  Dynamical symmetries of the collisionless Boltzmann transport equation, or
Vlasov equation, but under the influence of an external driving force, are
derived from non-standard representations of the $2D$ conformal algebra. In the
case without external forces, the symmetry of the conformally invariant
transport equation is first generalised by considering the particle momentum as
an independent variables. This new conformal representation can be further
extended to include an external force. The construction and possible physical
applications are outlined.
