Graphical methods are developed by which the guiding centre orbit topology of fast ions in tokamaks is efficiently obtained and displayed.
For constant energy we characterize the orbits by a new set of constant of motion variables
(S,\chi) describing the radial position and pitch angle of the orbits as they intersect with
the stagnation surface.
This surface is a generalization of the equatorial plane for non-top-bottom symmetric magnetic
profiles. The orbit topology is obtained simply by studying the contours of the magnitude of
the magnetic moment \mu and canonical angular momentum p_{\phi} in the (S,\chi) plane. The methods, suitable for routine analysis, can also be applied to evaluate the orbit topology in advanced tokamak scenarios where the presence of special orbit types (co-pinch orbits) causes first orbit loss of fusion products.