Electron beam impact parameters for the creation of excited species in N2 gas

Abstract

The number of electron–ion pairs and the distribution of excited species created by the passage of an intense electron beam in a gas are important parameters for many applications. The previously published values for molecular nitrogen rely on a differential ionization cross section that uses a number of fitting parameters and excitation cross sections determined from analytical fitting functions [S. P. Slinker, A. W. Ali, and R. D. Taylor, J. Appl. Phys. 67, 679 (1990)]. Slinker used cross section fits to solve the Boltzmann equation which was then used to compute the important beam-impact parameters. In this work, it is shown that an alternative approach based on the continuous slowing down approximation (CSDA) can be used to compute the energy expended per electron-ion pair and the distribution of excited gas species. This method results in an integral equation that can be solved iteratively and converges rapidly. The binary-encounter Bethe (BEB) differential ionization cross section is used [Y. K. Kim and M. E. Rudd, Phys. Rev. A 50, 3954 (1994); W. Hwang, Y.-K. Kim and M. E. Rudd, J. Chem. Phys. 104, 2956 (1996)]. The BEB model naturally extends to relativistic energies and has no free parameters. This makes the BEB considerably easier to use than previous models based on fitting parameters. The BEB model requires orbital constants obtained from quantum chemistry calculations. To demonstrate the technique, the electron-beam impact parameters are computed for nitrogen gas. The tabulated low-energy excitation cross sections are extended to relativistic energies using Bethe's asymptotic value for the inelastic cross sections [M. Inokuti, Rev. Mod. Phys. 43, 297 (1971)]. It is shown that the results for the energy expended per electron–ion pair as well as the distribution of excited states agree with published experimental values and are similar to previously published theoretical results.