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\title{Analyzing magnetic helicity in parts of a dynamo domain}
\author{}
\date{\today,~ $ $Revision: 1.3 $ $}
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\maketitle

\section{Introduction}

Magnetic helicity is an important characteristic of a turbulent dynamo.
For an $\alpha$ effect dynamo, for example, the magnetic field is known
to have a bihelical spectrum, i.e., the magnetic helicity spectrum has
different signs at different wave numbers.
This particular feature is not necessarily expected for other types
of dynamos.
The large-scale dynamo of the Sun is expected to be of the type of
an $\alpha$ effect dynamo, but it could also be of some other type.
An example is the dynamo driven by the Roberts flow-II , which works
based on the memory effect of turbulent pumping.
Whether or not this effect can also occur in the Sun is unclear.

Here we address the question to what extent the detailed spectral
properties of magnetic helicity can be detected observationally.
In particular, we ask whether we can tell such dynamos
apart by only measuring the magnetic field in parts of the domain.
As an example, we consider here the Roberts flows I and II in a periodic
cubic domain, which allows us to compute magnetic energy spectra.

By restricting ourselves to subvolumes, we can still compute magnetic
helicity spectra for those, but this can only be an approximation,
because these subvolumes are no longer periodic, which is required when
performing a Fourier decomposition.
Nevertheless, it will be of interest to find out how different such a
spectrum will be and what can be learned from such as spectrum.
Moreover, it will be of interest to know the properties of various
one-dimensional spectra, which might be accessible under the Taylor
hypothesis through a time series representing a chunk of turbulence
passing by a spacecraft.
Such a method was originally developed by \cite{MGS82} and was also
applied to the solar wind at high heliographic latitudes \citep{BSBG11}.

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\bibitem[Brandenburg et al.(2011)]{BSBG11}
Brandenburg, A., Subramanian, K., Balogh, A., \& Goldstein, M. L.\yapj{2011}{734}{9}
%Brandenburg, A., Subramanian, K., Balogh, A., \& Goldstein, M. L.\yapjN{2011}{734}{9}
%{Scale-dependence of magnetic helicity in the solar wind}

\bibitem[Matthaeus et al.(1982)]{MGS82}
Matthaeus, W. H., Goldstein, M. L., \& Smith, C.\yprl{1982}{48}{1256}
%{1259}{Evaluation of magnetic helicity in homogeneous turbulence}

\end{thebibliography}

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