The structure of waves around a magnetic X point is analyzed. A parado
x is noted, in which theory implies that waves cannot propagate along
the field past an X point, but experiment shows that they do anyway. T
he paradox may arise from the theoretical ''eikonal in the perpendicul
ar direction'' ansatz, in which waves follow field lines to lowest ord
er. This paper demonstrates that waves can encounter a boundary layer
in which this ansatz is violated. Such waves can propagate around the
X-point region, thus avoiding the large wave number increase from magn
etic shear, allowing them to correlate through such a region, This res
ult has some unexpected implications concerning mode structure in the
edge and scrape-off layer of a diverted tokamak, and possibly for the
core as well. (C) 1995 American Institute of Physics.