Self Excitation of the Ballooning Tearing Mode And the Nature of Anomalous Trans
Self Excitation of the Ballooning Tearing Mode And the Nature of Anomalous Trans
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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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To quickly assess the difficulty of the text, read a short excerpt:
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.
What to read after Self Excitation of the Ballooning Tearing Mode And the Nature of Anomalous Trans?
You can find similar books in the "Read Also" column, or choose other free books by L E Zakharov to read onlineMoreLess
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