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Content uploaded by Kolemann Lutz
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All content in this area was uploaded by Kolemann Lutz on Jul 22, 2022
Content may be subject to copyright.
51st International Conference Environmental Systems ICES-2022-339
10-14 July 2022, St. Paul, Minnesota
Design and Build of HelmHoltz Coils to Generate Hypomagnetic
Field for Low Cost Space Biology Experiments
Terry Trevinoa, Terry Rectorb, Kolemann Lutzc,Nicolas Vasquezd, Herve Cadiouce
Magneto Space, San Francisco, CA, 94105
Zero field and near null magnetic field (NNMF) studies demonstrate that a lack of electric and magnetic fields
beyond Earth's 20-70uT (.2-.7 Gauss) geomagnetic field introduces biological challenges to the health of organisms,
bacteria, plants, and humans. Electromagnetic Helmholtz (HH) coils cancel out the Earth's electromagnetic field and
reproduce a highly uniform 3D magnetic field with an MF intensity approaching zero inside the coils.
In spring 2022, researchers designed and built two HH coils with the goal to test effects of NNMF and planetary
crustal fields (CF) on plants, microorganisms, algae, and other systems in vitro. The first 25kg HH coil apparatus
with COTS components yielded NNMF strength of 3-5mG and 8 cm per side or 530 cm^3 NNMF volume in centre
with 100 coil turns, 500 milliwatt max coil current and 12V operating voltage. Due to changes in coil radius,
substrates, and materials, it is a challenge to create a truly uniform field accommodating the right current and
amplitude. A larger helmholtz coil apparatus (250mm x 240mm x 230mm) is under development with 6 aluminium
coils, turns of copper, and 24 3D printed parts. 3D CAD designs of coils and Magpylib free Python Package were
used to develop 3D analytical models of magnetic fields and interactions.
Research study outlines softwares, mathematics, subsystem design, materials, images, and build of the first and
second generation HH coil prototypes. The research study provides a guidebook to design, build, and test Helmholtz
coils with COTS parts at orders of magnitude lower cost to enable low cost space biology experiments to sustain
biological function in hypomagnetic field (HMF) space environments on Moon, Mars, Venus, and beyond.
Nomenclature
CAD = Computer Aided Design
COTS = Commercial off the Shelf
HH = Helmholtz Coil
mG = MilliGauss
NNMF = Near Null Magnetic Field
PEMF = Pulsed Electromagnetic Field
uT = Micro Tesla
I. Introduction
The Helmholtz (HH) Coil is an apparatus with two identical circular magnetic coils that are placed
symmetrically along a common axis and separated by their radius. Named after the German physicist Hermann von
Helmholtz (1821 – 1894), HH coils generate fairly uniform magnetic fields and cancel external magnetic fields to
produce a near null magnetic field (NNMF) or hypomagnetic field (HMF). Most Helmholtz coils use DC (direct)
current to produce a static magnetic field. If the coils are set up parallel to the lines of magnetic force from the Earth,
and if enough power to equal the Earth’s field but arranged to have the opposite polarity, then inside the coils you’ll
have some space where there’s no magnetic field at all. Most Helmholtz coils use DC (direct) current to produce a
static magnetic field. Commercial off the shelf (COTS) coils can yield Accuracy above 1% HH coils have often
been used to measure the accuracy of magnets, superconducting magnets, magnetometers, and particle accelerators
and are beginning to gain more interest for space biology experiments. HH coils can be used to cancel out the
planetary magnetic field to simulate NNMF fields of other planetary bodies that lack intrinsic magnetic fields and in
microgravity space environments. After passing current through two parallel coils with Radius R, the resulting
magnetic field forms a 3D sinusoidal shape that is perpendicular to the coil winding. The two parallel helmholtz
coils combine to yield 66.67% the magnetic field strength [B/B0] of each individual coil perpendicular to the coil
winding direction, as depicted in Figure 1 below.
