Stokes' Parameters Compared to Astrophysical Magnetic Turbulence Parameters

Since the divergence of a magnetic field is zero, the Fourier transform of fluctuations $\delta $\textbf{B(k}) must be perpendicular to \textbf{k}, so $\delta $\textbf{B(k}) has components only in the plane perpendicular to \textbf{k}. When there is also a mean field \textbf{B}, the obvious choice of coordinates to describe $\delta $\textbf{B(k}) are the unit vectors \textbf{t }in the direction\textbf{ B x k} and \textbf{p} in the direction \textbf{(Bxk) x k}, called the ``toroidal'' and ``poloidal'' directions, respectively. Oughton, et al. (1997) as elucidated by Wicks et al. (2012) showed that the power spectral tensor P$_{\mathrm{ij}}$(\textbf{k}) of magnetic fluctuations is described by four scalar functions of \textbf{k}, multiplying the tensors \textbf{t:t}, \textbf{p:p}, \textbf{t:p}$+$\textbf{p:t}, and \textbf{t:p}-\textbf{p:t} so that the Hermitian Pij(\textbf{k}) $=$Tor(\textbf{k}) \textbf{t:t }$+$ Pol(\textbf{k}) \textbf{p:p }$+$ C(\textbf{k}) [\textbf{t:p}$+$\textbf{p:t] }$+i$kH(\textbf{k}) [\textbf{t:p}-\textbf{p:t}]. Since the electromagnetic fluctuations $\delta $\textbf{B(k}) and $\delta $\textbf{E(k}) in a beam of light are also perpendicular to their \textbf{k}, the four scalar functions of magnetic turbulence in astrophysics which scatters cosmic rays and allows their acceleration, are analogs of the Stokes' parameters. Using Chandrasekhar's (1960) notation [I,Q,U,V]: I$=$ Tor $+$ Pol $=$Tr(P$_{\mathrm{ij}}$(\textbf{k}); Q$=$Tor-Pol; U$=$C; we speculate that V corresponds to magnetic helicity kH in turbulence. We are studying projections of P$_{\mathrm{ij}}$(\textbf{k}) observed by spacecraft in the solar wind.