We give a rigorous derivation of a theorem showing that charged particles in
an arbitrary electromagnetic field with at least one ignorable spatial
coordinate remain forever tied to a given magnetic-field line. Such a situation
contrasts the significant motions normal to the magnetic field that are
expected in most real three-dimensional systems. It is pointed out that, while
the significance of the theorem has not been widely appreciated, it has
important consequences for a number of problems and is of particular relevance
for the acceleration of cosmic rays by shocks.Comment: 7 pages, emulateapj format, including 1 eps figure, to appear in The
Astrophysical Journal, Dec. 10 1998 issu