Sommario
Si esaminano gli effetti di una rotazione uniforme sulla propagazione di piccole perturbazioni in un plasma anisotropo privo di urti. Tali effetti si manifestano in vario modo sui noti fenomeni di instabilità “hose”, “mirror” e magnetogravitazionale del tipo di Jeans. Nella prima parte si considerano perturbazioni piane, nella seconda di tipo cilindrico. Alcune considerazioni sulla stabilità e sulle onde idromagnetiche in un plasma anisotropo privo di urti sono svolte in Appendice.
Summary
The effects of a uniform rotation on the propagation of small perturbations through an anisotropic collisionless plasma are investigated. These effects are present in various ways on the well-known “hose”, “mirror” and gravitational instabilities. In Part I we consider plane perturbations, in Part II cylindrical. Some remarks about stability and hydromagnetic waves in an anisotropic collisionless plasma are given in Appendix.
References
B. Lehnert,Magneto-hydrodynamic waves under the action of the Coriolis force, Astrophysical Journal, Vol. 119, pp. 647–654, 1954.
B. Lehnert,Magneto-hydrodynamic waves under the action of the Coriolis force II, Astrophysical Journal, Vol. 121, pp. 481–490, 1955.
H. Alfvén,Cosmical electrodynamics, University Press, Oxford, 1963.
S. Chandrasekhar,Hydrodynamic and hydromagnetic stability, University Press, Oxford, 1961.
G. Mattei, Sulla propagazione di piccole perturbazioni magnetofluidodinamiche in un fluido comprimibile in rotazione uniforme, Rendiconti Seminario Matematico Università Padova, Vol. 37, pp. 324–340, 1967.
T. G. Cowling,Magneto-hydrodynamic oscillations of a rotating fluid globe, Proceedings Royal Society, A Vol. 233, pp. 319–322, 1956.
P. C. Kendall,Hydromagnetic oscillations of a rotating liquid sphere, Quarterly Journal Mechanics Applied Mathematics, Vol. 13, pp. 285–299, 1960.
P. C. Kendall andC. Plumpton,Magnetohydrodynamics with hydrodynamics, Vol. I, Pergamon Press, London, 1964.
G. Mattei, Sulla influenza della forza di Coriolis in un problema magnetofluidodinamico, Annali Scuola Normale Pisa, Vol. 20, pp. 703–717, 1966.
S. Chandrasekhar,The gravitational instability of an infinite homogeneous medium when Coriolis acceleration is acting, Vistas in Astronomy, Vol. I, Ed. A. Beer, pp. 344–347, 1955.
S. Chandrasekhar,The gravitational instability of an infinite homogeneous medium when Coriolis force is acting and a magnetic field is present, Astrophysical Journal, Vol. 119, pp. 7–9, 1954.
A. G. Pacholczyk,Sulla instabilità gravitazionale e magnetogravitazionale di sistemi compressibili, Magnetofluidodinamica, Corso CIME, Cremonese, Roma, 1962.
G. Mattei, Sulla instabilità magnetogravitazionale secondo Jeans di un mezzo comprimibile dissipativo, Atti Seminario Matematico Università Modena, Vol. 16, pp. 77–88, 1967.
V. C. A. Ferraro andC. Plumpton,An introduction to Magnetofluid Mechanics, II Ed. University Press, Oxford, 1966.
R. Hide andP. H. Roberts,Elementary problems in Magnetohydrodynamics, Advances in Applied Mechanics, Vol. 7, pp. 216–313, 1962.
S. Rionero, Su un tipo di oscillazioni magnetoidrodinamiche finite possibili in una massa fluida ellissoidale ruotante ed altamente conduttrice, Atti Accademia Scienze Torino, Vol. 98, pp. 1–17, 1963–64.
W. M. Elsasser,Hydromagnetic dynamo theory, Reviews Modern Physics, Vol. 28, pp. 135–163, 1956.
B. Lehnert,The decay of magneto-turbulence in the presence of a magnetic field and Coriolis force, Quarterly Applied Mathematics, Vol. 12, pp. 321–341, 1955.
J. Carstoiu, Sur les ondes magnétohydrodynamiques dans un fluide en rotation uniform, Comptes Rendus Académie Sciences Paris, Vol. 258, pp. 2745–47, 1964.
S. D. Nigam andP. D. Nigam,Magnetohydrodynamic waves in rotating liquids, Proceedings Royal Society, A Vol. 272, pp. 529–541, 1963.
