Patent Publication Number: US-2023160262-A1

Title: Multi-piece corrugated waveguide

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This Application is a continuation is U.S. Pat. Application No. 17/367,800, filed on Jul. 6, 2021 entitled “MULTI-PIECE CORRUGATED WAVEGUIDE”, the entire contents of which is incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     The subject matter described herein relates to a waveguide for use in transmitting electromagnetic waves. 
     BACKGROUND 
     A waveguide is a structure that guides waves, such as electromagnetic waves or sound, with minimal loss of energy by restricting the transmission of energy to one direction. Waveguides can be used in non-conventional drilling techniques, such as thermal drilling and/or millimeter wave drilling, to form a borehole of a well. Waveguides can be used to transmit electromagnetic waves into the borehole to enable drilling at deeper subsurface depths than conventional, rotary drilling. Specific internal features, such as corrugated grooves, can be included in a waveguide and can enhance the transmission efficiency of the electromagnetic waves provided into the borehole. Forming and deploying corrugated waveguides in single lengths of tubes can be expensive, require specialized materials and equipment, and be prone to manufacturing errors which can result in inventory waste, operational downtime of a well, and inefficient transmission of electromagnetic energy. 
     SUMMARY 
     In one aspect, an apparatus is provided. In one embodiment, the apparatus can include a tube including an inner surface, an inner diameter, and a length. The apparatus can also include a coil spring. The coil spring can include an outer surface, an outer diameter, and a plurality of coil elements arranged along a length of the coil spring. The coil spring can be positioned within the tube and the outer diameter of the coil spring can be less than the inner diameter of the tube. 
     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 can include a conductive material. In another embodiment, the coil spring can include a coating of copper, gold, silver, or platinum. In another embodiment, the apparatus can further include an insulative layer between the tube and the coil spring. In another embodiment, the outer surface of the coil spring can include a dielectric material. 
     In another embodiment, at least one coil element of the plurality of coil elements can be defined by one full turn of the at least one coil element with respect to a circumference of the coil spring. In another embodiment, at least one coil element of the plurality of coil elements can include a base portion and a protruding portion extending from the base portion, the protruding portion including 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. In another embodiment, the plurality of coil elements can include one of a trapezoidal cross-sectional shape, circular cross-sectional shape, a cross-sectional rectangular shape, a cross-sectional elliptical shape, or a tapered shape along a length of the plurality of coil elements. 
     In another embodiment, the coil spring can include a copper wire and/or an aluminum wire. In another embodiment, the tube can include a carbon steel tube. In another embodiment, a plurality of coil springs can be positioned within the tube. In another embodiment, a first coil spring and a second coil spring of the plurality of coil springs can be coupled via a coupling spring positioned within the tube. In another embodiment, a first end of the coupling spring can be attached to a first end of the first coil spring and a second end of the coupling spring can be attached to a second end of the second coil spring, the coupling spring can be configured to reduce an amount of axial travel of the first coil spring and the second coil spring relative to one another due to thermal expansion of the first coil spring and/or the second coil spring. 
     In another embodiment, the coil spring and/or a cross-sectional profile of each coil element of the plurality of coil elements can be dimensioned to propagate an electromagnetic wave. In another embodiment, the coil spring and the cross-sectional profile of the coil spring can be dimensioned to propagate the electromagnetic wave in an HE11 mode. In another embodiment, the length of the tube can be greater than 1 meter. In another embodiment, the length of the tube can be greater than 5 meters. In another embodiment, the length of the tube can be greater than 9 meters. 
     In another embodiment, the plurality of coil elements can be dimensioned so as include a space between two or more coil elements of the plurality of coil elements, the space can be dimensioned to be ⅙ of a wavelength of an electromagnetic wave injected into the borehole of the well via the waveguide assembly. In another embodiment, the plurality of coil elements can be dimensioned so as include a pitch between two or more coil elements of the plurality of coil elements, the pitch can be dimensioned to be ⅓ of a wavelength of an electromagnetic wave injected into the borehole of the well via the waveguide assembly. In another embodiment, the plurality of coil elements can be dimensioned so as include a width dimensioned to be less than a wavelength of an electromagnetic wave injected into the borehole of the well via the waveguide assembly. 
     In another embodiment, the coil spring within the tube can form a helical groove. In another embodiment, the helical groove can be configured to propagate an electromagnetic wave. In another embodiment, the helical groove can be configured to propagate the electromagnetic wave in an HE11 mode, a transverse electric mode, a transverse magnetic mode, or a combination of a transverse electric mode and a 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 bent tube. In another embodiment, the tube and the coil spring can be included in a casing and are configured to extend or retract from within the casing. 
     In another aspect, a method is provided. In one embodiment, the method can include extruding a wire including a cross-sectional profile. The method can also include forming the wire into a coil spring having an outer diameter and a plurality of coil elements arranged along a length of the coil spring. The method can further include inserting the coil spring into a tube having an inner diameter greater than the outer diameter of the coil spring, the tube can have a length along which the coil spring extends within the tube. 
     In another embodiment, the method can include coating the wire with a conductive material. The method can also include coating the coil spring with a conductive material. The method can further include coating an inner surface of the tube with an insulative material. In another embodiment, the conductive material can include one or more of copper, silver or gold. In another embodiment, a gap can be formed between an inner surface of the tube and an outer surface of the coil spring when the coil spring is inserted into the tube. 
     In another embodiment, the method can further include forming a channel on an inner surface of the tube, the channel can extend axially along the length of the tube. In another embodiment, the cross-sectional profile of the wire can include base portion and a protruding portion extending from the base portion, the protruding portion can include one of a trapezoidal profile, a circular profile, a square profile, a rectangular profile, or a sinusoidal profile. In another embodiment, forming the wire into a coil spring can include wrapping the wire around a mandrel such that a shape of each coil element of the plurality of coil elements can correspond to a 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 can include at least one of a trapezoidal shape, circular shape, a rectangular shape, an elliptical shape, or a tapered shape. 
     In another embodiment, the wire can be a copper wire or an aluminum wire. In another embodiment, the method can further include forming multiple coil springs and inserting the multiple coil springs into the tube. 
     In another aspect, an apparatus is provided. In one embodiment, the apparatus can include an outer tube. The outer tube can have an inner surface, an inner diameter, and a length. The apparatus can also include an inner tube. The inner tube can have an inner surface, an outer surface, an outer diameter, and a helical-shaped groove formed on the inner surface and extending along a length of the inner tube. The inner tube can be positioned within the outer tube and the outer diameter of the inner tube can be less than the inner diameter of the outer tube. 
     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, the helical-shaped grooved can form a waveguide. In another embodiment, the inner surface of the inner tube and/or the helical-shaped groove can include a conductive material. In another embodiment, the apparatus can further include an insulative layer between the outer tube and the inner tube. In another embodiment, the outer surface of the inner tube can include a dielectric material. In another embodiment, the helical-shaped groove can be configured to propagate a millimeter electromagnetic wave. In another embodiment, the helical-shaped groove can be configured to propagate the millimeter electromagnetic wave in an HE11 mode. 
     In another aspect, a system is provided. In one embodiment, the system can include a waveguide assembly. The waveguide assembly can include a tube. The tube can include an inner surface, an inner diameter, and a length. The wave guide assembly can also include a coil spring. The coil spring can include an outer surface, an outer diameter, and a plurality of coil elements arranged along a length of the coil spring. The coil spring can be positioned within the tube and the outer diameter of the coil spring is less than the inner diameter of the tube. The system can also include a millimeter wave drilling apparatus. The millimeter wave drilling apparatus can include a gyrotron configured to inject millimeter wave radiation energy into a borehole of a well via the waveguide assembly. 
     In another embodiment, the system can include multiple waveguide assemblies underground for directing the millimeter wave radiation energy to drill a portion of the borehole or to remove material from the borehole. In another embodiment, the multiple coil springs can be stacked within one or more tubes to a distance 15 km below a surface of the well. 
     In another aspect, a method is provided. In one embodiment, the method can include forming a plurality of corrugation features on a first side of a sheet of metal sock. The sheet can include a first edge and a second edge. The method can also include forming the sheet of metal stock into a first tube. The method can also include welding the first edge and the second edge together to seal the first tube. The sealed first tube can form a corrugated waveguide. 
     In another embodiment, the method can include inserting the sealed first tube into a second tube to form a multi-piece corrugated waveguide. 
     In another aspect, a method is provided. In one embodiment, the method can include receiving a sheet of metal stock having a first surface, a first edge and a second edge. The method can also include receiving a corrugated element atop the first surface of the sheet of metal stock. The corrugation element can include a plurality of corrugation features. The method can further include forming the sheet of metal stock into a first tube containing the corrugation element within the first tube. The method can also include welding the first edge and the second edge together to seal the first tube. The sealed first tube can form aa multi-piece corrugated waveguide. 
     In another embodiment, the corrugation element is a coil spring. In another embodiment, the corrugation element is a second tube including a plurality of corrugation features formed on an inner surface of the second tube. 
