LECTURES ON THE HYDROMAGNETIC STABILITY OF A CYLINDRICAL PLASMA. II. INVESTIGATIONS OF STABILITY USING INTEGRAL PROPERTIES OF THE HYDROMAGNETIC EQUATIONS

Technical Report · Tue Sep 01 04:00:00 EDT 1959

OSTI ID:4219921

Tayler, R J

In some stability problems it is either impossible or inconvenient to solve the normal mode equations completely. Then it is sometimes possible to obtain more limited information about the stability of the system by studying integral properties of the hydromagnetic equations. One such method can be used if the system is in static equilibrium and possesses a constant energy; then the stability against any penturbation can be investigated by finding whether or not the perturbation increases the potential energy of the system. A brief account of the hydromagnetic energy principle is given and from it are deduced some general stability properties of a cylindrical plasma. It is also shown that, in problems to which the energy principle cannot be applied, stability criteria can sometimes be obtained by studving volume integrals of the solutions of the normal mode equations. In such cases the reality or sign of the disturbance growth rate can be found without the normal mode equations being solved. (auth)

• Research Organization: United Kingdom Atomic Energy Authority. Research Group. Atomic Energy Research Establishment, Harwell, Berks, England
• NSA Number: NSA-14-004029
• OSTI ID: 4219921
• Report Number(s): AERE-L-103
• Country of Publication: United Kingdom
• Language: English

Related Subjects

CYLINDERS
DIFFERENTIAL EQUATIONS
DISTURBANCES
ENERGY
MAGNETOHYDRODYNAMICS
PHYSICS
PLASMA
STABILITY