## Abstract

We construct a non-local kinetic equation for a plasma in a very strong magnetic field B where the charged particles coincide with their guiding centres and have zero drifts. It is shown that, although in this system mass transport occurs only along the field lines, heat transport cannot be confined only in the direction of the magnetic field. In particular, we estimate that a finite cross field heat flux scaling as ${\textstyle\frac{3}{2}}$n $\partial $T/$\partial $t = $\partial $($\kappa _{\perp}^{\infty}\partial $T/$\partial $x)$\partial $x; $\kappa _{\perp}^{\infty}$ = ${\textstyle\frac{3}{2}}\pi ^{\frac{1}{2}}$(n$^{2}$e$^{4}$/m$^{\frac{1}{2}}$T$^{\frac{3}{2}}$)L$_{\perp}^{2}$ can be driven by collisions between like particles at the limit B $\rightarrow \infty $. Hence, the classical B$^{-2}$ dependence of $\kappa _{\perp}$ must be modified to comply with this result. The choice of the cut-off length L$_{\perp}$, representing the distance across B over which electrostatic interactions can be sustained, is discussed briefly at the end of the present work.