Observing Electric Currents in Space

ABSTRACT
To find evidence for electric currents in cosmic plasma requires both that the currents be looked for, and that data be available to indicate their presence. This paper focuses on the second requirement, the available data, and how the flow of electric current in plasma naturally will be difficult to observe from a distance. Coaxial current flow predicted and observed in plasma is examined in some detail showing that even very large total current flow can give, when seen from a distance, very little signal. Examples are given from active galactic nuclei, planetary magnetospheres, and plasma ejections from moons. Suggestions are given for how to analyze existing astrophysical data and also for new measurements to be made that will show the presence of cosmic electric currents.
Key words: Plasmas – ISM: evolution – ISM: structure – galaxies: jets

1 INTRODUCTION
In 1977, Hannes Alfven (Alfven & Carlqvist 1978) wrote that at
the galactic scale, electric currents of 10^17-10^19 amperes would be
natural. Forty years later measured estimates are of 10^18 amperes
in jets from active galactic nuclei (Kronberg & Lovelace 2015),
(Gabuzda et al. 2018). The accuracy of the 1977 prediction, so far
in advance of observation is a strong testament to Alfven and his
colleagues, and an indication that more attention should be given to
their work.

Kristian Birkeland is often credited with first describing cosmic
electric currents in his 1908 model of electric currents flowing from
the Sun to the Earth causing the aurora borealis (Dall 1915). For
60 years Birkeland’s theory of large-scale electrical connection was
ignored in favor of the mathematical models of Sydney Chapman,
where planets are electrically insulated from the Sun and solar wind.
The first in-situ measurements of cosmic-scaled electric currents
were provided by Zmuda et al. with a single axis magnetometer
on board the navigation satellite 1963–1938C (Zmuda et al. 1970).
Today the presence of cosmic electric currents is acknowledged, but
the debate remains if the electric fields and currents can be causal,
or are merely a consequence of thermodynamic and ponderomotive
processes.

Electric current flow in a coaxial configuration was first described
in Oliver Heaviside’s 1880 patent (Nahin 2002). Attempted
telegraph cables that sent current in only one direction required
more energy and incurred substantial information loss compared
to cables with a built-in design to accommodate a return current.
Coaxial current flow, now commonplace to the electrical engineer,
is a new idea to many in the astronomical community. This pa-
per will elaborate the morphology of electric current flow in low
density plasma, and present several examples observed in cosmic
plasma. The argument is advanced that coaxial current flow is to
be expected in cosmic plasma, though its presence will be difficult
to observe remotely. The paper will conclude with suggested
observations needed to advance this topic.

2 THE MAGNITUDE OF COSMIC ELECTRIC
CURRENTS
When electric current flows through astronomical plasma there must
be an electric field that is causing the electric charges to move. The
movement of charge will create a circular magnetic field which
will constrict the flow of charges into a narrow line. Gravitational
attraction will condense the mass of the plasma. The mass of the
plasma will be dissipated and expanded by random thermal motions
and by the total energy stored in the magnetic field. When all these
forces are in a stable state, we set the energies that condense equal
to the energies that expand. Consider an electric current flowing
along a tube through a cosmic plasma, the width of the tube is R0
(Peratt 2015, eq 2.52). These expressions are in units of energy per
unit length.

 The integrated linear current density out to radius R0 is given
by I; m is the mean particle mass averaged over electrons, ions, and
neutrals; N is the integrated linear particle number out to radius R0;

is the difference of magnetic field energy between the total
energy inside the tube and that at the boundary of the tube;

 is the difference of kinetic energy between the total inside the tube
and that at the boundary of the tube. 

This formulation was proposed by Carlqvist in 1988 (Carlqvist
1988), showing the relative importance of the electromagnetic
force, gravitational force, and thermal motions for any given cosmic
plasma setting. Using this relation, Alfven and Carlqvist argue we
should expect above the Earth currents on the order of 1.0-10.0
million ampere, which the Iridium satellite network has verified
(Coxon et al. 2014). The relation in Eq 1 implies that sunspots and
coronal loops should have currents on the order of 10^11 amps. Since
no satellites yet fly through coronal loops, the magnitude of electric
currents are inferred from magnetic fields which are inferred from
the polarization of light coming from the regions. Such modelling
shows electric currents on the order of 10^11 amperes. For the magnitude
of electric current flowing through an entire star - which can be
defined as the gravitating mass and the larger magnetic body of the
heliosphere - the Carlqvist relation predicts currents on the order of
10^9 amps. This number has been confirmed for the electric current
flowing into the Sun along the heliospheric current sheet (Israelevich
et al. 2001). The magnitude of the heliospheric current sheet is
not directly measured, our existing satellite sensors cannot identify
such a low current density, but is inferred from the magnetic fields
that exist above and below the plane of the solar system. During the
course of the 22-year solar cycle electric current flows alternately inward/
outward radially along the equator, and outward/inward from
each pole, closing at the heliosphere, or in some models continuing
to the interstellar medium.

