Ideal instabilities in a high-β rotating cylindrical plasma in the presence of an azimuthal magnetic field and a gravitational field

Abstract

Magnetohydrodynamic (MHD) theory of ideal instabilities in a high-β rotating cylindrical plasma with an azimuthal magnetic field and a radial gravitational field is developed (β is the ratio of the plasma and magnetic field pressures). The basis of this theory is a system of two first-order differential equations for the Frieman-Rotenberg variable (the sum of the perturbed plasma and magnetic field pressures) and the radial plasma displacement, which leads to the second-order differential equation for the displacement. The sausage instability criterion is derived which generalizes the earlier results for a plasma without gravitation. It is shown that this instability can occur for both the decreasing and increasing plasma pressures. The non-axisymmetric modes are also considered. This analysis is related to the MHD instability theory in a nonrotating plasma dealing with snake instabilities. A number of rotational and gravitational effects on both the m = 1 and m > 1 modes are revealed, where m is the azimuthal mode number. The eigenmode equation describing the Suydam modes in the presence of rotational and gravitational effects is derived. These modes can be responsible, in particular, for the Velikhov and rotational-convective instabilities.

Corotational instability, magnetic resonances and global inertial-acoustic oscillations in magnetized black hole accretion discs

“…They also agree with system (14) in Blokland et al (2005) 5 in the kz → 0 and barotropic limit, although their equations are cast on slightly different variables (δΠ instead of δh). The Hameiri-Bondeson-Iacono-Bhattacharjee (HBIB) type of equations presented in Blokland et al (2005) have been derived before by Hameiri (1981) and Bondeson et al (1987) [see also Mikhailovskii et al (2009); Goossens et al (1992) (hereafter GHS92) and reference therein] for a magnetized rotating flow in the absence of external gravity. The equations including gravity were obtained by Keppens et al (2002) (hereafter KCP02) using the same Frieman-Rotenberg technique (Frieman & Rotenberg 1960).…”

Density gradient effects on the magnetorotational instability

“…It is believed that the instability is one of the main factors driving plasma turbulence [4] and determining the angular momentum transport rate in most astrophysical discs [5]. Owing to its important role in the astrophysics (see, for example, three excellent reviews [5][6][7]), MRI has attracted much attention in the past twenty years and many studies have been devoted to analytical exploration, numerical analysis and experimental investigation of this magnetohydrodynamic (MHD) instability and MRI is indeed becoming a basic plasma physical phenomenon (see, for example, [8][9][10][11][12][13][14][15][16][17][18] and references therein).…”

Magnetorotational instability in dissipative dusty plasmas

“…5-14͒, protoplanetary disks, [15][16][17][18][19][20] stellar disks, 21,22 core-collapse supernovae, [23][24][25][26] and protoneutron stars 27,28 since MRI is believed to be one of the leading candidate in driving plasma turbulence. [29][30][31][32][33] Spurred by the astrophysical significance of MRI ͑see, for example, three excellent reviews [34][35][36] ͒ in conjunction with a deceptively simple setup, namely, the Couette-flow configuration, [37][38][39][40][41][42][43][44] studies of MRI have proliferated in terms of both theoretical analyses 37,[45][46][47][48][49] and experimental studies. 38,[50][51][52][53] In recent years, many analytical and numerical studies have been carried out by taking into account increasingly complex and realistic assumptions to investigate the linear and nonlinear properties of MRI, including effects due to the resistivity and viscosity, 37,46,[54]…”