methods we employ are also valid in the case $D = \mathbb{I}$, and hence provide an improved global existence theorem for the systems studied by Lai, Yu-Yang, and Chae, but with less regularity imposed on the initial data. Finally, Theorem \[T1\] can be altered slightly to accommodate friction terms which may arise within the formulation of the model. In this case, the Maxwell equations are unchanged and the Vlasov equation undergoes very minor alterations, taking the form $$\partial_t f + \hat{v}_1 \partial_x f + K \cdot \nabla_v f = \nabla_v \cdot \left ( D \nabla_v f + vf \right ).$$ The new terms are lower order and have no additional effect on the results we present. Lai has already displayed this within the context of his methods [@Lai2], though the additional friction term in [@Lai2] is $\hat{v} f$ and not $vf$. Additionally, we note that the friction term destroys the Lorentz-invariant structure of the equation.

This paper proceeds as follows. In the next section, we will derive *a priori* estimates in order to simplify the proof of the existence and uniqueness theorem. In Section $3$, we prove the lemmas of Section $2$, and then sketch the proof of global-in-time existence 