Bulletin KRASEC. Phys. & Math. Sci, 2015, V. 11, №. 2, pp. 63-72. ISSN 2313-0156

Back to contents

DOI: 10.18454/2313-0156-2015-11-2-63-72

PHYSICS

MSC 65D15

PRESERVATION OF THE THIRD ADIABATIC INVARIANT OF MOTION IN THE EQUATORIAL PLANE OF MAGNETIC FIELD WITH WEAK AXIAL ASYMMETRY

V.V. Bogdanov, A.V. Kaisin

Institute of Cosmophysical Research and Radio Wave Propagation, Far-Eastern Branch, Russian Academy of Sciences, 684034, Kamchatskiy Kray, Paratunka, Mirnaya st., 7, Russia.
E-mail: vbogd@ikir.ru.

The paper considers the question of preservation of the third adiabatic invariant of motion of charged particles vII = 0 (equatorial plane) in flow and in canonical forms in magnetic fields having weak asymmetry. Transition to the coordinate system rotating with drift angular velocity allows us to reduce the problem to the one already been solved, namely, to the problem of preservation of the third adiabatic invariant in an axially symmetric but time-variable magnetic field.

Key words: adiabatic invariant of motion, weak asymmetry of magnetic field, drift approximation.

References

  1. Bogdanov V.V., Pletnev V.D. K voprosu o tochnosti sokhraneniya tret’ego adiabaticheskogo invarianta dvizheniya zaryazhennoi chastitsy v aksial’no-simmetrichnykh polyakh [To the question on the accuracy of preservation of the third adiabatic invariant of charged particle motion in axially-symmetric fields].
    Kosmicheskie Issledovaniya – Cosmic Research, 1972, V.10, I. 3, pp. 358-367.
    2. Bogdanov V.V., Pletnev V.D. K voprosu o tochnosti sokhraneniya tret’ego adiabaticheskogo invarianta dvizheniya zaryazhennoi chastitsy v aksial’no-simmetrichnykh polyakh [To the question on the accuracy of preservation of the third adiabatic invariant of charged particle motion in axially-symmetric fields].
    Kosmicheskie Issledovaniya – Cosmic Research, 1972, V.10, I.4, pp. 528-531.
    3. Bogdanov V.V. Dinamika magnitosfernoi plazmy v dreifovom priblizhenii [Dynamics of the magnetosphere plasma in drift approximation]. Vladivostok, Dal’nauka, 2006, 140 p.
    4. Bogolyubov N.N., Zubarev D.N. Metod asimptoticheskogo priblizheniya dlya sistem s vrashchayushcheisya fazoi i ego primenenie k dvizheniyu zaryazhennykh chastits v magnitnom pole [Method of asymptotic approximation for the systems with rotating phase and its application for charged particle motion in the magnetic field]. Ukrainskii Matematicheskii Zhurnal – Ukrainian Mathematical Journal, 1955, I.1, pp. 5-17.
    5. Bogolyubov N.N., Mitropol’skii Yu.A. Asimptoticheskie metody v teorii nelineinykh kolebanii [Asymptotic methods in the theory of nonlinear oscillations]. Moscow, Fizmatlit, 1963. 410 p.
    6. Berkowitz, Gardner C. Communz, Pure and Appl. Math., 1959, Vol. 12. P. 501.
    7. Fairfield D.H. The average magnetic field configuration of outer magnetosphere // J. Geophys. Res. 1968. Vol.73. P. 7329-7338.
    8. Landau L.D., Lifshits E.M. Mekhanika [Mechanics]. Moscow, Nauka 1965. 204 p.
    9. Landau L.D., Lifshits E.M. Teoriya polya [Theory of a field]. Moscow, Nauka, 1988. 509 p.
    10. Rederer Kh. Dinamika radiatsii, zakhvachennoi geomagnitnym polem [Dynamics of radiation trapped by geomagnetic field]. Moscow, Mir, 1972, 192 p.

For citation: Bogdanov V.V., Kaysin A.V. Preservation of the third adiabatic invariant of motion in the equatorial plane of magnetic field with weak axial asymmetry. Bulletin KRASEC. Physical and Mathematical Sciences 2015, vol. 11, issue 2, 63-72. DOI: 10.18454/2313-0156-2015-11-2-63-72.

Original article submitted: 09.11.2015

Bogd
   Bogdanov Vadim Vasilevich – Dr. Sci. (Phys. & Math.), Head of Lab. Atmosphere Physics, Institute of Cosmophysical Researches and Radio Wave Propagation FEB RAS.

1

ew

цв


kaisin
 Kaisin Alexandr Vladimirovich – Researcher of Lab. Atmosphere Physics, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS.

Download article Bogdanov V.V., Kaisin A.V.