Theory of Long Period Magnetic Pulsations

Cover Theory of Long Period Magnetic Pulsations
Theory of Long Period Magnetic Pulsations
Satoshi Hamaguchi
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In the region II, Eq. (3. 24) becomes where a = k = kxd A^ - — 19 We now solve Eq. (3. 28) by means of the WKB method. For the range of the variable if such that 1^^ — a^ :7"^ 0, we transform ( to Za (-a ^ + Q and therefore we have dt] = d( -{e{r, )-a'y6 = 0.
(3. 29) Then Eq. (3. 22) is transformed to drj^ For (f^ not near q^, the WKB method yields the asymptotic solution of Eq. (3. 29) in terms of ^ as 6 = A+ {e - a'y'^\xpi + A. {e - a^y''' exp{-0. (3. 30) The boundary conditions to be applied
... at z = ±(f are that the normal velocity viy{y) and the normal component of the stress pi + BqBiz be continuous. Since u>'{y) = u — kxVo{y) is continuous a± z = ±d, the continuous normal velocity conditions are [^]. =±. = 0, (3. 31) where [ ]^ indicates the change in the value of the enclosed quantity across the discontinuity surface at z. Since Eq. (3. 23) may be written as . Pu)' dS (pi + BoBu) = -i- kx dy' the continuous normal stress conditions are given by = 0.
d( (3. 32) Equation (3.


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