Electromotive force plays a central role in the turbulent dynamo mechanism
and carries important information on the nature of the turbulent fields. In
this study, an analysis method is developed for the electromotive force and
the transport coefficients such as those for the

The essential part in the dynamo mechanism amplifying the large-scale
magnetic field lies in the existence of electromotive force. In the theory of
mean-field electrodynamics, the electromotive force is defined as a
statistically averaged vectorial quantity, and it is a cross product between the
fluctuating flow velocity

In the mean-field dynamo theory, the electromotive force is assumed to be
linear in the mean magnetic field

A simpler form or a minimal expression of the electromotive force for a
dynamo mechanism is composed of the two terms associated with the mean
magnetic field only

It is important to note that the electromotive force is a second-order
fluctuation quantity and is in the same class as the energy densities of the
fluctuating fields (for the magnetic field and the flow velocity) and the
helicity densities (magnetic helicity, kinetic helicity, and cross helicity).
The electromotive force appears as off-diagonal elements of the covariance
matrix composed of the fluctuating magnetic field and fluctuating velocity

Here we propose an analysis method to determine the electromotive force using
in situ spacecraft data in space plasma. While a large number of studies on
turbulent space plasmas (e.g., solar wind turbulence) concentrate on
the behavior of the energy and helicity quantities (see, e.g., reviews and
monographs such as

When modeling with

The inputs to the calculation of the coefficients

The estimator for the electromotive force and that for the transport
coefficients (

The electromotive force

The electromotive force increases from about

The transport coefficients

The coefficient

In contrast, the coefficient

A close inspection shows that the curl of the mean magnetic field is even
much smaller than the estimate above and is about 10

Time series plots of magnetic field magnitude

The electromotive force is a second-order quantity such as the energy densities (magnetic energy and kinetic energy) and the helicity densities (magnetic helicity, kinetic helicity, and cross helicity) of the fluctuating fields, but its analysis using the in situ spacecraft data in space plasma has largely been overlooked in earlier studies. Although assumptions have to be incorporated, such as the use of one-dimensional advected structure in the time series data, it is possible to observationally evaluate the electromotive force and determine the transport coefficients using the mean field model for the dynamo theory. Studies on the transport coefficients in the turbulence and dynamo theories can be performed not only by the analytic or numerical methods but also by the observational method. The advantage of the presented method is that even data with different sampling rates can be used to the studies of the electromagnetic force and the transport coefficients at the cost of first-order accuracy approximation in the gradient computation.

Although the proposed method is rather a simple or a naive one, the analysis
shows an enhancement of the electromotive force at the magnetic cloud event
by 1 or 2 orders of magnitude. This result indicates a scenario that the
enhanced or strong magnetic fields in the heliosphere are not merely
generated in the Sun or in the solar atmosphere and stream into the
heliosphere, but they can be actively amplified in the heliosphere by the flow
shear or twist. We believe, however, that the dynamo action is unlikely to
occur in the heliosphere. The enhanced electromotive force or the

There are various ways to improve the method presented here. First, from an
accuracy point of view, the regularly sampled data are preferred because the
second-order central difference method can be applied to the calculation of
the derivatives. Second, for a further evaluation of the mean-field dynamo
theory, one may test the relations on the transport coefficients

Helios plasma and magnetic field data are available at CDAWeb

The authors declare that they have no conflict of interest.

This work is financially supported by the Austrian Space Applications Programme (ASAP) at Austrian Research Promotion Agency, FFG ASAP12 SOPHIE, under contract 853994 and Austrian Science Fund (FWF) under contract P28764-N27. Discussion and collaboration with Philippe Bourdin and Bernhard Hofer in the preparation of the manuscript are acknowledged in the framework of the ASAP project. Yasuhito Narita is grateful to Masahiro Hoshino and his group at the University of Tokyo for their hospitality during his research stay, which was supported by the Japan Society for the Promotion of Science, Invitational Fellowship for Research in Japan (short-term) under grant FY2017 S17123. The topical editor, Georgios Balasis, thanks Octav Marghitu for help in evaluating this paper.