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The conventional definition of the ballooning D (as the ratio of the coefficients of the small to large series solutions) may lead to divergences in the asymptotic solution of the ideal ballooning equation for tokamaks. These problems occur for equilibria which do not exhibit up-down symmetry. In the limit of these divergences the terms in the small and large solutions are interchangeable and thus the definition of D becomes ambiguous. By mixing the solutions, the divergences may be cancelled. This 'mixing' is shown to be the correct procedure by evaluating the solution in an ideal inertial layer and matching onto the marginal ideal solution. The conventional D is not meaningful as a measure of stability to ballooning modes when the series become divergent.

Additional information

Authors: WILSON H R, UKAEA, Culham Laboratory, Abingdon (GB)
Bibliographic Reference: Report: CLM-P874 EN (1989) 23 pp.
Availability: Available from the Librarian, UKAEA, Culham Laboratory, Abingdon, Oxon. OX14 3DB (GB)
Record Number: 199011403 / Last updated on: 1994-12-01
Original language: en
Available languages: en