B. Lehnert,Plasma physics on cosmical and laboratory scale, Suppl. Nuovo Cimento, Vol. 13, pp. 59–110, 1959.
B. Lehnert,Dynamics of charged particles, North-Holland Publishing Company, Amsterdam, 1964.
V. C. A. Ferraro,Lezioni sulla dinamica dei gas ionizzati, Istituto Matematico Università di Firenze, 1967.
E. N. Parker,The plasma in a magnetic field, ed. Rolf K. M. Landshoff, Stanford, p. 77, 1958.
B. Abraham -Shrauner,Propagation of hydromagnetic waves through an anisotropic plasma, Journal Plasma Physics, Vol. I, pp. 361–378, 1967.
Y. Kato, M. Tajiri andT. Taniuti,Propagation of hydromagnetic waves in collisionless plasma I, Journal Physical Society Japan, Vol. 21, pp. 765–777, 1966.
J. E. C. Gliddon,Gravitational instability of anisotropic plasma, Astrophysical Journal, Vol. 145, pp. 583–588, 1966.
Y. M. Lynn,Discontinuities in an anisotropic plasma, Physics of Fluids, Vol. 10, pp. 2278–2280, 1967.
P. K. Bathia,Gravitational instability of a rotating anisotropic plasma, Physics of Fluids, Vol. 10, pp. 1652–53, 1967.
S. K. Trehan,Macroscopic theory of plasma waves, Plasma Physics, AIEA, Vienna, 1965.
A. G. Pacholczyk andJ. S. Stodolkiewicz,The magnetogravitational instability of an infinite homogeneous medium when a Coriolis force is acting and viscosity is taken into account, Bullettin Académie Polonaise Sciences, Vol. 7, pp. 429–434, 1959.
A. G. Pacholczyk andJ. S. Stodolkiewicz,The magnetogravitational instability of the medium of finite electrical conductivity, ibidem, pp. 681–85.
K. Kossacki,On the magnetogravitational instability of a homogeneous, infinite, viscous and rotating medium with finite electrical conductivity. Acta Astronomica, Vol. 11, pp. 83–86, 1961.
Mircea Vasiu,Sur l'équation de dispersion d'un fluide visqueux à conductivité électrique finie, dans le mouvement de rotation uniforme, Studia Universitatis Babes-Bolyai, pp. 117–131, Cluj, 1963.
Mircea Vasiu,ibidem, pp. 123–138, 1964.
E. N. Parker,Dynamical instability in an anisotropic ionized gas of low density, Physical Review, Vol. 109, pp. 1874–76, 1958.
S. Chandrasekhar, A. N. Kaufmann andK. M. Watson,The stability of the pinch, Proceedings Royal Society, A Vol. 245, pp. 435–455, 1958.
W. B. Thompson,An introduction to Plasma Physics, Pergamon Press, Oxford, 1962.
S. Chandrasekhar andE. Fermi,Problems of gravitational stability in the presence of a magnetic field, Astrophysical Journal, Vol. 118, pp. 116–141, 1953.
A. A. Vedenov andR. Z. Sagdeev,Some properties of a plasma with an anisotropic ion velocity distribution in a magnetic field, Plasma Physics and problems of controlled Thermonuclear Reactions III, Pergamon Press, Oxford, pp. 332–339, 1959.
G. Mattei,On the propagation of cylindrical waves in a magnetized self-gravitating collisionless plasma, Journal Plasma Physics, Vol. II, pp. 9–15, 1968.
B. Finzi andM. Pastori,Calcolo tensoriale e applicazioni, Zanichelli, Bologna, 1961.
J. Serrin,Mathematical principles of classical fluid mechanics, Handbuch Physik VIII/1, 1959.
A. Jeffrey,Magnetohydrodynamics, Oliver and Boyd, London, 1966.
C. C. Lin,The theory of hydrodynamic stability, Cambridge University Press, 1966.
R. Lust,Int. Summer Course in Plasma Physics, Ed. C. F. Wandel, Danish Atomic Energy Commission, p. 201, 1960.
G. Mattei, Varietà caratteristiche e propagazione ondosa in un plasma magnetizzato privo di urti, Annali Scuola Normale Pisa, Vol. 21, pp. 745–763, 1967.
B. Finzi, Caratteristiche dei sistemi differenziali e propagazione ondosa, L'energia elettrica, Vol. 27, pp. 189–195, 1950.
R. Nardini, Sui fronti d'onda nella Magneto-idrodinamica, Rivista Matematica Università Parma, Vol. 7, pp. 3–32, 1956.
H. Grad andC. K. Chu,Magnetofluid Dynamics, inResearch Frontiers in Fluid Dynamics, Interscience Publishers, pp. 317–325, 1965.
