Gyro and drift kinetic equations in toroidal plasmas

Fusion Technology

Volumn 29, Issue 2 SPEC. ISS., 1996, Pages 81-90

  Rogister, André L ^a  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRONS; IONS; KINETIC THEORY; MATHEMATICAL MODELS; PLASMA STABILITY;

BALLOONING FORMALISM; DRIFT KINETIC EQUATIONS; GYRO KINETIC EQUATIONS; MAGNETIC FIELD LINES; TOROIDAL MAGNETIC FIELDS .; TOROIDAL PLASMAS;

PLASMAS;

EID: 0030092334     PISSN: 07481896     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. The definition of magnetic surfaces is given in M.D. KRUSKAL and R.M. KULSRUD, Phys. Fluids 1, 265 (1958): in an ionized gas, if the pressure p(r̄) is not constant in any (small) 3-dimensional region, then a surface of constant pressure p(r̄)=P is (excepting a set of values of P of measure zero) traversed ergodically and consequently determined by any line of force contained in it. It can be shown that such a surface must be a toroid, i.e. a topological torus.
2. I.e. any change in it vanishes more rapidly than any power of the ratio of the Larmor radius of the particles to the scale of the magnetic field inhomogeneity or, when the field is changing in time, than any power of the ratio of the particles' Larmor period to the variation time-scale of the field. Cf. M.D. KRUSKAL, Proceeding of the Terzo Congresso Internazionale sui Fenomeni di Ionizzazione nei Gas, p. 562 Venezia (1957)
3. and R.M. KULSRUD, Phys. Rev. 106, 205 (1957).
4. i)/N, where N refers to the equilibrium electron density. When oscillations coherent over distances larger than the Debye length occur, the charge density fluctuations within the Debye sphere are expected to be of the order of the coherent electron and ion density oscillations, these being (almost) equal.
5. A. ROGISTER and G. HASSELBERG, Plasma Phys. Contr. Fusion 27, 193 (1985);
6. other representations to reconcile the requirement for long parallel wave-lengths with the toroidal nature of the equilibrium have been considered by J.W. CONNOR, R.J. HASTIE and J.B. TAYLOR, Proc. R. soc. Lond. A.365, 1 (1979),
7. J.W. VAN DAM, Ph. Thesis (Univ. of California, Los Angeles, 1979),
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9. See the lecture on Micro-Instabilities Theory in Tokamak Plasmas.
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11. F. TROYON, Plasma Phys. Control. Fusion 26, 209 (1984);
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13. A. ROGISTER and D. LI, Phys. Fluids B4, 804 (1992).
14. L. SPITZER, Physics of Fully Ionized Gases (Interscience Publishers, 1962) p. 131-132.
15. P.J. CATTO, W.M. TANG and D.E. BALDWIN, Plasma Phys. 23, 639 (1981). This derivation of the gyrokinetic equation is based on a fully different mathematical technique, namely integration along the unperturbed orbits.
16. 0 + π; hence the name ballooning mode. Note the similarity with the quantum theory of solids [C. KITTEL, Introduction to Solid State Physics (J. Wiley, New York, 1976), Ch. 7]
17. where the wave eigenfunction has one of the periodicities of the lattice [F. BLOCH, Z. Phys. 52, 555 (1928)].
18. M.J. LIGHTHILL, Fourier Analysis and Generalized Functions (University Press, Cambridge, 1962), p. 67-71.