Nonlinear stability of an infinite cylinder in the presence of a uniform axial magnetic field

1989 ◽  
Vol 158 (1) ◽  
pp. 67-88 ◽  
Author(s):  
R. K. Chhabra ◽  
S. K. Trehan
Keyword(s):  
Magnetic Field ◽  
Nonlinear Stability ◽  
Axial Magnetic Field ◽  
Infinite Cylinder

EXPANSION OF LASER-PRODUCED ION BEAMS IN AN AXIAL MAGNETIC FIELD

2002 ◽  
Vol 6 (4) ◽  
pp. 8
Author(s):  
J. Wolowski ◽  
J. Badziak ◽  
P. Parys ◽  
E. Woryna ◽  
J. Krasa ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Axial Magnetic Field ◽  
Ion Beams

A Slotless PM Variable Reluctance Resolver with Axial Magnetic Field

2021 ◽  
pp. 1-1
Author(s):  
Le Sun ◽  
Zhejun Luo ◽  
Jun Hang ◽  
Shichuan Ding ◽  
Wei Wang
Keyword(s):  
Magnetic Field ◽  
Axial Magnetic Field ◽  
Variable Reluctance

Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field

2021 ◽  
Vol 76 (3) ◽  
pp. 265-283
Author(s):  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Axial Magnetic Field ◽  
Order Approximation ◽  
Ideal Gas ◽  
Field Region ◽  
First Order ◽  
First Order Approximation ◽  
Flow Variables

Abstract The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.

The behavior of TIG welding arc in a high-frequency axial magnetic field

2020 ◽  
Vol 65 (1) ◽  
pp. 95-104
Author(s):  
H. Wu ◽  
Y. L. Chang ◽  
Alexandr Babkin ◽  
Boyoung Lee
Keyword(s):  
Magnetic Field ◽  
High Frequency ◽  
Axial Magnetic Field ◽  
Tig Welding ◽  
Welding Arc

On the application of the Kelvin–Arnol'd energy principle to the stability of forced two-dimensional inviscid flows

1998 ◽  
Vol 356 ◽  
pp. 221-257 ◽  
Author(s):  
P. A. DAVIDSON
Keyword(s):  
Magnetic Field ◽  
Nonlinear Stability ◽  
Broad Class ◽  
Mhd Flow ◽  
Two Dimensional ◽  
Energy Principle ◽  
Inviscid Flows ◽  
Virtual Displacement ◽  
Euler Flows ◽  
Universal Procedure

Arnol'd developed two distinct yet closely related approaches to the linear stability of Euler flows. One is widely used for two-dimensional flows and involves constructing a conserved functional whose first variation vanishes and whose second variation determines the linear (and nonlinear) stability of the motion. The second method is a refinement of Kelvin's energy principle which states that stable steady Euler flows represent extremums in energy under a virtual displacement of the vorticity field. The conserved-functional (or energy-Casimir) method has been extended by several authors to more complex flows, such as planar MHD flow. In this paper we generalize the Kelvin–Arnol'd energy method to two-dimensional inviscid flows subject to a body force of the form −ϕ∇f. Here ϕ is a materially conserved quantity and f an arbitrary function of position and of ϕ. This encompasses a broad class of conservative flows, such as natural-convection planar and poloidal MHD flow with the magnetic field trapped in the plane of the motion, flows driven by electrostatic forces, swirling recirculating flow, self-gravitating flows and poloidal MHD flow subject to an azimuthal magnetic field. We show that stable steady motions represent extremums in energy under a virtual displacement of ϕ and of the vorticity field. That is, d1E=0 at equilibrium and whenever d2E is positive or negative definite the flow is (linearly) stable. We also show that unstable normal modes must have a spatial structure which satisfies d2E=0. This provides a single stability test for a broad class of flows, and we describe a simple universal procedure for implementing this test. In passing, a new test for linear stability is developed. That is, we demonstrate that stability is ensured (for flows of the type considered here) whenever the Lagrangian of the flow is a maximum under a virtual displacement of the particle trajectories, the displacement being of the type normally associated with Hamilton's principle. A simple universal procedure for applying this test is also given. We apply our general stability criteria to a range of flows and recover some familiar results. We also extend these ideas to flows which are subject to more than one type of body force. For example, a new stability criterion is obtained (without the use of Casimirs) for natural convection in the presence of a magnetic field. Nonlinear stability is also considered. Specifically, we develop a nonlinear stability criterion for planar MHD flows which are subject to isomagnetic perturbations. This differs from previous criteria in that we are able to extend the linear criterion into the nonlinear regime. We also show how to extend the Kelvin–Arnol'd method to finite-amplitude perturbations.

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