    
    
     
       DESCRIPTION OF DRAWINGS 
       These and other features will be more readily understood from the following detailed description taken in conjunction with the accompanying drawings, in which: 
         FIG.  1    is a diagram illustrating an exemplary embodiment of a millimeter wave drilling system including a multi-piece corrugated waveguide as described herein; 
         FIG.  2    is a diagram illustrating a cross sectional view of a borehole including a waveguide for low loss transmission of millimeter wave radiation as described herein; 
         FIG.  3    is a flowchart illustrating one exemplary embodiment of a method for forming a multi-piece corrugated waveguide as described herein; 
         FIG.  4    is a flowchart illustrating one exemplary embodiment of a method for coating portions of a multi-piece corrugated wave guide as described herein; 
         FIG.  5    is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide as described herein; 
         FIG.  6    is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including a dielectric material and /or a thermal insulative material on an outer surface of a coil spring of a multi-piece corrugated waveguide as described herein; 
         FIG.  7    is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including an insulative layer between a tube and a coil spring of a multi-piece corrugated waveguide as described herein; 
         FIG.  8    is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including a dielectric material and /or a thermal insulative material on an inner surface of a tube of a multi-piece corrugated waveguide as described herein; 
         FIG.  9    is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including an inner tube having a helical groove formed on an inner surface of the inner tube as described herein; 
         FIG.  10    is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including an inner tube having a helical groove and a dielectric material on an outer surface of an inner tube of a multi-piece corrugated waveguide as described herein; 
         FIG.  11    is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including an inner tube having a helical groove and an insulative layer between a tube and a coil spring of a multi-piece corrugated waveguide as described herein; 
         FIG.  12    is a diagram illustrating 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; 
         FIG.  13    is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide including a bent tube as described herein; 
         FIGS.  14 A- 14 B  are diagrams illustrating cross-sectional views of exemplary embodiments of a multi-piece corrugated waveguide including a casing from which the tube and coil spring can extend as described herein; 
         FIG.  15    is a diagram illustrating an exemplary embodiment of manufacturing of a coil tubing product for use in a multi-piece corrugated waveguide as described herein. 
         FIG.  16    is a diagram illustrating an exemplary embodiment of manufacturing a multi-piece corrugated waveguide as described herein including a coil tubing product. 
         FIGS.  17 A- 17 G  are diagrams illustrating exemplary embodiments of coil springs included in a multi-piece corrugated waveguide as described herein; 
         FIGS.  18 A- 18 E  are diagrams illustrating exemplary embodiments a cross-sectional shape of a plurality of coil elements included in a multi-piece guide as described herein; 
         FIG.  19 A  is a diagram illustrating an exemplary embodiment of a square cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein; 
         FIG.  19 B  is a diagram illustrating an exemplary embodiment of a plurality of coil elements, each coil element including a square cross-sectional profile of a protruding portion as described herein; 
         FIG.  20 A  is a diagram illustrating an exemplary embodiment of a trapezoidal cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein; 
         FIG.  20 B  is a diagram illustrating an exemplary embodiment of a plurality of coil elements, each coil element including a trapezoidal cross-sectional profile of a protruding portion as described herein; 
         FIG.  21 A  is a diagram illustrating another exemplary embodiment of a trapezoidal cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein; 
         FIG.  21 B  is a diagram illustrating another exemplary embodiment of a plurality of coil elements, each coil element including a trapezoidal cross-sectional profile of a protruding portion as described herein; 
         FIG.  22 A  is a diagram illustrating an exemplary embodiment of a rectangular cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein; 
         FIG.  22 B  is a diagram illustrating an exemplary embodiment of a plurality of coil elements, each coil element including a rectangular cross-sectional profile of a protruding portion as described herein; 
         FIG.  23 A  is a diagram illustrating an exemplary embodiment of a circular cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein; 
         FIG.  23 B  is a diagram illustrating an exemplary embodiment of a plurality of coil elements, each coil element including a circular cross-sectional profile of a protruding portion as described herein; 
         FIG.  24 A  is a diagram illustrating an exemplary embodiment of a sinusoidal cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein; 
         FIG.  24 B  is a diagram illustrating an exemplary embodiment of a plurality of coil elements, each coil element including a sinusoidal cross-sectional profile of a protruding portion as described herein; 
         FIG.  25 A  is a diagram illustrating an exemplary embodiment of a protruding portion of a coil element including multiple cross-sectional profiles as described herein; 
         FIG.  25 B  is a diagram illustrating an exemplary embodiment of a plurality of coil elements, each coil element including a protruding portion having multiple cross-sectional profiles as described herein; 
         FIGS.  26 A- 26 C  are diagrams illustrating an exemplary embodiment of a multi-piece corrugated waveguide formed from two (2) nested coil springs as described herein; and 
         FIG.  27    is a diagram illustrating an exemplary embodiment of the multi-piece corrugated waveguide of  FIG.  26 C . 
     
    
    
     It is noted that the drawings are not necessarily to scale. The drawings are intended to depict only typical aspects of the subject matter disclosed herein, and therefore should not be considered as limiting the scope of the disclosure. 
     DETAILED DESCRIPTION 
     A waveguide is a structure that guides waves, such as electromagnetic waves or sound, with minimal loss of energy by restricting the transmission of energy to one direction. Waveguides can be employed, for example, in millimeter wave drilling operations, to efficiently convey electromagnetic waves to depths necessary to form a well. The design and materials used to form the waveguide can affect the transmission efficiency of the electromagnetic waves transmitted in a particular transmission mode. For example, radio frequency (RF) waves can be transmitted over long distances using a waveguide including a series of corrugated features. The corrugated features can include a pattern of repeating ridges or grooves that can extend within a length of a tube. The pattern of corrugated features (e.g., ridges, grooves, or the like) can be shaped to aid the propagation of the electromagnetic wave and can be dimensioned according to the properties (e.g., frequency) of the wave that the waveguide is designed to efficiently propagate. Often, corrugated waveguides can include a dielectric or conductive coating that can improve the transmission efficiency of the waveguide. 
     Some existing approaches to forming a corrugated waveguide include machining, rotary cutting, tapping, or boring an inner surface of a tube to form the corrugation features. Stacks of rings can also be configured within a tube to form the corrugation features. But these approaches can be difficult to perform for long waveguide lengths and therefore can result in errors in the dimensions of the corrugated features. These errors can reduce the transmission efficiency of the waveguide. 
     In addition, forming waveguides having long lengths using some existing methods can leave residual materials, such as turnings, burrs, or the like that can also reduce the transmission efficiency of the waveguide. And some existing methods are not amenable to subsequent machining of long lengths of tube to correct defects of the corrugated features. Thus repair and replacement costs of waveguides formed in long tubes using some traditional methods can be high. And coating inner surfaces of long lengths of tube (and the corrugation features therein), for example with a conductive coating, can be challenging, expensive, and labor intensive. 
     The multi-piece corrugated waveguide described herein can be employed in a variety of industries and applications wherein electromagnetic waves are transmitted, such as oil and gas production industry, nuclear energy, fusion reactors, drilling and mining operations, and sound or audio applications. The design and manufacturing approach of the multi-piece corrugated waveguide can provide a less expensive alternative for any industry or application compared to purchasing long corrugated waveguides with configured corrugation features formed via traditional manufacturing methods. Accordingly, some implementations of the current subject matter can include a multi-piece corrugated waveguide formed of a coil spring arranged within a tube. The coil spring can be shaped to provide the corrugation features of the waveguide while the tube can provide structural support. By utilizing a coil spring inside of a tube as a waveguide, longer-length waveguides can be produced without the errors in dimensions of the corrugated features that are introduced by some existing approaches to forming waveguides. And by reducing errors in dimensions of the corrugated features, the waveguide can more efficiently propagate electromagnetic waves (e.g., millimeter waves) thereby resulting in an improved waveguide. 
     In some embodiments, the multi-piece corrugated waveguide can be configured for use in millimeter wave drilling during formation of a well. In some implementations, the coil springs and inner surfaces 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 dimensioning features of the coil springs, such as a width, a depth, and a pitch of the coil springs in regard to a particular transmission mode. Some implementations of the multi-piece corrugated waveguide described herein can provide efficient transmission of electromagnetic waves in a variety of transmission modes. 
     Some implementations of the multi-piece corrugated waveguide described herein can be formed by assembling multiple individual components. In some implementations, each of the individual components can be formed with greater precision, compared to existing methods of machining corrugation features within single, long pieces of tube. Forming components individually can ensure that the corrugation features have been formed with the desired properties necessary for efficient and frequency dependent electromagnetic wave transmission. And individually manufacturing components of some implementations of the multi-piece corrugated waveguide described herein can reduce operating and maintenance costs because the coil spring and tube can be assembled together in a greater range of tube lengths compared to machining fixed lengths of tube. 
     In some implementations, repair and replacement costs can be reduced since the coil springs can be easily removed and replaced within a tube. In contrast, repair and replacement costs can be higher for existing methods as re-machining long lengths of tube can require specialized equipment and extensive downtime. In addition, re-machining the tube multiple times can result in insufficient material remaining to reform the desired corrugation features of the waveguide. 
       FIG.  1    is a diagram illustrating an exemplary embodiment of a millimeter wave drilling (MMWD) system  100  including an example multi-piece corrugated waveguide  108 . The MMWD system  100  shown in  FIG.  1    includes a gyrotron  102  connected via power cable  104  to a power supply  106  supplying 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 described herein. The waveguide  108  can include a waveguide bend  118 , a window  120 , a waveguide section  126  with opening  128  for off gas emission and pressure control. A section of the waveguide is below ground  130  to help seal the borehole. 
     As part of the waveguide  108  transmission line there is an isolator  110  to prevent reflected power from returning to the gyrotron  102  and an interface for diagnostic access  112 . The diagnostic access is connected to diagnostics electronics and data acquisition  116  by low power waveguide  114 . At the window  120  there is a pressurized gas supply unit  122  connected by plumbing  124  to the window to inject a clean gas flow across the inside window surface to prevent window deposits. A second pressurization unit  136  is connected by plumbing  132  to the waveguide opening  128  to help control the pressure in the borehole  148  and to introduce and remove borehole gases as needed. The window gas injection unit  122  can be operated at slightly higher pressure relative to the borehole pressure unit  136  to maintain a gas flow across the window surface. A branch line  134  in the borehole pressurization plumbing  132  can be connected to a pressure relief valve  138  to allow exhaust of volatized borehole material and window gas through a gas analysis monitoring unit  140  followed by a gas filter  142  and exhaust duct  144  into the atmosphere  146 . In some embodiments, the exhaust duct  144  can return the gas to the pressurization unit  136  for reuse. 
