Bulg. J. Phys. vol.37 no.1 (2010), pp. 48-55

Fictitious Roots in the Dispersion Relation

S. Chandra, G.M. Dak, M. Sharma
School of Physics, Shri Mata Vaishno Devi University, Katra 182 320 (J&K), India
Abstract. For application of magnetohydrodynamics (MHD) in solar physics as well as in plasma physics, dispersion relation plays key role. For a common set of equations, some authors have derived the dispersion relation as a sixth degree polynomial in ω, whereas the others have derived a fifth degree polynomial. Both groups are claiming that their dispersion relation is correct and consequently their results for the fast and slow mode waves are correct. We have shown that for the same set of equations, one can have a fifth degree, sixth degree or even seventh degree polynomial, depending on the way used in solving the set of equations. For these polynomials however the five roots are found to be common and they are the actual roots giving the same results for the fast and slow mode waves. Other roots (one for the sixth degree polynomial and two for the seventh degree polynomial) are fictitious. It explicitly shows that the results for the fast and slow mode waves do not depend on the degree of the polynomial for the dispersion relation.

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