Multi-piece corrugated waveguide

Abstract

We offer multi-piece corrugated waveguides. [Solution] The apparatus includes a tube having an inner surface, an inner diameter, and a length. The apparatus also includes a coil spring. The coil spring includes an outer surface, an outer diameter, and a plurality of coil elements arranged along the length of the coil spring. The coil spring can be positioned within the tube, and the outer diameter of the coil spring can be smaller than the inner diameter of the tube. The coil spring can form a waveguide. Related manufacturing methods and systems are also described herein. In one embodiment, a gap is defined between the outer surface of the coil spring and the inner surface of the tube.

Description

Technical Field

[0001] Cross - reference to Related Applications This application claims priority under 35 U.S.C. § 119(e) to U.S. Patent Application No. 17 / 367,800, filed Jul. 6, 2021, entitled "MULTI - PIECE CORRUGATED WAVEGUIDE", the entire content of which is hereby incorporated by reference in its entirety.

[0002] The subject matter described herein relates to a waveguide for use in transmitting electromagnetic waves.

Background Art

[0003] A waveguide is a structure that guides waves such as electromagnetic waves or sound by restricting the transmission of energy in one direction to minimize energy loss. Waveguides can be used in non - conventional drilling techniques such as thermal drilling and / or millimeter - wave drilling to form boreholes in wells. Waveguides can be used to transmit electromagnetic waves within a borehole to enable drilling at deeper underground depths than conventional rotary drilling. Specific internal features such as corrugated grooves can be included in the waveguide and can enhance the transmission efficiency of the electromagnetic waves provided within the borehole. Forming and deploying a corrugated waveguide within a single length of tube can be expensive, may require special materials and equipment, and tends to be prone to manufacturing errors, which can result in wasted inventory, downtime in the well operation, and inefficient transmission of electromagnetic energy.

Summary of the Invention

Means for Solving the Problems

[0004] In one embodiment, an apparatus is provided. In one embodiment, the apparatus may include a tube having an inner surface, an inner diameter, and a length. The apparatus may also include a coil spring. The coil spring may include an outer surface, an outer diameter, and a plurality of coil elements arranged along the length of the coil spring. The coil spring may be positioned within the tube, and the outer diameter of the coil spring may be smaller than the inner diameter of the tube.

[0005] In another embodiment, a gap can be defined between the outer surface of the coil spring and the inner surface of the tube. In another embodiment, the coil spring can form a waveguide. In another embodiment, the inner surface of the coil spring may include a conductive material. In another embodiment, the coil spring may include a coating of copper, gold, silver, or platinum. In another embodiment, the device may further include an insulating layer between the tube and the coil spring. In another embodiment, the outer surface of the coil spring may include a dielectric material.

[0006] In another embodiment, at least one of the plurality of coil elements can be defined by one turn of the at least one coil element around the coil spring. In another embodiment, at least one of the plurality of coil elements may include a base portion and a projection portion extending from the base portion, the projection portion including one of a trapezoidal, circular, square, rectangular, or sinusoidal cross-sectional shape. In another embodiment, the plurality of coil elements may include one of a trapezoidal, circular, rectangular, elliptical cross-sectional shape, or a tapered shape along the length of the plurality of coil elements.

[0007] In another embodiment, the coil spring may include copper wire and / or aluminum wire. In another embodiment, the tube may include a carbon steel tube. In another embodiment, a plurality of coil springs may be positioned within the tube. In another embodiment, a first coil spring and a second coil spring of the plurality of coil springs may be coupled via a coupling spring positioned within the tube. In another embodiment, the first end of the coupling spring may be attached to the first end of the first coil spring, and the second end of the coupling spring may be attached to the second end of the second coil spring, and the coupling spring may be configured to reduce the amount of axial movement of the first coil spring and the second coil spring relative to each other due to thermal expansion of the first coil spring and / or the second coil spring.

[0008] In another embodiment, the cross-sectional shape of each coil element of the coil spring and / or a plurality of coil elements can be sized to propagate electromagnetic waves. In another embodiment, the cross-sectional shape of the coil spring and the coil spring can be sized to propagate electromagnetic waves in HE11 mode. In another embodiment, the length of the pipe can be longer than 1 meter. In another embodiment, the length of the pipe can be longer than 5 meters. In another embodiment, the length of the pipe can be longer than 9 meters.

[0009] In another embodiment, the coil elements can be dimensioned to include space between two or more of the coil elements, and the space can be dimensioned to be 1 / 6 of the wavelength of the electromagnetic waves injected into the borehole of the well via the waveguide assembly. In another embodiment, the coil elements can be dimensioned to include a pitch between two or more of the coil elements, and the pitch can be dimensioned to be 1 / 3 of the wavelength of the electromagnetic waves injected into the borehole of the well via the waveguide assembly. In yet another embodiment, the coil elements can be dimensioned to include a width that is shorter than the wavelength of the electromagnetic waves injected into the borehole of the well via the waveguide assembly.

[0010] In another embodiment, the coil spring inside the tube can form a helical groove. In another embodiment, the helical groove can be configured to propagate electromagnetic waves. In another embodiment, the helical groove can be configured to propagate electromagnetic waves in HE11 mode, transverse electric mode, transverse magnetic mode, or a combination of transverse electric mode and transverse magnetic mode. In another embodiment, the tube can be a tapered tube, and the coil spring can be a tapered coil spring. In another embodiment, the tube can be a curved tube. In another embodiment, the tube and coil spring can be contained within a casing, and are configured to extend from or retract into the casing.

[0011] In another embodiment, a method is provided. In one embodiment, the method may include extruding a wire including a cross-sectional outer shape. The method may also include forming the wire into a coil spring having an outer diameter and a plurality of coil elements arranged along the length of the coil spring. The method may further include inserting the coil spring into a tube having an inner diameter larger than the outer diameter of the coil spring, wherein the tube may have a length along which the coil spring extends.

[0012] In another embodiment, the method may include coating the wire with a conductive material. The method may also include coating the coil spring with a conductive material. The method may further include coating the inner surface of the tube with an insulating material. In another embodiment, the conductive material may include one or more of copper, silver, or gold. In another embodiment, a gap may be formed between the inner surface of the tube and the outer surface of the coil spring when the coil spring is inserted into the tube.

[0013] In another embodiment, the method may further include forming a channel on the inner surface of a tube such that the channel can extend axially along the length of the tube. In another embodiment, the cross-sectional shape of the wire may include a base portion and a projection portion extending from the base portion, the projection portion may include one of a trapezoidal, circular, square, rectangular, or sinusoidal shape. In another embodiment, forming the wire into a coil spring may include winding the wire around a mandrel such that the shape of each coil element of a plurality of coil elements can correspond to the cross-sectional shape of the mandrel along at least a portion of the length of the coil spring. In another embodiment, the cross-sectional shape of the mandrel may include at least one of a trapezoidal, circular, rectangular, elliptical, or tapered shape.

[0014] In another embodiment, the wire may be a copper wire or an aluminum wire. In another embodiment, the method may further include forming a plurality of coil springs and inserting the plurality of coil springs into a tube.

[0015] In another embodiment, the apparatus is provided. In one embodiment, the apparatus may include an outer tube. The outer tube may have an inner surface, an inner diameter, and a length. The apparatus may also include an inner tube. The inner tube may have an inner surface, an outer surface, an outer diameter, and a helical groove formed on the inner surface and extending along the length of the inner tube. The inner tube may be positioned within the outer tube, and the outer diameter of the inner tube may be smaller than the inner diameter of the outer tube.

[0016] In another embodiment, a gap can be defined between the outer surface of the inner tube and the inner surface of the outer tube. In another embodiment, a helical groove can form a waveguide. In another embodiment, the inner surface of the inner tube and / or the helical groove may include a conductive material. In another embodiment, the device may further include an insulating layer between the outer tube and the inner tube. In another embodiment, the outer surface of the inner tube may include a dielectric material. In another embodiment, the helical groove may be configured to propagate millimeter electromagnetic waves. In another embodiment, the helical groove may be configured to propagate millimeter electromagnetic waves in HE11 mode.

[0017] In another embodiment, a system is provided. In one embodiment, the system may include a waveguide assembly. The waveguide assembly may include a tube. The tube may include an inner surface, an inner diameter, and a length. The waveguide assembly may also include a coil spring. The coil spring may include an outer surface, an outer diameter, and a plurality of coil elements arranged along the length of the coil spring. The coil spring may be positioned within the tube, and the outer diameter of the coil spring is smaller than the inner diameter of the tube. The system may also include a millimeter-wave drilling device. The millimeter-wave drilling device may include a gyrotron configured to inject millimeter-wave radiation energy into the borehole of a well via the waveguide assembly.

[0018] In another embodiment, the system may include multiple waveguide assemblies underground for directing millimeter-wave radiation energy to excavate a portion of a borehole or to remove material from a borehole. In yet another embodiment, multiple coil springs may be stacked in one or more tubes up to a distance of 15 km below the well surface.

[0019] In another embodiment, a method is provided. In one embodiment, the method may include forming a plurality of corrugation features on a first side surface of a metal material sheet. The sheet may include a first edge and a second edge. The method may also include forming the metal material sheet into a first tube. The method may also include sealing the first tube by welding the first edge and the second edge together. The sealed first tube may form a corrugated waveguide.

[0020] In another embodiment, the method may include inserting a sealed first tube into a second tube to form a multi-piece corrugated waveguide.

[0021] In another embodiment, a method is provided. In one embodiment, the method may include receiving a metal material sheet having a first surface, a first edge, and a second edge. The method may also include receiving a corrugated element at the top of the first surface of the metal material sheet. The corrugated element may include a plurality of corrugated features. The method may further include forming the metal material sheet into a first tube containing the corrugated element within the first tube. The method may also include sealing the first tube by welding the first edge and the second edge together. The sealed first tube may form a multi-piece corrugated waveguide.

