  Plastic deformation, at all strain rates, is accommodated by the collective
motion of crystalline defects known as dislocations. Here, we extend an
analysis for the energetic stability of a straight dislocation, the so-called
line tension ($\Gamma$), to steady-state moving dislocations within elastically
anisotropic media.
  Upon simplification to isotropy, our model reduces to an explicit analytical
form yielding insight into the behavior of $\Gamma$ with increasing velocity.
We find that at the first shear wave speed within an isotropic solid, the screw
dislocation line tension diverges positively indicating infinite stability. The
edge dislocation line tension, on the other hand, changes sign at approximately
$80\%$ of the first shear wave speed, and subsequently diverges negatively
indicating that the straight configuration is energetically unstable.
  In anisotropic crystals, the dependence of $\Gamma$ on the dislocation
velocity is significantly more complex; At velocities approaching the first
shear wave speed within the plane of the crystal defined by the dislocation
line, $\Gamma$ tends to diverge, with the sign of the divergence strongly
dependent on both the elastic properties of the crystal, and the orientation of
the dislocation line. We interpret our analyses within the context of recent
molecular dynamics simulations (MD) of the motion of dislocations near the
first shear wave speed. Both the simulations and our analyses are indicative of
instabilities of nominally edge dislocations within fcc crystals approaching
the first shear wave speed. We apply our analyses towards predicting the
behavior of dislocations within bcc crystals in the vicinity of the first shear
wave speed.
