Ion skin depth ($d_i=c/{\omega }_{pi}$)

For a singly charged ion species in Gaussian units, ${\omega }_{pi}=(4\pi n{e}^2/m_i{)}^{1/2}$ is its plasma frequency and $d_i=c\sqrt{m_i/(4\pi n{e}^2)}$. The ion skin depth marks a characteristic scale below which ion and electron motion can separate in a magnetized plasma. Together with the Alfvén speed, it satisfies $v_A{d}_i=c{B}_0/(4\pi en)$, the coefficient of guide-field propagation in electron magnetohydrodynamics.