Ballooning Stability of Separatrix Spanning Modes

The ideal ballooning stability of the near-separatrix tokamak plasma and its possible relation to the Greenwald density limit, as discussed in [1], motivates the present work. We consider a sequence of CORSICA-generated equilibrium shapes with varying elongation and examine the marginal stability of infinite-n and finite-n separatrix-spanning modes using the 2DX [2] and ArbiTER [3] eigenvalue codes. The elongation scaling of the result provides a test of the proposed density-limit theory. A new computationally efficient technique for dealing with the phase variation of moderate-n modes across the branch cut in field-line following coordinates will also be discussed.\\[4pt] [1] R. J. Goldston and T. Eich, 24th IAEA Fusion Energy Conference, San Diego, USA, October 8 - 13, 2012, paper IAEA-CN-197/TH/P4-19 \newline [2] D. A. Baver, J. R. Myra and M.V. Umansky, Comp. Phys. Comm. \textbf{182}, 1610 (2011). \newline [3] D. A. Baver et al., this conference