Within the interstellar medium, the Carlqvist relation predicts
electric currents on the order of 10^14 amperes. The Planck, Herschel,
and SOFIA telescopes have greatly increased the available
data for the interstellar medium. Verschuur recently calculated currents
of 10^14 amperes in the A0 molecular cloud through neutral
Hydrogen emission measurements (Verschuur 2013). Stars form
along filaments, the filaments extend for hundreds of light years
without broadening, filaments have a trunk-and-branch morphology,
the filaments abruptly change direction at bright points, and
different molecular species and energy states are segregated within
the filaments. These are all features to be expected from electric
currents in a plasma. The cause of these features is not primarily
due to gravity.

At the galactic scale Alfven proposed electric currents should
be on the order of 10^18 amps, from a balance of magnetic pressure,
thermal expansion, gravity, and helical magnetic fields. Works by
Kronberg and Lovelace Kronberg & Lovelace (2015) and Gabuzda
(Gabuzda et al. 2018) have deduced 10^18 amperes of current flowing
into and out of galaxies in a columnated form. The technique relies
on measuring the polarization of light coming from the regions of
these jets.

3 MEASURING COSMIC CURRENTS
3.1 Model
In 1950 Lundqvist proposed a force free current flow in a plasma,
meaning that the electric current flowing through the plasma feels
no Lorentz force from ambient magnetic fields (Lundquist 1950)
(Lundquist 1951). This is a very special case, maybe never actually
realized in Nature, but if there is any truth in the model it will
give predictive power and new insights. In such a lowest energy
configuration the current and magnetic field must be flowing in the
same direction. This arrangement of current and magnetic field seen
in the force-free flow is much more complicated than a single wire
carrying a current with the azimuthal magnetic field curling around.
In equation form, we write for the force free condition,

Where mu and alpha are scalars which possibly depend upon position
and plasma characteristics. J  is the electric current density vector. B 
is the magnetic field vector.

Scott (Scott 2015) extended Lundqvist’s
model to values of radius large enough to see reversals of both
magnetic and current directions. In the simplest case of current
flow in cylindrical symmetry, the solutions to a force free state are
Bessel functions.

where

are the (z, theta) directions of the magnetic
field and electric current density. If the electric current is to be
in a lowest energy configuration, the electric current and magnetic
field flow in the same direction, and form a series of concentric
shells, like multiple coaxial cables. With increasing R the current
and magnetic field, both pointing in the same direction, twist and
eventually flow back in the opposite direction, Fig 2. That a return
current will be present in a lowest energy configuration harkens
back to Heaviside’s telegraph equation showing that a unidirectional
current requires more energy and loses information.

With increasing total current, the direction of flow will again
reverse itself, flowing in the direction of the center core. The exact
physical conditions that dictate the number of reversals is not yet
known. Some magnetic clouds at 1 AU show single reversals with
10^9 ampere currents (Lepping et al. 2006). Single reversals - simple
coaxial - are seen in 10^18 ampere galactic jets, while multiple
reversals are seen in 10^10 ampere polar currents on Earth. Hence
magnitude of current is not the only factor determining if current is
unidirectional or if there is also a return current. The reverse current
is also seen in particle in cell simulations, where a current injected
into a plasma can only continue if a return current is created (Peratt
2015, p. 75).

3.2 Applying the model
Filaments are ubiquitous in the interstellar medium, see Fig 3 for
one example. The Herschel and Planck telescope projects are repositories
for hundreds of such images. If electric current were flowing
through the filament, and were doing so according to the coaxial
model, how would such a morphology be detected? We will look
at several detection techniques: polarization changes due to magnetic
fields, Doppler shifts due to relative motion, and segregation
of atoms and molecules by ionization potential.

Consider a coaxial filament, with current flow along the z-direction,
Fig 1. The viewer stands far away on the y-axis. The x-z
plane is the plane of the sky. We are looking "side-on" towards the
filament. Interesting measurements such as changes in light polarization
or Doppler shift will depend upon the integrated magnetic
field along our line of sight. We first consider a filament that has
current flowing only in one direction, with no return current. 

Figure 4 shows the numerically integrated projection of the components of
the magnetic field along the y-axis, that is, the line of sight while
looking through the filament. For any given point in the filament, the
horizontal component of the magnetic field, Bx, will have a mirror
point in front or behind the center which has the opposite horizontal
component. Hence all Bx fields will tend to cancel. The By values
have a different symmetry: fields pointing away on one side of the
center will point towards us on the other side of the filament. This is
shown in Fig 4 where the By component changes sign on either side
of the center. The Bz component will always flow in the positive
direction, but drops off to zero at the outer boundary as the flow
rotates to a purely azimuthal direction.

Next consider a current flow with a coaxial return flow, Fig. 5.

The central current flow in the positive z-direction is surrounded
by a return flow in the negative z-direction. The projection of the
magnetic field components is shown. The same symmetries apply
as in the previous case, but with more reversals. Figures 4 and 5
were solved on the same scale.