aSpace Studies Master’s Graduate, American Military University, terry.trevino@prodigy.net
bPhD Candidate, University of North Dakota, terry.rector@und.edu
cCofounder, Magneto Space and Mars University, kole@mars.university
dPhysics Graduate Student, Washington University, nvasquez172@gmail.com
eInstitut des Neurosciences Cellulaires et Intégratives, cadiou@unistra.fr
Figure 1. Helmholtz Coil Magnetic Field Strength
In the 1960’s, NASA conducted electromagnetic field experiments primarily focused on testing magnetometers
and preparing spacecraft and electronics for the space environment. The Goddard Space Flight Center Spacecraft
Magnetic Test Facility (SMTF) was constructed to simulate the geomagnetic and interplanetary magnetic field
environments. SMTF includes a three axis Braunbek coil system with 12 loops, 4 loops on each of the three
orthogonal axes. The 2004 study reviews the history of the facility, mission requirements, and plans for restoring the
facility (Vernier, et al, 2004).
Magnetic field modulation is important to understand and improve the detection sensitivity of instrumentation.
The ability to detect low frequency magnetic fields with magnetoresistive (MR) sensors is seriously affected by 1/f
noise. A Helm-Holtz coil significantly reduces 1/f noise observed from DC current, prevents DC sensor current
drift, sharp zero-crossing (1st harmonic) or well defined peak (2nd harmonic) to lock onto, can be shared on same
modulation waveform as DC cancelling signal, and allows for detection of electron-nuclear hyperfine interactions.
More recently, researchers designed a 3D Helmholtz coil that generates magnetic fields of up to 5 mT with an
expected angular precision of 0.2 mrad. (Fontanet, et al, 2019).
In 2004, Dr. Thomas Goodwin led a NASA study to determine the greatest efficacy of PEMF therapy was from
TVEMF low 10Hz frequencies, and low intensities ~10-200 milligauss (1-20 µT). The TVEMF human brain cells
exhibited 2.5 to 4.0X increase in cell tissue regeneration (Goodwin, 2004). Another 2005 study from NASA
Engineering Directorate at Johnson Space Centre entitled, Pulsed Electromagnetic Fields – A Countermeasure for
Bone Loss and Muscle Atrophy, developed the hardware for stable magnetic control with a helmholtz coil design
and a software to evaluate the most effective PEMF frequencies, waveforms, and pulse durations. Byerly et al.
performed the field characterization of the magnetic fields in terms of frequency, sine wave/pulsed inputs, frequency
response, field amplitude, and harmonics to reverse bone loss and muscle atrophy. The long-term objective was
produce a garment with a PEMF device to be worn by astronauts as a noninvasive countermeasure. (Byerly, Diane et
al, 2005)
II. Equations and Calculations
The magnetic field for an induced current in the solenoid shape of the electromagnetic can be calculated
accordingly:
B=μ0n L (1)
B is the magnetic field in Teslas, μ
0 ("mu naught") is the permeability of free space (a constant value ~1.257 x 10-6
or 4π x 10-7 T*m / A), L is the length of a metal object parallel to the field and n is the number of loops around the
electromagnet. Derived from Biot Savart's law, Ampere's Law can be used to calculate current (I):
B= (2)
𝐿µ 𝐼
𝐿
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Ampere's Law and the mathematical equation derive magnetic field intensity changes depending on the geometry of
the EM generator. Torrodoil transformers and magnets (donut-shaped electromagnet) are used in the medical field
and creating biomedical devices. The field can be derived using the below equation:
B= (3)
2π𝑟
µ 𝑛𝐼
Helmholtz (HH) coils reproduce a highly uniform 3-dimensional magnetic field with an intensity much closer to
zero inside the coils. To calculate the uniform field strength in a Helmholtz coil at the centre, the following equation
may be used where I = current [A], N is the number of turns of coil, r is the coil radius [m].