[0022] In another embodiment, the corrugated element is a coil spring. In another embodiment, the corrugated element is a second tube including a plurality of corrugated features formed on the inner surface of the second tube. The present invention provides, for example, the following items: (Item 1) It is a device, A tube including its inner surface, inner diameter, and length, A coil spring, comprising an outer surface, an outer diameter, and a plurality of coil elements arranged along the length of the coil spring, wherein the coil spring is positioned within the tube and the outer diameter of the coil spring is smaller than the inner diameter of the tube, and a device comprising the coil spring. (Item 2) The device according to item 1, wherein a gap is defined between the outer surface of the coil spring and the inner surface of the tube. (Item 3) The device according to any one of the preceding items, wherein the coil spring forms a waveguide. (Item 4) The device according to any one of the preceding items, wherein the inner surface of the coil spring contains a conductive material. (Item 5) The device according to any one of the preceding items, wherein the coil spring contains a coating of copper, gold, silver, or platinum. (Item 6) The device according to any one of the preceding items, further comprising an insulating layer between the tube and the coil spring. (Item 7) The device according to any one of the preceding items, wherein the outer surface of the coil spring contains a dielectric material. (Item 8) The device according to any one of the preceding items, wherein at least one of the plurality of coil elements is defined by one rotation of the at least one coil element around the coil spring. (Item 9) The device according to any one of the preceding items, wherein at least one of the plurality of coil elements includes a base portion and a protruding portion extending from the base portion, and the protruding portion includes one of a trapezoidal cross-sectional shape, a circular cross-sectional shape, a square cross-sectional shape, a rectangular cross-sectional shape, or a sinusoidal cross-sectional shape. (Item 10) The device according to any one of the preceding items, wherein the plurality of coil elements includes one of a trapezoidal cross-sectional shape, a circular cross-sectional shape, a rectangular cross-sectional shape, an elliptical cross-sectional shape, or a tapered shape along the length of the plurality of coil elements. (Item 11) The apparatus according to any one of the preceding items, wherein the coil spring includes copper wire and / or aluminum wire. (Item 12) The apparatus according to any one of the preceding items, wherein the pipe includes a carbon steel pipe. (Item 13) The apparatus according to any one of the preceding items, wherein multiple coil springs are positioned within the tube. (Item 14) The apparatus according to item 13, wherein a first coil spring and a second coil spring among the plurality of coil springs are connected via a coupling spring positioned within the tube. (Item 15) The apparatus according to item 14, wherein the first end of the coupling spring is attached to the first end of the first coil spring, and the second end of the coupling spring is attached to the second end of the second coil spring, and the coupling spring is configured to reduce the amount of axial movement of the first coil spring and the second coil spring relative to each other due to thermal expansion of the first coil spring and / or the second coil spring. (Item 16) The apparatus according to any one of the preceding items, wherein the cross-sectional shape of each coil element of the coil spring and / or the plurality of coil elements is sized to allow electromagnetic waves to propagate. (Item 17) The apparatus according to item 16, wherein the coil spring and the cross-sectional outer shape of the coil spring are dimensionally set to propagate the electromagnetic waves in HE11 mode. (Item 18) The apparatus according to any one of the preceding items, wherein the length of the pipe is longer than 1 meter. (Item 19) The apparatus according to any one of the preceding items, wherein the length of the pipe is longer than 5 meters. (Item 20) The apparatus according to any one of the preceding items, wherein the length of the pipe is longer than 9 meters. (Item 21) The apparatus according to any one of the preceding items, wherein the plurality of coil elements are sized to include space between two or more of the plurality of coil elements, and the space is sized to be 1 / 6 of the wavelength of electromagnetic waves injected into the borehole of the well via the waveguide assembly. (Item 22) The apparatus according to any one of the preceding items, wherein the plurality of coil elements are dimensioned to include a pitch between two or more of the plurality of coil elements, and the pitch is dimensioned to be one-third of the wavelength of electromagnetic waves injected into the borehole of the well through the waveguide assembly. (Item 23) The apparatus according to any one of the preceding items, wherein the plurality of coil elements are dimensioned to include a width that is shorter than the wavelength of the electromagnetic waves injected into the borehole of the well via the waveguide assembly. (Item 24) The apparatus according to any one of the preceding items, wherein the coil spring inside the tube forms a helical groove. (Item 25) The apparatus according to item 24, wherein the helical groove is configured to propagate electromagnetic waves. (Item 26) The apparatus according to item 25, wherein the helical groove is configured to propagate the electromagnetic wave in HE11 mode, transverse electric mode, transverse magnetic mode, or a combination of transverse electric mode and transverse magnetic mode. (Item 27) The apparatus according to any one of the preceding items, wherein the tube is a tapered tube and the coil spring is a tapered coil spring. (Item 28) The apparatus described in any one of the preceding items, wherein the pipe is a curved pipe. (Item 29) The apparatus according to any one of the preceding items, wherein the tube and the coil spring are contained within a casing and are configured to extend from or retract into the casing. (Item 30) It is a method, Extrusion molding of a wire including its cross-sectional shape, The process involves forming the wire into a coil spring, wherein the coil spring has an outer diameter and a plurality of coil elements arranged along the length of the coil spring. A method comprising inserting the coil spring into a tube having an inner diameter larger than the outer diameter of the coil spring, wherein the tube has a length along which the coil spring extends. (Item 31) The wire is coated with a conductive material. Coating the coil spring with a conductive material, and / or The method according to item 30, further comprising coating the inner surface of the tube with an insulating material. (Item 32) The method according to item 31, wherein the conductive material comprises one or more of copper, silver, or gold. (Item 33) The method according to any one of items 30 to 32, wherein a gap is formed between the inner surface of the tube and the outer surface of the coil spring when the coil spring is inserted into the tube. (Item 34) The method according to any one of items 30 to 33, further comprising forming a channel on the inner surface of the tube, wherein the channel extends axially along the length of the tube. (Item 35) The method according to any one of items 30 to 34, wherein the cross-sectional shape of the wire includes a base portion and a projection extending from the base portion, the projection including one of a trapezoidal, circular, square, rectangular, or sinusoidal shape. (Item 36) The method according to any one of items 30 to 35, wherein forming the wire into a coil spring involves winding the wire around the mandrel such that the shape of each of the plurality of coil elements corresponds to the cross-sectional shape of the mandrel along at least a portion of the length of the coil spring. (Item 37) The method according to item 36, wherein the cross-sectional shape of the mandrel includes at least one of a trapezoidal shape, a circular shape, a rectangular shape, an elliptical shape, or a tapered shape. (Item 38) The method according to any one of items 30 to 37, wherein the wire is a copper wire or an aluminum wire. (Item 39) The method described above is Forming multiple coil springs, The method according to any one of items 30 to 38, further comprising inserting the plurality of coil springs into the tube. (Item 40) It is a device, An outer tube having an inner surface, an inner diameter, and a length, An apparatus comprising: an inner tube having an inner surface, an outer surface, an outer diameter, and a helical groove formed on the inner surface and extending along the length of the inner tube, wherein the inner tube is positioned within the outer tube, and the outer diameter of the inner tube is smaller than the inner diameter of the outer tube. (Item 41) The apparatus according to item 40, wherein a gap is defined between the outer surface of the inner tube and the inner surface of the outer tube. (Item 42) The apparatus according to item 40 or 41, wherein the helical groove forms a waveguide. (Item 43) The apparatus according to any one of items 40 to 42, wherein the inner surface and / or the helical groove of the inner tube comprises a conductive material. (Item 44) The apparatus according to any one of items 40 to 43, wherein the apparatus further includes an insulating layer between the outer tube and the inner tube. (Item 45) The apparatus according to any one of items 40 to 44, wherein the outer surface of the inner tube comprises a dielectric material. (Item 46) The apparatus according to any one of items 40 to 45, wherein the helical groove is configured to propagate millimeter electromagnetic waves. (Item 47) The apparatus according to item 46, wherein the helical groove is configured to propagate the millimeter electromagnetic waves in HE11 mode. (Item 48) It is a system, Waveguide assembly, A tube including its inner surface, inner diameter, and length, A waveguide assembly comprising: a coil spring having an outer surface, an outer diameter, and a plurality of coil elements arranged along the length of the coil spring, wherein the coil spring is positioned within the tube, and the outer diameter of the coil spring is smaller than the inner diameter of the tube; A system comprising a millimeter-wave drilling apparatus, including a gyrotron configured to inject millimeter-wave radiation energy into a borehole of a well via the waveguide assembly. (Item 49) The system according to item 48, further comprising a plurality of waveguide assemblies underground for directing the millimeter-wave radiation energy to excavate a portion of the borehole or to remove material from the borehole. (Item 50) The system according to item 49, wherein the plurality of coil springs are stacked in one or more pipes up to a distance of 15 km below the surface of the well. (Item 51) It is a method, The method involves forming a plurality of corrugation features on a first side surface of a metal material sheet, wherein the sheet includes a first edge and a second edge. The aforementioned metal material sheet is formed into a first tube, A method comprising sealing the first tube by welding the first edge and the second edge together, wherein the sealed first tube forms a corrugated waveguide. (Item 52) The method according to item 51, further comprising inserting the sealed first tube into the second tube to form a multi-piece corrugated waveguide. (Item 53) It is a method, To receive a metal material sheet having a first surface, a first edge, and a second edge, The receiving of a corrugation element at the uppermost part of the first surface of the metal material sheet, wherein the corrugation element includes a plurality of corrugation features, The metal material sheet is formed in the first tube, which includes the corrugation element inside the first tube. A method comprising sealing the first tube by welding the first edge and the second edge together, wherein the sealed first tube forms a multi-piece corrugated waveguide. (Item 54) The method according to item 53, wherein the corrugated element is a coil spring. (Item 55) The method according to item 53 or 54, wherein the corrugated element is a second tube comprising a plurality of corrugated features formed on the inner surface of the second tube.

[0023] These and other features will be more readily understood from the following detailed description, which is provided in conjunction with the attached drawings. [Brief explanation of the drawing]

[0024] [Figure 1] This figure shows an exemplary embodiment of a millimeter-wave drilling system including a multi-piece corrugated waveguide as described herein. [Figure 2] This figure shows a cross-sectional view of a borehole containing a waveguide for transmitting millimeter-wave radiation with low loss as described herein. [Figure 3] This flowchart shows an exemplary embodiment of a method for forming a multi-piece corrugated waveguide as described herein. [Figure 4] This flowchart shows an exemplary embodiment of a method for coating a portion of a multi-piece corrugated waveguide as described herein. [Figure 5]This figure shows a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide described herein. [Figure 6] This figure shows a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide described herein, which includes a dielectric material and / or a thermal insulating material on the outer surface of the coil spring of the multi-piece corrugated waveguide. [Figure 7] This figure shows a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide described herein, which includes an insulating layer between the tube and the coil spring. [Figure 8] This figure shows a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide described herein, in which a dielectric material and / or a thermal insulating material is included on the inner surface of the tube. [Figure 9] This figure shows a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide, including an inner tube having a helical groove formed on the inner surface of the inner tube, as described herein. [Figure 10] This figure shows a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide described herein, which includes an inner tube having a helical groove and dielectric material on the outer surface of the inner tube. [Figure 11] This figure shows a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide described herein, which includes an inner tube having a helical groove and an insulating layer between the tube and the coil spring. [Figure 12] This figure shows a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including a tapered tube and a tapered coil spring as described herein. [Figure 13] This figure shows a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including a curved tube as described herein. [Figure 14A] This figure shows a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide, including a casing into which the tubes and coil springs described herein can extend. [Figure 14B]This figure shows a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide, including a casing into which the tubes and coil springs described herein can extend. [Figure 15] This figure shows an exemplary embodiment for manufacturing a coil tube product for use in the multi-piece corrugated waveguide described herein. [Figure 16] This figure shows an exemplary embodiment for manufacturing a multi-piece corrugated waveguide as described herein, including a coil tube product. [Figure 17A] This figure shows an exemplary embodiment of a coil spring included in a multi-piece corrugated waveguide as described herein. [Figure 17B] This figure shows an exemplary embodiment of a coil spring included in a multi-piece corrugated waveguide as described herein. [Figure 17C] This figure shows an exemplary embodiment of a coil spring included in a multi-piece corrugated waveguide as described herein. [Figure 17D] This figure shows an exemplary embodiment of a coil spring included in a multi-piece corrugated waveguide as described herein. [Figure 17E] This figure shows an exemplary embodiment of a coil spring included in a multi-piece corrugated waveguide as described herein. [Figure 17F] This figure shows an exemplary embodiment of a coil spring included in a multi-piece corrugated waveguide as described herein. [Figure 17G] This figure shows an exemplary embodiment of a coil spring included in a multi-piece corrugated waveguide as described herein. [Figure 18A] This figure shows exemplary embodiments of the cross-sectional shapes of multiple coil elements included in the multi-piece guide described herein. [Figure 18B] This figure shows exemplary embodiments of the cross-sectional shapes of multiple coil elements included in the multi-piece guide described herein. [Figure 18C]This figure shows exemplary embodiments of the cross-sectional shapes of multiple coil elements included in the multi-piece guide described herein. [Figure 18D] This figure shows exemplary embodiments of the cross-sectional shapes of multiple coil elements included in the multi-piece guide described herein. [Figure 18E] This figure shows exemplary embodiments of the cross-sectional shapes of multiple coil elements included in the multi-piece guide described herein. [Figure 19A] This figure shows an exemplary embodiment of the square cross-sectional shape of the protruding portion of the coil element of a multi-piece corrugated waveguide described herein. [Figure 19B] This figure shows an exemplary embodiment of a plurality of coil elements, each of which has a square cross-sectional outer shape of a protruding portion, as described herein. [Figure 20A] This figure shows an exemplary embodiment of the trapezoidal cross-sectional shape of the protruding portion of the coil element of the multi-piece corrugated waveguide described herein. [Figure 20B] This figure shows an exemplary embodiment of a plurality of coil elements, each of which has a trapezoidal cross-sectional shape of a protruding portion, as described herein. [Figure 21A] This figure shows another exemplary embodiment of the trapezoidal cross-sectional shape of the protruding portion of the coil element of the multi-piece corrugated waveguide described herein. [Figure 21B] This figure shows another exemplary embodiment of a plurality of coil elements, each of which coil elements described herein includes a trapezoidal cross-sectional outer shape of a protruding portion. [Figure 22A] This figure shows an exemplary embodiment of the rectangular cross-sectional shape of the protruding portion of the coil element of a multi-piece corrugated waveguide described herein. [Figure 22B] This figure shows an exemplary embodiment of a plurality of coil elements, each of which has a rectangular cross-sectional outline of a protruding portion, as described herein. [Figure 23A] This figure shows an exemplary embodiment of the circular cross-sectional shape of the protruding portion of the coil element of a multi-piece corrugated waveguide described herein. [Figure 23B] This figure shows an exemplary embodiment of a plurality of coil elements, each of which has a circular cross-sectional outer shape of a protruding portion, as described herein. [Figure 24A] This figure shows an exemplary embodiment of the sinusoidal cross-sectional shape of the protruding portion of the coil element of the multi-piece corrugated waveguide described herein. [Figure 24B] This figure shows an exemplary embodiment of a plurality of coil elements, each of which has a sinusoidal cross-sectional shape of a protruding portion, as described herein. [Figure 25A] This figure shows an exemplary embodiment of a protruding portion of a coil element, including multiple cross-sectional shapes described herein. [Figure 25B] This figure shows an exemplary embodiment of a plurality of coil elements, each of which has a protruding portion having a plurality of cross-sectional shapes, as described herein. [Figure 26] This figure shows an exemplary embodiment of a multi-piece corrugated waveguide formed from two nested coil springs as described herein. [Figure 27] Figure 26C shows an exemplary embodiment of a multi-piece corrugated waveguide.

[0025] Please note that the drawings are not necessarily to scale. The drawings are intended to show only typical embodiments of the subject matter disclosed herein and should not be considered to limit the scope of this disclosure. [Modes for carrying out the invention]

[0026] A waveguide is a structure that guides waves, such as electromagnetic waves or sound waves, by restricting energy transmission to one direction, thereby minimizing energy loss. Waveguides can be used, for example, in millimeter-wave drilling to efficiently transport electromagnetic waves to the required depth and form a well. The design and materials used to form the waveguide can affect the transmission efficiency of electromagnetic waves transmitted in a particular transmission mode. For example, high-frequency (RF) waves can be transmitted over long distances using waveguides that include a series of corrugated features. The corrugated features may include repeating ridge or groove patterns that can extend within the length of the tube. The pattern of the corrugated features (e.g., ridges, grooves, etc.) can be shaped to assist the propagation of electromagnetic waves and can be dimensionally set according to the characteristics of the wave (e.g., frequency) for which the waveguide is designed to propagate efficiently. Often, corrugated waveguides can include dielectric or conductive coatings that can improve the waveguide's transmission efficiency.

[0027] Several existing methods for forming corrugated waveguides involve machining, rotary cutting, tapping, or perforating the inner surface of the tube to create the corrugation feature. Alternatively, a stack of rings can be constructed within the tube to form the corrugation feature. However, these methods can be difficult to implement when the waveguide is long, and therefore may introduce errors in the dimensions of the corrugation feature. Such errors can reduce the transmission efficiency of the waveguide.

[0028] In addition, forming long waveguides using some existing methods may leave behind residual materials such as shavings and burrs, which can also reduce the waveguide's transmission efficiency. Furthermore, some existing methods are not suitable for subsequent machining of long tubes to correct defects in the corrugated features. Consequently, the repair and replacement costs of waveguides formed in long tubes using some conventional methods can be high. Coating the inner surface of long tubes (and the corrugated features within them) with, for example, a conductive coating can be difficult, expensive, and labor-intensive.