Applying this to telescope observations, low intensity current
flow, Fig 4, will have magnetic fields close to the filament that
are parallel to the filament. Those parallel fields will decrease in
intensity at the boundary of the filament. More intense current
flow, Fig 5, will show fields along the filament to reverse direction.
Observations highlighting the By component will appear in Doppler
shifts, since flowing charged particles will drag neutrals. From the
observer’s point of view, the azimuthal flow around the filament
axis will be moving away from the observer on one side of the
filament and moving towards the observer on the other side. Look
for opposite Doppler shifts on either side of the filament center.

Additional observations should focus on spatial segregation of
atoms and molecules. The current flow in the force-free model is
also very efficient at collecting ions into shells segregated by ionization
potential, see (Marklund 1979). Spectrographic data can be
examined to look for atoms and molecules with low ionization potential
collecting near the center of the filament and high ionization
potential species concentrated on the periphery.

The ongoing debate as to whether magnetic fields are aligned
with or perpendicular to interstellar molecular filaments is rooted in
the fact that both are true. The general form of cosmic currents and
their associated magnetic fields will be coaxial, with directions constantly
shifting from parallel, perpendicular, to anti-parallel, with
the number of reversals dependent upon the setting. 

As an example,
on a smaller scale, the polar electric currents on Earth form concentric
shells, with the number of shells increasing with the current,
Fig 6. Imagine trying to estimate the electric current flow in the
Earth’s aurora, but doing so by observing shifts in the polarization
of light passing through the aurora. When viewed from outside the
Earth, the net change in polarization due to magnetic fields will be
close to zero. Hence a current flow of billions of amperes can result
in very little net change of polarization, and lead to the conclusion
that no appreciable electric current exists in the Earth’s aurora. It
is arguable that planetary polar currents have underlying physics
different from the model presented in this paper. If that is so, they
still provide a clear example of how increased current causes additional
counter-flowing shells and how remote sensing will greatly
underestimate the actual current flowing.

The Cassini probe provides another example of how a large
current flow can be seen as very small when viewed from a distance.
When the Cassini probe flew through the plumes of Enceladus, the
Langmuir probe, while flying through the plumes, measured charge
densities indicating 10^7 amps of current flowing from the moon
towards Saturn. But the magnetometer aboard, measuring from a
distance, only measured a magnetic field that would be produced
by 10^5 amps. Farrell et al suggest that an ion dust sheath forms
around the central flow of electrons, which serves to shield the bulk
of current flow (Farrell et al. 2017). But is is unlikely that these ions
are stationary, and more likely that they form a return current of a
force-free Birkeland current. Regardless, this represents a clear case
where the electric current inferred from a distance is 1/100th that
found through direct measurement. When viewed from the outside,
magnetic fields produced by the main central flow will be partly
cancelled by the outer sheath flowing in the opposite direction.
Remote sensing tends to show only the net current, which in many
cases will be much smaller than the number of charges flowing.

The methods described in this paper provide clear qualitative
criteria for identifying force-free currents in cosmic plasma. The
more quantitative Carlqvist relation, Eq 1, can be used in a wide
variety of cosmic settings. We suggest that the voluminous data of
filaments in the interstellar medium available in Herschel, Planck,
VLA, HI4PI, and other surveys be examined using the Carlqvist
relation to map the morphology of electric currents in the galaxy.
The method for such analysis, assuming uni-directional current flow,
is presented clearly in (Verschuur 2013). Extending that method to
the more general case of coaxial current flow will be the subject of
a future paper.

The primary observational requirement, to apply the methods
in this paper, is high resolution polarization and spectra cube data
with beam width easily resolving 0.1pc distance, which is the average
ISM filament width. Interstellar filaments in regions of high
star formation are likely candidates, such as protostars in filaments
in the Orion A molecular clouds: RA [42:00.00 to 34:00.00] Dec
[-9:00:00 to -5:00:00].

4 CONCLUSIONS
Electric currents are ubiquitous in cosmic plasma, having been observed
in planetary, solar, interstellar, and galactic levels. Considerations
from basic plasma physics lead us to expect that in cosmic
settings, electric current will flow in a coaxial form: a primary current
flow will be matched by a surrounding return current. There
may even be multiple reversals of current, as in planetary polar currents.
When light passes through a coaxial current, the polarization
changes will tend to cancel out, making it very difficult to determine
the actual amount of current flowing. Likewise, any magnetic field
measurements taken from outside such a coaxial current tube will
greatly underestimate the current, since the reversing directions of
current flow will cause a cancellation of magnetic field strength as
seen from the outside. The ongoing debate as to whether magnetic
fields are aligned with or perpendicular to interstellar molecular
filaments is rooted in the fact that both are true. Force-free current
flow can also be identified from Doppler shift morphology and the
segregation of atoms and molecules by ionization potential. The
wealth of recent high resolution data in infrared, millimeter, and
radio frequencies can be examined to distinguish different models
for the flow of electric current in cosmic plasma.

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