     Pressure in the borehole can be increased in part or in whole by the partial volatilization of the subsurface material being melted. A thermal melt front  152  at the end of the borehole  148  can be propagated into the subsurface strata under the combined action of the millimeter wave power and gas pressure leaving behind a ceramic (e.g., glassy) borehole wall  150 . This wall can act as a dielectric waveguide to transmit the millimeter wave beam to the thermal front  152 . 
       FIG.  2    is a diagram illustrating a cross sectional view of an example borehole including a multi-piece corrugated waveguide, which can be configured for low loss transmission of millimeter wave radiation.  FIG.  2    provides a more detailed view of MMWD and corresponds to the MMWD system described in U.S. Pat. No. 8,393,410 to Woskov et. al, entitled “Millimeter-wave Drilling System.” The borehole  200  with annulus  205 , glassy/ceramic wall  210  and permeated glass  215  has a waveguide assembly  220  inserted to improve the efficiency of millimeter wave beam propagation. In some embodiments, the waveguide assembly can include a multi-piece corrugated waveguide as will be described herein. In some embodiments, multiple waveguide assemblies can be inserted into the borehole. For example, multiple waveguide assemblies can be stacked upon one another to a distance of 1 km, 5 km, 10 km or more below a surface of a well. 
     As shown in  FIG.  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 melt front  235  of the borehole is far enough to allow the launched millimeter wave beam divergence  240  to fill  245  the dielectric borehole  200  with the guided millimeter-wave beam. The standoff distance  230  is also far enough to keep the temperature at the waveguide assembly  220  low enough for survivability. The inserted waveguide assembly  220  also acts as a conduit for a pressurized gas flow  250  from the surface. This gas flow keeps the waveguide clean and contributes to the extraction/displacement of the rock material from the bore hole. The gas flow from the surface  250  mixes  255  with the volatilized out gassing of the rock material  260  to carry the condensing rock vapor to the surface through annular space  225 . The exhaust gas flow  265  is sufficiently large to limit the size of the volatilized rock fine particulates and to carry them all the way to the surface. 
       FIG.  3    is a flowchart illustrating one exemplary embodiment of a method for forming a multi-piece corrugated waveguide as described herein. At  305 , a wire including a cross-sectional profile can be extruded. Extruding or roll forming a wire to form a coil spring (e.g., the corrugated features of the waveguide described herein) can advantageously improve the quality of the manufactured waveguide because the extrusion is less likely to leave burrs or machined material within the waveguide compared to traditional methods which can machine, tap, or otherwise bore corrugated grooves on an inner surface of the waveguide. The wire can be made from any standard metal or non-metal material. In some embodiments, the wire can include a metal wire or other electrically conductive material, such as a copper wire, aluminum wire or copper chromium zirconium alloy wire. The extrusion can form a cross-sectional profile of the wire. The cross-sectional profile can include a base portion and protruding portion extending from the base portion, as shown and described in relation to  FIGS.  19 - 25   . 
     The base portion and the protruding portion can include profiles that can be shaped in a variety of geometries and dimensions. For example, in some embodiments, the profile of the protruding portion can include a trapezoidal profile, a circular profile, a square profile, a rectangular profile, or a sinusoidal profile. In some embodiments, the base portion can include a rectangular profile or a curved profile. Other profile shapes are possible. 
     The protruding portion can include a width and a depth which can correspond to a mode and/or frequency of electromagnetic waves which are transmitted through the multi-piece corrugated waveguide described herein. For example, the width and depth of the protruding portion can be formed to correspond to the optimum transmission of electromagnetic waves, such as millimeter waves and microwaves in HE11 mode or any other modes with low attenuation. 
     The width and depth of the protruding portion of the corrugated waveguide can be configured with respect to a frequency of the waves transmitted through the waveguide. For example, for optimal transmission in the HE11 mode, the width of the corrugations can be less than a sixth of the wavelength and the depth of the corrugations can be approximately a quarter of the wavelength of the beam. For other modes of propagation, the corrugations can take different geometrical characteristics. 
     At  310 , the wire can be formed into a coil spring having an outer diameter and a plurality of coil elements arranged along a length of the coil spring. In some embodiments, the coil spring can be formed by wrapping the wire around a form, such as a mandrel, to form the wire into the coil spring. In this way, a cross-sectional shape of the coil spring (e.g., the shape observed when viewing the coil spring from a perspective that is parallel with an axis extending along a length of the coil spring) and the shape of each coil element of the coil spring can correspond to a cross-sectional shape of the mandrel (e.g., the shape observed when viewing the mandrel from a perspective that is parallel with an axis extending along a length of the mandrel). The cross-sectional shape of the mandrel (and thus, the cross-sectional shape of a coil element, a plurality of coil elements, and a coil spring) can include a trapezoidal shape, a circular shape, a rectangular shape, a square shape, or an elliptical shape, for example, as shown in  FIGS.  18 A- 18 E . Other shapes are possible. 
     In some embodiments, the coil spring can be a tapered coil spring that can be formed using a tapered mandrel. In some embodiments, the cross-sectional shape of a plurality of coil elements and thus, the coil spring, can vary along the length of the plurality of coil elements and/or the coil spring. In some embodiments, the coil spring can include multiple cross-sectional profiles along the length of the coil spring. 
     A coil element of the coil spring can correspond to a single turn of the wire around the 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 the plurality of coil elements forming the coil spring. As shown in regard to  FIG.  17 A , a plurality of coil elements can include a pitch defined between a center of two coil springs. The pitch can correspond to a mode and/or frequency of electromagnetic waves which are transmitted through the multi-piece corrugated waveguide described herein. In addition, the coil element can include a protruding portion. The protruding portion can be formed with a width and a depth to correspond to optimal transmission of millimeter waves in HE11 mode, for example. Profiles of coil elements illustrating the width and depth of the protruding portion are shown and described in relation to  FIGS.  19 - 25   . 
     In some embodiments, the coil spring can be formed as a compression spring or an extension spring. Depending on the desired pitch between coil elements, it can be advantageous to use a compression spring (e.g., a coil spring having a larger pitch between coil elements as shown in  FIG.  17 A ) instead of an extension spring (e.g., a coil spring having a smaller pitch between coil elements as shown in  FIG.  17 B ). In some embodiments, multiple coil springs can be formed in the manner described in relation to operation  310 . In some embodiments, the coil spring can be formed to include an attachment point at each end of the coil spring, so that multiple coil springs can be linked or joined together, as shown in  FIGS.  17 B and  17 C . For example, the attachment points can include semi-circular attachment points configured at each end of the coil spring. The semi-circular attachment point at one end of one coil spring can couple with a semi-circular attachment point at a one end of another, adjacent coil spring. 
     At  315 , the coil spring can be inserted into a tube. The tube can provide structural rigidity to the coil spring and can be designed to provide gas or liquid tight (e.g., pressurized) containment. In some embodiments, the tube can be a continuous tube, a coil tubing product, or a pipe tubing product. In some embodiments, the tube can be a gas injector or pump out device. The tube can have an inner diameter that can be greater than the outer diameter of the coil spring. The tube can have a length along which the coil can extend within the tube. When inserted into the tube, the coil spring can form a plurality of corrugation features within the tube, as illustrated in  FIGS.  5 - 8 ,  12 - 13 , and  14 A- 14 B . The corrugation features can enable the coil spring and tube to transmit electromagnetic waves there through efficiently in a variety of transmission modes, such as HE11 mode. The corrugation features can be further defined as a result of extruding the wire with a particular cross-sectional profile and pitch so that the transmission efficiency is achieved by the coil spring within tube and the cross-sectional profile of the plurality of coil elements. 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 alloys, molybdenum alloys, tungsten alloys, copper alloys, aluminum alloys, or copper chromium zirconium. In some embodiments, multiple coil springs can be inserted into the tube. 
     In some embodiments, a gap can be formed between an inner surface of the tube and an outer surface of the coil spring when the coil spring is inserted into the tube, as illustrated in  FIGS.  5 - 8 , and  12 - 13   . The gap can enable variations in the coil spring materials due to thermal expansion during electromagnetic wave transmission through tube and coil spring. The gap allows gas from the surface to flow down to the bottom of the borehole while allowing cooling of the corrugation on the inside and outside of the coiled spring, which cannot be achieved with conventional waveguide pipe. The tube can act as an additional barrier for any electromagnetic waves which may leak through the coil spring to the environment. In some embodiments, a channel can be formed on an inner surface of the tube and can enable gas flow from the surface to be bottom of the borehole. In some embodiments, the channel can extend axially along the length of the tube. 
       FIG.  4    is a flowchart illustrating one exemplary embodiment of a method  400  for coating portions of a multi-piece corrugated wave guide as described herein. Coating or dipping portions of the multi-piece corrugated waveguide described herein can increase the transmission efficiency of transmitted electromagnetic waves and can aid in managing thermal conditions within the multi-piece corrugated waveguide. Compared to traditional methods of coating the inner surfaces of long tubes that have been bored or machined to form corrugated waveguide features within the long tubes, it can be easier to coat portions of the multi-piece corrugated waveguide described herein because the coil spring and tube can be formed separately and can be coated separately. In addition, the use of shorter length coil springs described herein can also make application of coating materials easier prior to insertion into the tube. 