[0029] The multi-piece corrugated waveguides described herein can be used in a variety of industries and applications where electromagnetic waves are transmitted, such as the oil and gas manufacturing industry, nuclear energy, fusion reactors, drilling and extraction operations, and sound or audio applications. The design and manufacturing methods of multi-piece corrugated waveguides can provide a less expensive alternative for any industry or application compared to purchasing long corrugated waveguides with corrugated features formed by conventional manufacturing methods. For this reason, some implementations of this subject matter can include multi-piece corrugated waveguides formed from coil springs placed inside a tube. The coil springs can be shaped to provide the corrugated features of the waveguide, while the tube can provide structural support. By utilizing coil springs inside a tube as the waveguide, longer waveguides can be manufactured without the dimensional errors of the corrugated features that are introduced by some existing methods for forming waveguides. By reducing dimensional errors in the corrugated features, waveguides can propagate electromagnetic waves (e.g., millimeter waves) more efficiently, resulting in improved waveguides.

[0030] In some embodiments, the multi-piece corrugated waveguide can be configured for use in millimeter-wave drilling during well formation. In some implementations, the coil springs and the inner surface of the tube can be coated with, for example, a conductive coating. The transmission efficiency of some implementations of the multi-piece corrugated waveguide described herein can also be improved by dimensionalizing the coil spring characteristics, such as the width, depth, and pitch of the coil springs, with respect to a particular transmission mode. Some implementations of the multi-piece corrugated waveguide described herein can provide efficient transmission of electromagnetic waves in various transmission modes.

[0031] Several configurations of the multi-piece corrugated waveguide described herein can be formed by assembling multiple individual components. In some configurations, each individual component can be formed with greater precision compared to existing methods of machining corrugation features within a single long piece of tube. Forming the components individually ensures that corrugation features with the desired properties necessary for efficient and frequency-dependent electromagnetic wave transmission are formed. Furthermore, since the coil springs and tubes can be assembled together over a longer length range compared to machining a fixed-length tube, individually manufacturing the components of some configurations of the multi-piece corrugated waveguide described herein can reduce labor and maintenance costs.

[0032] In some implementations, the coil spring can be easily removed and replaced within the tube, thereby reducing repair and replacement costs. In contrast, existing methods may require specialized equipment and long downtime to remachine long tubes, potentially leading to higher repair and replacement costs. In addition, remachining the tube multiple times may leave insufficient material to reshape the desired corrugation features of the waveguide.

[0033] Figure 1 shows an exemplary embodiment of a millimeter-wave drilling (MMWD) system 100, including an exemplary multi-piece corrugated waveguide 108. The MMWD system 100 shown in Figure 1 includes a gyrotron 102 connected via a power cable 104 to a power source 106 that supplies power to the gyrotron 102. The high-power millimeter-wave beam output by the gyrotron 102 is guided by a waveguide 108, such as a multi-piece corrugated waveguide as described herein. The waveguide 108 may include a waveguide curve 118, a waveguide section 126 having a window 120, and an opening 128 for off-gas discharge and pressure control. The waveguide section is below ground 130 to assist in sealing the borehole.

[0034] As part of the transmission line of waveguide 108, there is an isolator 110 to prevent reflected power from returning to the interface for gyrotron 102 and diagnostic access 112. Diagnostic access is connected to diagnostic electronic components and data acquisition 116 by low-power waveguide 114. Window 120 has a pressurized gas supply unit 122 connected to the window by piping 124 to inject a clean gas flow over the entire inside of the window to prevent deposits on the window. A second pressurized unit 136 is connected to the waveguide opening 128 by piping 132 to control the pressure in the borehole 148 and assist in introducing and removing borehole gas as needed. Window gas injection unit 122 can be operated at a slightly higher pressure than borehole pressure unit 136 to maintain a gas flow across the entire window surface. Branch lines 134 within the borehole pressurizing piping 132 can be connected to a pressure relief valve 138, allowing volatile borehole material and window gas to be discharged into the atmosphere 146 through a gas analysis monitoring unit 140, followed by a gas filter 142, and an exhaust duct 144. In some embodiments, the exhaust duct 144 can return the gas to the pressurizing unit 136 for reuse.

[0035] The pressure inside the borehole may increase partially or entirely due to the partial volatilization of the molten subsurface material. The thermal molten front 152 at the end of the borehole 148 can be propagated into the subsurface formation under the combined action of millimeter-wave power and gas pressure, leaving behind a ceramic (e.g., vitreous) borehole wall 150. This wall can act as a dielectric waveguide for transmitting the millimeter-wave beam to the thermal front 152.

[0036] Figure 2 shows a cross-sectional view of an exemplary borehole including a multi-piece corrugated waveguide that can be configured to transmit millimeter-wave radiation with low loss. Figure 2 provides a more detailed diagram corresponding to the MMWD and MMWD system described in U.S. Patent No. 8,393,410, entitled "Millimeter-wave Drilling System" by Woskov et al. A borehole 200 comprising a ring 205, a vitreous / ceramic wall 210, and a transparent glass 215 has a waveguide assembly 220 inserted to improve the propagation efficiency of the millimeter-wave beam. In some embodiments, the waveguide assembly may include a multi-piece corrugated waveguide as described herein. In some embodiments, multiple waveguide assemblies may be inserted into the borehole. For example, multiple waveguide assemblies may be stacked on top of each other to a distance of 1 km, 5 km, 10 km or more below the surface of the well.

[0037] As shown in Figure 2, the diameter of the waveguide assembly 220 can be smaller than the borehole diameter to create an annular gap 225 for exhaust / extraction. The standoff distance 230 of the leading edge of the multi-piece corrugated waveguide 220 from the thermal melting front 235 of the borehole is far enough to allow the emitted millimeter-wave beam spread 240 to fill the dielectric borehole 200 with the induced millimeter-wave beam 245. The standoff distance 230 is also far enough to keep the temperature of the waveguide assembly 220 sufficiently low for persistence. The inserted waveguide assembly 220 also acts as a conduit for pressurized gas flow 250 from the surface. This gas flow keeps the waveguide clean and contributes to the extraction / removal of rock material from the borehole. The gas flow from the surface 250 mixes with volatile outgassable rock material 260 255, transporting the condensed rock vapor through the annular space 225 to the surface. The exhaust gas flow 265 is large enough to limit the size of the volatile rock particles and transport them to the surface.

[0038] Figure 3 is a flowchart illustrating an exemplary embodiment of a method for forming a multi-piece corrugated waveguide as described herein. In 305, a wire including the cross-sectional shape can be extruded. Extrusion can favorably improve the quality of the manufactured waveguide because, compared to conventional methods in which corrugated grooves can be machined, tapped, or otherwise perforated on the inner surface of the waveguide, there is a lower possibility of burrs or machined material remaining inside the waveguide. Extrusion or roll forming of a wire to form a coil spring (e.g., the corrugated feature of the waveguide described herein) can favorably improve the quality of the manufactured waveguide. The wire can be made from any standard metallic or non-metallic material. In some embodiments, the wire can include metallic wires or other conductive materials, such as copper wire, aluminum wire, or copper-chromium-zirconium alloy wire. Extrusion can form the cross-sectional shape of the wire. The cross-sectional shape can include a base portion and a projection extending from the base portion, as shown and described with respect to Figures 19 to 25.

[0039] The base and protruding portions may include external shapes that can be defined in various geometries and dimensions. For example, in some embodiments, the external shape of the protruding portion may include a trapezoidal, circular, square, rectangular, or sinusoidal shape. In some embodiments, the base portion may include a rectangular or curved shape. Other external shapes are possible.

[0040] The protruding portion may include a width and depth that can accommodate the modes and / or frequencies of electromagnetic waves transmitted through the multi-piece corrugated waveguide described herein. For example, the width and depth of the protruding portion may be shaped to accommodate the optimal transmission of electromagnetic waves such as millimeter waves and microwaves in HE11 mode or any other mode with low attenuation.

[0041] The width and depth of the protrusions in a corrugated waveguide can be configured with respect to the frequency of the wave transmitted through the waveguide. For example, for optimal transmission of the HE11 mode, the width of the corrugation can be shorter than 1 / 6 of the wavelength, and the depth of the corrugation can be about 1 / 4 of the beam wavelength. For other propagation modes, the corrugation can have different geometric characteristics.

[0042] In 310, the wire can be formed into a coil spring having multiple coil elements arranged along the outer diameter and length of the coil spring. In some embodiments, the coil spring can be formed by winding the wire around a mold such as a mandrel in order to form the wire into a coil spring. In this way, the cross-sectional shape of the coil spring (e.g., the shape observed when the coil spring is viewed from a viewpoint parallel to the axis extending along the length of the coil spring) and the shape of each coil element of the coil spring can correspond to the cross-sectional shape of the mandrel (e.g., the shape observed when the mandrel is viewed from a viewpoint parallel to the axis extending along the length of the mandrel). The cross-sectional shape of the mandrel (and therefore the cross-sectional shape of the coil element, the multiple coil elements, and the coil spring) can include, for example, the trapezoidal, circular, rectangular, square, or elliptical shapes shown in Figures 18A to 18E. Other shapes are possible.

[0043] In some embodiments, the coil spring can be a tapered coil spring, which can be formed using a tapered mandrel. In some embodiments, the cross-sectional shape of the multiple coil elements, and therefore the cross-sectional shape of the coil spring, can be varied along the length of the multiple coil elements and / or the coil spring. In some embodiments, the coil spring can include multiple cross-sectional shapes along the length of the coil spring.

[0044] The coil elements of a coil spring can correspond to one turn of wire around a mandrel. Each coil element can have a circumference and a diameter. The diameter of each coil element can correspond to the diameter of the coil spring and to the number of coil elements forming the coil spring. As shown with respect to Figure 17A, the number of coil elements can include a pitch defined between the centers of two coil springs. The pitch can correspond to the mode and / or frequency of electromagnetic waves transmitted through the multi-piece corrugated waveguide described herein. In addition, the coil elements can include protrusions. The protrusions can be formed with a width and depth that corresponds to optimal transmission of millimeter waves in HE11 mode, for example. The external shape of the coil elements showing the width and depth of the protrusions is shown and described with respect to Figures 19 to 25.

[0045] In some embodiments, the coil spring can be formed as a compression spring or a tension spring. Depending on the desired pitch between the coil elements, it may be advantageous to use a compression spring (e.g., a coil spring with a larger pitch between the coil elements, as shown in Figure 17A) instead of a tension spring (e.g., a coil spring with a smaller pitch between the coil elements, as shown in Figure 17B). In some embodiments, multiple coil springs can be formed in the manner described with respect to work 310. In some embodiments, as shown in Figures 17B and 17C, the coil spring can be formed to include mounting points at each end of the coil spring so that multiple coil springs can be connected or joined together. For example, the mounting points may include semicircular mounting points configured at each end of the coil spring. A semicircular mounting point at one end of one coil spring can be connected to a semicircular mounting point at one end of another adjacent coil spring.

[0046] In 315, a coil spring can be inserted into a tube. The tube can provide structural rigidity to the coil spring and can be designed to provide airtight or liquidtight (e.g., pressurized) containment. In some embodiments, the tube can be a continuous tube, a coil tube product, or a pipe tube product. In some embodiments, the tube can be a gas injector or a pump discharge device. The tube can have an inner diameter that can be larger than the outer diameter of the coil spring. The tube can have a length that allows the coil to extend along it. As shown in Figures 5-8, 12-13, and 14A-14B, when the coil spring is inserted into the tube, it can form multiple corrugation features within the tube. The corrugation features can enable the coil spring and tube to efficiently transmit electromagnetic waves through them in various transmission modes, such as HE11 mode. The corrugation features can be further defined as a result of extruding wire having a specific cross-sectional shape and pitch such that transmission efficiency is achieved by the cross-sectional shape of the coil spring and multiple coil elements within the tube. In some embodiments, the tube can be formed from a metallic or non-metallic material. In some embodiments, the tube can be formed from carbon steel, stainless steel, Inconel, titanium alloy, molybdenum alloy, tungsten alloy, copper alloy, aluminum alloy, or copper-chromium-zirconium. In some embodiments, multiple coil springs can be inserted into the tube.

[0047] In some embodiments, as shown in Figures 5-8 and 12-13, a gap can be formed between the inner surface of the tube and the outer surface of the coil spring when the coil spring is inserted into the tube. The gap can allow deformation of the coil spring material due to thermal expansion during electromagnetic wave transmission through the tube and coil spring. The gap allows gas to flow from the ground to the bottom of the borehole, while also allowing cooling of the inner and outer corrugations of the coil spring, which cannot be achieved with conventional waveguide pipes. The tube can act as an additional barrier against any electromagnetic waves that may leak into the environment through the coil spring. In some embodiments, a channel can be formed on the inner surface of the tube, which can allow gas to flow from the ground to the bottom of the borehole. In some embodiments, the channel can extend axially along the length of the tube.

[0048] Figure 4 is a flowchart illustrating an exemplary embodiment of Method 400 for coating a portion of a multi-piece corrugated waveguide as described herein. Coating or immersing a portion of a multi-piece corrugated waveguide as described herein can improve the transmission efficiency of the transmitted electromagnetic waves and help control the thermal conditions within the multi-piece corrugated waveguide. Compared to conventional methods of coating the inner surface of a long tube that has been perforated or machined to form corrugated waveguide features within the long tube, coating a portion of a multi-piece corrugated waveguide as described herein is easier because the coil spring and the tube can be formed and coated separately. In addition, the use of shorter coil springs as described herein also makes it easier to apply the coating material before insertion into the tube.

[0049] In 405, the wire can be coated with a conductive material. In some embodiments, the wire can be coated with a conductive material such as copper, silver, platinum, or gold. The coating process can include vapor deposition, chemical or electrochemical coating, spraying, rotating, dipping, film application, etc. In some embodiments, the wire can be coated with a dielectric material.

[0050] In 410, the coil spring can be coated with a conductive material. In some embodiments, the outer diameter of the coil spring can be coated with a conductive material, as shown in Figure 17B. In some embodiments, the coil spring can be coated with a conductive material such as copper, silver, platinum, or gold. In some embodiments, the coil spring can be coated with a dielectric material. The coating process can include vapor deposition, chemical or electrochemical coating, spraying, rotating, dipping, film application, etc.

