Self Excitation of the Ballooning Tearing Mode And the Nature of Anomalous Trans

L E Zakharov

The book Self Excitation of the Ballooning Tearing Mode And the Nature of Anomalous Trans was written by author L E Zakharov Here you can read free online of Self Excitation of the Ballooning Tearing Mode And the Nature of Anomalous Trans book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Self Excitation of the Ballooning Tearing Mode And the Nature of Anomalous Trans a good or bad book?

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Bers for a stimulating discussion.
This work was supported by U. S. Department of Energy Grant No. DE-FG02-86ER53223.
APPENDIX: TWISTING MODE We will now calculate the nonlinear behavior of the odd twisting mode in physical space. We exactly reproduce the results of Zakharov, Semenov and Riedel, however our present calculation is substantially simpler and more intuitive than the previous analysis in Fourier space. We again base our analysis on the theory of nearest equilibrium and therefore ana...lyze the stability of the nested flux surface equilibrium with a pressure distribution given in Fig. 2.
Our starting point is the energy function given in Eq. (2). The analysis of the twisting mode requires the determination of the next order terms and the retention of the second satellite harmonic. The general Euler equations are ^ ('n-Sx)2 i. F, - (m-Sx)2F, = f^ ^ [_ . AU)F^ - - [F^, i*F^_i) ^ - [-^^ - -^^] ^ - [ g j (Al) This equation can be solved with a Green's function to yield e-|x-t|f F„(x) = - - -, — (A2) "> 2 J-a> (m-Sx)(m-St) The following identities will be useful f" dx dF^ r^ e^'-^rjt) [xS(x)]'f^(x) X (m-Sx)(m-St) (m-Sx) F„ - "1 dx dF^ rx et-^f^(t) [xS(x)]'f^(x) ^^^^ -OD (m-Sx)(m-St) (m-Sx) We assume the standard ballooning mode ordering, that a is small, 2 the shear S and the magnetic well W are order a and that the width of the island is also small.

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