Perpendicular plasma pressure ($p_{\perp }=m\int (v_{\perp }^2/2)f{d}^{3}v$)

The equal normal stresses in the two directions perpendicular to the local magnetic field for a gyrotropic phase-space distribution function. The factor one half averages the two perpendicular velocity components. With first adiabatic invariant $\mu =v_{\perp }^2/(2B)$, the integrand is $m\mu Bf$.