[0051] In 415, the inner surface of the tube can be coated with an insulating material. For example, as shown in Figure 8, the inner surface of the tube can be coated with a dielectric material. The insulating material can be thermally insulating and can also be used between the inner surface of the tube and the outer surface of the coil spring to isolate the heat in the well bore ring 205 from the coil spring. This allows the purge gas from the ground to cool the coil spring down to the bottom of the borehole without losing its cooling capacity due to interaction with the inner surface of the tube (contact with the hot gas rising through the ring 205). In some embodiments, the insulating material can include glass fiber, open-cell foam, closed-cell foam, polystyrene, ceramic fiber, carbon composite, silica fiber, rock wool, and the like.

[0052] While multi-piece corrugated waveguides are described herein in relation to drilling operations, embodiments of multi-piece corrugated waveguides herein can be developed in various other configurations for transmitting electromagnetic waves. Drilling operations require inserting the MCG into the ground and possibly flowing gas in or around the MCG, but other applications of the embodiments of MCG described herein can be carried out using a fixed above-ground placement of the MCG. For example, in nuclear energy or sound transmission applications, the MCG can be configured on the ground surface and positioned relative to a target from which electromagnetic waves are transmitted.

[0053] Figure 5 is a cross-sectional view of an exemplary embodiment of the multi-piece corrugated waveguide 500 described herein. Several implementations of the multi-piece corrugated waveguide (MCG) described herein can be formed according to methods 300 and 400 described with respect to Figures 3 and 4. The exemplary MCG described herein can be configured to operate within the system 100 described with respect to Figure 1 and to deploy the borehole 200 described with respect to Figure 2.

[0054] As shown in Figure 5, the MCG 500 can be deployed into a borehole 505 on a surface 510 where a well or other subsurface drilling operation is being performed. The MCG 500 can deliver electromagnetic energy 515, such as RF waves, into the borehole 505. The MCG 500 may include a tube 520 and a coil spring 525 positioned within the tube 520. The tube 520 may include an inner surface, an outer surface, an inner diameter defined between opposing inner surfaces, an outer diameter defined between opposing outer surfaces, and a length defined between the end 520 of a first tube and the end 520 of a second tube. In some embodiments, the length of the tube 520 may be longer than 1 meter, longer than 5 meters, or longer than 9 meters. In embodiments in which the tube includes a continuous tube, a coiled tube product, or a pipe tube product, the length of the tube 520 may be longer than 10 km. When forming a borehole, tens to hundreds of pipes 520 can be deployed to reach a sufficient depth to form the well.

[0055] The coil spring 525 may include a plurality of coil elements 530 arranged along the length of the tube 520 and may also form a waveguide. The plurality of coil elements 530 may include two or more coil elements 535. The coil spring 525 may include an outer surface in contact with the inner surface of the tube 520 and an outer diameter defined between the opposing outer surfaces of the coil spring 525. The outer diameter of the coil spring 525 may be smaller than the inner diameter of the tube 520.

[0056] As shown in Figure 5, a gap 540 can be defined between the outer surface of the coil spring 525 and the inner surface of the tube 520. This gap allows the coil spring 525 to expand within the tube 520 as a result of thermal expansion of the coil spring 525 during the transmission of electromagnetic waves through the MCG 500. The gap 540 can also allow gas to pass from the ground to the bottom of the borehole. Additionally, a second gap 545 can be defined between the outer surface of the tube 520 and the wall of the borehole 505.

[0057] In some embodiments, the cross-sectional shape of each of the coil springs 525 and coil elements 535 can be sized to propagate electromagnetic waves through the MCG 500. For example, the cross-sectional shapes of the coil springs 525 and coil elements 535 can be formed and sized to propagate millimeter electromagnetic waves with low attenuation. The cross-sectional shapes of the coil springs 525 and coil elements 535 can be sized to transmit electromagnetic waves in one or more transmission modes. For example, the cross-sectional shapes of the coil springs 525 and coil elements 535 can be sized to transmit millimeter electromagnetic waves in HE11 mode.

[0058] In some embodiments, the cross-sectional shape of the coil spring 525 and the coil element 535 can be dimensionally set based on the wavelength and / or frequency of the electromagnetic wave being transmitted.

[0059] As shown in Figure 5, the coil spring 525 can form a helical groove 550. In some implementations, the helical groove 550 can extend continuously along the length of the coil spring 525 along the inner surface of the coil spring 525. The helical groove 550 can be formed by opposing protruding portions of each coil element 535. In some embodiments, the coil spring 525 may include an inner diameter 555 measured between the protruding portions of each coil element 535. In some embodiments, the inner diameter 555 can include diameters of 5.0mm to 15.0mm, 10.0mm to 20.0mm, 15.0mm to 25.0mm, 20.0mm to 30.0mm, 25.0mm to 35.0mm, 30.0mm to 40.0mm, 45.0mm to 55.0mm, 50.0mm to 60.0mm, 55.0mm to 65.0mm, 60.0mm to 70.0mm, 65.0mm to 75.0mm, 70.0mm to 80.0mm, 75.0mm to 90.0mm, or 85.0mm to 200.0mm. In some embodiments, the inner diameter can be greater than 200.0mm or less than 5.0mm. Other inner diameters are possible. In some embodiments, the inner diameter 555 may include tolerances such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, or ±0.2 mm, ±0.225 mm, or ±0.25 mm, but other tolerances are possible.

[0060] Figure 6 shows a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide 600, which includes a dielectric material and / or thermal insulation material on the outer surface of the coil spring of the multi-piece corrugated waveguide described herein. As shown in Figure 6, the MCG 600 may include a tube 605, a coil spring 610, and a dielectric material 615 on the outer surface of the coil spring 610. In some embodiments, the dielectric material may include glass, ceramic, porcelain, and most plastics. The dielectric material 615 may be applied as a coating to the outer diameter of the coil spring 610, or the dielectric material 615 may be an independent component added to the assembled MCG 600. The dielectric material 615 can electrically insulate the tube 605 from the coil spring 610 to prevent an electrical short circuit between them.

[0061] In some embodiments, the coil spring 610 may include an inner diameter 620 measured between the protruding portions of each coil element of the coil spring 610. In some embodiments, the inner diameter 620 may include diameters of 5.0mm to 15.0mm, 10.0mm to 20.0mm, 15.0mm to 25.0mm, 20.0mm to 30.0mm, 25.0mm to 35.0mm, 30.0mm to 40.0mm, 45.0mm to 55.0mm, 50.0mm to 60.0mm, 55.0mm to 65.0mm, 60.0mm to 70.0mm, 65.0mm to 75.0mm, 70.0mm to 80.0mm, 75.0mm to 90.0mm, or 85.0mm to 200.0mm. In some embodiments, the diameter may be greater than 200.0mm or less than 5.0mm. Other diameters are possible. In some embodiments, the inner diameter 620 may include tolerances such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, but other tolerances are possible.

[0062] Figure 7 is a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide 700 described herein, which includes an insulating layer between the tube and the coil spring. As shown in Figure 7, the MCG 700 may include a tube 705, a coil spring 710, and an insulating layer 715. The insulating layer 715 may be thermally insulating and may be positioned between the tube 705 and the coil spring 710. In some embodiments, the insulating layer may be formed from an insulating material such as glass fiber, open / closed-cell foam, polystyrene, ceramic fiber, carbon composite, silica fiber, or rock wool. The insulating material may be positioned between the inner surface of the tube 705 and the outer surface of the coil spring 710 to isolate heat within the well bore ring 205 from the coil spring 710. This allows the purge gas from the ground surface to cool the coil spring 710 down to the bottom of the borehole without losing its cooling capacity due to interaction with the inner surface of the tube 705 (contact with the hot gas rising through the ring 205).

[0063] In some embodiments, the coil spring 710 may include an inner diameter 720 measured between the protruding portions of each coil element of the coil spring 710. In some embodiments, the inner diameter 720 may include diameters of 5.0mm to 15.0mm, 10.0mm to 20.0mm, 15.0mm to 25.0mm, 20.0mm to 30.0mm, 25.0mm to 35.0mm, 30.0mm to 40.0mm, 45.0mm to 55.0mm, 50.0mm to 60.0mm, 55.0mm to 65.0mm, 60.0mm to 70.0mm, 65.0mm to 75.0mm, 70.0mm to 80.0mm, 75.0mm to 90.0mm, or 85.0mm to 200.0mm. In some embodiments, the diameter may be greater than 200.0mm or less than 5.0mm. Other diameters are possible. In some embodiments, the inner diameter 720 may include tolerances such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, but other tolerances are possible.

[0064] Figure 8 is a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide 800, which includes a dielectric material and / or thermal insulation material on the inner surface of the tube of the multi-piece corrugated waveguide described herein. As shown in Figure 8, the MCG 800 may include a tube 805, a coil spring 810, and a dielectric material 815 on the inner surface of the tube 815. In some embodiments, the dielectric material and / or thermal insulation material may include glass fibers, open / closed-cell foam, polystyrene, ceramic fibers, carbon composites, silica fibers, rock wool, and the like.

[0065] In some embodiments, the coil spring 810 may include an inner diameter 820 measured between the protruding portions of each coil element of the coil spring 810. In some embodiments, the inner diameter 820 may include diameters of 5.0mm to 15.0mm, 10.0mm to 20.0mm, 15.0mm to 25.0mm, 20.0mm to 30.0mm, 25.0mm to 35.0mm, 30.0mm to 40.0mm, 45.0mm to 55.0mm, 50.0mm to 60.0mm, 55.0mm to 65.0mm, 60.0mm to 70.0mm, 65.0mm to 75.0mm, 70.0mm to 80.0mm, 75.0mm to 90.0mm, or 85.0mm to 200.0mm. In some embodiments, the diameter may be greater than 200.0mm or less than 5.0mm. Other diameters are possible. In some embodiments, the inner diameter 820 may include tolerances such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, but other tolerances are possible.

[0066] Figure 9 is a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide 900, which includes inner tubes having helical grooves formed on the inner surface of the inner tubes as described herein. As shown in Figure 9, the MCG 900 may include an outer tube 905. The outer tube 905 may include an inner surface, an inner diameter defined between opposing inner surfaces, and a defined length between the end 905 of the first tube and the end 905 of the second tube. The MCG 900 may also include one or more inner tubes, such as inner tubes 910 and 915. Each inner tube may include an inner surface, an outer surface, an outer diameter defined between opposing outer surfaces, and helical grooves 920 formed on the inner surface of the inner tubes 910 and 915. The inner tubes 910 and 915 can be positioned within the outer tube 905 as a result of their outer diameters being smaller than the inner diameter of the outer tube 905. In some embodiments, for example, when multiple inner tubes are positioned within an outer tube 905, two or more inner tubes 910 and 915 can be joined via screw connections, by welding one inner tube to a second inner tube, or by bolting one inner tube to a second inner tube. In some embodiments, the inner tubes 910 and / or 915 can be fixed within the outer tube 905 via projections formed on the inner surface of the outer tube 905. In some embodiments, the inner tubes 910 and 915 can be joined via magnetic connectors or retainer rings that can surround the overlapping portion of the inner tubes 910 and 915. In some embodiments, the inner tubes 910 and 915 can be formed from a flat sheet of stock material wound into a tubular shape. In such embodiments, corrugation features can be formed on the surface of the flat sheet of stock material, and the corrugation features may include helical corrugations as well as non-helical corrugations formed as peaks and valleys on the surface of the flat sheet of stock material. In some embodiments, the inner tubes 910 and 915 can be formed by additive manufacturing.

[0067] The helical groove 920 can be formed as a continuous or semi-continuous groove that can extend along the length of the inner tubes 910 and 915. The helical groove 920 can form a waveguide configured to transmit electromagnetic waves through the MCG 900. For example, the helical groove 920 can be configured to propagate millimeter electromagnetic waves in one or more transmission modes. In some embodiments, the helical groove 920 can be configured to propagate millimeter electromagnetic waves in HE11 transmission mode, but other transmission modes such as transverse electric mode (TE) or transverse magnetic mode (TM), or a combination of TE and TM, can also be propagated through the helical groove 920.

[0068] As further shown in Figure 9, in some embodiments, a gap 925 can be defined between the outer surfaces of the inner tubes 910 and 915 and the inner surface of the outer tube 905. The gap 925 can allow the inner tubes 910 and 915 to expand within the tube 905 as a result of thermal expansion of the inner tubes 910 and 915 during electromagnetic wave transmission through the MCG 900. The gap 925 can also allow gas to pass from the ground to the bottom of the borehole.

[0069] As further shown in Figure 9, in some embodiments, the helical groove 920 may include a conductive material 930. The conductive material 930 may be present on the surface of the helical groove 920. In some embodiments, the inner surfaces of the inner tubes 910 and / or 915 may include a conductive material 935. The conductive material may include copper, silver, platinum, or gold.

[0070] In some embodiments, the MCG900 may include an inner diameter 940 measured between the protruding portions of each inner tube 910 and 915. The protruding portions may be formed by helical grooves 920. In some embodiments, the inner diameter 940 may include diameters of 5.0mm to 15.0mm, 10.0mm to 20.0mm, 15.0mm to 25.0mm, 20.0mm to 30.0mm, 25.0mm to 35.0mm, 30.0mm to 40.0mm, 45.0mm to 55.0mm, 50.0mm to 60.0mm, 55.0mm to 65.0mm, 60.0mm to 70.0mm, 65.0mm to 75.0mm, 70.0mm to 80.0mm, 75.0mm to 90.0mm, or 85.0mm to 200.0mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 940 may include tolerances such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, but other tolerances are possible.

[0071] Figure 10 shows an exemplary embodiment of a multi-piece corrugated waveguide 1000 described herein, which includes an inner tube having a helical groove and dielectric material on the outer surface of the inner tube. As shown in Figure 10, the MCG 1000 may include an outer tube 1005 and an inner tube 1010. In the embodiment shown in Figure 10, a single inner tube 1010 is configured inside the outer tube 1005. The inner tube 1010 includes a helical groove 1015 formed on its inner surface. The helical groove 1015 may be a continuous groove formed along the length of the inner tube 1010 and may also form a waveguide. The MCG 1000 may include a dielectric material 1020 on the outer surface of the inner tube 1010. The dielectric material 1020 may include glass, ceramic, porcelain, or plastic, and may be applied as a coating to the outer diameter of the inner tube 1020, or the dielectric material 1020 may be an independent component added to the MCG1000 assembly. The dielectric material 1020 can electrically insulate the outer tube 1005 from the inner tube 1010 and prevent electrical short circuits between them.

