Abstract
In swarm studies, one generally is less interested in \(f(\mathbf {r},\mathbf {v},t)\) than in its moments, i.e., integrals of particular functions of \(\mathbf {v}\) multiplied by the ion vdf, \(f(\mathbf {v})\) . In this case, one is better off converting the Boltzmann equation to an equation governing the moments themselves and then solving the resulting moment equations. We shall do this in the rest of this chapter, after first reviewing moment methods that have been suggested previously.
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References
G. Balla, A.D. Koutselos, J. Chem. Phys. 119, 1137 (2003)
T. Berge, H.R. Skullerud, Phys. Rev. A 13, 1975 (1976)
G.L. Braglia, Phys. C 92, 91 (1977)
G.L. Braglia, in Theory of Electron Motion in Gases. I. Stochastic Theory of Homogeneous Systems (IFPR Report no. 174, Univ (Parma, Italy, 1978)
D. Burnett, Proc. Lond. Math. Soc. 39, 385 (1935a)
D. Burnett, Proc. Lond. Math. Soc. 40, 382 (1935b)
G. Cavalleri, S.L. Paveri-Fontana, Phys. Rev. A 6, 327 (1972)
C. Cercignani, The Boltzmann Equation and Its Applications (Springer, New York, 1988)
S. Chapman, T.G. Cowling, The Mathematical Theory of Non-uniform Gases, 3rd edn. (Cambridge Mathematical Library, Cambridge, 1970), pp. 62–64
H. Date, S. Yachi, K. Kondo, H. Tagashira, J. Phys. D 25, 42 (1992a)
H. Date, S. Yachi, K. Kondo, H. Tagashira, J. Phys. D 25, 1330 (1992b)
H. Date, K. Kondo, H. Tagashira, J. Phys. D 26, 1211 (1993)
A.Y. Ender, I.A. Ender, A.B. Gerasimenko, Open plasma. Phys. J. 2, 24 (2009)
L. Ferrari, Phys. A 93, 531 (1978)
J.L.A. Francey, D.A. Jones, J. Phys. D 9, 457 (1976)
J.B. French, T.E. Darcie, J. Chem. Phys. 84, 1764 (1986)
D.E. Goeringer, L.A. Viehland, J. Phys. B 38, 4027 (2005)
I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1980)
W. Kaplan, Advanced Calculus (Addison-Wesley, Reading, 1959), pp. 417–424
T. Kihara, Rev. Mod. Phys. 25, 844 (1953)
K. Kitamori, H. Tagashira, Y. Sakai, J. Phys. D 13, 535 (1980)
A.D. Koutselos, J. Chem. Phys. 106, 7117 (1997)
K. Kumar, Ann. Phys. (N.Y.) 37, 113 (1966)
K. Kumar, Aust. J. Phys. 20, 205 (1967)
K. Kumar, Aust. J. Phys. 23, 505 (1976)
K. Kumar, Aust. J. Phys. 33, 449 (1980)
K. Kumar, H.R. Skullerud, R.E. Robson, Aust. J. Phys. 33, 343 (1980)
S.L. Lin, J.N. Bardsley, J. Chem. Phys. 66, 43 (1977)
S.L. Lin, L.A. Viehland, E.A. Mason, Chem. Phys. 37, 411 (1979)
E.A. Mason, E.W. McDaniel, Transport Properties of Ions in Gases (Wiley, New York, 1988)
J.C. Maxwell, Philos. Trans. R. Soc. Lond. 157, 49 (1867). A reprint is available in S.G. Brush, Kinetic Theory, Vol. 2, Irreversible Processes (Pergamon, Oxford, 1966)
H.B. Milloy, R.O. Watts, R.E. Robson, M.T. Elford, Aust. J. Phys. 27, 787 (1974)
K.F. Ness, R.E. Robson, Transp. Theory Stat. Phys. 14, 257 (1985)
K.F. Ness, L.A. Viehland, Chem. Phys. 148, 255 (1990)
S.L. Paveri-Fontana, The moment method applied to the validation of Davydov’s approximate results for weakly ionized gases, in Proceedings of 9th International Symposium on Rarified Gas Dynamics, ed. by M. Becker, M. Fiebig (DFVLR, Porz-Wahn, 1974)
R. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965)
R.E. Robson, Introductory Transport Theory for Charged Particles in Gases (World Scientific, Singapore, 2006)
R.E. Robson, K.F. Ness, Phys. Rev. A 33, 2068 (1986)
N. Sato, H. Tagashira, J. Phys. D 18, 2451 (1985)
H.R. Skullerud, J. Phys. D 6, 728 (1973)
H.R. Skullerud, J. Phys. B 17, 913 (1984)
H. Tagashira, T. Taniguchi, K. Kitamori, Y. Sakai, J. Phys. D 11, L43 (1978)
L.A. Viehland, Chem. Phys. 179, 71 (1994)
L.A. Viehland, J. Stat. Phys. 163, 175 (2015)
L.A. Viehland, Y. Chang, Comput. Phys. Commun. 181, 1687 (2010)
L.A. Viehland, D.E. Goeringer, J. Chem. Phys. 120, 9090 (2004)
L.A. Viehland, D.E. Goeringer, J. Phys. B 38, 3987 (2005)
L.A. Viehland, S.L. Lin, Chem. Phys. 43, 135 (1979)
L.A. Viehland, E.A. Mason, Ann. Phys. (N.Y.) 91, 499 (1975)
L.A. Viehland, E.A. Mason, Ann. Phys. (N.Y.) 110, 287 (1978)
L.A. Viehland, W.F. Siems, J. Am. Soc. Mass Spectrom. 23, 1841 (2012)
L.A. Viehland, E.A. Kabbe, V.V. Dixit, J. Phys. B 38, 4011 (2005)
U. Weinert, Phys. Rep. 91, 297 (1982)
U. Weinert, Physica 125A, 498 (1984)
J.H. Whealton, Phys. Rev. A 11, 2 (1975)
J.H. Whealton, Phys. Rev. A 13, 1977 (1976)
S. Yachi, H. Date, K. Kitamori, N. Tagashira, J. Phys. D 24, 573 (1991)
A. Yousef, S. Shrestha, L.A. Viehland, E.P.F. Lee, B.R. Gray, V.L. Ayles, T.G. Wright, W.H. Breckenridge, J. Chem. Phys. 127, 154309 (2007)
M. Yousfi, A. Hennad, O. Eichwald, J. Appl. Phys. 84, 107 (1998)
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Viehland, L.A. (2018). Moment Methods for Solving the Boltzmann Equation. In: Gaseous Ion Mobility, Diffusion, and Reaction. Springer Series on Atomic, Optical, and Plasma Physics, vol 105. Springer, Cham. https://doi.org/10.1007/978-3-030-04494-7_5
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