Kink mode m = 1 in thin plasma flex with discontinuous vertical magnetic field
1Cheremnykh, OK, 2Kryshtal, AN, 1Tkachenko, AA 1Space Research Institute under NAS and National Space Agency of Ukraine, Kyiv, Ukraine 2Main Astronomical Observatory of the National Academy of Sciences of Ukraine, Kyiv, Ukraine |
Kinemat. fiz. nebesnyh tel (Online) 2017, 33(3):3-24 |
https://doi.org/10.15407/kfnt2017.03.003 |
Start Page: Solar Physics |
Language: Russian |
Abstract: In this paper, we study conditions of realization and stability of kink modes with azimuthal wave numbers m=±1 in cylindrical plasma flex with twisted magnetic field and homogeneous current along its axis. We assume permanent vertical magnetic fields inside and outside the flex, which is surrounded by currentless plasma, and outside its boundary azimuthal magnetic field decreases inversely proportional to the distance from the flex’s border. We derive dispersion equations for stable and unstable modes in approximation of «thin» plasma flex. Analysis of equations for the case of discontinuous vertical magnetic field on flex’s boundary is provided. Conditions of propagation of wave modes have been defined. We have obtained that unstable modes with m=±1 can’t be realized. Results can be applied for interpretation of solar magnetic tubes behavior, using measurements provided by the spacecrafts. |
Keywords: kink modes, magnetic field, thin plasma flex |
1.G. Bateman, MHD Instabilities (MIT Press, Cambridge, 1978; Energoizdat, Moscow, 1982).
2.A. Bernshtein, “Variational principle for stability problems in ideal magnetohydrodynamics,” in Fundamentals of Plasma Physics, Ed. by A. A. Galeev and R. Sudan (Energoatomizdat, Moscow, 1983), Vol. 1, pp. 365–392 [in Russian].
3.M. Goossens, “MHD waves and wave heating in nonuniform plasmas,” in Advances in Solar System Magnetohydrodynamics, Ed. by E. R. Priest and A. W. Hood (Cambridge Univ. Press, Cambridge, 1991; Mir, Moscow, 1995), p. 137–172.
4.A. G. Zagorodnii and O. K. Cheremnykh, Introduction to Plasma Physics (Naukova Dumka, Kyiv, 2014) [in Russian].
5.B. B. Kadomtsev, “Hydromagnetic stability of plasma,” in Questions of Plasma Theory, Ed. by M. A. Leontovich (Atomizdat, Moscow, 1964), Vol. 2, 132–176 [in Russian].
6.K. Miyamoto, Fundamentals of Plasma Physics and Controlled Fusion (National Inst. of Fusion Science, Tokio, 2000; Fizmatlit, Moscow, 2007).
7.Yu. P. Ladikov-Roev, “Magneto-vortex rings,” Izv. Akad. Nauk SSSR, Ser. Mekh. Mashinostr., No. 4, 7–13 (1960).
8.Yu. P. Ladikov-Roev and O. K. Cheremnykh, “Propagation of incompressible kink modes in a thin magnetic flux tube,” J. Autom. Inf. Sci. 48, 54–64 (2016).
https://doi.org/10.1615/JAutomatInfScien.v48.i3.60
9.E. Parker, Cosmical Magnetic Fields: Their Origin and Their Activity (Clarendon Press, Oxford, 1979; Mir, Moscow, 1982).
10.B. Roberts, “MHD waves in the Sun,” in Advances in Solar System Magnetohydrodynamics, Ed. by E. R. Priest and A. W. Hood (Cambridge Univ. Press, Cambridge, 1991; Mir, Moscow, 1995), pp. 105–136.
11.B. P. Filippov, Eruptive Processes in the Sun (Fizmatlit, Moscow, 2007) [in Russian].
12.Yu. T. Tsap, Yu. G. Kopylova, and A. V. Stepanov, “Ballooning instability and oscillations of coronal loops,” Astron. Rep. 50, 1026–1035 (2006).
https://doi.org/10.1134/S1063772906120079
13.O. K. Cheremnykh, D. Yu. Klimushkin, and D. V. Kostarev, “On the structure of azimuthally small-scale ULF oscillations of hot space plasma in a curved magnetic field. Modes with continuous spectrum,” Kinematics Phys. Celestial Bodies 30, 209–222 (2014).
https://doi.org/10.3103/S088459131405002X
14.O. K. Cheremnykh, “On the theory of transversally small-scale modes in the cylindrical plasma column,” Kinematics Phys. Celestial Bodies 31, 213–224 (2015).
https://doi.org/10.3103/S0884591315050025
15.O. K. Cheremnykh, D. Yu. Klimushkin, and P. N. Mager, “On the structure of azimuthally small-scale ULFoscillations of a hot space plasma in a curved magnetic field: Modes with discrete spectra,” Kinematics Phys. Celestial Bodies 32, 120–128 (2016).
https://doi.org/10.3103/S0884591316030028
16.V. D. Shafranov, “On the question of hydromagnetic stability of plasma thread with a current in a strong magnetic field,” Zh. Tekh. Fiz. 40, 241–253 (1970).