[0072] In some embodiments, the MCG1000 may include an inner diameter 1025 measured between protruding portions of the inner tube 1010. The protruding portions may be formed by helical grooves 1015. In some embodiments, the inner diameter 1025 may include diameters of 5.0mm to 15.0mm, 10.0mm to 20.0mm, 15.0mm to 25.0mm, 20.0mm to 30.0mm, 25.0mm to 35.0mm, 30.0mm to 40.0mm, 45.0mm to 55.0mm, 50.0mm to 60.0mm, 55.0mm to 65.0mm, 60.0mm to 70.0mm, 65.0mm to 75.0mm, 70.0mm to 80.0mm, 75.0mm to 90.0mm, or 85.0mm to 200.0mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 1025 may include tolerances such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, but other tolerances are possible.

[0073] Figure 11 is a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide 1100 described herein, which includes an inner tube having a helical groove and an insulating layer between the tube and the coil spring of the multi-piece corrugated waveguide. As shown in Figure 11, the MCG 1100 may include an outer tube 1105, an inner tube 1110, and a helical groove 1115 formed on the inner surface of the inner tube 1110. The MCG 1100 may also include an insulating layer 1120. The insulating layer 1120 may be positioned between the outer tube 1105 and the inner tube 1110. In some embodiments, the insulating layer 1120 may be formed from an insulating material such as glass fiber, open-cell foam, closed-cell foam, polystyrene, ceramic fiber, carbon composite, silica fiber, or rock wool. The insulating material 1120 is positioned between the inner surface of the outer tube 1105 and the outer surface of the inner tube 1110, thereby separating the heat inside the well bore ring 205 from the inner tube 1110. This allows the purge gas from the ground to cool the inner tube 1110 down to the bottom of the borehole without losing its cooling capacity due to interaction with the inner surface of the outer tube 1105 (contact with the hot gas rising through the ring 205).

[0074] In some embodiments, the MCG1100 may include an inner diameter 1125 measured between protruding portions of the inner tube 1110. The protruding portions may be formed by helical grooves 1115. In some embodiments, the inner diameter 1125 may include diameters of 5.0mm to 15.0mm, 10.0mm to 20.0mm, 15.0mm to 25.0mm, 20.0mm to 30.0mm, 25.0mm to 35.0mm, 30.0mm to 40.0mm, 45.0mm to 55.0mm, 50.0mm to 60.0mm, 55.0mm to 65.0mm, 60.0mm to 70.0mm, 65.0mm to 75.0mm, 70.0mm to 80.0mm, 75.0mm to 90.0mm, or 85.0mm to 200.0mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 1125 may include tolerances such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, but other tolerances are possible.

[0075] Figure 12 is a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide 1200 including a tapered tube and a tapered coil spring as described herein. As shown in Figure 12, the MCG 1200 may include a tube 1205 and a coil spring 1210 within the tube 1205. The tube 1205 may be a tapered tube. The tapered tube 1205 may have a first diameter defined between opposing surfaces of the tube 1205 at a first end 1215 of the MCG 1200 and a second diameter defined between opposing surfaces of the tube 1205 at a second end 1220 of the MCG 1200. Thus, the diameter of the tube 1205 can vary from the first end 1215 to the second end 1220. For example, the first diameter of the tube 1205 at the first end 1215 can be smaller than the second diameter of the tube 1205 at the second end 1220. As further shown in Figure 12, the coil spring 1210 can be a tapered coil spring. Similar to the tube 1205, the coil spring 1210 can have a diameter that changes from the first end 1215 to the second end 1220. The tapered coil spring 1210 can be formed using a tapered mandrel as described with respect to Figure 3. The two-piece design can advantageously reduce the machining difficulty of creating the tapered corrugation feature within the tapered tube 1205.

[0076] In some embodiments, the MCG1200 may include an inner diameter 1225 measured between the protruding portions of the inner tube 1210 at the first end 1215 of the MCG1200. In some embodiments, the inner diameter 1225 may include diameters of 5.0mm to 15.0mm, 10.0mm to 20.0mm, 15.0mm to 25.0mm, 20.0mm to 30.0mm, 25.0mm to 35.0mm, 30.0mm to 40.0mm, 45.0mm to 55.0mm, 50.0mm to 60.0mm, 55.0mm to 65.0mm, 60.0mm to 70.0mm, 65.0mm to 75.0mm, 70.0mm to 80.0mm, 75.0mm to 90.0mm, or 85.0mm to 200.0mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 1225 may include tolerances such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, but other tolerances are possible.

[0077] In some embodiments, the MCG1200 may include an inner diameter 1230 measured between the protruding portion of the inner tube 1210 at the second end 1230 of the MCG1200. In some embodiments, the inner diameter 1230 may include diameters of 5.0mm to 15.0mm, 10.0mm to 20.0mm, 15.0mm to 25.0mm, 20.0mm to 30.0mm, 25.0mm to 35.0mm, 30.0mm to 40.0mm, 45.0mm to 55.0mm, 50.0mm to 60.0mm, 55.0mm to 65.0mm, 60.0mm to 70.0mm, 65.0mm to 75.0mm, 70.0mm to 80.0mm, 75.0mm to 90.0mm, or 85.0mm to 200.0mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 1230 may include tolerances such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, but other tolerances are possible.

[0078] Figure 13 is a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide 1300 including a curved tube as described herein. As shown in Figure 13, the MCG 1300 may include a tube 1305 (showing only the inner surface for clarity) and a coil spring 1310 within the tube 1305. The curved tube 1305 can enable the deployment of the MCG 1300 in various borehole configurations that are not predominantly vertical or predominantly horizontal geometry. For example, the MCG 1300 can be used during transitions between vertical and horizontal borehole configurations, or vice versa. The MCG 1300 can be deployed to manipulate or steer electromagnetic waves around subsurface obstacles or geological formations that, otherwise, could limit the transmission efficiency of the transmitted electromagnetic waves. In some embodiments, the tube 1305 may be a bellows tube including a plurality of retractable segments configured to form a curved section within the tube 1305.

[0079] In some embodiments, the coil spring 1310 may include an inner diameter 1315 measured between the protruding portions of each coil element of the coil spring 1310. In some embodiments, the inner diameter 1315 may include diameters of 5.0 mm to 15.0 mm, 10.0 mm to 20.0 mm, 15.0 mm to 25.0 mm, 20.0 mm to 30.0 mm, 25.0 mm to 35.0 mm, 30.0 mm to 40.0 mm, 45.0 mm to 55.0 mm, 50.0 mm to 60.0 mm, 55.0 mm to 65.0 mm, 60.0 mm to 70.0 mm, 65.0 mm to 75.0 mm, 70.0 mm to 80.0 mm, 75.0 mm to 90.0 mm, or 85.0 mm to 200.0 mm. In some embodiments, the diameter may be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 1315 may include tolerances such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, but other tolerances are possible.

[0080] Figures 14A and 14B show cross-sectional views of exemplary embodiments of a multi-piece corrugated waveguide 1400, including a casing into which a tube and coil spring described herein can extend. The MCG 1400 may include a tube 1405, a coil spring 1410 within the tube 1405, and a casing 1415. As shown in Figure 14A, the MCG 1400 is shown in a retracted position. The tube 1405 and coil spring 1410 are retracted into the casing 1415. In Figure 14B, the MCG 1400 is shown in an extended position. In Figure 14B, the tube 1405 and coil spring 1410 extend from within the casing 1415. In this way, the tube 1405 and coil spring 1410 can be retracted in a nested manner within the casing 1415 and extend from there. By placing the coil spring 1410 over the length of the casing 1415 and the tube 1505, millimeter waves can be contained regardless of the position or bending angle of the MCG 1400. Furthermore, since the spring 1405 is a one-piece unit, there is no step between the inner diameter of the casing 1415 and the inner diameter of the tube 1405. This eliminates the millimeter wave power loss that can be associated with abrupt diameter changes.

[0081] In some embodiments, the coil spring 1410 may include an inner diameter 1420 measured between the protruding portions of each coil element of the coil spring 1410. In some embodiments, the inner diameter 1420 may include diameters of 5.0 mm to 15.0 mm, 10.0 mm to 20.0 mm, 15.0 mm to 25.0 mm, 20.0 mm to 30.0 mm, 25.0 mm to 35.0 mm, 30.0 mm to 40.0 mm, 45.0 mm to 55.0 mm, 50.0 mm to 60.0 mm, 55.0 mm to 65.0 mm, 60.0 mm to 70.0 mm, 65.0 mm to 75.0 mm, 70.0 mm to 80.0 mm, 75.0 mm to 90.0 mm, or 85.0 mm to 200.0 mm. In some embodiments, the diameter may be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 1420 may include tolerances such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, but other tolerances are possible.

[0082] Figure 15 shows an exemplary embodiment for manufacturing a coiled tube product for use in the multi-piece corrugated waveguide described herein. In some embodiments, the multi-piece corrugated waveguide can be formed from a continuous tube, a coiled tube product, or a pipe tube product. The continuous tube and the coiled tube product or pipe tube product can be formed from sheet metal in long strips. The long strips of metal can be configured on reels. The metal strips can be welded together at the ends of the metal strips and then wound via rollers to form a tube. The tubes can then be welded closed to form tubes of extremely long continuous lengths, such as tubes longer than 10 km. In embodiments including continuous tubes, coiled tube products, or pipe tube products, the length of the tube can be longer than 10 km.

[0083] In some embodiments, corrugated features such as ridges and / or grooves can be rolled or punched into a strip of sheet metal. Thus, when the coil tube is formed from the strip of sheet metal, the corrugated features are provided on the inner surface of the coil tube. In this way, the first tube can be formed to include pre-configured corrugated features on its inner surface. The first tube can then be inserted into the second tube to form a multi-piece corrugated waveguide as described in the embodiments herein.

[0084] As shown in Figure 15, a long strip of stock metal 1505 can be brought into contact with a roller 1510. The roller 1510 may include grooves and ridges that can form corrugation features 1515 on the strip of metal. The corrugation features 1515 can be formed on the surface of the metal material 1505 that can correspond to the inner surface of the tube to be formed. The metal material 1505 can be conveyed through one or more shaping rollers 1520 to deform the metal material 1505 into a tube 1525. The tube 1525 may have an open seam where the opposing edges of the metal material 1505 are close to each other. The seam can be welded via a welding device 1530 to form a fully closed tube or pipe 1535 including the corrugation features 1515.

[0085] Figure 16 shows an exemplary embodiment for manufacturing a multi-piece corrugated waveguide including a coil tube product as described herein. For example, a long strip of metal material 1605 can be received in one or more shaping rollers 1610. While the metal material is being formed by the shaping rollers 1610, a coil spring 1615 or a previously formed coil tube product 1615 can be fitted into a portion of the metal material 1605. In some embodiments, the coil tube product 1615 can be formed as described with respect to Figure 15. Once fitted, the metal material 1605 can be fully formed into a tube and welded closed. The resulting tube 1620 can contain the coil spring 1615 or coil tube product 1615 and provide the corrugation features described herein. In some embodiments, the coil spring or coil tube product 1605 can be fitted before the tube is fully enclosed and welded closed. In some embodiments, the coil spring or coil tube product 1615 can be fitted into the coil tube when the tube is being formed and welded closed.

[0086] Figures 17A to 17G show exemplary embodiments of coil springs included in the multi-piece corrugated waveguide described herein. The coil springs shown in Figures 17A to 17G can correspond to the coil springs described in the embodiments herein and may include embodiments of coil springs configured as compression springs or tension springs. In some embodiments, a combination of compression and tension coil springs can be used in the waveguide described herein.

[0087] As shown in Figure 17A, one embodiment of a compression coil spring having a length of 1705 is shown. The coil spring may include an inner diameter of 1710 and a width of 1715. In some embodiments, the inner diameter 1710 may include diameters of 5.0 mm to 15.0 mm, 10.0 mm to 20.0 mm, 15.0 mm to 25.0 mm, 20.0 mm to 30.0 mm, 25.0 mm to 35.0 mm, 30.0 mm to 40.0 mm, 45.0 mm to 55.0 mm, 50.0 mm to 60.0 mm, 55.0 mm to 65.0 mm, 60.0 mm to 70.0 mm, 65.0 mm to 75.0 mm, 70.0 mm to 80.0 mm, 75.0 mm to 90.0 mm, or 85.0 mm to 200.0 mm. In some embodiments, the diameter can be greater than 200.0 mm or less than 5.0 mm. Other diameters are possible. In some embodiments, the inner diameter 1710 may include tolerances such as ±0.075 mm, ±0.1 mm, ±0.125 mm, ±0.150 mm, ±0.175 mm, ±0.2 mm, ±0.225 mm, or ±0.25 mm, but other tolerances are possible.

[0088] In some embodiments, the width 1715 can be dimensionally set to be shorter than the wavelength of the electromagnetic waves provided through the MCG described herein. For example, the width 1715 can be shorter than the wavelength of the millimeter electromagnetic waves injected into the borehole of the well. In some embodiments, the width 1715 can be 1 / 3 to 1 / 4 of the frequency of the RF signal transmitted in the MCG described herein. The width 1715 of the coil can correspond to the pitch and corrugation features of the spring formed in the MCG described herein.

