The flat coil gained widespread popularity thanks to the work and patents of Nikola Tesla [1], who was one of the first to note the advantages of a helical winding constructed in a single plane. In his research, Tesla considered this design not simply as a way to compactly arrange the conductor, but as a means of increasing the coil's capacitance and improving its resonant properties.

Unlike traditional cylindrical windings, a flat spiral allows adjacent turns to be spaced over a large area, which enhances the electrical interaction between them and makes the coil more efficient in high-frequency resonant systems. Thanks to these properties, flat coils have found application in radio engineering, wireless power transmission, medicine, inductive sensors, and numerous experimental devices.

In addition to its well-known properties related to inductance and interturn capacitance, a flat coil is also of interest due to the existence of a second magnetic field, which presumably has a different spatial structure compared to the classical vortex magnetic field described by Maxwell's equations. According to the results of several experiments conducted by the author, a flat spiral geometry can create more favorable conditions for the generation and detection of such a field. This makes a flat coil not only an effective resonant element but also a convenient tool for studying additional electromagnetic effects, insufficiently explored within the framework of traditional electrodynamics.

The author has conducted studies of flat coils in several papers:

• Distribution of magnetic fields in a Tesla bifilar coil;
• Mutual induction of bifilar coils at resonance of the first and second kinds;
• Nuclear magnetic resonance of some materials in an inductor coil;
• Method of detecting and amplifying a second magnetic field;
• Healing coil with a second magnetic field.

In many cases, an effect was observed in which the second magnetic field was enhanced. This effect was most pronounced when several flat coils were placed one above the other. This observation served as the starting point for research into a new design, which consists of a set of flat spiral coils combined into a single multilayer element.

The multilayer flat spiral coil is a development of the flat Tesla coil, in which several spiral windings are arranged one above the other to form a compact spatial structure. By successively decreasing the diameter of each subsequent layer, a unique stepped pyramid is created, possessing a high winding density and a number of unusual electromagnetic properties.

The peculiarity of this design is that Interaction between adjacent spirals occurs simultaneously through inductive and capacitive channels. Each layer influences all the others, forming a complex system of coupled resonators. As a result, the magnetic field distribution differs significantly from that of a conventional flat coil: the energy is concentrated in the central region of the structure, and the shape of the magnetic field lines takes on a distinct three-dimensional character. This makes the multilayer spiral coil interesting not only as an inductive element, but also as a model for studying the second magnetic field and other unconventional modes of electromagnetic interaction.

The combination of high inductance, significant interlayer capacitance, and compact size opens up possibilities for the use of such coils in resonant systems, wireless power transmission, sensors, high-frequency filters, and experimental devices. Furthermore, the unusual geometry of such coils makes them a convenient tool for studying the distribution of electromagnetic fields and the influence of the spatial configuration of conductors on resonant processes.

The design of such a coil can be represented by a set of (multilayer) printed circuit boards with inductive tracks arranged in a pyramidal pattern. This distinguishes it from the well-known set of flat coils in a columnar pattern [2]. With this geometry, each spiral coil is located within the magnetic field of adjacent layers. As a result, the contributions of individual layers may not simply sum up, but rather be amplified due to mutual interaction.

If we assume that the strengths of the second magnetic field are added in a similar manner, then increasing the number of layers should lead to a significant increase in its total energy. In this case, the theoretical increase in the energy of the second magnetic field can reach the values ​​obtained in formula (1.20) from this work. In this case, it should be assumed that \(2 a^2 = 1\), then \(N\) is the number of layers in the coil. To obtain the field strength gain, we need to take the square root of the resulting formula: \[\tag{1} K_H = \sqrt{\frac{N^3}{3} + \frac{N^2}{2} + \frac{N}{8}} \] The distance between layers should presumably be kept to a minimum, and the number of layers should be maximized.

The analysis shows that a multilayer flat helical coil is a promising development of the classic flat Tesla coil. The placement of multiple helical layers in a single structure leads to increased mutual inductive and capacitive interactions between them, and also creates a more complex spatial distribution of the electromagnetic field. According to the theoretical model discussed, increasing the number of layers can lead to a significant increase in the energy and strength of the second magnetic field, making this design particularly interesting for further research.

The multilayer coil is of particular interest for medical research, as it theoretically allows for significantly higher levels of the second magnetic field compared to single flat coils. This opens up opportunities for further study of the effects of such fields on biological tissue, the body's healing processes, and the development of new methods of electromagnetic therapy.

The practical implementation of the coil as a set of printed circuit boards allows for the creation of compact multilayer structures with highly repeatable parameters and a large number of layers. Such coils can be used not only as resonant elements but also as an experimental platform for studying the properties of the second magnetic field, testing theoretical models of its amplification, and exploring new applications in electromagnetic devices. Further research should be aimed at experimentally confirming the obtained relationships and studying the influence of the structure's geometry on the characteristics of the generated fields.