the electron energy conservation equation reveals that indeed the electronic excitation of the Na first level dominates the electron energy exchange processes for the Na and the Na He/Xe mixtures. For example, in pure Na 100% of the electron energy is transferred to the Na(3 P) state in the E/N range 5×10−16 to 5×10−15 V cm2. In both the NaHe (1:99) and the NaXe (1:7600) mixtures, over 90% of the electron energy is transferred to this same Na(3 P) level in the E/N range of 5×1017 to 4×10−16 and (1.2–7) ×10−17 V cm2, respectively. At the second Na electronic level, 4P, electron energy transfer is down from that of the Na(3 P) by nearly three orders of magnitude for all of the mixtures. For the optimum values of E/N as cited above the mean electron energy for the Na, NaHe, and NaXe mixture lies in the range 0.6–1.4, 0.92–2.4, and 1.2–2.7 eV, respectively. Also, the normalized collision rates, ν/N (cm3 sec−1), for the Na(3 P) level are shown to have a value approximately 10–100 times that calculated for the normalized vibrational excitation rates of CO and CO2 laser discharges. These high pumping rates are a direct result of the large resonant transition cross section and give these systems excellent potential for high-power high-efficiency cw laser operation. Other discharge transport properties, like drift velocities and characteristics energies, are presented. Electron-electron interactions have negligible effects on the ’’tail’’ of distribution for partial ionization ratios, ne/N, values up to 10−3 due to the large Na(3 P) inelastic cross. The results and their generalizations to all the alkali systems along with recommended cross-section data needed are discussed.