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1 Mechanics and Mechanical Engineering

1 2001

1 Radwan A. E. A. E.

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Nonlinear MHD analysis for force-free magnetic field instability of magnetized flud cylinder

100%

Radwan A. E. A. E.

tom Vol. 5, nr 2

203-221

The linear and nonlinear instabilities of force-free magnetic fields of perfectly conducting fluid cylinder have been analyzed. Indeed, the instability of force-free magnetized flows poses a challenge to our physical understanding and mathematical skills. Equilibrium state is studied by taking Lundquist field (1951) and it is found that the fluid kinetic pressure is non-uniform. Normal mode analysis is utilized for investigating the linear perturbation technique while in nonlinear ones an iteration procedure (see Radwan (1989)) is used. The stability criterion is discussed analytically and numerically and the unstable domains are identified. Surprising results are obtained due to Lundquist Bessel model effect. The second order perturbation equations are derived and solved. Upon applying appropriate conditions, the coefficients control nonlinear theory are identified in general and in the case in which the force-free tenuous field is unperturbed in the linear analysis. Second order analysis does not alter in a direct way the unstable domains. However, it gives corrections and domain of validity for the linear analysis, since no linear theory can predict its domain of validity.