17.Z. M. Andrushchenko, S. M. Revenchuk, and O. K. Cheremnykh, “Steady MHD flows in a cylindrical plasma column,” Plasma Phys. Rep. 19 (1993). OSTI id.: 102 964
18.K. Bennet, B. Roberts, and U. Narain, “Waves in twisted magnetic flux tubes,” Sol. Phys. 185, 41–59 (1999).
https://doi.org/10.1023/A:1005141432432
19.O. S. Burdo, O. K. Cheremnykh, S. M. Revenchuk and V. D. Pustovitov, “General geometric dispersion relations for toroidal plasma configuration,” Plasma Phys. Controlled Fusion 36, 641–656 (1994).
https://doi.org/10.1088/0741-3335/36/4/006
20.O. K. Cheremnykh, “Dispersion equation and stability limit for ballooning flute modes in a tokamak with circular magnetic surfaces and an arbitrary pressure profile,” Nucl. Fusion 29, 1899–1904 (1989).
https://doi.org/10.1088/0029-5515/29/11/005
21.O. K. Cheremnykh, Z. M. Andrushchenko, J. W. Edenstrasser, and V. B. Taranov, “Relaxation of a nonideal magnetohydrodynamic plasma in a cylindrical column,” Phys. Plasmas 1, 2525–2530 (1994).
https://doi.org/10.1063/1.870580
22.O. K. Cheremnykh, “On the motion of vortex rings in an incompressible media,” Nelineinaya Din. 4, 417–428 (2003).
https://doi.org/10.20537/nd0804003
23.P. M. Edwin and B. Roberts, “Wave propagation in a magnetic cylinder,” Sol. Phys. 88, 179–191 (1983).
https://doi.org/10.1007/BF00196186
24.R. Erdelyi and V. Fedun, “Sausage MHD waves in in compressible flux tubes with twisted magnetic fields,” Sol. Phys. 238, 41–59 (2006).
https://doi.org/10.1007/s11207-006-0217-z
25.R. Erdélyi and V. Fedun, “Linear MHD sausage waves in compressible magnetically twisted flux tubes,” Sol. Phys. 246, 101–118 (2007).
https://doi.org/10.1007/s11207-007-9022-6
26.K. Hain and R. Z. Lust, “Zur Stability zylindersymmetrischer Plasmakonfigurationen mit Volumenströmen,” Z. Naturforsch., A: Phys. Sci. 13, 936–940 (1958).
https://doi.org/10.1515/zna-1958-1103
27.A. N. Kryshtal, S. V. Gerasimenko, A. D. Voitsekhovska, and O. K. Cheremnykh, “One type of three-wave interaction of low-frequency waves in magnetoactive plasma of the solar atmosphere,” Kinematics Phys. Celestial Bodies 30, 147–154 (2014).
https://doi.org/10.3103/S0884591314030052
28.Yu. P. Ladikov-Roev, S. O. Cheremnykh, and V. A. Yatsenko, “Axisymmetric force free magnetic configurations in plasma flux,” J. Autom. Inf. Sci. 45 (4), 48–58 (2013).
https://doi.org/10.1615/JAutomatInfScien.v45.i6.50
29.Y. P. Ladikov-Roev, A. A. Loginov, and O. K. Cheremnykh, “Nonstationary model of solar spicule,” J. Autom. Inf. Sci. 46 (10), 20–29 (2014).
https://doi.org/10.1615/JAutomatInfScien.v46.i10.30
30.M. S. Ruderman, “Nonaxisymmetric oscillations of thin twisted magnetic tubes,” Sol. Phys. 246, 119–131 (2007).
https://doi.org/10.1007/s11207-007-9024-4
31.M. S. Ruderman, “Propagating kink waves in thin twisted magnetic tubes with continuous equilibrium magnetic field,” Astron. Astrophys. 575, A130 (2015).
https://doi.org/10.1051/0004-6361/201424611
32.A. V. Stepanov, K. Shibasaki, Yu. G. Kopylova, and Yu. T. Tsap, “MHD-oscillations of coronal loops and diagnostics of flare plasma,” in Solar Physics with Nobeyama Radioheliograph: Proc. of Nobeyama Symp. 2004, Kiyosato, Japan, October 26–29, 2004 (Nobeyama Solar Radio Obs., 2004), pp. 23–31.
33.J. A. Wesson, “Hydromagnetic stability of Tokamaks,” Nucl. Fusion 18, 87–132 (1978).
https://doi.org/10.1088/0029-5515/18/1/010