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\title{On is the possibility of measuring magnetic helicity in laboratory plasmas through the cancelation of Faraday depolarization}
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\date{\today,~ $ $Revision: 1.4 $ $}
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%\section{}

Faraday depolarization can arise when the plasma itself emits linearly
polarized radiation with the plane of polarization being aligned with
the electric field vector, which is $90\degr$ rotated relative to the
magnetic field vector.
If the magnetic field has a net component along the line of sight (the $z$
direction, say), the perpendicular component will be rotated by an amount
\begin{equation}
\delta\phi=K\int_{z_1}^{z_2} n_{\rm e} B_z\,\dd z,
\end{equation}
where $K$ is a constant, $n_{\rm e}$ is the electron density, and $B_z$
is the $z$ component of the magnetic field.
In a medium that is sufficiently optically thin, the superposition of
emission from different positions leads to a cancellation of the observed
net polarized emission from differently rotated perpendicular components.
This means the medium is Faraday thick.
In radioastronomy, where Faraday rotation is often quite prominent because
of long wavelengths and large distances, this is usually regarded as a
problem in that the direction of the magnetic field cannot be measured
accurately.
Under certain conditions, however, this can also be beneficial, because
a helical magnetic field also leads to a rotation of the perpendicular
field component--similarly to Faraday rotation.

Consider, as an example, a magnetic field of the form
$\BB\propto(\sin kz, \cos kz, B_z)$.
We see that, over the distance $z$, the perpendicular component of the
field is rotated by an amount $kz$.
If those two effects cancel, the effect of Faraday depolarization is
being canceled.

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