(4)
According to the law of Biot-Savart-Laplace, the resulting field of the two coils is equal to the vector sum of the
fields generated by each coil. The axial field of one coil of a predetermined point can be calculated according to (1):
B (z) = (5)
µ0 𝑁𝐼𝑅2
2(𝑅2+ (𝑧−ℎ)2 ) 2/3
where μ0 is the magnetic permeability or susceptibility of vacuum, N is the the number of turns of the each coil; I is
the current through the coils, z is the coordinate of the point, m is the the distance of the coil centre from the
beginning of the coil centre coordinates. Axial field of two coils can be calculated by formula:
(6)
‘
(7)
Moreover, researchers from Columbia University developed a Taylor series approximation for the magnetic field
and computational model in COMSOL and compared the magnetic field distribution for both geometries.
(Resterepo, et al, 2012). Moreover, COMSOL Multiphysics software and website provides a 20 page description
outlining how to model Helmholtz coil magnetic field in COMSOL.
III. Methods
In the first HH Coil design and build, a 10 cm single Helmholz coil was used with a sawtooth pulse rate of an
average 300 milliseconds using a COTS pulse generator, generating an electromagnetic wave using 500 milliwatts
of converted Direct Current 12 V electricity. The electromagnetic wave field produced by the coil had a wave area
of 530 cm3. The volume of the coils and their sphere of influence is approximately 60% of volume inside the test
bed. As payload or objects tested inside Helmholtz coil systems are typically confined in size and mass, the 1.8 kg
coils influence a significant area of magnetic wavelength. A Pasco 200 Turn Field Coils EM6711A provides a frame
to wire the coils in a circular pattern. Instead of a COTS device, a small version 3-B Scientific Helmholtz Coils
Md1000906 can also be used. The 3-axis COTS magnetometer should be vertical and parallel with gravity. It is also
important to calibrate or zero magnetometer, which can be accomplished by placing a small Mu chamber to shield
from the ambient, local magnetic field.
3.1 Helmholtz Coil Design and Build
To improve the uniformity of the field in the space inside the coils, a third larger diameter coil, or Maxwell coil,
was positioned midway between two Helmholtz coils and moved in the y-direction. Pure copper coils with minimal
pollutant particles are tightly wound with no spacing in order to cancel out the horizontal and vertical component of
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International Conference on Environmental Systems
Earth’s magnetic field. Research on conductivity, ductility, and heat resistance of copper wire from manufacturers
should be conducted in addition to identifying trace non-cu materials in wires. A 2-3 uT vertical and 2 uT horizontal
field strength with at least 2 pairs of coils is recommended. Coils 1 and 2 on the horizontal plane direction are
positioned gravity vector, x-axis along Martian surface vector and inside the generated magnetic field closer to zero
in the centre of the magnetic field. Experiments should be conducted in a laboratory with low levels of
electromagnetic and electric field interference. A 3-axis magnetometer is recommended to determine the local MF
field strength. Additional equipment that can be used include a hall sensor, DC current source, cables, and a
waveform generator, which allows for the shaping of the electromagnetic wave generated.
Figure 3a. HH Coil Design and Build Version 1. 3b. HH Coil V1 tested over 300 hours.
For the first HH coil prototype, a 1m3HH coil was built to be reusable and modular to allow for an extended life
span with several biological experiments and minimal component replacement or maintenance should failures occur.
To build the 12V HH coil, 1mm copper wiring was wrapped 100 times around three sets of identical coils, 633mm in
length. Two small rings with 10 cm diameter, two middle rings with 30 cm diameter, and two large rings with 67 cm
were used due to the challenges of using same sized rings. A tubeless MD 50mm cycling wheel rim was used as the
frame or substrate. PVC ¾ inches was used to provide the structural frame with a total build time of two hours. As
it can be challenging to use the same size for all three rings, the top lines are big rings/middle rings, which was an
anomaly and the middle coil was uneven which skewed magnetic field measurements initially. The different sized
rings introduced different power requirements for each set of rings with different waveforms on each ring, which
introduced challenges to replicating a uniform NNMF field centre. Moreover, the smallest coils are plastic with
aluminium on the inside and mylar on the outside.
