Density gradient effects on the magnetorotational instability

Abstract

The effects of the equilibrium density gradient on non-axisymmetric magnetorotational instability are investigated in a pure axial magnetic field for ideal incompressible plasmas. A second-order ordinary differential equation is employed to determine the magnetic field perturbation and the full dispersion relationship regarding the non-axisymmetric magnetohydrodynamic instability in the presence of gravitation and density gradient effects. By means of local linear analysis, the reduced dispersion relationship is derived with a small azimuthal wavenumber. Spatial variations in the radial field perturbation magnitude cannot be neglected in the calculation since this term has the same order of magnitude as L D , which is the scale length of radial density gradient. The analytical expression of the instability growth rate is presented. Our analysis shows that the instability criterion is modified by the density gradient which has a stabilizing effect when increasing outwards and conversely a destabilizing effect when decreasing outwards. The growth rate increases with L D when L D is small. For a sufficiently large L D , the growth rate decreases with increasing L D . The magnetic field exerts a similar effect on the growth rate and can totally quench the instability. The non-axisymmetric effect introduces a frequency shift and increases the growth rate but does not affect the instability criterion.

Flow shear stabilization of rotating plasmas due to the Coriolis effect

“…[29] the perturbed pressure δp was not included so that the effect was missed. In a cylindrical geometry the effect is included in the original analysis of [30] or more recently in for example [31,32]. The fact that without axial variation the Coriolis force only modifies the pressure was already observed in Ref.…”

The effect of density gradient on the growth rate of relativistic Weibel instability

“…The pellet core is denser than its side by four orders of magnitude, so that the beam makes its way through an important density gradient. [11][12][13][14][15] The energy deposition of a relativistic electron beam in a plasma can be managed through sufficiently steep plasma density gradients. These beams then deposit most of their energy in a reasonably short flat density region.…”

Magnetorotational instability in plasmas with mobile dust grains

“…To take into account the field gradient effect, other boundary conditions are needed. 23 Furthermore, numerical evaluation is needed for the case with x $ OðX d Þ, which is beyond the scope of the present work.…”