... Fitzpatrick¹

In association with R.D. Hazeltine and F.L. Waelbroeck.

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... Solov'ev.²

A.I. Morozov, and L.S. Solev'ev, Motion of charged particles in electromagnetic fields, in Reviews of Plasma Physics, Vol. 2 (Consultants Bureau, New York NY, 1966).

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... Kruskal³

M. Kruskal, Asymptotic theory of Hamiltonian and other systems with all solutions nearly periodic, J. Math. Phys. 3, 806 (1962).

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... abandoned.⁴

This is not quite true. In fact, fusion scientists have developed advanced mirror concepts which do not suffer from the severe end-losses characteristic of standard mirror machines. Mirror research is still being carried out, albeit at a comparatively low level, in Russia and Japan. See, for instance, the following web site: http://www.inp.nsk.su/plasma.htm

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... written⁵

It is conventional to take account of the negative charge of electrons by making the electron gyrofrequency ${\Omega}_e$ negative. This approach is implicit in formulae such as Eq. (87).

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... 1989.⁶

Dst data is freely availabel from the following web site in Kyoto (Japan): http://swdcdb.kugi.kyoto-u.ac.jp/dstdir

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... Teller.⁷

T.G. Northrop, and E. Teller, Phys. Rev. 117, 215 (1960).

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... Northrup.⁸

T.G. Northrup, The adiabatic motion of charged particles (Interscience, New York NY, 1963).

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... particles.⁹

In general, this is not true. Atomic or nuclear processes operating in a plasma can give rise to local sources and sinks of particles of various species. However, if a plasma is sufficiently hot to be completely ionized, but still cold enough to prevent nuclear reactions from occurring, then such sources and sinks are usually negligible.

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... Cowling.¹⁰

S. Chapman, and T.G. Cowling, The mathematical theory of non-uniform gases (Cambridge University Press, Cambridge, UK, 1953).

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... S.I. Braginskii.¹¹

S.I. Braginskii, Transport processes in a plasma, in Reviews of Plasma Physics (Consultants Bureau, New York NY, 1965), Vol. 1, p. 205.

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...kinetic-MHD.¹²

Kinetic-MHD is described in the following two classic papers: M.D. Kruskal, and C.R. Oberman, Phys. Fluids 1, 275 (1958): M.N. Rosenbluth, and N. Rostoker, Phys. Fluids 2, 23 (1959).

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... theory¹³

Neoclassical transport theory in axisymmetric systems is described in the following classic papers: I.B. Bernstein, Phys. Fluids 17, 547 (1974): F.L. Hinton, and R.D. Hazeltine, Rev. Mod. Phys. 48, 239 (1976).

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....¹⁴

M. Abramowitz, and I.A. Stegun, Handbook of Mathematical Functions (Dover, New York NY, 1964), p. 446.

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... one,¹⁵

M. Abramowitz, and I.A. Stegun, Handbook of Mathematical Functions (Dover, New York NY, 1964), p. 358.

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... one,¹⁶

M. Abramowitz, and I.A. Stegun, Handbook of Mathematical Functions (Dover, New York NY, 1964), p. 374.

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... integrals,¹⁷

M. Abramowitz, and I.A. Stegun, Handbook of mathematical functions, (Dover, New York NY, 1965), Sect. 7.3.

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... decent.¹⁸

Léon Brillouin, Wave propagation and group velocity, (Academic press, New York NY, 1960).

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... Parker¹⁹

E.N. Parker, Astrophys. J. 128, 664 (1958).

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... data.²⁰

M. Neugebauer, C.W. Snyder, J. Geophys. Res. 71, 4469 (1966).

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... Chapman,²¹

S. Chapman, Smithsonian Contrib. Astrophys. 2, 1 (1957).

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... days.²²

To an observer orbiting with the Earth, the rotation period appears to be about 27 days.

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... Davis.²³

E.J. Weber, and L. Davis Jr., Astrophys. J. 148, 217 (1967).

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... 1919,²⁴

J. Larmor, Brit. Assoc. Reports, 159 (1919).

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... regimes.²⁵

E. Knobloch, Phys. Lett. 82A, 439 (1981).

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... solutions.²⁶

S. Vainshtein, and Ya. B. Zel'dovich, Sov. Phys. Usp. 15, 159 (1978).

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... Cowling.²⁷

T.G. Cowling, Mon. Not. Roy. Astr. Soc. 94, 39 (1934): T.G. Cowling, Quart. J. Mech. Appl. Math. 10, 129 (1957).

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... Ponomarenko.²⁸

Yu. B. Ponomarenko, J. Appl. Mech. Tech. Phys. 14, 775 (1973).

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....²⁹

M. Abramowitz, and I.A. Stegun, Handbook of Mathematical Functions (Dover, New York NY, 1964), p. 374.

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... by³⁰

M. Abramowitz, and I.A. Stegun, Handbook of Mathematical Functions (Dover, New York NY, 1964), p. 377.

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... problems.³¹

A. Gailitis, Topological Fluid Dynamics, edited by H.K. Moffatt, and A. Tsinober (Cambridge University Press, Cambridge, UK, 1990), p. 147.

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... Rosenbluth.³²

H.P. Furth, J. Killeen, and M.N. Rosenbluth, Phys. Fluids 6, 459 (1963).

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... function.³³

M. Abramowitz, and I.A. Stegun, Handbook of Mathematical Functions (Dover, New York NY, 1964), p. 686.

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... Rutherford,³⁴

P.H. Rutherford, Phys. Fluids 16, 1903 (1973).

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... Sweet³⁵

P.A. Sweet, Electromagnetic Phenomena in Cosmical Physics, (Cambridge University Press, Cambridge, UK, 1958).

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... Parker.³⁶

E.N. Parker, J. Geophys. Res. 62, 509 (1957).

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... Laboratory.³⁷

H. Ji, M. Yamada, S. Hsu, and R. Kulsrud, Phys. Rev. Lett. 80, 3256 (1998).

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... Petschek.³⁸

H.E. Petschek, AAS-NASA Symposium on the Physics of Solar Flares (NASA Spec. Publ. Sp-50, 1964), p. 425.

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... Biskamp³⁹

D. Biskamp, Phys. Fluids 29, 1520 (1986).

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... Forbes⁴⁰

E.R. Priest, and T.G. Forbes, J. Geophys. Res. 97, 16,757 (1992).

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... Landau⁴¹

L.D. Landau, Sov. Phys.-JETP 10, 25 (1946).

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... Conte.⁴²

B.D. Fried, and S.D. Conte, The Plasma Dispersion Function (Academic Press, New York NY, 1961.)

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