= Magnetic energy spectrum
{title2=$E_B(k)$}
The shell-integrated magnetic energy spectrum distributes <magnetic energy> over <wavenumbers>. With a <solenoidal isotropic spectral tensor> normalized to $\widehat C_{ii}=2H(k)$ and the inverse <Fourier transform> measure $d^3k/(2\pi)^3$, one has $\mathbb E|\mathbf B|^2=\pi^{-2}\int k^2H(k)dk$. In <Gaussian units>, $E_B(k)=k^2H(k)/(8\pi^3)$ integrates to the energy density $\mathbb E|\mathbf B|^2/(8\pi)$. A spectrum per unit mass or normalized to $B^2/2$ has different constant factors. Scale-local fluctuation estimates give $\delta B_l^2$ proportional to $kE_B(k)$ at $k\sim l^{-1}$ when the spectrum is normalized consistently.
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