## 6 Nonthermal and Coulomb Focusing Effects in Lorentzian (Kappa) Plasmas  
The neutral elements in a plasma can be detected by using spatially resolved plasma spectroscopy [25]. Since Fe and W atoms are important elements in astrophysical and laboratory plasmas, we shall consider the electron-atom bremsstrahlung process with those elements in nonthermal Lorentzian plasmas. In order to investigate the behavior of the electron-atom bremsstrahlung in wide spectral ranges such as the soft- and hard-photon ranges, we choose \(\overline{E}_{0}\,=\,15\,(>>1)\), i.e., \(E_{0}>>Ry\). Figure 1 shows the electron-ion bremsstrahlung cross sections \((d\overline{\sigma}_{b}/d\overline{\varepsilon})_{e-a}\) and the electron-atom bremsstrahlung cross sections \((d\overline{\sigma}_{b}/d\overline{\varepsilon})_{e-a}\) per photon energy in units of \(\pi a_{0}^{2}/Ry\) as functions of the scaled photon energy \(\overline{\varepsilon}\) for W and Fe atoms. In this figure, we see that the electron-atom bremsstrahlung cross section is quite different from the electron-ion bremsstrahlung cross section due to the screening  
effect caused by the bound electrons in the atom. We also see that the bremsstrahlung cross section is suppressed by the influence of bound atomic electrons. Figure 2 represents the scaled form of the electron-atom bremsstrahlung cross sections \((d\overline{\sigma}_{b}/d\overline{\varepsilon})_{e-n}\) per photon energy in units of \(\pi a_{0}^{2}/Ry\) as functions of the scaled photon energy \(\overline{\varepsilon}\) for W and Fe atoms. As shown in this figure, the Coulomb focusing enhances the bremsstrahlung cross section, especially for high-energy photons, for example, about 30% at \(\overline{\varepsilon}=6\). In addition, we see that the Coulomb focusing effect on the electron-atom bremsstrahlung cross section increases with an increase of the radiation photon energy. Hence, the Coulomb focused electron-atom bremsstrahlung cross sections including the influence of Coulomb focusing would be especially accurate for high-energy photons since the Coulomb focusing effect is significant near the cutoff spectral domain. Figure 3 shows the bremsstrahlung emission rate \(\overline{P}_{e}\) in units of \(P_{0}[\,=\,(32/3\pi^{1/2})r_{0}^{2}cn_{e}n_{a}]\) as a function of \(\overline{\varepsilon}\) for W atom with different values of \(\kappa\) when the Coulomb focusing is not considered. Figure 4 shows the Coulomb focused bremsstrahlung emission rate \(\overline{P}_{e,\,CF}\) in units of \(P_{0}[\,=\,(32/3\pi^{1/2})r_{0}^{2}cn_{e}n_{a}]\) as a function of \(\overline{\varepsilon}\) for W atom with different \(\kappa\) including the Coulomb focusing effect. Figure 5 shows \(\overline{P}_{e}\) as a function of \(\overline{\varepsilon}\) for Fe atom with different \(\kappa\) excluding the Coulomb focusing effect. Figure 6 shows \(\overline{P}_{e,\,CF}\) as a function of \(\overline{\varepsilon}\) for Fe atom with different \(\kappa\) including the effect of Coulomb focusing. As shown in Figures 3-6, the bremsstrahlung emission rates for the electron-atom bremsstrahlung process in Maxwellian plasmas are always greater than those in nonthermal plasmas. In addition, the nonthermal effects on the bremsstrahlung emission rate for the soft photon case are found to be more significant than those for the hard photon case. Moreover, the influence of Coulomb focusing on the bremsstrahlung emission rate decreases with a decrease of the spectral index \(\kappa\). Therefore, the Coulomb focusing effect on the bremsstrahlung emission rate is more significant in thermal plasmas and in hard spectral ranges. As shown in these figures, the nonthermal effect on \(\overline{P}_{e,\,CF}\) decreases with decreasing \(\overline{\varepsilon}\). Hence, the classification of the nonthermal character of plasmas by using the bremsstrahlung spectrum would be quite significant in hard spectral regions.