A New Approach to Magnetohydrodynamic Stability I a Practical Stability Concept
A New Approach to Magnetohydrodynamic Stability I a Practical Stability Concept
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In our eReader you can find the full English version of the book. Read A New Approach to Magnetohydrodynamic Stability I a Practical Stability Concept Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A New Approach to Magnetohydrodynamic Stability I a Practical Stability Concept
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(35)- However, since f and g are 2 non-singular functions of r and us for < r _< a and values of 2 us in one non-singular subinterval, we may as well restrict the equilibrium profiles to those which make f and g analytic functions 2 2 of both r and a> . The function R = R(n, us ) will then be analytic 2 in us and the expansion (39) can be analytically continued in the 2 2 2 complex as -plane. Then, one can choose [B(us ) ] < so that 2 2 2 2 6(us ) is imaginary and, consequently, us « us + 5(co ) is complex. 2 Equation (39) then gives for this complex us a possible real wall- position for which the boundary value problem x = at r =0 and for self-adjcint systems and we conclude that an extremum for 2 R as a function of us cannot occur. Hence, in each non-singular branches labelled by n. 2 Having proved that for fixed us R is an increasing function 2 of n, and for fixed n R is a monotonic function of us, it follows 2 that for fixed R us is a monotonic function of n. Choosing R = a, 2 we see that the solution as of the boundary value problem (35) is a monotonic function of n.
What to read after A New Approach to Magnetohydrodynamic Stability I a Practical Stability Concept?
You can find similar books in the "Read Also" column, or choose other free books by J P Goedbloed to read online
To quickly assess the difficulty of the text, read a short excerpt:
(35)- However, since f and g are 2 non-singular functions of r and us for < r _< a and values of 2 us in one non-singular subinterval, we may as well restrict the equilibrium profiles to those which make f and g analytic functions 2 2 of both r and a> . The function R = R(n, us ) will then be analytic 2 in us and the expansion (39) can be analytically continued in the 2 2 2 complex as -plane. Then, one can choose [B(us ) ] < so that 2 2 2 2 6(us ) is imaginary and, consequently, us « us + 5(co ) is complex. 2 Equation (39) then gives for this complex us a possible real wall- position for which the boundary value problem x = at r =0 and for self-adjcint systems and we conclude that an extremum for 2 R as a function of us cannot occur. Hence, in each non-singular branches labelled by n. 2 Having proved that for fixed us R is an increasing function 2 of n, and for fixed n R is a monotonic function of us, it follows 2 that for fixed R us is a monotonic function of n. Choosing R = a, 2 we see that the solution as of the boundary value problem (35) is a monotonic function of n.
What to read after A New Approach to Magnetohydrodynamic Stability I a Practical Stability Concept?
You can find similar books in the "Read Also" column, or choose other free books by J P Goedbloed to read online
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