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Author(s):
Y. Kondoh, T. Takahashi and H. Momota
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Title:
Revisit to the Helicity and the Generalized Self-organization Theory
Date of publication:
Sep. 2000
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Key words:
magnetic helicity, equation of change rate, conservation law, variational calculus, self-organization, auto-correlations, minimum change rate auto-correlation
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Abstract:
It is clarified that the so-called "helicity conservation law" is never "the conservation equation of the helicity K itsell", but is merely "the time change rate equation of K", which is passively and resultantly determined by the mutually independent volume and surface integral terms. It is shown that since the total helicity K can never be conserved in the real experimental systems, the conjecture of the total helicity invariance is not physically available to real magnetized plasmas in an exact sense. The well-known relaxation theory by Dr. J. B. Taylor is clarified to be neither the variational principle nor the energy principle, but be merely a mathematical calculation, using the variational calculus in order to find the minimum magnetic energy solution from the set of solutions having the same value of K. With the use of auto-correlations for physical quantities, it is presented that a novel basic formulation of an extended generalized self-organization theory, which is not based on neither the variational principle nor the energy principle. It is clarified that conservation equations concerning with all physical quantities for the dynamic system of interest are naturally embedded in the formulation of the generalized self-organization theory. The self-organized states of every physical quantities of interest may be realized during their own phases and the dynamical system may evolve repeatedly those out of phase organizations, depending on boundary conditions and input powers. It is shown that the conservation laws can be used to extend conventional methods of plasma current drives by energy injections with use of various types of energies, such as magnetic energies, electromagnetic wave energies, internal energies of plasmoids by plasma guns, which induce the thermal plasma flow velocity, various particle beam energies, and so on.
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