C. Truesdell andR. Toupin,The Classical field theories, Handbuch Physik III/1, 1960.
C. Truesdell,General and exact theory of waves in finite elastic strain, Archive Rational Mechanics Analysis, Vol. 8, pp. 263–296, 1961.
G. F. Chew, M. L. Goldberger andF. E. Low,The Boltzmann equation and one-fluid hydromagnetic equations in the absence of particle collisions, Proceedings Royal Society, A Vol. 236, pp. 112–118, 1956.
R. Kulsrud,General stability theory in Plasma Physics, Rendiconti Scuola Internazionale di Fisica E. Fermi. Vol. 25, Academic Press, pp. 54–96, 1964.
L. I. Rudakov andR. Z. Sagdeev,A quasi-hydrodynamic description of a rarefied plasma in a magnetic field, Plasma Physics and Problems of Controlled Thermonuclear Reactions, Vol. III, Pergamon Press, pp. 321–331, 1959.
B. B. Kadomtsev,Plasma dynamics in a strong magnetic field, ibidem, Vol. IV, pp. 438–449, 1960.
M. N. Rosenbluth andN. Rostoker,Theoretical structure of plasma equations, Physics Fluids, Vol. II, pp. 23–30, 1959.
G. Rowlands,Some aspects of theoretical Plasma Physics in the United Kingdom, Propagation and Instabilities in Plasmas, Stanford University Press, pp. 52–69, 1963.
A. Macmahon,Finite gyro-radius corrections to the hydromagnetic equations for a Vlasov Plasma, Physics Fluids, Vol. VIII, pp. 1840–1845, 1965.
T. F. Volkov,Hydrodynamic description of a collisionless plasma, Reviews of Plasma Physics, Ed. Leontovich, Vol. IV, pp. 1–21, Consultants Bureau, New York, 1966.
E. Frieman, R. Davidson andB. Langdon,Higher order corrections to the Chew-Goldberger-Low theory, Physics Fluids, Vol. IX, pp. 1475–1482, 1966.
I. B. Bernstein, E. A. Frieman, M. D. Kruskal andR. M. Kulsrud,An energy principle for hydromagnetic stability problems, Proceedings Royal Society London, Vol. A 244, pp. 17–40, 1958.
M. D. Kruskal andG. R. Oberman,On the stabiilty of plasma in static equilibrium, Physics Fluids, Vol. I, pp. 275–280, 1958.
C. Oberman,Hydromagnetic stability, Plasma Physics, AIEA, pp. 137–162, Vienna, 1965.
J. B. Tayor,Some stable plasma equilibria in combined mirrorcusp fields, Physics Fluids, Vol. VI, pp. 1529–1536, 1963.
J. B. Taylor,Plasma confinement in magnetic wells, Plasma Physics, AIEA, pp. 449–481, Vienna, 1965.
T. G. Northrop,The adiabatic motion of charged particles, Interscience Publishers, Ch. IV, D, New York, 1963.
N. Rostoker,Plasma stability, fromPlasma Physics in Theory and Application, Ed. W. B. Kunkel, Mc Graw-Hill, pp. 122–125, New York, 1966.
B. Abraham-Shrauner,Shock jump conditions for an anisotropic plasma, Journal Plasma Physics, Vol. I, 379–381, 1967.
S. P. Talwar,Kelvin-Helmholtz instability in an anisotropic plasma, Physics Fluids, Vol. VIII, pp. 1295–1299, 1965.
K. Hida andM. Tajiri,Note on the CGL approximation for treating a collisionless plasma flow, Bulletin American Physical Society, Vol. X, pp. 730, 1965.
I. A. Akhiezer, R. V. Polovin andN. L. Tsintsadze,Simple waves in the Chew-Goldberger-Low approximation, Soviet Physics JETP, Vol. 37, pp. 539–542, 1960.
C. P. Yu andJ. V. Sanborn,Internal gravitational instability in a stratified anisotropic plasma, Physics Fluids, Vol. X, pp. 2436–2441, 1967.
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This work was carried out while the author was a member of the Gruppo di Ricerca no. 44 per la Matematica del CNR, 1967–68.
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Mattei, G. Wave propagation and instabilities in a rotating anisotropic plasma. Meccanica 3, 214–230 (1968). https://doi.org/10.1007/BF02186941
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DOI: https://doi.org/10.1007/BF02186941