     At  405 , the wire can be coated with a conductive material. In some embodiments, the wire can be coated with an electrically conductive material such as copper, silver, platinum, or gold. The process of coating can include vapor deposition, chemical or electrochemical coating, spraying, rolling, dipping, applying a film, or the like. In some embodiments, the wire can be coated with a dielectric material. 
     At  410 , the coil spring can be coated with a conductive material. In some embodiments, an outer diameter of the coil spring can be coated with a conductive material, as shown in  FIG.  17 B . In some embodiments, the coil spring can be coated with an electrically conductive material such as copper, silver, platinum, or gold. In some embodiments, the coil spring can be coated with a dielectric material. The process of coating can include vapor deposition, chemical or electrochemical coating, spraying, rolling, dipping, applying a film, or the like. 
     At  415 , an inner surface of the tube can be coated with an insulative material. For example as shown in  FIG.  8   , the inner surface of the tube can be coated with a dielectric material. Insulative material can be thermally insulative and can be used between the inner surface of the tube and the outer surface of the coil spring to separate the heat in the wellbore annulus  205  from the coil spring. This can allow purge gas from the surface to cool the coil springs all the way down to the bottom of the borehole without losing cooling capability due to the interaction with the inner surface of the tube (which is in contact with hot gas rising up through the annulus  205 ). In some embodiments, the insulative material can include fiberglass, open cell foam, closed cell foam, polystyrene, ceramic fiber, carbon composite, silica fiber, rockwool, or the like. 
     While the multi-piece corrugated waveguide is described herein in relation to drilling operations, embodiments of the multi-piece corrugated waveguide herein can be deployed in a variety of other configurations to transmit electromagnetic waves. While drilling operations can require insertion of the MCG into the ground and possibly flowing a gas in or around the MCG, other applications of embodiments of the MCG described here can be performed using an above-ground, stationary arrangement of the MCG. For example, in nuclear energy or sound transmission applications, the MCG can be configured on an above-ground surface and positioned relative to a target at which electromagnetic waves are to be transmitted. 
       FIG.  5    is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide  500  as described herein. Some implementations of the multi-piece corrugated waveguide (MCG) described herein can be formed according to methods  300   and  400  described in relation to  FIGS.  3  and  4   . The example MCG described herein can be configured for operation within the system  100  described in relation to  FIG.  1    and for deployment in the borehole  200  described in relation to  FIG.  2   . 
     As shown in  FIG.  5   , the MCG  500  can be deployed into a borehole  505  at a surface  510  at which a well or other subsurface drilling operation is being performed. The MCG  500  can convey electromagnetic energy  515 , such as RF waves, into the borehole  505 . The MCG  500  can include a tube  520  and a coil spring  525  positioned within the tube  520 . The tube  520  can 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 a first end of the tube  520  and a second end of the tube  520 . In some embodiments, the length of the tube  520  can be greater than one meter, greater than 5 meters, or greater than 9 meters. In embodiments where the tube includes a continuous tube, a coil tubing product, or a pipe tubing product the length of the tube  520  can be greater than 10 km. When forming a borehole, 10 s and 100 s of tubes  520  can be deployed to reach sufficient depths necessary to form a well. 
     The coil spring  525  can include a plurality of coil elements  530  arranged along a length of the tube  520  and can form a waveguide. The plurality of coil elements  530  can include two or more coil elements  535 . The coil spring  525  can include an outer surface interfacing with the inner surface of the tube  520  and an outer diameter defined between opposing outer surfaces of the coil spring  525 . The outer diameter of the coil spring  525  can be less than the inner diameter of the tube  520 . 
     As shown in  FIG.  5   , a gap  540  can be defined between an outer surface of the coil spring  525  and the inner surface to the tube  520 . The gap can enable the coil spring  525  to expand within the tube  520  as a result of thermal expansion of the coil spring  525  during electromagnetic wave transmission through MCG  500 . The gap  540  can also allow gas to pass from the surface to the bottom of the borehole. Additionally, a second gap  545  can be defined between the outer surfaces of the tube  520  and the walls of the borehole  505 . 
     In some embodiments, the coil spring  525 , as well as a cross-sectional profile of each of the coil elements  535  can be dimensioned to propagate electromagnetic waves through the MCG  500 . For example, the coil spring  525  and the cross-sectional profile of the coil elements  535  can be formed and dimensioned to propagate a millimeter electromagnetic wave with low attenuation. The coil spring  525  and the cross-sectional profile of the coil elements  535  can be dimensioned to transmit the electromagnetic wave in one or more transmission modes. For example, the coil spring  525  and the cross-sectional profile of the coil elements  535  can be dimensioned to transmit the millimeter electromagnetic wave in HE11 mode. 
     In some embodiments, the coil spring  525  and the cross-sectional profile of the coil elements  535  can be dimensioned based on a wavelength and/or a frequency of the transmitted electromagnetic wave. 
     As shown in  FIG.  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  on the inner surface of the coil spring  525 . The helical groove  550  can be formed by opposing and protruding portions of each coil element  535 . In some embodiments, the coil spring  525  can include an inner diameter  555  measured between protruding portions of each coil element  535 . In some embodiments, the inner diameter  555  can include a diameter of 5.0 mm -15.0 mm, 10.0 mm - 20.0 mm, 15.0 mm - 25.0 mm, 20.0 mm - 30.0 mm, 25.0 mm - 35.0 mm, 30.0 mm - 40.0 mm, 45.0 mm - 55.0 mm, 50.0 mm - 60.0 mm, 55.0 mm - 65.0 mm, 60.0 mm -70.0 mm, 65.0 mm - 75.0 mm, 70.0 mm - 80.0 mm, 75.0 mm - 90.0 mm, or 85.0 mm - 200.0 mm. In some embodiments, the inner diameter can be greater than 200.0 mm or less than 5.0 mm. Other inner diameters are possible. In some embodiments, the inner diameter  555  can include a tolerance range, 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, although other tolerance ranges are possible. 
       FIG.  6    is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide  600  including a dielectric material and/or a thermal insulative material on an outer surface of a coil spring of a multi-piece corrugated waveguide as described herein. As shown in  FIG.  6   , the MCG  600  can 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 can include glass, ceramics, porcelain and most plastics. The dielectric material  615  can be applied to the outer diameter of the coil spring  610  as a coating or the dielectric material  615  can be a standalone component that is added to the assembled MCG  600 . The dielectric material  615  can electrically isolate the tube  605  from the coil spring  610  and prevent electrical shorting between them. 
     In some embodiments, the coil spring  610  can include an inner diameter  620  measured between protruding portions of each coil element of the coil spring  610 . In some embodiments, the inner diameter  620  can include a diameter of 5.0 mm - 15.0 mm, 10.0 mm - 20.0 mm, 15.0 mm - 25.0 mm, 20.0 mm - 30.0 mm, 25.0 mm - 35.0 mm, 30.0 mm - 40.0 mm, 45.0 mm -55.0 mm, 50.0 mm - 60.0 mm, 55.0 mm - 65.0 mm, 60.0 mm - 70.0 mm, 65.0 mm - 75.0 mm, 70.0 mm - 80.0 mm, 75.0 mm - 90.0 mm, or 85.0 mm - 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  620  can include a tolerance range, 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, although other tolerance ranges are possible. 
       FIG.  7    is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide  700  including an insulative layer between a tube and a coil spring of a multi-piece corrugated waveguide as described herein. As shown in  FIG.  7   , the MCG  700  can include a tube  705 , a coil spring  710 , and an insulative layer  715 . The insulative layer  715  can be thermally insulative and can be positioned between the tube  705  and the coil spring  710 . In some embodiments, the insulative layer can be formed from an insulative material, such as fiberglass, open / closed cell foam, polystyrene, ceramic fiber, carbon composite, silica fiber, rockwool, or the like. Insulative materials can be positioned in between the inner surface of the tube  705  and the outer surface of the coil spring  710  to separate the heat in a wellbore annulus  205  from the coil spring  710 . This can allow purge gas from the surface to cool the coil spring  710  all the way down to the bottom of the borehole without losing cooling capability due to the interaction with the inner surface of the tube  705  (which is in contact with hot gas rising up through the annulus  205 ). 
     In some embodiments, the coil spring  710  can include an inner diameter  720  measured between protruding portions of each coil element of the coil spring  710 . In some embodiments, the inner diameter  720  can include a diameter of 5.0 mm - 15.0 mm, 10.0 mm - 20.0 mm, 15.0 mm - 25.0 mm, 20.0 mm - 30.0 mm, 25.0 mm - 35.0 mm, 30.0 mm - 40.0 mm, 45.0 mm -55.0 mm, 50.0 mm - 60.0 mm, 55.0 mm - 65.0 mm, 60.0 mm - 70.0 mm, 65.0 mm - 75.0 mm, 70.0 mm - 80.0 mm, 75.0 mm - 90.0 mm, or 85.0 mm - 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  720  can include a tolerance range, 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, although other tolerance ranges are possible. 
       FIG.  8    is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide  800  including a dielectric material and/or thermal insulative material on an inner surface of a tube of a multi-piece corrugated waveguide as described herein. As shown in  FIG.  8   , the MCG  800  can include a tube  805 , a coil spring  810 , and a dielectric material  815  on an inner surface of the tube  815 . In some embodiments, the dielectric material and/or thermal insulative material can include fiberglass, open / closed cell foam, polystyrene, ceramic fiber, carbon composite, silica fiber, rockwool, or the like. 