[0089] The coil element 1720 of a coil spring can be defined as one rotation (e.g., 360 degrees) of the coil spring when measured along the circumference of the coil spring. Multiple coil elements 1720 can form a coil spring having a length 1705. The coil spring may include a space 1725 between two or more coil elements 1720. For example, the space 1725 may be wider than the frequency of the electromagnetic waves injected into the MCG described herein, but the spring may be configured to compress so that the space 1725 is reduced to at least 1 / 10 of the frequency of the injected electromagnetic waves to prevent leakage of electromagnetic waves. In some embodiments, the space 1715 may be 0.1–0.2 mm, 0.15–0.25 mm, 0.3–0.4 mm, 0.35–0.45 mm, or 0.5–0.6 mm. In some embodiments, the space may be greater than 0.6 mm or less than 0.1 mm. Other space sizes may be included.

[0090] In some embodiments, a coil spring and a plurality of coil elements 1720 may include a pitch 1730 between the coil elements 1720. The pitch can be measured from the center point of a first coil element to the center point of a second coil element adjacent to the first coil element. In some embodiments, the pitch 1730 can be sized to be one-third of the wavelength of the electromagnetic waves provided through the MCG described herein. For example, the pitch 1730 can be one-third of the wavelength of the millimeter electromagnetic waves injected into the borehole of the well. For example, the pitch can be between 0.3 mm and 7.0 mm.

[0091] Figures 17B to 17G show additional exemplary embodiments of coil springs for use with the MCG embodiments described herein. Any and all of the coil springs shown in Figures 17B to 17G may have the coil spring diameter, coil element width, pitch between coil elements, and space between coil elements, as shown and described with respect to the coil springs shown in Figure 17A. For example, Figure 17B shows a tension spring. The tension spring may be coated with material 1735 such as a conductive material. The spring may also be coated with a highly conductive metallic material such as gold, platinum, copper, or aluminum, which can optimize transmission efficiency. The tension spring may include a first coupling portion at a first end and a second coupling portion at a second end. A compression coil spring is shown as shown in Figure 17C. The compression spring may include a first coupling portion at a first end and a second coupling portion at a second end.

[0092] As shown in Figure 17D, in some embodiments, the coil spring may include a tapered coil spring. The tapered coil spring may include a diameter that changes along the length of the coil spring. As shown in Figure 17E, in some embodiments, the coil spring may include multiple tapered portions. In the embodiment shown in Figure 17E, the coil spring has an upper tapered portion and a lower tapered portion, with a non-tapered portion between the upper tapered portion and the lower tapered portion.

[0093] As shown in Figure 17F, in some embodiments, the coil spring may include a tapered portion having a larger diameter than the non-tapered portion between the upper tapered portion and the lower tapered portion. As shown in Figure 17G, in some embodiments, the coil spring may include multiple pitch configurations between the coil elements at two or more locations along the length of the coil spring. For example, the coil spring may include a first pitch 1740 and a second pitch 1750. The first pitch 1740 may be smaller than the second pitch 1750. In some embodiments, the first pitch may be larger than the second pitch. Similarly, in some embodiments, the coil spring may have a first space 1745 between the first plurality of coil elements and a second space 1755 between the second plurality of coil elements.

[0094] Figures 18A to 18E show exemplary embodiments of the cross-sectional shapes of multiple coil elements included in the multi-piece guide described herein. The cross-sectional shapes of multiple coil elements included in the coil spring described herein can be formed according to work 310 in Figure 3. As shown in Figure 18A, in some embodiments, the multiple coil elements may include a rectangular cross-sectional shape. As shown in Figure 18B, in some embodiments, the multiple coil elements may include an elliptical cross-sectional shape. As shown in Figure 18C, in some embodiments, the multiple coil elements may include an oval cross-sectional shape. As shown in Figure 18D, in some embodiments, the multiple coil elements may include a circular cross-sectional shape. As shown in Figure 18E, in some embodiments, the multiple coil elements may include a trapezoidal cross-sectional shape. In some embodiments, the multiple coil elements may include a square, triangular, or polygonal shape. Although the cross-sectional shapes shown in Figures 18A to 18E are described in the context of multiple cross-sectional shapes of coil elements, the cross-sectional shapes shown in Figures 18A to 18E may also correspond to the cross-sectional shapes of the mandrel used to form the multiple coil elements.

[0095] Figures 19A to 25B show various embodiments of the cross-sectional shape of the coil element. The cross-sectional shape can be formed as shown in operation 305 of Figure 3. The wires forming the coil spring and the coil elements of the coil spring can be extruded to have the cross-sectional shapes shown in Figures 19A to 25B. Various cross-sectional shapes can be formed in this way and can be configured for use in various embodiments of the MCG described herein. For example, in some embodiments, the cross-sectional shape may include triangular or pointed cross-sectional shapes in addition to the cross-sectional shapes shown in Figures 19A to 25B. Other cross-sectional shapes are possible.

[0096] Figure 19A shows an exemplary embodiment of the square cross-sectional shape of a protruding portion of a coil element of a multi-piece corrugated waveguide described herein. As shown in Figure 19A, the coil element 1900 may include a base portion 1905 and a protruding portion 1925 extending from the base portion 1905. The base portion 1905 may include a height 1910, a width 1915, and a back surface 1920. The base portion 1905 is shown with a rectangular shape, but additional base portion shapes can be implemented. Similarly, the back surface 1920 is shown with a flat back surface, but additional back surface shapes or shapes can be implemented. In some embodiments, the height 1910 can include heights of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 1.0mm, 2.0mm to 5.0mm, 4mm to 8mm, 6mm to 10mm, or 12mm to 15mm. In some embodiments, the height can be greater than 15mm or less than 0.2mm. Other heights are possible.

[0097] As shown in Figure 19A, the coil element 1900 may include a protruding portion 1925 extending from the base portion 1905. The protruding portion 1925 may include a square shape as shown in Figure 19A, but other shapes can be implemented. The protruding portion 1925 may include a height 1930, a width 1935, and an offset 1940. In some embodiments, the height 1930 may include heights of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, or 0.6mm to 1.0mm. In some embodiments, the height may be greater than 1.0mm or less than 0.2mm. Other heights are possible. In some embodiments, the height 1930 may include tolerances such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, but other tolerances are possible.

[0098] In some embodiments, the width 1935 may include widths of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 0.8mm, 0.7mm to 0.9mm, or 0.8mm to 1.0mm. In some embodiments, the width may be greater than 1.0mm or less than 0.2mm. Other widths are possible. In some embodiments, the width 1935 may include tolerances such as ±0.050mm, ±0.060mm, ±0.070mm, ±0.080mm, or ±0.090mm, but other tolerances are possible.

[0099] In some embodiments, the offset 1940 may include offsets of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 0.8mm, 0.7mm to 0.9mm, or 0.8mm to 1.0mm. In some embodiments, the offset may be greater than 1.0mm or less than 0.2mm. Other offsets are possible. In some embodiments, the offset 1940 may include tolerances such as ±0.050mm, ±0.060mm, ±0.070mm, ±0.080mm, or ±0.090mm, but other tolerances are possible.

[0100] Figure 19B shows an exemplary embodiment of a plurality of coil elements, each of which a coil element described herein includes a square cross-sectional outline of a protruding portion. As shown in Figure 19B, the plurality of coil elements 1945 can be formed such that each coil element (e.g., coil elements 1900A to 1900C) has the same cross-sectional outline and dimensions as those described with respect to the coil elements shown in Figure 19A. The plurality of coil elements 1945 can include a space 1950 between adjacent protruding portions 1925 of adjacent coil elements. In some embodiments, the space 1950 can be sized to be 1 / 4 of the wavelength of the electromagnetic waves provided through the MCG described herein. For example, the space 1950 can be 1 / 6 of the wavelength of the millimeter electromagnetic waves injected into the borehole of the well. As further shown in Figure 19B, the plurality of coil elements 1945 can include a pitch 1955. The pitch 1955 can be sized to be 1 / 3 of the wavelength of the electromagnetic waves provided through the MCG described herein. For example, a pitch of 1955 can be one-third the wavelength of the millimeter electromagnetic waves injected into the borehole of the well. Other dimensions can also be implemented.

[0101] Figure 20A shows an exemplary embodiment of the trapezoidal cross-sectional shape of a projecting portion of a coil element of a multi-piece corrugated waveguide described herein. As shown in Figure 20A, the coil element 2000 may include a base portion 2005 and a projecting portion 2025 extending from the base portion 2005. The base portion 2005 may include a height 2010, a width 2015, and a back surface 2020. The base portion 2005 is shown with a rectangular shape, but additional base portion shapes can be implemented. Similarly, the back surface 2020 is shown with a flat back surface, but additional back surface shapes or shapes can be implemented. In some embodiments, the height 2010 can include heights of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 1.0mm, 2.0mm to 5.0mm, 4mm to 8mm, 6mm to 10mm, or 12mm to 15mm. In some embodiments, the height can be greater than 15mm or less than 0.2mm. Other heights are possible.

[0102] As shown in Figure 20A, the coil element 2000 may include a protruding portion 2025 extending from the base portion 2005. The protruding portion 2025 may include a trapezoidal shape as shown in Figure 20A, but other shapes can be implemented. The protruding portion 2025 may include a height 2030, a width 2035, and an offset 2040. In some embodiments, the height 2030 may include heights of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, or 0.6mm to 1.0mm. In some embodiments, the height may be greater than 1.0mm or less than 0.2mm. Other heights are possible. In some embodiments, the height 2030 may include tolerances such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, but other tolerances are possible.

[0103] In some embodiments, the width 2035 may include widths of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 0.8mm, 0.7mm to 0.9mm, or 0.8mm to 1.0mm. In some embodiments, the width may be greater than 1.0mm or less than 0.2mm. Other widths are possible. In some embodiments, the width 2035 may include tolerances such as ±0.010mm, ±0.020mm, ±0.030mm, ±0.040mm, or ±0.050mm, but other tolerances are possible.

[0104] In some embodiments, the offset 2040 may include offsets of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 0.8mm, 0.7mm to 0.9mm, or 0.8mm to 1.0mm. In some embodiments, the offset may be greater than 1.0mm or less than 0.2mm. Other offsets are possible. In some embodiments, the offset 2040 may include tolerances such as ±0.010mm, ±0.020mm, ±0.030mm, ±0.040mm, or ±0.050mm, but other tolerances are possible.

[0105] In some embodiments, the protruding portion 2025 may include an angle 2060 formed with respect to the surface of the base portion 2005 on which the protruding portion 2025 extends. In some embodiments, the angle 2060 may be 0 to 3.0 degrees, 1.5 to 5.0 degrees, 4.0 to 6.0 degrees, 5.5 to 7.0 degrees, 6.0 to 8.0 degrees, 7.5 to 9.0 degrees, 8.0 to 10.0 degrees, 9.0 to 12.0 degrees, 11.0 to 13.0 degrees, or 12.0 to 15.0 degrees, but other angles are possible. In some embodiments, the angle may be greater than 15 degrees. Other angles are possible.

[0106] Figure 20B shows an exemplary embodiment of a plurality of coil elements, each of which coil elements described herein includes a trapezoidal cross-sectional shape of the protruding portion. As shown in Figure 20B, the plurality of coil elements 2045 can be formed such that each coil element (e.g., coil elements 2000A to 2000C) has the same cross-sectional shape and dimensions as those described with respect to the coil elements shown in Figure 20A. The plurality of coil elements 2045 can include a space 2050 between adjacent protruding portions 2025 of adjacent coil elements. In some embodiments, the space 2050 can be sized to be 1 / 6 of the wavelength of the electromagnetic waves provided through the MCG described herein. For example, the space 2050 can be 1 / 6 of the wavelength of the millimeter electromagnetic waves injected into the borehole of the well. As further shown in Figure 20B, the plurality of coil elements 2045 can include a pitch 2055. The pitch 2055 can be sized to be 1 / 3 of the wavelength of the electromagnetic waves provided through the MCG described herein. For example, a pitch of 2055 can be one-third the wavelength of the millimeter electromagnetic waves injected into the borehole of the well. Other dimensions can also be implemented.

[0107] Figure 21A shows another exemplary embodiment of the trapezoidal cross-sectional shape of the projection portion of a coil element of a multi-piece corrugated waveguide described herein. As shown in Figure 21A, the coil element 2100 may include a base portion 2105 and a projection portion 2125 extending from the base portion 2105. The base portion 2105 may include a height 2110, a width 2115, and a back surface 2120. The base portion 2105 is shown with a rectangular shape, but additional base portion shapes can be implemented. Similarly, the back surface 2120 is shown with a flat back surface, but additional back surface shapes or shapes can be implemented. In some embodiments, the height 2110 can include heights of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 1.0mm, 2.0mm to 5.0mm, 4mm to 8mm, 6mm to 10mm, or 12mm to 15mm. In some embodiments, the height can be greater than 15mm or less than 0.2mm. Other heights are possible.

[0108] As shown in Figure 21A, the coil element 2100 may include a protruding portion 2125 extending from the base portion 2105. The protruding portion 2125 may have a trapezoidal shape as shown in Figure 21A, but other shapes can be implemented. The protruding portion 2125 may include a height 2130, an offset 2135, and a width 2140. In some embodiments, the offset 2135 may be the same or different on both sides of the protruding portion 2125. In some embodiments, the height 2130 may include heights of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, or 0.6mm to 1.0mm. In some embodiments, the height may be greater than 1.0mm or less than 0.2mm. Other heights are possible. In some embodiments, the height 2130 may include tolerances such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, but other tolerances are possible.

[0109] In some embodiments, the offset 2135 may include offsets of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 0.8mm, 0.7mm to 0.9mm, or 0.8mm to 1.0mm. In some embodiments, the offset may be greater than 1.0mm or less than 0.2mm. Other offsets are possible. In some embodiments, the offset 2135 may include tolerances such as ±0.010mm, ±0.020mm, ±0.030mm, ±0.040mm, or ±0.050mm, but other tolerances are possible.

[0110] In some embodiments, the width 2140 may include widths of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 0.8mm, 0.7mm to 0.9mm, or 0.8mm to 1.0mm. In some embodiments, the width may be greater than 1.0mm or less than 0.2mm. Other widths are possible. In some embodiments, the width 2140 may include tolerances such as ±0.010mm, ±0.020mm, ±0.030mm, ±0.040mm, or ±0.050mm, but other tolerances are possible.

