  Solutions to the differential equations of linear elasticity in the continuum
limit in arbitrary crystal symmetry are known only for steady-state
dislocations of arbitrary character, i.e. line defects moving at constant
velocity. Troubled by singularities at certain `critical' velocities (typically
close to certain sound speeds), these dislocation fields are thought to be too
idealized, and divergences are usually attributed to neglecting the finite size
of the core and to the restriction to constant velocity. In the isotropic
limit, accelerating pure screw and edge dislocations were studied some time
ago. A generalization to anisotropic crystals has been attempted for pure screw
and edge dislocations only for some special cases. This work aims to fill the
gap of deriving a general anisotropic solution for pure screw dislocations
applicable to slip systems featuring a reflection symmetry, a prerequisite to
studying pure screw dislocations without mixing with edge dislocations. Further
generalizations to arbitrary mixed dislocations as well as regularizations of
the dislocation core are beyond the scope of this paper and are left for future
work.
