Ion Transport Notes HELIUM He+ drift velocity He: I recommend the empirical mobility formula of L. S. Frost, Phys. Rev. 105, 354 (1957), which can be written in terms of the drift velocity as W+ = 29.6 (E/n)/[1+0.01288*(E/n)]^0.5 (m/s) where E/N is in Td and 1 Td = 10^-21 V m^2. This formula gives results comparable with those of the formulas of A. L. Ward, J. Appl. Phys. 33, 2789 (1962). The two Ward formulas have the disadvantage that many models require switching formulas in the middle of the calculation. Both fits are based on the data of J. A. Hornbeck, Phys. Rev. 84, 615 (1951) and M. A. Biondi and L. M. Chanin, ibid. 94, 910 (1954). I have not attempted to update the Frost formula by comparison with more recent experimental data. He+ transverse diffusion coefficient in He: Below is DT/mu data at 294 K from T. Stefansson, T. Berge, R. Lausund, and H. R. Skullerud, J. Phys. D 21, 1359 (1988). I have not tried to fit this data with an empirical relation. E/n(Td) DT/mu (mV) 15 27.1 20 27.9 30 29.7 40 32.1 50 33.9 60 36.2 70 37.8 80 40.6 100 44.8 120 48.7 150 55.0 200 64.6 300 85.2 400 102.1 500 118.9 600 132.3 700 147.1 800 158.3 1000 181.4 1200 198.6 1500 216.4 2000 251.8 He+ longitudinal diffusion coefficient in He Apparently, there are no published experimental values for DL*N or DL/mu for He+ in He. Formulas for estimating DL/mu for charge exchange dominated inteactions are given by H. R. Skullerud, J. Phys. B 2, 86 (1969). However, Mason and McDaniel, "The Mobility and Diffusion of Ions in Gases", (Wiley, 1973, New York), page 212 appear to correct a numerical error in Skullerud's Eq. (22). NEON Ne+ drift velocity Ne: I recommend the empirical mobility formula of L. S. Frost, Phys. Rev. 105, 354 (1957), which can be written in terms of the drift velocity as W+ = 11.27 (E/n)/[1+0.01288*(E/n)]^0.5 (m/s) where E/N is in Td and 1 Td = 10^-21 V m^2. This formula gives results comparable with those of the formulas of A. L. Ward, J. Appl. Phys. 33, 2789 (1962). The two Ward formulas have the disadvantage that many models require switching formulas in the middle of the calculation. Both fits are based on the data of J. A. Hornbeck, Phys. Rev. 84, 615 (1951) and M. A. Biondi and L. M. Chanin, ibid. 94, 910 (1954). I have not attempted to update the Frost formula by comparison with more recent experimental data. Ne+ transverse diffusion coefficient in Ne: from T. Stefansson, J. Phys. B 22, 3541 (1989) Table 2 T= 294 K E/n(Td)DT/mu(mV) 20 26.3 30 27.3 40 28.9 50 30.2 60 31.8 70 33.3 80 36.1 100 37.7 120 41.7 150 47.0 200 54.6 300 67.4 400 80.1 500 90.6 600 101.8 700 114.5 800 129.8 1000 143.4 1200 168.9 1500 202 2000 250 The accuracy claimed is +- 4% for E/n > 120 Td and +- 8% for lower E/n. ARGON Ar+ drift velocity in Ar From Eq. B(9) of Z. Lj. Petrovic and A. V. Phelps, Plasma Sources Sci. Technol. 8, R21 (1999), the drift velocity W+ data is fit by W+ = 4.00 (E/n)/[1+(0.007*E/n)^1.5]^0.33 (m/s) where E/n is in Td. This formula is based on a review of published data and is somewhat different in detail from that of L. S. Frost, Phys. Rev. 105, 354 (1957). In addition to being fits to older data, the two ion mobility formulas suggested by A. L. Ward, J. Appl. Phys. 33, 2789 (1962) have the disadvantage that many models require switching between formulas in the middle of the calculation. Ar+ transverse diffusion coefficient in Ar: See the DT/mu data of T. Stefansson, Joint Symposium on Electron and Ion Swarms and Low Energy Electron Scattering, Trondheim, July 1991. I have not tried to fit this data with an empirical relation. E/n (Td) DT/mu (eV) 4.98637E+01 2.70075E-02 6.00921E+01 2.72885E-02 6.94773E+01 2.81490E-02 7.94999E+01 2.87377E-02 9.88338E+01 2.99523E-02 1.17879E+02 3.22028E-02 1.51175E+02 3.46223E-02 2.02084E+02 3.83974E-02 3.05918E+02 4.53123E-02 4.00547E+02 5.07758E-02 5.08388E+02 5.93030E-02 6.06354E+02 6.50921E-02 7.01055E+02 6.99827E-02 8.02188E+02 7.68143E-02 9.97274E+02 9.06476E-02 1.18945E+03 1.01577E-01 1.47871E+03 1.22377E-01 1.97668E+03 1.45918E-01 2.96147E+03 1.85134E-01 Tgas= 294.5 K. The number of significant figures is determined by the digitizing software. The accuracy claimed is +- 5% for E/n < 1200 Td decreasing to +- 10% for E/n = 4000 Td. Note that his theoretical Ar+ - Ar scattering model yields DT/mu values only slightly above these values. Ar+ longitudinal diffusion coefficient in Ar: Apparently, there are no published experimental values for DL*N or DL/mu for Ar+ in Ar. Formulas for estimating DL/mu for charge exchange dominated inteactions are given by H. R. Skullerud, J. Phys. B 2, 86 (1969). However, Mason and McDaniel, "The Mobility and Diffusion of Ions in Gases", (Wiley, 1973, New York), page 212 appear to correct a numerical error in Skullerud's Eq. (22). The following Ar+ + Ar data are taken from A. V. Phelps, J. Phys. Chem. Ref. Data 20, 557 (1991). Table 8. Calculated drift velocities, steady-state energies and reaction coefficients for Ar+ in Ar. The QCT values listed below are out of date and should be ignored. Use those given above. The use of different slightly QCT will change the W+ and T+ values correspondingly. E/n QCT T+ W+ Q(e) Q(UV) Q(488) Q(811) Td m2 eV m/s m2 m2 m2 m2 1000 5.7E-19 1.754 1641 8.22E-31 1.67E-28 -a - 2000 5.4E-19 3.70 2380 1.28E-26 5.13E-25 1.02E-35 1.13E-31 3000 5.2E-19 5.77 2980 4.40E-25 8.55E-24 1.05E-31 1.06E-28 5000 4.9E-19 10.20 3960 9.45E-24 9.10E-23 1.23E-28 2.15E-26 10000 4.6E-19 21.7 5780 1.32E-22 6.08E-22 1.85E-26 1.08E-24 20000 4.2E-19 47.6 8550 8.02E-22 1.91E-21 3.62E-25 1.06E-23 30000 4.0E-19 75 10730 1.73E-21 2.92E-21 1.27E-24 2.56E-23 50000 3.7E-19 135.1 14400 3.81E-21 4.26E-21 4.67E-24 5.79E-23 100000 3.3E-19 303 21600 8.48E-21 5.75E-21 1.74E-23 1.16E-22 Table 10. Reaction coefficients for Ar + Ar tabulated by product. The Qm values listed below are out of date and should be ignored. Use those given above. Note that the E/n and T+ values are those for the Ar+ that produces the fast Ar by charge transfer. E/n T+ Q(e),Q(UV) Q(811) Q(795) Qm Td eV m2 m2 m2 m2 500 0.862 -a - - 1.51E-19 1000 1.754 - - - 1.22E-19 2000 3.70 1.46E-27 2.61E-27 2.47E-31 9.29E-20 3000 5.77 1.03E-25 1.46E-25 2.23E-28 7.81E-20 5000 10.20 4.90E-24 4.65E-24 4.49E-26 6.21E-20 10000 21.7 1.41E-22 7.76E-23 2.20E-24 4.61E-20 20000 47.6 1.13E-21 4.13E-22 2.17E-23 3.44E-20 30000 75 2.44E-21 7.72E-22 5.53E-23 2.94E-20 50000 135.1 4.96E-21 1.37E-21 1.39E-22 2.44E-20 100000 303 9.56E-21 2.22E-21 3.16E-22 1.93E-20 a Too small to list NITROGEN The following N+, N2+, and N2 in N2 data are taken from A. V. Phelps, J. Phys. Chem. Ref. Data 20, 557 (1991). Table 2. Calculated drift velocities and cross sections versus E/n for N+ in N2. (The cross sections are in units 1E-20 m2) E/n Wm T+ Qd(N+) Q(391) Q(e) Td m/s eV 149 1173 0.1 - - - 199 1564 0.1778 - - - 265 2090 0.316 - - - 359 2780 0.562 - - - 473 3710 1 - - - 640 4950 1.778 0.051 - - 877 6600 3.16 0.083 - - 1177 8800 5.62 0.164 - - 1559 11730 10 1.45 - - 2040 15650 17.78 4.25 - - 2610 20870 31.6 4.95 - 0.004 3190 27830 56.2 4.73 - 0.0085 3870 37100 100 4.65 - 0.0137 4270 49500 177.8 4.6 0.00093 0.0217 4300 57100 237 4.6 0.0015 0.0272 Table 4. Calculated transport coefficients and average cross sections for N2+ in N2. E/n Qm T+ W+ Q(N+) Q(391nm) Q(N3+) Q(e) Td m2 eV m/s m2 m2 m2 m2 500 5.70E-19 0.877 1387 4.06E-29 1.00E-34 4.04E-29 1.00E-34 1000 4.90E-19 2.04 2120 3.47E-25 1.00E-34 2.65E-25 1.10E-31 2000 4.30E-19 4.65 3190 6.35E-23 2.04E-34 1.86E-23 5.95E-27 3000 3.90E-19 7.69 4110 4.50E-22 1.34E-29 6.91E-23 2.21E-25 5000 3.60E-19 13.89 5520 1.69E-21 1.39E-26 1.36E-22 3.20E-24 10000 3.48E-19 28.7 7940 4.12E-21 1.27E-24 1.57E-22 3.91E-23 20000 3.24E-19 61.7 11640 6.37E-21 1.29E-23 1.14E-22 2.96E-22 50000 3.00E-19 166.7 19100 8.03E-21 6.14E-23 5.45E-23 1.92E-21 100000 2.76E-19 362 28200 8.79E-21 1.42E-22 2.72E-23 5.46E-21 Table 6. Reaction coefficients for N2 + N2 collisions. Note that the E/n and T+ values are those for the N2+ that produces the fast N2 by charge transfer. E/n T+ Q(2nd Pos.) Q(e) Qm Td eV m2 m2 m2 500 0.877 -a - 2.03E-19 1000 2.04 - - 1.73E-19 2000 4.65 3.21E-25 - 1.44E-19 3000 7.69 4.92E-24 2.70E-27 1.28E-19 5000 13.89 4.06E-23 6.33E-25 1.11E-19 10000 28.7 2.08E-22 2.71E-23 9.39E-20 20000 61.7 5.65E-22 2.78E-22 7.75E-20 50000 166.7 1.06E-21 1.91E-21 5.63E-20 100000 362 1.32E-21 5.43E-21 3.98E-20