Pressure-anisotropy-modified magnetic tension ($\mathcal{T}=B^2/(4\pi )+p_{\perp }-p_{\parallel }$)

In Gaussian units, the gyrotropic pressure tensor adds directional stress to the magnetic tension. A transverse displacement of a uniform magnetic field obeys $\rho {\partial }_t^2{\mathbf{\xi }}_{\perp }=\mathcal{T}{\partial }_{\parallel }^2{\mathbf{\xi }}_{\perp }$. Positive $\mathcal{T}$ gives a restoring force; negative $\mathcal{T}$ gives the fluid firehose instability. This follows by combining $-\nabla \cdot \mathsf{P}$ with the divergence of the Maxwell stress tensor. In SI replace $B^2/(4\pi )$ by $B^2/{\mu }_0$.