     In some embodiments, the coil spring  810  can include an inner diameter  820  measured between protruding portions of each coil element of the coil spring  810 . In some embodiments, the inner diameter  820  can include a diameter of 5.0 mm - 15.0 mm, 10.0 mm - 20.0 mm, 15.0 mm - 25.0 mm, 20.0 mm - 30.0 mm, 25.0 mm - 35.0 mm, 30.0 mm - 40.0 mm, 45.0 mm -55.0 mm, 50.0 mm - 60.0 mm, 55.0 mm - 65.0 mm, 60.0 mm - 70.0 mm, 65.0 mm - 75.0 mm, 70.0 mm - 80.0 mm, 75.0 mm - 90.0 mm, or 85.0 mm - 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  820  can include a tolerance range, 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, although other tolerance ranges are possible. 
       FIG.  9    is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide  900  including an inner tube having a helical groove formed on an inner surface of the inner tube as described herein. As shown in  FIG.  9   , the MCG  900  can include an outer tube  905 . The outer tube  905  can include an inner surface, an inner diameter defined between opposing inner surfaces, and a length defined between a first end of the tube  905  and a second end of the tube  905 . The MCG  900  can also include one or more inner tubes, such as inner tubes  910  and  915 . Each inner tube can include an inner surface, an outer surface, an outer diameter defined between opposing outer surfaces, and a helical-shaped groove  920  formed on the inner surface of the inner tube(s)  910  and  915 . The inner tube(s)  910  and  915  can be positioned within the outer tube  905  as a result of the outer diameter of the inner tube(s)  910  and  915  being less than the inner diameter of the outer tube  905 . In some embodiments, for example, when multiple inner tubes are positioned within the outer tube  905 , two or more inner tubes  910  and  915  can be joined via a threaded connection, via welding one inner tube to a second inner tube, or via bolting one inner tube to a second inner tube. In some embodiments, the inner tube(s)  910  and/or  915  can be secured within the outer tube  905  via protrusions formed on the inner surface of the outer tube  905 . In some embodiments, the inner tubes  910  and  915  can be joined via a magnetic coupling or a retainer ring that can encircle overlapping portions of the inner tubes  910  and  915 . In some embodiments, the inner tube(s)  910  and  915  can be formed from a flat sheet of stock material that is rolled into a tube shape. In such an embodiment, the corrugation features can be formed on a surface of the flat sheet of stock material and the corrugation features can include helical corrugations, as well as non-helical corrugations formed as ridges and valleys on the surface of the flat sheet of stock material. In some embodiments, the inner tube(s)  910  and  915  can be formed via additive manufacturing methods. 
     The helical-shaped groove  920  can be formed as a continuous or semi-continuous groove that can extend along a length of the inner tube(s)  910  and  915 . The helical-shaped groove  920  can form a waveguide configured to transmit electromagnetic waves through the MCG  900 . For example, the helical-shaped groove  920  can be configured to propagate a millimeter electromagnetic wave in one or more transmission modes. In some embodiments, the helical-shaped groove  920  can be configured to propagate the millimeter electromagnetic wave in an HE11 transmission mode, although other transmission modes can be propagated via the helical-shaped groove  920 , such as transverse electric mode (TE) or transverse magnetic mode (TM) or combination of TE &amp; TM. 
     As further shown in  FIG.  9   , in some embodiments, a gap  925  can be defined between the outer surface of the inner tube(s)  910  and  915  and the inner surface of the outer tube  905 . The gap  925  can enable the inner tube(s)  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 MCG  900 . The gap  925  can also allow gas to pass from the surface to the bottom of the borehole. 
     As further shown in  FIG.  9   , in some embodiments, the helical-shaped groove  920  can include a conductive material  930 . The conductive material  930  can be on the surface of the helical groove  920 . In some embodiments, the inner surface of the inner tube(s)  910  and/or  915  can include a conductive material  935 . The conductive material can include copper, silver, platinum, or gold. 
     In some embodiments, the MCG  900  can include an inner diameter  940  measured between protruding portions of each inner tube  910  and  915 . The protruding portions can be formed by the helical-shaped groove  920 . In some embodiments, the inner diameter  940  can include a diameter of 5.0 mm - 15.0 mm, 10.0 mm - 20.0 mm, 15.0 mm - 25.0 mm, 20.0 mm -30.0 mm, 25.0 mm - 35.0 mm, 30.0 mm - 40.0 mm, 45.0 mm - 55.0 mm, 50.0 mm - 60.0 mm, 55.0 mm - 65.0 mm, 60.0 mm - 70.0 mm, 65.0 mm - 75.0 mm, 70.0 mm - 80.0 mm, 75.0 mm - 90.0 mm, or 85.0 mm - 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  940  can include a tolerance range, 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, although other tolerance ranges are possible. 
       FIG.  10    is a diagram illustrating an exemplary embodiment of a multi-piece corrugated waveguide  1000  including an inner tube having a helical groove and a dielectric material on an outer surface of an inner tube of a multi-piece corrugated waveguide as described herein. As shown in  FIG.  10   , the MCG  1000  can include an outer tube  1005 , and an inner tube  1010 . In the embodiment, shown in  FIG.  10    a single inner tube  1010  is configured inside the outer tube  1005 . The inner tube  1010  includes a helical-shaped groove  1015  formed on an inner surface of the inner tube  1010 . The helical-shaped groove  1015  can be a continuous groove formed along the length of the inner tube  1010  and can form a waveguide. The MCG  1000  can include a dielectric material  1020  on the outer surface of the inner tube  1010 . The dielectric material  1020  can include glass, ceramics, porcelain or plastics and can be applied to the outer diameter of the inner tube  1020  as a coating or the dielectric material  1020  can be a standalone component that is added to the MCG  1000  assembly. The dielectric material  1020  can electrically isolate the outer tube  1005  from the inner tube  1010  and can prevent electrical shorting between them. 
     In some embodiments, the MCG  1000  can include an inner diameter  1025  measured between protruding portions of the inner tube  1010 . The protruding portions can be formed by the helical-shaped groove  1015 . In some embodiments, the inner diameter  1025  can include a diameter of 5.0 mm - 15.0 mm, 10.0 mm - 20.0 mm, 15.0 mm - 25.0 mm, 20.0 mm - 30.0 mm, 25.0 mm - 35.0 mm, 30.0 mm - 40.0 mm, 45.0 mm - 55.0 mm, 50.0 mm - 60.0 mm, 55.0 mm - 65.0 mm, 60.0 mm - 70.0 mm, 65.0 mm - 75.0 mm, 70.0 mm - 80.0 mm, 75.0 mm -90.0 mm, or 85.0 mm - 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  1025  can include a tolerance range, 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, although other tolerance ranges are possible. 
       FIG.  11    is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide  1100  including an inner tube having a helical groove and an insulative layer between a tube and a coil spring of a multi-piece corrugated waveguide as described herein. As shown in  FIG.  11   , the MCG  1100  can include an outer tube  1105 , an inner tube  1110 , and a helical-shaped grooved  1115  formed on an inner surface of the inner tube  1110 . The MCG  1100  can also include an insulative layer  1120 . The insulative layer  1120  can be positioned between the outer tube  1105  and the inner tube  1110 . In some embodiments, the insulative layer  1120  can be formed from an insulative material, such as fiberglass, open cell foam, closed cell foam, polystyrene, ceramic fiber, carbon composite, silica fiber, rockwool, or the like. Insulative material  1120  can be positioned in between the inner surface of the outer tube  1105  and the outer surface of the inner tube  1110  to separate the heat in a wellbore annulus  205  from the inner tube  1110 . This can allow purge gas from the surface to cool the inner tube  1110  all the way down to the bottom of the borehole without losing cooling capability due to the interaction with the inner surface of the outer tube  1105  (which is in contact with hot gas rising up through the annulus  205 ). 
     In some embodiments, the MCG  1100  can include an inner diameter  1125  measured between protruding portions of the inner tube  1110 . The protruding portions can be formed by the helical-shaped groove  1115 . In some embodiments, the inner diameter  1125  can include a diameter of 5.0 mm - 15.0 mm, 10.0 mm - 20.0 mm, 15.0 mm - 25.0 mm, 20.0 mm - 30.0 mm, 25.0 mm - 35.0 mm, 30.0 mm - 40.0 mm, 45.0 mm - 55.0 mm, 50.0 mm - 60.0 mm, 55.0 mm - 65.0 mm, 60.0 mm - 70.0 mm, 65.0 mm - 75.0 mm, 70.0 mm - 80.0 mm, 75.0 mm -90.0 mm, or 85.0 mm - 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  1125  can include a tolerance range, 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, although other tolerance ranges are possible. 
       FIG.  12    is a diagram illustrating 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  FIG.  12   , the MCG  1200  can include a tube  1205  and a coil spring  1210  within the tube  1205 . The tube  1205  can be a tapered tube. The tapered tube  1205  can 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 . The diameter of the tube  1205  can thus 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  FIG.  12   , the coil spring  1210  can be a tapered coil spring. Similarly 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 in relation to  FIG.  3   . The two-piece design can advantageously reduce the machining difficulty of making tapered corrugation features within a tapered tube  1205 . 
     In some embodiments, the MCG  1200  can include an inner diameter  1225  measured between protruding portions of the inner tube  1210  at the first end  1215  of the MCG  1200 . In some embodiments, the inner diameter  1225  can include a diameter of 5.0 mm - 15.0 mm, 10.0 mm - 20.0 mm, 15.0 mm - 25.0 mm, 20.0 mm - 30.0 mm, 25.0 mm - 35.0 mm, 30.0 mm -40.0 mm, 45.0 mm - 55.0 mm, 50.0 mm - 60.0 mm, 55.0 mm - 65.0 mm, 60.0 mm - 70.0 mm, 65.0 mm - 75.0 mm, 70.0 mm - 80.0 mm, 75.0 mm - 90.0 mm, or 85.0 mm - 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  1225  can include a tolerance range, 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, although other tolerance ranges are possible. 
