  A unified ballooning theory, constructed on the basis of two special theories
[Y. Z. Zhang, S. M. Mahajan, X. D. Zhang, Phys. Fluids B4, 2729 (1992); Y. Z.
Zhang, T. Xie, Nucl. Fusion & Plasma Phys. 33, 193 (2013)], shows that a weak
up-down asymmetric mode structure is normally formed in an up-down symmetric
equilibrium; the weak up-down asymmetry in mode structure is the manifestation
of non-trivial higher order effects beyond the standard ballooning equation. It
is shown that the asymmetric mode may have even higher growth rate than
symmetric modes. Salient features of the theory are illustrated by
investigating a fluid model for the ion temperature gradient (ITG) mode. The
two dimensional (2D) analytical form of ITG mode, solved in ballooning
representation, is then converted into the radial-poloidal space to provide the
natural boundary condition for solving the 2D mathematical local eigenmode
problem. We find the analytical expression of mode structure in good agreement
with finite difference solution. This sets a reliable framework for
quasi-linear computation.
