Theoretical Research On Thermal Convective And Rotational Instability In Magnetized Plasmas

When the particle gyroradius is much less than the mean collisional free path, the heat is restricted to being transported primarily along the magnetic force lines. The anisotropic heat conduction will introduce a kind of convective magnetohydrodynamic (MHD) instability, which is referred to as the magnetothermal instability (MTI). MTI has attracted more and more attention due to its important application on astrophysical bodies. Another MHD instability considered in this dissertation is the so-called magne-torotational instability (MRI) which is induced by differential rotation. MRT was first discovered in 1959 and has significant application on many astrophysical bodies such as accretion disks, protoplanetary disks as well as core-collapse supernovae and so on. It is sufficient for us to use MHD equations to describe the two instabilities. The present dissertation is based on the previous method and results to investigate MTI and MRI. The main content are as follows.1.When the gyro time is much less than the mean collisional time, we investigate the anisotropic resistivity and viscosity dissipative effects on the MTI due to the parallel heat transporting on the basis of the non-ideal MHD equations. The general dispersion relation is obtained by using the Wentzel-Kramers-Brillouin (WKB) approximation to simplify the linearized perturbed MHD equations in the Boussinesq limit. We discuss the effects on the MTI due to the resistivity and viscosity and obtained the growth rates for weak dissipation and strong dissipation, respectively. The perturbations are damped when the temperature decreases in the direction of gravity. When the temperature in-creases in the direction of gravity, the system is MTI unstable. Resistivity and viscosity are shown to reduce the value of MTI growth rate, which is then less than the growth rate obtained in the ideal MHD case.2.The density gradient effect on the MTI in an arbitrary magnetic field is exam-ined by using ideal MHD equations. We obtained the second-order ordinary differen-tial equation (ODE) describing the axial perturbed velocity and derived the instability criterion and growth rate under the fixed boundary condition. It is shown that the per-turbation is MTI unstable when the temperature increases in the direction of gravity. The growth rate increases monotonically as Ld increases at first, where LD is the scale length of density gradient. When LD is greater than a critical value LDc, the growth rate starts to decrease as LD increases. Finally, magnetic fields show stabilizing effect on the MTI and can totally quench the instability. 3.The magnetorotational instability (MRI) in differential rotating dusty plasmas with dissipative effects is investigated by using local linear analysis on the basis of non-ideal MHD equations. We assume that the dust grains are heavy enough to be immobile. The general local dispersion relation is derived under the WKB approximation. Two limiting cases, (?)Rd/(?)lnr>>Rd≥0 and Rm>>Rd,丨(?)Rd/(?)lnr丨>>Rd, are discussed with respect to the dust-induced effect in detail, where Rm is the normalized rotation frequency and Rd is the normalized effective dusty rotation frequency. The instability criteria in the different limiting cases are presented and the growth rate of local MRI in the last case is demonstrated.4. The local MTI and MRI in differential rotating plasmas are investigated in the ideal MHD framework which contains immobile dusty grains effects. By adopting the WKB and Boussinesq approximations, the general dispersion relation of MTI as-sociated with MRI is derived and presented in the high-βlimit. For entropy-gradient mode, density inhomogeneity has significant effect on the instability criterion. Density gradient shows stabilizing effect on the instability when increasing outward whereas has destabilizing effect when increasing inward. For the MTI combined with MRI, the instability criteria and growth rate show that dust has stabilizing effect on the MTI whereas the rotation changes the instability criterion. Even if the temperature decreases in the direction of gravity, the MTI will come into being provided that rΩ2 is greater than the gravity acceleration g.5.Anisotropic resistivity and viscosity effect on the MTI and MRI is examined. We obtain the full general dispersion relation as well as the reduced dispersion rela-tion and growth rate in the high-βlimit. It is found that in our model, the anisotropic dissipative terms do not affect the instability criterion, which is identical with the one obtained in the ideal MHD case. On the other hand, both resistivity and viscosity re-duce the value ofγ. That is, they have stabilizing effect on the thermal convective and magnetorotational instability and modify the growth rate remarkably.6.The density gradient and non-axisymmetric effects on the MRI are finally in-vestigated in the presence of axial magnetic field by using the ideal MHD equations. Our results show that density gradient has no effect on the instability criterion. We also obtain the instability growth rate and discuss the weak field case in detail. For positiveκ2, it is found that when the scale length of density gradient is small, density gradient shows destabilizing effect on the MRI. When the scale length exceeds a crit-ical value, density gradient has stabilizing effect on the instability. The MRI will be totally quenched by the density gradient when the latter exceeds ge/κ2. For negativeκ2, density gradient shows similar effect on the instability but the MRI can not be to-tally quenched and the growth rate goes to a constant independent of LD.Ignoring the density gradient, we then obtain the dispersion relation and instability criterion in weak fields limit with non-axisymmetric effect modifications. Similar to the density gradient, non-axisymmetric effect in this case do not change the MRI criterion.