Different PEMF Devices
Single PEMF Coil
Many PEMFT machines use a single-coil or multiple coils, each working as a single coil without an amplifying effect.
Examples are handheld coils or mattress-type devices.
The problem with Single Coil PEMF devices is the limited penetration depth of the healing magnetic flux.
With a simple formula, Inverse Square Law (the formula overestimates the magnetic field), we see that if we move a distance away from the coil, the magnetic strength decreases by a factor equal to the square of the distance ratio.
Imaging that the magnetic field 1mm out of the coil is 100 μT,
at only 1 cm (factor 10) out of the coil, the magnetic field will drop to only 1 μT.
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The penetration depth can be improved using two (single) coils in a flat butterfly configuration.
Tilting the coils of a butterfly configuration can further enhance the penetration depth.
Examples are the Elmag Pro and the Medtronic (now Magventure) Coils for Deep Transcranial Magnetic Stimulation.

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Helmholtz PEMF Coils
The drawback of most PEMF devices is that the magnetic field lines in the magnetic field volume of use are curved to return to the opposite pole, resulting in limited penetration into the field volume of use for healing purposes.
To create a valuable area of a nearly uniform magnetic field and not have to deal with the limited penetration depth of single coils, Hernamm von Helmholtz developed a setup of two coils on the same axis. He obtained a homogeneous magnetic inside and between the two coils.
Interestingly, the magnetic flux density, B, in a Helmholtz configuration is about 40% stronger than the magnetic flux density generated by each coil.
Multiple coils on the same axis function as a magnetic flux density amplifier.
Sometimes butterfly coils are tilted so far that they almost reach a Helmholtz configuration.
When using a Helmholtz Coils configuration in a whole-body machine, the coils have to be giant to fit the body between the coils. Such huge coils result in very low magnetic flux densities and huge losses.



Multiple Coils, on same Axis
Helmholtz coils only deliver relatively small Homogeneous magnetic fields in the center of the coils.
However, we can add coils to the same axis to further extend the useful homogeneous magnetic field volume.
The configuration is called an improved Helmholtz or Maxwell Coil when a third coil is added.
Not only does the magnetic field volume increase, but the magnetic field flux density is also further amplified.
The amplification factor for a Helmholtz coil is about 50%. For a Maxwell coil, this increases up to 90%.
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Lorem X has eight coils generating a large homogeneous unipolar magnetic field, covering a whole person for treating purposes and achieving a magnetic amplification factor of + 160%.




REFERENCES
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J. C. Maxwell, “A Treatise on Electricity and Magnetism,” Clarendon, Oxford, 1873.
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M. Hosoya, E. Goto, Coils for generating uniform fields in a cylindrical ferromagnetic shield, Review of Scientific Instruments, 1991, vol. 62, pp. 2472–2475.
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P.M. Fishbane, S. Gasiorowicz, S.T. Thornton, “Physics for Scientists and Engineers,” 2nd ed., Prentice Hall, New York, 1996, Chap. 30.
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Po Gyu Park, et al., “AC magnetic flux density standards in the low frequency range,” in Proc. Conf. Dig. CPEM, June 2008, pp. 456–457.
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D. Lorrain, D. R. Corson, “Electromagnetism,” Freeman, San Francisco, 1979, Chap. 8.
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J. D. Kraus, “Electromagnetics,” 2nd ed., McGraw–Hill, New York, 1973, Chap. 4.
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V. E. Baranova, P. F. Baranov, "The Helmholtz Coils Simulating and Improved in COMSOL", DOI: 10.1109/Dynamics.2014.7005634.
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J. Yang, Y. Wang, J. Pan, "Note: Parametric tuning of the Helmholtz coil and its optimal designs with thick winding pairs", AIP Advances 8, 085115 (2018).
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J. Wang, S. She, S. Zhang, "An improved Helmholtz coil and analysis of its magnetic field homogeneity", Review of Scientific Instruments 73, 2175-2179 (2002).
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R. Merritt, C. Purcell, G. Stroink, "Uniform magnetic field produced by three, four, and five square coils", Review of Scientific Instruments 54, 879-882 (1983).
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L. Xiang, T Jianbo, "Simulation for the polygonal coil magnetic field," Progress in Applied Mathematics, 2013 - 52.196.142.242.
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Sasada, Y. Nakashima, "Planar coil system consisting of three coil pairs for producing a uniform magnetic field", Journal of Applied Physics 99, 08D904 (2006).
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J, García-Farieta, A. Hurtado, "Exploring the magnetic field of Helmholtz and Maxwell coils: a computer-based approach exploiting the superposition principle. Revista Brasileira de Ensino de Física. 42. 10.1590/1806-9126-RBEF-2020-0282 (2020).
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K. Hug, M. Röösli, "Therapeutic effects of whole-body mat devices applying pulsed electromagnetic fields (PEMF): A systematic literature review", Bio Electric Magnetics, Volume 33, Issue 2, 95-102, 2012.