Figure 4. HH Coil 1 Parameters
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Figure 5. HH V1 Experiment Payload Test bed
With the near zero field at the centre of the apparatus, biological experiments are conducted within the
150-200 cm3test bed or payload carrier. Lined with Aluminium and Coated with a Mylar Sheeting, the current test
bed design accommodates ten pods each inside the payload area to conduct concurrent biological HMF experiments
with small to micro plants, fungi, and soil microorganisms. The current design does not accommodate an adjustable
coil on each axis, which helps to align distance, coil axes and planarity. The HH coils should be grounded with a
cable to the piping system or some insulating surface, which removes the excess charge on an object by introducing
electrons and preventing a buildup of positive charge. Grounding rods made of solid copper, stainless steel, or
galvanised rods may also be used and should be spaced at least eight feet deep vertically into the ground. An
accurate layer winding of the coils ensures good field quality and tightly wound wires help ensure MF field
uniformity, minimal background noise, and cancellation of planetary magnetic field. The non conductive
environment helps avoid eddy-currents in case of dynamic operation. An EM Probe was installed in the position
with its “X” axis top (-X) to down (+X), the “Y” axis (labelled on the probe’s end) is right (+Y) to left (-Y). Lastly
the “Z” axis is facing forward, front (+Z) to back (-Z). A Bartington 3D fluxgate Mag-03MS1000 can be used to
measure the magnetic field intensity in addition to magnetic field, metal detecting and measuring mobile phone
applications such as Max-see and Magnetic Detector. Vernier Graphical analysis software was used to visualise data
collected from magnetic field probes and sensors in real time. An infrared FLIR camera connected to the iPhone was
used to collect high resolution image quality and thermal data on the HH Coil temperatures in real time. Infrared
imaging and data analysis is important in order to not exceed the maximum cooling power.
Figure 6. 4’x8’ Switchboard to interconnect and individually power six coils.
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3.2 Developing Models and Simulations of Helmholtz and Magnetic Fields
Images and magnetic field models were developed with Magpylib, a light-weight and free Python package used
to compute magnetic fields of permanent magnets, currents and moments based on analytical models. Magpylib is a
Python package for calculating 3D static magnetic fields of magnets, line currents and other sources with user
friendly geometry interface and quick and easy access to magnetic field computation (Ortner, et al, 2020).It is also
available on Github.
Figure 7. Build and Model of V1 HelmHoltz Coil developed with FreeCAD 0.19
Figure 8. V1 HelmHoltz Coil Magnetic Field Strength in the XZ Plane.
Figure 8 highlights a birds eye view of combined magnetic fields from each of the HH coils on XY Plane with the
payload project box fixed at the centre. Bars indicate payload boxes Y Coils are Red, Z Coils are Orange). The
.04-.05 milliTesla (40-50uT) field strength anomalies form a diagonal field and are likely a product of the different
coil radius sizes and materials. Other factors influencing abnormal field uniformity include spacing of coils.
Figure 9. Magnitude of Generated Magnetic Field in the X (Blue), Y (Orange), and Z (Red) direction along the X Axis
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Figure 10. Shows the near null electromagnetic field averaging mG of 8.6 (.86 uT).
3.3 HH Coil Design and Build Version 2
A subsequent coil design, previously tested, built and discussed in Merritt et al, (2010), is under development
that will accommodate an increase in the number of test subjects inserted into the near null field, and a larger size,
energised with a supplied 12-volt power supply, weighing approximately 27 kg, with a larger test bed. The second
prototype is being designed and built in the San Francisco Lab of Magneto Space with X,Y and Z sets of merit coils,
where the test bed will approximately double in size. The electromagnetic wave expected to be generated will
perform similarly to the Helmholtz Coils. The required energy to generate the electromagnetic field will be identical
to the HH coils design and the only significant change in the design is the shape of the coils. The coils are square
and constructed of basic aluminium channels, allowing for inexpensive construction. No bending is required since
the channels will be connected by corners 3D printed in house. In addition, these simpler parts make the system
more modular and easier to maintain. Mechanical faults can be replaced and potential upgrades can be added
without compromising the rest of the coils. Consideration is being given to the potential use of the 18 gauge wire
combined and wrapped, finished off with copper conductive tape, approximately .03 mm in thickness and with a
width of ½ inch. The rings will be made of similar sized copper wire in the range of 18 gauge, hand wrapped, and
manufactured of different material when compared to the first HH coil prototype.
