Contribution of electron-atom collisions to the plasma conductivity of noble gases

We present an approach which allows the consistent treatment of bound states in the context of dc conductivity in dense partially ionized noble gas plasmas. Besides electron-ion and electron-electron collisions, further collision mechanisms owing to neutral constituents are taken into account. Especially at low temperatures of ${10}^4\text{to}{10}^5$ K, electron-atom collisions give a substantial contribution to the relevant correlation functions. We suggest an optical potential for the description of the electron-atom scattering which is applicable for all noble gases. The electron-atom momentum-transfer cross section is in agreement with experimental scattering data. In addition, the influence of the medium is analyzed, the optical potential is advanced including screening effects. The position of the Ramsauer minimum is influenced by the plasma. Alternative approaches for the electron-atom potential are discussed. Good agreement of calculated conductivity with experimental data for noble gas plasmas is obtained.

Figure 1

Screened optical potential, Eq. (35), for electron-argon interaction at zero wave number ($k=0$) for different screening parameters $\kappa a_0$ in comparison to the unscreened optical potential, Eq. (28). The asymptotes, Eq. (41), are also shown.

Figure 2

Momentum-transfer cross section for the noble gases: (a) He, (b) Ne, (c) Ar, (d) Kr, and (e) Xe. The calculations are performed using the optical potential Eq. (28) in the present work (full line), Eqs. (26), (27), (31), and (34), in comparison with the optical potential used in [24] (crosses). Also shown are experimental data [39, 40, 43, 44, 45, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64].

Figure 3

Screening effects on the momentum-transfer cross section for (a) argon and (b) helium at various screening parameters $\kappa$.

Figure 4

Ionization degree of partially ionized noble gases at $T=20000$ K according to Ref. [12] (a) as a function of $n_{\mathrm{heavy}}$, $\times$ indicates the value of $\mathrm{\Theta }=100$, $+$ the value $\mathrm{\Theta }=10$; and (b) as a function of $\mathrm{\Theta }$, $*$ indicates the value $n_{\mathrm{heavy}}={10}^{21}{\mathrm{cm}}^{-3}$.

Figure 5

Correlation functions (a) $d_{11}$ and (b) $d_{33}$ relative to $d$, Eq. (43), for the different considered scattering mechanisms $e\text{−}i$ (dashed line), $e\text{−}e$ (dash-dotted line), and $e\text{−}a$ (full lines) at $T=20000$ K (two scales).

Figure 6

Conductivity of partially ionized noble gases (PIP) using the optical potential for the $e\text{−}a$ interaction (full lines): (a) helium (red) and argon (green) at $20000$ K in comparison with experimental data (•[65, 66, 67]), fully ionized plasma (FIP) model $n_{\mathrm{a}}=0$ (dash-dotted lines) and neglecting $e\text{−}a$ interaction $V_{\mathrm{ea}}=0$ (dashed lines); and (b) helium (red), neon (orange), argon (green), krypton (blue), and xenon (violet) at $20000$ K in comparison with the experimental data (•[65, 66, 67]).

Figure 7

Conductivity of partially ionized noble gases (PIP) using the optical potential for the $e\text{−}a$ interaction (full lines): (a) argon at temperatures $T=10000$ K (cyan), $15000$ K (brown), and $20000$ K (black) in comparison with calculations using the polarization potential [15] (dashed line) and experimental data around these temperatures [67, 68] (•, Ref. [67]; $\blacksquare$, Ref. [68]; and $\diamond$, calculations at experimental conditions); and (b) xenon at temperatures $T=10000$ K (cyan), $15000$ K (brown), and $25000$ K (black) in comparison with calculations using the polarization potential [15] (dashed) and experimental data around these temperatures [67, 68, 69] (•, Ref. [67]; $\blacksquare$, Ref. [68]; $▴$, Ref. [69]; and $\diamond$, calculations at experimental conditions).