     In some embodiments, the MCG  1200  can include an inner diameter  1230  measured between protruding portions of the inner tube  1210  at the second end  1230  of the MCG  1200 . In some embodiments, the inner diameter  1230  can include a diameter of 5.0 mm - 15.0 mm, 10.0 mm - 20.0 mm, 15.0 mm - 25.0 mm, 20.0 mm - 30.0 mm, 25.0 mm - 35.0 mm, 30.0 mm -40.0 mm, 45.0 mm - 55.0 mm, 50.0 mm - 60.0 mm, 55.0 mm - 65.0 mm, 60.0 mm - 70.0 mm, 65.0 mm - 75.0 mm, 70.0 mm - 80.0 mm, 75.0 mm - 90.0 mm, or 85.0 mm - 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  1230  can include a tolerance range, 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, although other tolerance ranges are possible. 
       FIG.  13    is a diagram illustrating a cross-sectional view of an exemplary embodiment of a multi-piece corrugated waveguide  1300  including a bent tube as described herein. As shown in  FIG.  13   , the MCG  1300  can include a tube  1305  (of which only the inner surface is shown for clarity) and a coil spring  1310  within the tube  1305 . The bent tube  1305  can enable the MCG  1300  to be deployed in a variety of borehole configurations which are not mostly vertical or mostly horizontal geometries. For example, MCG  1300  can be utilized in transitions between vertical borehole configurations and horizontal borehole configurations, or vice versa. MCG  1300  can be deployed to maneuver or otherwise steer electromagnetic waves around subsurface obstacles or geologic formations which may otherwise limit the transmission efficiency of the transmitted electromagnetic waves. In some embodiments, the tube  1305  can be a bellowed tube including a plurality of collapsible segments configured to form a bend in the tube  1305 . 
     In some embodiments, the coil spring  1310  can include an inner diameter  1315  measured between protruding portions of each coil element of the coil spring  1310 . In some embodiments, the inner diameter  1315  can include a diameter of 5.0 mm - 15.0 mm, 10.0 mm - 20.0 mm, 15.0 mm - 25.0 mm, 20.0 mm - 30.0 mm, 25.0 mm - 35.0 mm, 30.0 mm - 40.0 mm, 45.0 mm -55.0 mm, 50.0 mm - 60.0 mm, 55.0 mm - 65.0 mm, 60.0 mm - 70.0 mm, 65.0 mm - 75.0 mm, 70.0 mm - 80.0 mm, 75.0 mm - 90.0 mm, or 85.0 mm - 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  1315  can include a tolerance range, 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, although other tolerance ranges are possible. 
       FIGS.  14 A- 14 B  are diagrams illustrating cross-sectional views of exemplary embodiments of a multi-piece corrugated waveguide  1400  including a casing from which the tube and coil spring can extend as described herein. The MCG  1400  can include a tube  1405 , a coil spring  1410  within the tube  1405 , and a casing  1415 . As shown in  FIG.  14 A , the MCG  1400  is shown in a retracted position. The tube  1405  and the coil spring  1410  are retracted within the casing  1415 . In  FIG.  14 B , the MCG  1400  is shown in an extended position. In  FIG.  14 B , the tube  1405  and the coil spring  1410  have been extended from within the casing  1415 . In this way, the tube  1405  and coil spring  1410  can telescopically retract into and extend from the casing  1415 . By having the coiled spring  1410  span the length of the casing  1415  and the tube  1505 , the millimeter wave can be contained regardless of what position or angle of flexion the MCG  1400  is in. And since the spring  1405  is one piece, there is no step change between the inner diameter of the casing  1415  and inner diameter of the tube  1405 . This can eliminates loss of power of millimeter wave that can be associated with abrupt diameter changes. 
     In some embodiments, the coil spring  1410  can include an inner diameter  1420  measured between protruding portions of each coil element of the coil spring  1410 . In some embodiments, the inner diameter  1420  can include a diameter of 5.0 mm - 15.0 mm, 10.0 mm - 20.0 mm, 15.0 mm - 25.0 mm, 20.0 mm - 30.0 mm, 25.0 mm - 35.0 mm, 30.0 mm - 40.0 mm, 45.0 mm -55.0 mm, 50.0 mm - 60.0 mm, 55.0 mm - 65.0 mm, 60.0 mm - 70.0 mm, 65.0 mm - 75.0 mm, 70.0 mm - 80.0 mm, 75.0 mm - 90.0 mm, or 85.0 mm - 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  1420  can include a tolerance range, 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, although other tolerance ranges are possible. 
       FIG.  15    is a diagram illustrating an exemplary embodiment of manufacturing of a coil tubing product for use in a multi-piece corrugated waveguide as described herein. In some embodiments, the multi-piece corrugated waveguide can be formed from a continuous tube, a coil tubing product, or a pipe tubing product. Continuous tubes and coil or pipe tubing products can be formed from long strips of sheet metal. The long strips of metal may be configured on a reel. The strips of metal can be welded together at the ends of the strips of metal and then can be rolled to form a tube via rollers. The tube can then be welded shut to form tubes of extremely long continuous lengths, such as tubes in excess of 10 km in length. In embodiments including a continuous tube, a coil tubing product, or a pipe tubing product the length of the tube can be greater than 10 km. 
     In some embodiments, corrugation features, such as ridges and/or grooves, can be rolled or stamped into the strips of sheet metal. In this way, when the coil tube is formed from the strips of sheet metal, the corrugation features are provided on an inner surface of the coil tube. In this way, a first tube can be formed to include corrugation features preconfigured on an inner surface of the first tube. The first tube can then be inserted into a second tube to form a multi-piece corrugated waveguide as described in embodiments herein. 
     As shown in  FIG.  15   , a long strip of stock metal  1505  can be brought into contact with a roller  1510 . The roller  1510  can include grooves and ridges, which can form corrugation features  1515  in the strip of metal. The corrugation features  1515  can be formed on a surface of the metal stock  1505  which can correspond to an inner surface of a tube to be formed. The metal stock  1505  can be conveyed through one or more shape roller  1520  to transform the metal stock  1505  into a tube  1525 . The tube  1525  can have an open seam at which opposing edges of the metal stock  1505  are in proximity to each other. The seam can be welded via a welding device  1530  to form a fully enclosed tube or pipe  1535  including the corrugation features  1515  within. 
       FIG.  16    is a diagram illustrating an exemplary embodiment of manufacturing a multi-piece corrugated waveguide as described herein including a coil tubing product. For example, a long strip of metal stock  1605  can be received in one or more shape rollers  1610 . A coil spring  1615  or a previously formed coil tubing product  1615  can be inserted into a portion of the metal stock  1605  as the metal stock is being formed by the shape rollers  1610 . In some embodiments, the coil tubing product  1615  can be formed as described in relation to  FIG.  15   . Once inserted, the metal stock  1605  can be fully formed into a tube and welded shut. The resulting tube  1620  can include the coil spring  1615  or the coil tubing product  1615  therein, which can provide corrugation features described herein. In some embodiments, the coil spring or the coil tubing product  1605  can be inserted before the tube is fully enclosed and welded shut. In some embodiments, the coil spring or the coil tubing product  1615  can be inserted into the coil tube as the tube is being formed and welded shut. 
       FIGS.  17 A- 17 G  are diagrams illustrating exemplary embodiments of coil springs included in a multi-piece corrugated waveguide as described herein. The coil springs shown in  FIGS.  17 A- 17 G  can correspond to the coil springs described in the embodiments herein and can include embodiments of coil springs configured as compression springs or extension springs. In some embodiments, a combination of compression coil springs and extension coil springs can be used within a tube as described herein. 
     As shown in  FIG.  17 A , an embodiment of a compression coil spring is shown having a length  1705 . The coil spring can include an inner diameter  1710  and a width  1715 . In some embodiments, the inner diameter  1710  can include a diameter of 5.0 mm- 15.0 mm, 10.0 mm -20.0 mm, 15.0 mm - 25.0 mm, 20.0 mm - 30.0 mm, 25.0 mm - 35.0 mm, 30.0 mm - 40.0 mm, 45.0 mm - 55.0 mm, 50.0 mm - 60.0 mm, 55.0 mm - 65.0 mm, 60.0 mm - 70.0 mm, 65.0 mm -75.0 mm, 70.0 mm - 80.0 mm, 75.0 mm - 90.0 mm, or 85.0 mm - 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  can include a tolerance range, 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, although other tolerance ranges are possible. 
     In some embodiments, the width  1715  can be dimensioned to be less than a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the width  1715  can be less than a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. In some embodiments, the width  1715  can be ⅓ to ¼ of the frequency of the RF signal being transmitted the MCG described herein. The width  1715  of the coil can correspond to the pitch of the spring and the corrugation features formed within the MCG described herein. 
     A coil element  1720  of the coil spring can be defined as a complete turn, e.g.,  360  degrees, of the coil spring as measured along a circumference of the coil spring. A plurality of coil elements  1720  can form the coil spring to have a length  1705 . The coil spring can include a space  1725  between two or more coil elements  1720 . For example, the space  1725  can be larger than the frequency of the electromagnetic wave injected into the MCG described herein, but the spring can be configured to compress so that the space  1725  is reduced to at least ⅒ of the frequency of the of the injected electromagnetic wave to prevent it from leaking through. In some embodiments, the space  1715  can 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 can be greater than 0.6 mm or less than 0.1 mm. Other space sizes can be included. 