[0111] In some embodiments, the projection 2125 may include an angle 2160 formed with respect to the surface of the base portion 2105 on which the projection 2125 extends. In some embodiments, the angle 2160 may be 0–3.0 degrees, 1.5–5.0 degrees, 4.0–6.0 degrees, 5.5–7.0 degrees, 6.0–8.0 degrees, 7.5–9.0 degrees, 8.0–10.0 degrees, 9.0–12.0 degrees, 11.0–13.0 degrees, or 12.0–15.0 degrees, but other angles are possible. In some embodiments, the angle may be greater than 15 degrees. In some embodiments, the angle 2160 may be the same on both sides of the projection 2125. In some embodiments, the angle 2160 on one side of the projection 2125 may be different from the angle 2160 on the opposite side of the projection 2125.

[0112] Figure 21B shows another exemplary embodiment of a plurality of coil elements, in which each coil element described herein includes a trapezoidal cross-sectional shape of the protruding portion. As shown in Figure 21B, the plurality of coil elements 2145 can be formed such that each coil element (e.g., coil elements 2100A to 2100C) has the same cross-sectional shape and dimensions as those described with respect to the coil elements shown in Figure 21A. The plurality of coil elements 2145 can include a space 2150 between adjacent protruding portions 2125 of adjacent coil elements. In some embodiments, the space 2150 can be sized to be 1 / 6 of the wavelength of the electromagnetic waves provided through the MCG described herein. For example, the space 2150 can be 1 / 6 of the wavelength of the millimeter electromagnetic waves injected into the borehole of the well. As further shown in Figure 21B, the plurality of coil elements 2145 can include a pitch 2155. The pitch 2155 can be sized to be 1 / 3 of the wavelength of the electromagnetic waves provided through the MCG described herein. For example, a pitch of 2155 can be one-third the wavelength of the millimeter electromagnetic waves injected into the borehole of the well. Other dimensions can also be implemented.

[0113] Figure 22A shows an exemplary embodiment of the rectangular cross-sectional shape of a protruding portion of a coil element of a multi-piece corrugated waveguide described herein. As shown in Figure 22A, the coil element 2200 may include a base portion 2205 and a protruding portion 2225 extending from the base portion 2205. The base portion 2205 may include a height 2210, a width 2215, and a back surface 2220. The base portion 2205 is shown with a rectangular shape, but additional base portion shapes can be implemented. Similarly, the back surface 2220 is shown with a flat back surface, but additional back surface shapes or shapes can be implemented. In some embodiments, the height 2210 can include heights of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 1.0mm, 2.0mm to 5.0mm, 4mm to 8mm, 6mm to 10mm, or 12mm to 15mm. In some embodiments, the height can be greater than 15mm or less than 0.2mm. Other heights are possible.

[0114] As shown in Figure 22A, the coil element 2200 may include a protruding portion 2225 extending from the base portion 2205. The protruding portion 2225 may have a rectangular shape as shown in Figure 22A, but other shapes can be implemented. The protruding portion 2225 may include a height 2230, an offset 2235, and a width 2240. In some embodiments, the offset 2235 may be the same or different on both sides of the protruding portion 2225.

[0115] In some embodiments, the height 2230 can be greater than or less than 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, or 0.6mm to 1.0mm, but other heights are possible. In some embodiments, the height 2230 can include tolerances such as ±0.010mm, ±0.020mm, ±0.030mm, ±0.040mm, or ±0.050mm, but other tolerances are possible.

[0116] In some embodiments, the offset 2235 may include offsets of 0.05mm to 0.1mm, 0.075mm to 0.15mm, 0.1mm to 0.15mm, 0.125mm to 0.175mm, 0.15mm to 0.2mm, 0.175mm to 0.25mm, 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, or 0.6mm to 1.0mm. In some embodiments, the offset may be greater than 1.0mm or less than 0.2mm. Other offsets are possible. In some embodiments, the offset 2235 may include tolerances such as ±0.010mm, ±0.020mm, ±0.030mm, ±0.040mm, or ±0.050mm, but other tolerances are possible. In some embodiments, the offset 2235 can be the same on both sides of the protruding portion 2225. In some embodiments, the offset 2235 on one side of the protruding portion 2225 may be different from the offset 2235 on the opposite side of the protruding portion 2225.

[0117] In some embodiments, the width 2240 may include widths of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 0.8mm, 0.7mm to 0.9mm, or 0.8mm to 1.0mm. In some embodiments, the width may be greater than 1.0mm or less than 0.2mm. Other widths are possible. In some embodiments, the width 2240 may include tolerances such as ±0.010mm, ±0.020mm, ±0.030mm, ±0.040mm, or ±0.050mm, but other tolerances are possible.

[0118] Figure 22B shows an exemplary embodiment of a plurality of coil elements, each of which coil elements described herein includes a rectangular cross-sectional outline of a protruding portion. As shown in Figure 22B, the plurality of coil elements 2245 can be formed such that each coil element (e.g., coil elements 2200A to 2200C) has the same cross-sectional outline and dimensions as those described with respect to the coil elements shown in Figure 22A. The plurality of coil elements 2245 can include spaces 2250 between adjacent protruding portions 2225 of adjacent coil elements. In some embodiments, the spaces 2250 can be sized to be 1 / 6 of the wavelength of electromagnetic waves provided through the MCG described herein. For example, the spaces 2250 can be 1 / 6 of the wavelength of millimeter electromagnetic waves injected into the borehole of a well. As further shown in Figure 22B, the plurality of coil elements 2245 can include a pitch 2255. The pitch 2255 can be sized to be 1 / 3 of the wavelength of electromagnetic waves provided through the MCG described herein. For example, a pitch of 2255 can be one-third the wavelength of the millimeter electromagnetic waves injected into the borehole of the well. Other dimensions can also be implemented.

[0119] Figure 23A shows an exemplary embodiment of the circular cross-sectional shape of a protruding portion of a coil element of a multi-piece corrugated waveguide described herein. As shown in Figure 23A, the coil element 2300 may include a base portion 2305 and a protruding portion 2325 extending from the base portion 2305. The base portion 2305 may include a height 2310, a width 2315, and a back surface 2320. The base portion 2305 is shown with a rectangular shape, but additional base portion shapes can be implemented. Similarly, the back surface 2320 is shown with a flat back surface, but additional back surface shapes or shapes can be implemented. In some embodiments, the height 2310 can include heights of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 1.0mm, 2.0mm to 5.0mm, 4mm to 8mm, 6mm to 10mm, or 12mm to 15mm. In some embodiments, the height can be greater than 15mm or less than 0.2mm. Other heights are possible.

[0120] As shown in Figure 23A, the coil element 2300 may include a protruding portion 2325 extending from the base portion 2305. The protruding portion 2325 may have a circular shape as shown in Figure 23A, but other shapes can be implemented. The protruding portion 2325 may include a height 2330, an offset 2335, and a width 2340. In some embodiments, the offset 2335 may be the same or different on both sides of the protruding portion 2325.

[0121] In some embodiments, the height 2330 may include heights of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, or 0.6mm to 1.0mm. In some embodiments, the height may be greater than 1.0mm or less than 0.2mm. Other heights are possible. In some embodiments, the height 2330 may include tolerances such as ±0.010mm, ±0.020mm, ±0.030mm, ±0.040mm, or ±0.050mm, but other tolerances are possible.

[0122] In some embodiments, the offset 2335 may include offsets of 0.05mm to 0.1mm, 0.075mm to 0.15mm, 0.1mm to 0.15mm, 0.125mm to 0.175mm, 0.15mm to 0.2mm, 0.175mm to 0.25mm, 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, or 0.6mm to 1.0mm. In some embodiments, the offset may be greater than 1.0mm or less than 0.2mm. Other offsets are possible. In some embodiments, the offset 2335 may include tolerances such as ±0.010mm, ±0.020mm, ±0.030mm, ±0.040mm, or ±0.050mm, but other tolerances are possible. In some embodiments, the offset 2335 can be the same on both sides of the protruding portion 2325. In some embodiments, the offset 2335 on one side of the protruding portion 2325 may be different from the offset 2335 on the opposite side of the protruding portion 2325.

[0123] In some embodiments, the width 2340 may include widths of 0.2 to 0.4 mm, 0.3 to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, 0.6 mm to 0.8 mm, 0.7 mm to 0.9 mm, or 0.8 mm to 1.0 mm. In some embodiments, the width may be greater than 1.0 mm or less than 0.2 mm. Other widths are possible. In some embodiments, the width 2340 may include tolerances such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, but other tolerances are possible.

[0124] Figure 23B shows an exemplary embodiment of a plurality of coil elements, each of which coil elements described herein includes a circular cross-sectional shape of the protruding portion. As shown in Figure 23B, the plurality of coil elements 2345 can be formed such that each coil element (e.g., coil elements 2300A to 2300C) has the same cross-sectional shape and dimensions as those described with respect to the coil elements shown in Figure 23A. The plurality of coil elements 2345 can include a space 2350 between adjacent protruding portions 2325 of adjacent coil elements. In some embodiments, the space 2350 can be sized to be 1 / 6 of the wavelength of the electromagnetic waves provided through the MCG described herein. For example, the space 2350 can be 1 / 6 of the wavelength of the millimeter electromagnetic waves injected into the borehole of the well. As further shown in Figure 23B, the plurality of coil elements 2345 can include a pitch 2355. The pitch 2355 can be sized to be 1 / 3 of the wavelength of the electromagnetic waves provided through the MCG described herein. For example, a pitch of 2355 can be one-third the wavelength of the millimeter electromagnetic waves injected into the borehole of the well. Other dimensions can also be implemented.

[0125] Figure 24A shows an exemplary embodiment of the sinusoidal cross-sectional shape of a protruding portion of a coil element of a multi-piece corrugated waveguide described herein. As shown in Figure 24A, the coil element 2400 may include a base portion 2405 and a protruding portion 2425 extending from the base portion 2405. The base portion 2405 may include a height 2410, a width 2415, and a back surface 2420. The base portion 2405 is shown with a rectangular shape, but additional base portion shapes can be implemented. Similarly, the back surface 2420 is shown with a flat back surface, but additional back surface shapes or shapes can be implemented. In some embodiments, the height 2410 can include heights of 0.2–0.4 mm, 0.3–0.5 mm, 0.4 mm–0.6 mm, 0.5 mm–0.7 mm, 0.6 mm–1.0 mm, 2.0 mm–5.0 mm, 4 mm–8 mm, 6 mm–10 mm, or 12 mm–15 mm. In some embodiments, the height can be greater than 15 mm or less than 0.2 mm. Other heights are possible.

[0126] As shown in Figure 24A, the coil element 2400 may include a protruding portion 2425 extending from the base portion 2405. The protruding portion 2425 may include a symmetrical sinusoidal shape as shown in Figure 24A, but other sinusoidal shapes can be implemented. In some embodiments, the protruding portion 2425 may have an angular shape, such as a triangular shape. In some embodiments, multiple protruding portions 2425 may extend from the base portion, and each protruding portion may have the same or different shape. The protruding portion 2425 may include a height 2430, an offset 2435, and a width 2440. In some embodiments, the protruding portion 2425 may be positioned between two offsets 2435.

[0127] In some embodiments, the height 2430 may include heights of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, or 0.6mm to 1.0mm. In some embodiments, the height may be greater than 1.0mm or less than 0.2mm. Other heights are possible. In some embodiments, the height 2430 may include tolerances such as ±0.010mm, ±0.020mm, ±0.030mm, ±0.040mm, or ±0.050mm, but other tolerances are possible.

[0128] In some embodiments, the offset 2435 may include offsets of 0.05mm to 0.1mm, 0.075mm to 0.15mm, 0.1mm to 0.15mm, 0.125mm to 0.175mm, 0.15mm to 0.2mm, 0.175mm to 0.25mm, 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, or 0.6mm to 1.0mm. In some embodiments, the offset may be greater than 1.0mm or less than 0.2mm. Other offsets are possible. In some embodiments, the offset 2435 may include tolerances such as ±0.010mm, ±0.020mm, ±0.030mm, ±0.040mm, or ±0.050mm, but other tolerances are possible. In some embodiments, the offset 2435 can be the same on both sides of the protruding portion 2425. In some embodiments, the offset 2435 on one side of the protruding portion 2425 may be different from the offset 2435 on the opposite side of the protruding portion 2425.

[0129] In some embodiments, the width 2440 may include widths of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 0.8mm, 0.7mm to 0.9mm, or 0.8mm to 1.0mm. In some embodiments, the width may be greater than 1.0mm or less than 0.2mm. Other widths are possible. In some embodiments, the width 2440 may include tolerances such as ±0.010mm, ±0.020mm, ±0.030mm, ±0.040mm, or ±0.050mm, but other tolerances are possible.

[0130] Figure 24B shows an exemplary embodiment of a plurality of coil elements, each of which a coil element described herein includes a sinusoidal cross-sectional shape of a protruding portion. As shown in Figure 24B, the plurality of coil elements 2445 can be formed such that each coil element (e.g., coil elements 2400A to 2400C) has the same cross-sectional shape and dimensions as those described with respect to the coil elements shown in Figure 24A. The plurality of coil elements 2445 can include a space 2450 between adjacent protruding portions 2425 of adjacent coil elements. In some embodiments, the space 2450 can be sized to be 1 / 6 of the wavelength of the electromagnetic waves provided through the MCG described herein. For example, the space 2450 can be 1 / 6 of the wavelength of the millimeter electromagnetic waves injected into the borehole of the well. As further shown in Figure 24B, the plurality of coil elements 2445 can include a pitch 2455. The pitch 2455 can be sized to be 1 / 3 of the wavelength of the electromagnetic waves provided through the MCG described herein. For example, a pitch of 2455 can be one-third the wavelength of the millimeter electromagnetic waves injected into the borehole of the well. Other dimensions can also be implemented.

