How fluctuations continue through an X point

The structure of waves around a magnetic X point is analyzed. A paradox is noted, in which theory implies that waves cannot propagate along the field past an X point, but experiment shows that they do anyway. The paradox may arise from the theoretical ‘‘eikonal in the perpendicular direction’’ ansatz, in which waves follow field lines to lowest order. 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 magnetic shear, allowing them to correlate through such a region. This result 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.