Energy of eigen-modes in magnetohydrodynamic flows of ideal fluids

Analytical expression for energy of eigen-modes in magnetohydrodynamic flows of ideal fluids is obtained. It is shown that the energy of unstable modes is zero, while the energy of stable oscillatory modes (waves) can assume both positive and negative values. Negative energy waves always correspond to non-symmetric eigen-modes -- modes that have a component of wave-vector along the equilibrium velocity. These results suggest that all non-symmetric instabilities in ideal MHD systems with flows are associated with coupling of positive and negative energy waves. As an example the energy of eigen-modes is calculated for incompressible conducting fluid rotating in axial magnetic field.Comment: 10 pages, 3 figure

Modeling the Parker instability in a rotating plasma screw pinch

We analytically and numerically study the analogue of the Parker (magnetic buoyancy) instability in a uniformly rotating plasma screw pinch confined in a cylinder. Uniform plasma rotation is imposed to create a centrifugal acceleration, which mimics the gravity required for the classical Parker instability. The goal of this study is to determine how the Parker instability could be unambiguously identified in a weakly magnetized, rapidly rotating screw pinch, in which the rotation provides an effective gravity and a radially varying azimuthal field is controlled to give conditions for which the plasma is magnetically buoyant to inward motion. We show that an axial magnetic field is also required to circumvent conventional current driven magnetohydrodynamic (MHD) instabilities such as the sausage and kink modes that would obscure the Parker instability. These conditions can be realized in the Madison Plasma Couette Experiment (MPCX). Simulations are performed using the extended MHD code NIMROD for an isothermal compressible plasma model. Both linear and nonlinear regimes of the instability are studied, and the results obtained for the linear regime are compared with analytical results from a slab geometry. Based on this comparison, it is found that in a cylindrical pinch the magnetic buoyancy mechanism dominates at relatively large Mach numbers (M>5), while at low Mach numbers (M<1) the instability is due to the curvature of magnetic field lines. At intermediate values of Mach number (1<M<5) the Coriolis force has a strong stabilizing effect on the plasma. A possible scenario for experimental demonstration of the Parker instability in MPCX is discussed

CHRONIC MYELOID LEUKEMIA: EPIDEMIOLOGY AND FIFTEENTH YEARS OF THERAPY IN THE NOVOSIBIRSK REGION

The incidence of chronic myeloid leukemia from 2004 to 2018 amounted to 0.63 per 100 000 people per year. The prevalence of chronic myeloid leukemia over the past 15 years has increased from 1.88 to 7.02 case per 100 000 people. We have analyzed the therapy outcomes of chronic myeloid leukemia of patients, received imatinib treatment for more than 12 month (165 patients). Complete hematologic response is attained in 88.5 % cases (146 patients), complete cytogenetic response (CCR) (ph+&lt;0 %) – in 72.1 % cases (119 patients), major molecular response (MMR) – in 50.3 % cases (83 patients). The primary resistance to imatinib is observed in 21.8 % cases (36 patients), secondary – in 6.1 % cases (10 patients – 7 patients have lost the complete hematologic response and CCR and 3 patients have lost the CCR and MMR). The thirteen patients of those, who have primary or secondary resistance to imatinib have been treated with second-generation tyrosine kinase inhibitors (nilotinib, dasatinib) and in 93,3 % cases (14 patients) CCR have been obtained, 10 patients (66.7 %) have attained the CCR and 9 patients (60 %) have achieved MMR. Among all those patients treated with I and II generations tyrosine kinase inhibitors, we have carried out the overall survival (OS) analysis and obtained following results: the median of OS have not been achieved, 5-year OS rate is estimated as 90 %, 10-year OS rate – more than 77 %, calculated 15-year OS – more than 60 %