Hankel inversion of a rotation-measure correlation ($H(k)=\frac{2\pi }{a_0^2{n}_e^{2}L}{\int }_0^{\infty }r{J}_0(kr)C_{\mathrm{RM}}(r)dr$)

Invert the two-dimensional Fourier transform in the long-path projection of a magnetic correlation, then perform the angular integration in polar coordinates. The angular integral is $2\pi J_0(kr)$, a Bessel function of the first kind, giving the displayed Hankel transform with the stated Fourier-Hankel normalization for an isotropic spectrum. The result recovers the scalar tensor coefficient $H$, whose shell-integrated magnetic energy spectrum has an additional factor $k^2$.