$$\hat{v} = \frac{v}{v_0}, \qquad v_0 = \sqrt{1 + \vert v \vert^2}.$$

In order to include collisions of particles with a background medium in the physical formulation, often a diffusive Fokker-Planck term is added to the Vlasov equation in (\[RVM\]). With this, the system is referred to as the relativistic Vlasov-Maxwell-Fokker-Planck equation. Since basic questions of well-posedness remain unknown even in lower dimensions, we study a dimensionally-reduced version of this model for which $x \in \bfR$ and $v \in \mathbb{R}^2$, the so-called “one and one-half dimensional” analogue, given by $$\label{RVMFP} \tag{RVMFP} \left \{ \begin{gathered} \partial_t f + \hat{v}_1 \partial_x f + K \cdot \nabla_v f = \nabla_v \cdot \left ( D \nabla_v f \right ) \\  D = \frac{1}{v_0} \left [ \begin{array}{lr} 1 + v_1^2 & v_1v_2\\ v_1v_2 & 1 + v_2^2 \end{array} \right ]\\
K_1 = E_1 + \hat{v}_2 B, \qquad K_2 = E_2 - \hat{v}_1 B\\  \rho(t,x) = \int f(t,x,v) \ dv - \phi(x), \quad j(t,x)= \int \hat{v}  f(t,x,v) \ dv \\  \partial_t E_2 = -\partial_x B - j_2, \quad \partial_t B = - \partial_x E_2, \quad \partial_x E_1 = \rho, \quad \partial_t E_1 = j_1.
\end{gathered} \right.$$ Here, we assume a single species of particles described by $f(t,x,v)$ 