Figure 11. 24 corners 3D printed made of PVC piping to attach the HH coil frames.
3.4 Characterisation and Calibration of HH Coils
When coil shielding is not available and background noise is an issue, characterising and calibrating large
Helmholtz coils of different sizes and fields in the X, Z, and Y directions can be a challenge. As temperature and
coil impedance influence the calibration process, magnetic field measurements made over a four year period are
recommended. Characterising and calibrating large Helmholtz coils can be performed with rulers, levels, plumb
lines, and inexpensive gaussmeters. When measuring the MF field intensity and vector, it is important that the Hall
effect sensor does not twist as measurements are taken from one point to another point, especially when measuring
null field components. Researchers from University of Nevada at Las Vegas developed a reliable calibration
technique to observe magnetic field with standard deviations of two milligauss and less over a uniform magnetic
field region. (Schill, 2001) Moreover, software such as ANSYS Maxwell can also be used to simulate the magnetic
shielding inside a magnetic field with frequencies between 0.1-60 Hz.
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IV. Discussion
The current HH Coil build has demonstrated the potential to cancel out Earth’s magnetic field. Due to the
changes in coil size, it is a challenge to create a truly uniform field accommodating the right current and amplitude.
The magnetic field on the Z-axis was initially around 1,200 uT, which was 60X higher than anticipated and was
offset by adjusting the current and resistance to achieve NNMF of within 8.6 mG (.86uT). As the larger ring
generates more magnetism, these issues can be mitigated by using different power supplies and voltages to achieve a
more uniform near null field.
Preliminary biological experiments are underway and HH Coil prototypes may be subsequently available for use
upon request for free or low cost experimentation. Results from over 300 hours of testing are showing little or no
negative effect in the growth rates of two species of plants, Arabadopsis and Ocimum Basilicum. Both species
performed well, with the plant root exudates appearing healthy. See figure 10 below. There are subtle tiny root
exudates that appear to be Rhizobia that emerge from the central tap root. These micro plants receive only water and
light in red and white wavelengths averaging 400 nm. The lab conditions are closely monitored, with the goal of
maintaining a stable atmosphere, a relative humidity in the range of 45%, temperature in the range of 19c and a
substrate that is replicable. The seeds are dropped in a NASA used, organic cotton, that easily soaks up water and
provides a seedling a hospitable environment to grow.
Figure 12. Evidence of a large exudate supply with two smaller root hairs, or extensions of root epidermal cells.
As the project scales up in size with a new test bed double the current volume, further research will be published.
As measurements of the oxygen production and the consumption of carbon dioxide is understood, the goal then
becomes to close the bioregenerative loop. The HH Coils are further planned to be utilised during academic
programs and conferences to provide hands-on experience and further experiment testing with biological organisms.
Future research will emphasise plants, bacteria, and organisms that may adapt better to NNMF. Future research may
further develop machine learning algorithms to automate and quantify the HH magnetic field, and pulsed
electromagnetic field (PEMF) interactions, and to explore novel, alternative applications of an artificial induced
NNMF with helmholtz coil-like architectures on macro and micro-scale for Earth, space, Solar system and beyond.
Author Contributions
The authors are the sole contributor to this work and are responsible for this article. Furthermore, the
author confirms this material or similar material has not been and will not be submitted to or published in
any other publication.
Author Disclosure Statements
There are no conflicts of interest to report related to this work and no competing financial interests exist.
Funding Information
No funding was received for this self funded research.
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