     In some embodiments, the coil spring and the plurality of coil elements  1720  can include a pitch  1730  between coil elements  1720 . The pitch can be measured from a center point of a first coil element to a center point of a second coil element that is adjacent to the first coil element. In some embodiments, the pitch  1730  can be dimensioned to be a ⅓ of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the pitch  1730  can be a ⅓ of a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. For example, the pitch can be 0.3 mm to 7.0 mm. 
       FIGS.  17 B- 17 G  illustrate additional, example embodiments of a coil spring for use with the MCG embodiments described herein. Any and all of the coil springs shown in  FIGS.  17 B- 17 G  can have a coil spring diameter, a coil element width, a pitch between coil elements, and a space between coil elements as described in relation to the coil spring shown and described in  FIG.  17 A . For example, in  FIG.  17 B , an extension spring is shown. The extension spring can be coated with a material  1735 , such as a conductive material. The spring can also be coated with a highly conductive metallic material, such as gold, platinum, copper or aluminum, which can optimize transmission efficiency. The extension spring can include a first coupling portion at a first end and a second coupling portion at a second end. As shown in  FIG.  17 C , a compression coil spring is shown. The compression spring can include a first coupling portion at a first end and a second coupling portion at a second end. 
     As shown in  FIG.  17 D , in some embodiments, the coil spring can include a tapered coil spring. The tapered coil spring can include a diameter that changes along a length of the coil spring. As shown in  FIG.  17 E , in some embodiments, the coil spring can include multiple tapered portions. In the embodiment shown in  FIG.  17 E , the coil spring can have an upper tapered portion and a lower tapered portion with a non-tapered portion between the upper tapered portion and the lower tapered portion. 
     As shown in  FIG.  17 F , in some embodiments, the coil spring can include tapered portions that have a larger diameter than a non-tapered portion between the upper and lower tapered portions. As shown in  FIG.  17 G , in some embodiments, the coil spring can include multiple pitch configurations between coil elements at two or more locations along the length of the coil spring. For example, the coil spring can include a first pitch  1740  and a second pitch  1750 . The first pitch  1740  can be smaller than the second pitch  1750 . In some embodiments, the first pitch can be larger than the second pitch. Similarly, in some embodiments, the coil spring can have a first space  1745  between a first plurality of coil elements and a second space  1755  between a second plurality of coil elements. 
       FIGS.  18 A- 18 E  are diagrams illustrating exemplary embodiments a cross-sectional shape of a plurality of coil elements included in a multi-piece guide as described herein. The cross-sectional shapes of the plurality of coil elements included in the coil springs described herein can be formed according to operation  310  of  FIG.  3   . As shown in  FIG.  18 A , in some embodiments, the plurality of coil elements can include a rectangular cross-sectional shape. In some embodiments, the plurality of coil elements can include an elliptical cross-sectional shape as shown in  FIG.  18 B . As shown in  FIG.  18 C , in some embodiments, the plurality of coil elements can include an oval cross-sectional shape. As shown in  FIG.  18 D , in some embodiments, the plurality of coil elements can include a circular cross-sectional shape. As shown in  FIG.  18 E , in some embodiments, the plurality of coil elements can include a trapezoidal cross-sectional shape. In some embodiments, the plurality of coil elements can include a square shape, a triangular shape, or a polygonal shape. Although the cross-sectional shapes shown in  FIGS.  18 A- 18 E  are described in the context of cross-sectional shapes of pluralities of coil elements, the cross-sectional shapes shown in  FIGS.  18 A- 18 E  can also correspond to cross-sectional shapes of mandrels used to form the pluralities of coil elements. 
       FIGS.  19 A- 25 B  illustrate various embodiments of cross-sectional profiles of coil elements. The cross-sectional profiles can be formed as described in operation  305  of  FIG.  3   . A wire forming the coil spring and the coil elements of the coil spring can be extruded to have a cross-sectional profile shown in  FIGS.  19 A- 25 B . A variety of cross-sectional profiles can be formed in this way and can be configured for use in the various MCG embodiments described herein. For example, in some embodiments, the cross-sectional profile can include a triangular or pointed cross-sectional profile in addition to those shown in  FIGS.  19 A- 25 B . Other cross-sectional profiles are possible. 
       FIG.  19 A  is a diagram illustrating an exemplary embodiment of a square cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein. As shown in  FIG.  19 A , a coil element  1900  can include a base portion  1905  and a protruding portion  1925  extending from the base portion  1905 . The base portion  1905  can include a height  1910 , a width  1915 , and a back surface  1920 . Although the base portion  1905  is shown with a rectangular-shaped profile, additional base portion profile shapes can be implemented. Similarly, although the back surface  1920  is shown as a flat-shaped back surface, additional back surface shapes or profiles can be implemented. In some embodiments, the height  1910  can include a height of 0.2 mm - 0.4 mm, 0.3 mm - 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. 
     As shown in  FIG.  19 A , the coil element  1900  can include a protruding portion  1925  extending from the base portion  1905 . The protruding portion  1925  can include a square-shaped profile as shown in  FIG.  19 A , although other profile shapes can be implemented. The protruding portion  1925  can include a height  1930 , a width  1935  and an offset  1940 . In some embodiments, the height  1930  can include a height of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, or 0.6 mm - 1.0 mm. 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  1930  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. 
     In some embodiments, the width  1935  can include a width of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, 0.6 mm - 0.8 mm, 0.7 mm - 0.9, or 0.8 mm -1.0 mm. In some embodiments, the width can be greater than 1.0 mm or less than 0.2 mm. Other widths are possible. In some embodiments, the width  1935  can include a tolerance range, such as +/- 0.050 mm, +/- 0.060 mm, +/- 0.070 mm, +/- 0.080 mm, or +/- 0.090 mm, although other tolerance ranges are possible. 
     In some embodiments, the offset  1940  can include an offset of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, 0.6 mm - 0.8 mm, 0.7 mm - 0.9, or 0.8 mm -1.0 mm. In some embodiments, the offset can be greater than 1.0 mm or less than 0.2 mm. Other offsets are possible. In some embodiments, the offset  1940  can include a tolerance range, such as +/- 0.050 mm, +/- 0.060 mm, +/- 0.070 mm, +/- 0.080 mm, or +/- 0.090 mm, although other tolerance ranges are possible. 
       FIG.  19 B  is a diagram illustrating an exemplary embodiment of a plurality of coil elements, each coil element including a square cross-sectional profile of a protruding portion as described herein. As shown in  FIG.  19 B , a plurality of coil elements  1945  can be formed such that each coil element (e.g., coil elements  1900 A- 1900 C) has the same cross-sectional profile and dimensions as described in relation to the coil element shown in  FIG.  19 A . 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 dimensioned to be a ¼ of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the space  1950  can be a ⅙ of a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. As further shown in  FIG.  19 B , the plurality of coil elements  1945  can include a pitch  1955 . The pitch  1955  can be dimensioned to be a ⅓ of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the pitch  1955  can be a ⅓ of a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. Other dimensions can be implemented as well. 
       FIG.  20 A  is a diagram illustrating an exemplary embodiment of a trapezoidal cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein. As shown in  FIG.  20 A , a coil element  2000  can include a base portion  2005  and a protruding portion  2025  extending from the base portion  2005 . The base portion  2005  can include a height  2010 , a width  2015 , and a back surface  2020 . Although the base portion  2005  is shown with a rectangular-shaped profile, additional base portion profile shapes can be implemented. Similarly, although the back surface  2020  is shown as a flat-shaped back surface, additional back surface shapes or profiles can be implemented. In some embodiments, the height  2010  can include a height of 0.2 mm - 0.4 mm, 0.3 mm - 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. 
     As shown in  FIG.  20 A , the coil element  2000  can include a protruding portion  2025  extending from the base portion  2005 . The protruding portion  2025  can include a trapezoidal-shaped profile as shown in  FIG.  20 A , although other profile shapes can be implemented. The protruding portion  2025  can include a height  2030 , a width  2035  and an offset  2040 . In some embodiments, the height  2030  can include a height of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, or 0.6 mm - 1.0 mm. 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  2030  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. 
     In some embodiments, the width  2035  can include a width of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, 0.6 mm - 0.8 mm, 0.7 mm - 0.9, or 0.8 mm -1.0 mm. In some embodiments, the width can be greater than 1.0 mm or less than 0.2 mm. Other widths are possible. In some embodiments, the width  2035  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. 
     In some embodiments, the offset  2040  can include an offset of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, 0.6 mm - 0.8 mm, 0.7 mm - 0.9, or 0.8 mm -1.0 mm. In some embodiments, the offset can be greater than 1.0 mm or less than 0.2 mm. Other offsets are possible. In some embodiments, the offset  2040  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. 
     In some embodiments, the protruding portion  2025  can include an angle  2060  that is formed relative to a surface of the base portion  2005  from which the protruding portion  2025  extends. In some embodiments, the angle  2060  can 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, although other angles are possible. In some embodiments, the angle can be greater than 15 degrees. Other angles are possible. 
       FIG.  20 B  is a diagram illustrating an exemplary embodiment of a plurality of coil elements, each coil element including a trapezoidal cross-sectional profile of a protruding portion as described herein. As shown in  FIG.  20 B , a plurality of coil elements  2045  can be formed such that each coil element (e.g., coil elements  2000 A- 2000 C) has the same cross-sectional profile and dimensions as described in relation to the coil element shown in  FIG.  20 A . 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 dimensioned to be a ⅙ of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the space  2050  can be a ⅙ of a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. As further shown in  FIG.  20 B , the plurality of coil elements  2045  can include a pitch  2055 . The pitch  2055  can be dimensioned to be a ⅓ of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the pitch  2055  can be a ⅓ of a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. Other dimensions can be implemented as well. 
