How are these "supplementary" or "satellite" Helmholtz coils used? Three mutually orthogonal pairs of Helmholtz coils can be used to produce a fairly uniform magnetic field of arbitrary direction within a certain volume, and/or to null/cancel an external field (e.g. Earth's) to make a nearly field-free region.
In this answer to my question Why is there a large wooden ball on Mariner 3's magnetometer? I link to the NASA video MAVEN Magnetometer which includes some clips of the MAVEN spacecraft's three-axis fluxgate magnetometer being tested in a large workspace surrounded by the standard three pairs of Helmholtz coils.
However, when I look closely I can see another six coils, smaller in diameter and at larger distances. I've annotated a screen shot below to make this clearer.
Is there a name for this 12-coil configuration? Do the extra coils improve the uniformity within the center, or extend the useful size of the uniform area, or both, or neither? 
If possible a link to the math is appreciated, but mostly I'd like to know if this is an established technique and what it's called.
I've done my best to indicate the primary three pairs and at least some of the secondary coils separately. I think one or two have been removed for access - so things can be wheeled in and out of the test volume.


 A: This arrangement of four coils per axis is called a Braunbek coil, a modified and improved Helmholtz coil developed in 1934 by Werner Braunbek.
Each of the four coils has the same number of windings and the coils are connected in series, the same current flowing through all four coils.

The Braunbek configuration chosen for the coil system affords a large
volume of  homogeneous field relative to its physical dimensions,
provides easy access to  the work space without the need for moving
and repositioning any coil loops,  and assures the simplest circuit
for maintaining a precise relationship among loop currents since all
loops on any given axis are connected in series.
Each of the  three orthogonal coil sets has two large inner coil loops
and two smaller outer  coil loops.  The orthogonal coil loops differ
slightly in diameter to avoid physical  interference. Each coil set
has seven separate windings differing in function,  number of turns,
and wire size.


Picture and quotes from this NASA paper about the

Goddard Space Flight Center Spacecraft Magnetic Test Facility (SMTF)
was constructed in the 1960's for the purpose of simulating
geomagnetic  and interplanetary magnetic field environments.
The facility includes a three axis Braunbek coil system consisting of
12 loops, 4 loops on each of the three orthogonal axes; a remote Earth
field sensing magnetometer and servo controller; and a remote power
control and instrumentation building. The inner coils of the Braunbek
system are 42-foot in diameter with a 10-foot by 10-foot opening
through the outer coils to accommodate spacecraft access into the test
volume. The physical size and precision of the facility are matched by
only two other such facilities in the world.
The facility was used
extensively from the late 1960's until the early 1990's when the
requirement for spacecraft level testing diminished. New NASA missions
planned under the Living with a Star, Solar Terrestrial Probes,
Explorer, and New Millennium Programs include precision,
high-resolution magnetometers to obtain magnetic field data that is
critical to fulfilling their scientific mission.
It is highly likely
that future Lunar and Martian exploration missions will also use
precision magnetometers to conduct geophysical magnetic surveys. To
ensure the success of these missions, ground testing using a magnetic
test facility such as the GSFC SMTF will be required.