[0131] Figure 25A shows an exemplary embodiment of a projecting portion of a coil element, including a plurality of cross-sectional shapes described herein. As shown in Figure 25A, the coil element 2500 may include a base portion 2505 and a projecting portion 2525 extending from the base portion 2505. The base portion 2505 may include a height 2510, a width 2515, and a back surface 2520. The base portion 2505 is shown with a rectangular outline, but additional base portion outlines can be implemented. Similarly, the back surface 2520 is shown with a flat back surface, but additional back surface shapes or outlines can be implemented. In some embodiments, the height 2510 and / or back surface 2520 can include heights of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 1.0mm, 2.0mm to 5.0mm, 4mm to 8mm, 6mm to 10mm, or 12mm to 15mm. In some embodiments, the height can be greater than 15mm or less than 0.2mm. Other heights are possible.

[0132] As shown in Figure 25A, the coil element 2500 may include a plurality of protruding portions 2525 extending from the base portion 2505. Each protruding portion 2525 may have a rectangular shape as shown in Figure 25A, but other shapes can be implemented. In some embodiments, each of the plurality of protruding portions 2525 may have the same shape as shown in Figure 25A. In some embodiments, one or more of the protruding portions 2525 may have a shape that is shaped differently from the shape of the other protruding portions 2525. A protruding portion 2525 may include a height 2530, a width 2535, an offset 2540, and a combined protruding portion width 2545. In some embodiments, the height 2530 may include heights of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, or 0.6mm to 1.0mm. In some embodiments, the height can be greater than 1.0 mm or less than 0.2 mm. Other heights are possible. In some embodiments, the height 2530 may include tolerances such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, but other tolerances are possible. In some embodiments, the height 2530 may be the same as or different from adjacent or non-adjacent protruding portions 2525.

[0133] In some embodiments, the width 2535 may include widths of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 0.8mm, 0.7mm to 0.9mm, or 0.8mm to 1.0mm. In some embodiments, the width may be greater than 1.0mm or less than 0.2mm. Other widths are possible. In some embodiments, the width 2535 may include tolerances such as ±0.010mm, ±0.020mm, ±0.030mm, ±0.040mm, or ±0.050mm, but other tolerances are possible. In some embodiments, the width 2535 may be the same as or different from adjacent or non-adjacent protruding portions 2525.

[0134] In some embodiments, the offset 2540 may include offsets of 0.05 to 0.1 mm, 0.075 to 0.15 mm, 0.1 mm to 0.15 mm, 0.125 mm to 0.175 mm, 0.15 mm to 0.2 mm, 0.175 mm to 0.25 mm, 0.2 mm to 0.4 mm, 0.3 mm to 0.5 mm, 0.4 mm to 0.6 mm, 0.5 mm to 0.7 mm, or 0.6 mm to 1.0 mm. In some embodiments, the offset may be greater than 1.0 mm or less than 0.2 mm. Other offsets are possible. In some embodiments, the offset 2540 may include tolerances such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, but other tolerances are possible. In some embodiments, the offset 2540 can be the same on both sides of the protruding portion 2525. In some embodiments, the offset 2540 on one side of the protruding portion 2525 may be different from the offset 2540 on the opposite side of the protruding portion 2525. In some embodiments, the offset 2540 may be the same or different for non-adjacent protruding portions 2525.

[0135] In some embodiments, the width 2545 of the combined protrusions can include widths of 0.2mm to 0.4mm, 0.3mm to 0.5mm, 0.4mm to 0.6mm, 0.5mm to 0.7mm, 0.6mm to 0.8mm, 0.7mm to 0.9mm, 0.8mm to 1.0mm, 0.9mm to 2.0mm, 1.5mm to 3.0mm, 2.5mm to 5.0mm, 4.0mm to 8.0mm, 6.0mm to 10.0mm, 8.0mm to 15.0mm, or 10.0mm to 20.0mm. In some embodiments, the width can be greater than 20mm or less than 0.2mm. Other widths of the combined protrusions are possible. In some embodiments, the width 2545 of the combined protruding portion may include tolerances such as ±0.010 mm, ±0.020 mm, ±0.030 mm, ±0.040 mm, or ±0.050 mm, but other tolerances are possible.

[0136] Figure 25B shows an exemplary embodiment of a plurality of coil elements, each of which a coil element described herein includes a protruding portion having a plurality of cross-sectional shapes. As shown in Figure 25B, the plurality of coil elements 2550 can be formed such that each coil element (e.g., coil elements 2500A to 2500C) has the same cross-sectional shape and dimensions as those described with respect to the coil element shown in Figure 25A. The plurality of coil elements 2550 can include spaces 2555 between adjacent protruding portions 2525 of adjacent coil elements. In some embodiments, the spaces 2555 can be sized to be 1 / 6 of the wavelength of the electromagnetic waves provided through the MCG described herein. For example, the spaces 2555 can be 1 / 6 of the wavelength of the millimeter electromagnetic waves injected into the borehole of the well. As further shown in Figure 25B, the plurality of coil elements 2550 can include a pitch 2560. The pitch 2560 can be sized to be 1 / 3 of the wavelength of the electromagnetic waves provided through the MCG described herein. For example, a pitch of 2560 can be one-third the wavelength of the millimeter electromagnetic waves injected into the borehole of the well. Other dimensions can also be implemented. The coil element 2550 can be axially fixed inside the outer tube of the MCG described herein by bolts or by using the parts available, thereby connecting the coil element together and / or connecting it to the outer tube of the MCG described herein.

[0137] Figures 26A to 26C show an exemplary embodiment of a multi-piece corrugated waveguide formed from two nested coil springs as described herein. As shown in Figure 26A, the first coil spring 2605 is inserted into the second coil spring 2610 by rotating the first coil spring 2605 into the second coil spring 2610, so that the coil elements of each coil spring can be screwed together, as shown in the assembled two-piece coil spring 2615 shown in Figure 26B. Figure 26C shows a cross-sectional view of the two-piece coil spring 2615.

[0138] Figure 27 shows an exemplary embodiment of the multi-piece corrugated waveguide of Figure 26C. As shown in Figure 27, detail A of Figure 26C is shown to illustrate how two coil springs are nested together to create the outer shape of the corrugation feature corresponding to the diameter and pitch of the first coil spring 2605 and the second coil spring 2610. The first coil spring 2605 may have an inner diameter 2705 that is larger than the inner diameter 2710 of the second coil spring 2610. In some embodiments, the first coil spring 2605 may be coated with a first material such as a dielectric or ferromagnetic material. The second coil spring 2610 may be coated with a second material such as a conductive material.

[0139] Several implementations of this subject matter can provide multi-piece corrugated waveguides suitable for use with electromagnetic wave transmission. For example, several implementations of this subject matter can enable the formation and use of corrugated waveguides suitable for drilling boreholes in wells using millimeter electromagnetic waves in various transmission modes, such as HE11 mode. Several implementations of the multi-piece configuration of corrugated waveguides described herein can reduce the complexity of manufacturing such devices by providing the corrugated waveguide features via coil springs that can be inserted into the tube, instead of machining the corrugation features into the long tube. As a result, several implementations of MCG described herein can be manufactured with higher tolerances than forming corrugated features via machining, tapping, or drilling, which can leave machined material inside the waveguide and reduce electromagnetic transmission. Additionally, instead of machining corrugation features onto long tubes and then coating or plating the long tubes with insulating, dielectric, or conductive materials, the insulating, dielectric, or conductive materials can be applied to individual components during manufacturing, thus making it easier to coat or plate the components of the MCG.

[0140] To provide an overall understanding of the structure, function, manufacturing and use principles of the systems, apparatus, and methods disclosed herein, certain exemplary embodiments are described. One or more examples of these embodiments are illustrated in the accompanying drawings. Those skilled in the art will understand that the systems, apparatus, and methods specifically described herein and shown in the accompanying drawings are non-limiting exemplary embodiments, and that the scope of the invention is defined solely by the claims. Features illustrated or described in relation to one exemplary embodiment may be combined with features of other embodiments. Such modifications and changes are intended to fall within the scope of the invention. Furthermore, in this disclosure, components with similar names in embodiments generally have similar features, and therefore, within a particular embodiment, each feature of each similarly named component is not necessarily fully described.

[0141] Throughout this specification and the claims, the approximate language used herein may be applied to modify any quantitative expression that may vary within an acceptable range without altering the fundamental function of the expression. Thus, values ​​modified by terms such as “about,” “approximately,” and “substantially” are not limited to the specified exact value. In at least some cases, the approximate language may correspond to the precision of an instrument used to measure a value. Throughout this specification and the claims, unless otherwise indicated by context or language, scope limitations may be combined and / or replaced, such scopes may be specified and include all sub-scopes contained therein.

[0142] Those skilled in the art will understand further features and advantages of the present invention based on the embodiments described above. Therefore, this application should not be limited by what is specifically shown and described, except as indicated by the appended claims. All publications and references cited herein are expressly incorporated by reference in their entirety.

Claims

1. An apparatus, wherein the apparatus is An outer tube having an inner surface, an inner diameter, and a length, An inner tube having an inner surface, an outer surface, an outer diameter, and a helical groove, wherein the helical groove is formed on the inner surface and extends along the length of the inner tube, the inner tube is located within the outer tube, and the outer diameter of the inner tube is less than the inner diameter of the outer tube, and A device equipped with the following features.

2. The apparatus according to claim 1, wherein a gap is defined between the outer surface of the inner tube and the inner surface of the outer tube.

3. The apparatus according to claim 1, wherein the spiral groove forms a waveguide.

4. The apparatus according to claim 1, wherein the inner surface and / or the helical groove of the inner tube comprises a conductive material.

5. The apparatus according to claim 1, further comprising an insulating layer between the outer tube and the inner tube.

6. The apparatus according to claim 1, wherein the outer surface of the inner tube includes a dielectric material.

7. The apparatus according to claim 1, wherein the spiral groove is configured to propagate millimeter electromagnetic waves.

8. The apparatus according to claim 7, wherein the spiral groove is configured to propagate the millimeter electromagnetic wave in HE11 mode.

9. A method, wherein the method is The method involves forming a plurality of corrugation features on a first side surface of a metal material sheet, wherein the sheet includes a first edge and a second edge. The aforementioned metal material sheet is formed inside the first tube, The first tube is sealed by welding both the first and second edges, and the sealed first tube forms a corrugated waveguide. Methods that include...

10. The method according to claim 9, further comprising forming a multi-piece corrugated waveguide by inserting the sealed first tube into the second tube.

11. A method, wherein the method is To receive a metal material sheet having a first surface, a first edge, and a second edge, The metal material sheet is configured to receive a corrugation element at the uppermost part of the first surface, wherein the corrugation element includes a plurality of corrugation features. The metal material sheet is formed inside the first tube, wherein the first tube includes the corrugation element inside the first tube. The first tube is sealed by welding both the first and second edges, and the sealed first tube forms a multi-piece corrugated waveguide. Methods that include...

12. The method according to claim 11, wherein the corrugation element is a coil spring.

13. The method according to claim 11, wherein the corrugation element is a second tube having a plurality of corrugation features formed on the inner surface of the second tube.

14. An apparatus, wherein the apparatus is An outer tube having an inner surface, an inner diameter, and a length, At least one inner tube having an inner surface, an outer surface, an outer diameter, and at least one corrugated feature, wherein the at least one corrugated feature is formed on the inner surface and extends along the length of the at least one inner tube, the at least one inner tube is located within the outer tube, and the outer diameter of the at least one inner tube is less than the inner diameter of the outer tube. A device equipped with the following features.

15. The apparatus according to claim 14, further comprising a dielectric material adjacent to the inner surface of the outer tube or the outer surface of the at least one inner tube.

16. The apparatus according to claim 15, wherein the outer surface of the at least one inner tube includes a coating of the dielectric material.

17. The apparatus according to claim 15, wherein the dielectric material is a material layer positioned between the inner surface of the outer tube and the outer surface of the at least one inner tube.

18. The apparatus according to claim 15, wherein the dielectric material includes one of glass, ceramic, porcelain, and plastic.

19. The apparatus according to claim 14, further comprising an insulating layer positioned between the outer tube and the at least one inner tube.

20. The apparatus according to claim 19, wherein the insulating layer comprises one of glass fibers, open-cell foam, closed-cell foam, polystyrene, ceramic fibers, carbon composite, silica fibers, and rock wool.

21. The apparatus according to claim 14, wherein the at least one inner tube comprises a plurality of inner tubes arranged longitudinally within the outer tube.

22. The apparatus according to claim 21, wherein each of the plurality of inner tubes is connected together to the outer tube via one of screw connections, welding, magnetic connections, or bolt connections.

23. The apparatus according to claim 21, wherein each of the plurality of inner tubes is connected to one another via retaining rings that surround the adjacent ends of two inner tubes.

24. The apparatus according to claim 14, wherein the at least one inner tube is formed by additive manufacturing.

25. The apparatus according to claim 14, wherein the outer tube comprises a continuous tube, a coiled tube, or a pipe tube.

26. The apparatus according to claim 14, wherein the outer tube comprises a gas injector or a pump discharge device.

27. ​​The apparatus according to claim 14, wherein the outer tube comprises a non-metallic material.

28. The apparatus according to claim 14, wherein the outer tube comprises carbon steel, stainless steel, Inconel, titanium alloy, molybdenum alloy, tungsten alloy, copper alloy, aluminum alloy, or copper-chromium-zirconium alloy.

29. The apparatus according to claim 14, wherein the at least one corrugated feature includes at least one groove adjacent to at least one ridge.

30. The apparatus according to claim 14, wherein the at least one corrugated feature includes a helical groove.

31. The apparatus according to claim 29, wherein the at least one corrugation feature is configured to propagate millimeter electromagnetic waves in HE11 mode.

32. The apparatus according to claim 29, wherein the at least one corrugated feature is configured to propagate millimeter electromagnetic waves, and the width of the at least one corrugated feature is shorter than 1 / 6 of the wavelength of the millimeter electromagnetic waves.

33. The apparatus according to claim 29, wherein the at least one corrugated feature is configured to propagate millimeter electromagnetic waves, and the depth of the at least one corrugated feature is one-quarter the wavelength of the millimeter electromagnetic waves.

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