       FIG.  21 A  is a diagram illustrating another exemplary embodiment of a trapezoidal cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein. As shown in  FIG.  21 A , a coil element  2100  can include a base portion  2105  and a protruding portion  2125  extending from the base portion  2105 . The base portion  2105  can include a height  2110 , a width  2115 , and a back surface  2120 . Although the base portion  2105  is shown with a rectangular-shaped profile, additional base portion profile shapes can be implemented. Similarly, although the back surface  2120  is shown as a flat-shaped back surface, additional back surface shapes or profiles can be implemented. In some embodiments, the height  2110  can include a height of 0.2 mm - 0.4 mm, 0.3 mm - 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. 
     As shown in  FIG.  21 A , the coil element  2100  can include a protruding portion  2125  extending from the base portion  2105 . The protruding portion  2125  can include a trapezoidal-shaped profile as shown in  FIG.  21 A , although other profile shapes can be implemented. The protruding portion  2125  can include a height  2130 , an offset  2135 , and a width  2140 . In some embodiments, the offset  2135  can be the same or different on either side of the protruding portion  2125 . In some embodiments, the height  2130  can include a height of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, or 0.6 mm - 1.0 mm. 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  2130  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. 
     In some embodiments, the offset  2135  can include an offset of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, 0.6 mm - 0.8 mm, 0.7 mm - 0.9, or 0.8 mm - 1.0 mm. In some embodiments, the offset can be greater than 1.0 mm or less than 0.2 mm. Other offsets are possible. In some embodiments, the offset  2135  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. 
     In some embodiments, the width  2140  can include an width of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, 0.6 mm - 0.8 mm, 0.7 mm - 0.9, or 0.8 mm - 1.0 mm. In some embodiments, the width can be greater than 1.0 mm or less than 0.2 mm. Other widths are possible. In some embodiments, the width  2140  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. 
     In some embodiments, the protruding portion  2125  can include an angle  2160  that is formed relative to a surface of the base portion  2105  from which the protruding portion  2125  extends. In some embodiments, the angle  2160  can 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, although other angles are possible. In some embodiments, the angle can be greater than 15 degrees. In some embodiments, the angle  2160  can be the same on either side of the protruding portion  2125 . In some embodiments, the angle  2160  on one side of the protruding portion  2125  can be different than an angle  2160  on an opposite side of the protruding portion  2125 . 
       FIG.  21 B  is a diagram illustrating another exemplary embodiment of a plurality of coil elements, each coil element including a trapezoidal cross-sectional profile of a protruding portion as described herein. As shown in  FIG.  21 B , a plurality of coil elements  2145  can be formed such that each coil element (e.g., coil elements  2100 A- 2100 C) has the same cross-sectional profile and dimensions as described in relation to the coil element shown in  FIG.  21 A . 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 dimensioned to be a ⅙ of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the space  2150  can be a ⅙ of a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. As further shown in  FIG.  21 B , the plurality of coil elements  2145  can include a pitch  2155 . The pitch  2155  can be dimensioned to be a ⅓ of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the pitch  2155  can be a ⅓ of a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. Other dimensions can be implemented as well. 
       FIG.  22 A  is a diagram illustrating an exemplary embodiment of a rectangular cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein. As shown in  FIG.  22 A , a coil element  2200  can include a base portion  2205  and a protruding portion  2225  extending from the base portion  2205 . The base portion  2205  can include a height  2210 , a width  2215 , and a back surface  2220 . Although the base portion  2205  is shown with a rectangular-shaped profile, additional base portion profile shapes can be implemented. Similarly, although the back surface  2220  is shown as a flat-shaped back surface, additional back surface shapes or profiles can be implemented. In some embodiments, the height  2210  can include a height of 0.2 mm - 0.4 mm, 0.3 mm - 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. 
     As shown in  FIG.  22 A , the coil element  2200  can include a protruding portion  2225  extending from the base portion  2205 . The protruding portion  2225  can include a rectangular-shaped profile as shown in  FIG.  22 A , although other profile shapes can be implemented. The protruding portion  2225  can include a height  2230 , an offset  2235 , and a width  2240 . In some embodiments, the offset  2235  can be the same or different on either side of the protruding portion  2225 . 
     In some embodiments, the height  2230  can include a height that can be greater than or less than 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, or 0.6 mm - 1.0 mm, although other heights are possible. In some embodiments, the height  2230  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. 
     In some embodiments, the offset  2235  can include an offset of 0.05 mm - 0.1 mm, 0.075 mm - 0.15 mm, 0.1 mm - 0.15 mm, 0.125 mm - 0.175 mm, 0.15 mm - 0.2 mm, 0.175 - 0.25 mm, 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, or 0.6 mm - 1.0 mm. In some embodiments, the offset can be greater than 1.0 mm or less than 0.2 mm. Other offsets are possible. In some embodiments, the offset  2235  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. In some embodiments, the offset  2235  can be the same on either side of the protruding portion  2225 . In some embodiments, the offset  2235  on one side of the protruding portion  2225  can be different than an offset  2235  on an opposite side of the protruding portion  2225 . 
     In some embodiments, the width  2240  can include a width of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, 0.6 mm - 0.8 mm, 0.7 mm - 0.9, or 0.8 mm -1.0 mm. In some embodiments, the width can be greater than 1.0 mm or less than 0.2 mm. Other widths are possible. In some embodiments, the width  2240  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. 
       FIG.  22 B  is a diagram illustrating an exemplary embodiment of a plurality of coil elements, each coil element including a rectangular cross-sectional profile of a protruding portion as described herein. As shown in  FIG.  22 B , a plurality of coil elements  2245  can be formed such that each coil element (e.g., coil elements  2200 A- 2200 C) has the same cross-sectional profile and dimensions as described in relation to the coil element shown in  FIG.  22 A . The plurality of coil elements  2245  can include a space  2250  between adjacent protruding portions  2225  of adjacent coil elements. In some embodiments the space  2250  can be dimensioned to be a ⅙ of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the space  2250  can be a ⅙ of a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. As further shown in  FIG.  22 B , the plurality of coil elements  2245  can include a pitch  2255 . The pitch  2255  can be dimensioned to be a ⅓ of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the pitch  2255  can be a ⅓ of a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. Other dimensions can be implemented as well. 
       FIG.  23 A  is a diagram illustrating an exemplary embodiment of a circular cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein. As shown in  FIG.  23 A , a coil element  2300  can include a base portion  2305  and a protruding portion  2325  extending from the base portion  2305 . The base portion  2305  can include a height  2310 , a width  2315 , and a back surface  2320 . Although the base portion  2305  is shown with a rectangular-shaped profile, additional base portion profile shapes can be implemented. Similarly, although the back surface  2320  is shown as a flat-shaped back surface, additional back surface shapes or profiles can be implemented. In some embodiments, the height  2310  can include a height of 0.2 mm - 0.4 mm, 0.3 mm - 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. 
     As shown in  FIG.  23 A , the coil element  2300  can include a protruding portion  2325  extending from the base portion  2305 . The protruding portion  2325  can include a circular-shaped profile as shown in  FIG.  23 A , although other profile shapes can be implemented. The protruding portion  2325  can include a height  2330 , an offset  2335 , and a width  2340 . In some embodiments, the offset  2335  can be the same or different on either side of the protruding portion  2325 . 
     In some embodiments, the height  2330  can include a height of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, or 0.6 mm - 1.0 mm. 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  2330  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. 
     In some embodiments, the offset  2335  can include an offset of 0.05 mm - 0.1 mm, 0.075 mm - 0.15 mm, 0.1 mm - 0.15 mm, 0.125 mm - 0.175 mm, 0.15 mm - 0.2 mm, 0.175 - 0.25 mm, 0.2 mm - 0.4 mm, 0.3 - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, or 0.6 mm - 1.0 mm. In some embodiments, the offset can be greater than 1.0 mm or less than 0.2 mm. Other offsets are possible. In some embodiments, the offset  2335  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040, or +/- 0.050 mm, although other tolerance ranges are possible. In some embodiments, the offset  2335  can be the same on either side of the protruding portion  2325 . In some embodiments, the offset  2335  on one side of the protruding portion  2325  can be different than an offset  2335  on an opposite side of the protruding portion  2325 . 
     In some embodiments, the width  2340  can include a width 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 - 0.8 mm, 0.7 mm - 0.9, or 0.8 mm - 1.0 mm. In some embodiments, the width can be greater than 1.0 mm or less than 0.2 mm. Other widths are possible. In some embodiments, the width  2340  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040, or +/- 0.050 mm, although other tolerance ranges are possible. 
       FIG.  23 B  is a diagram illustrating an exemplary embodiment of a plurality of coil elements, each coil element including a circular cross-sectional profile of a protruding portion as described herein. As shown in  FIG.  23 B , a plurality of coil elements  2345  can be formed such that each coil element (e.g., coil elements  2300 A- 2300 C) has the same cross-sectional profile and dimensions as described in relation to the coil element shown in  FIG.  23 A . 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 dimensioned to be a ⅙ of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the space  2350  can be a ⅙ of a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. As further shown in  FIG.  23 B , the plurality of coil elements  2345  can include a pitch  2355 . The pitch  2355  can be dimensioned to be a ⅓ of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the pitch  2355  can be a ⅓ of a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. Other dimensions can be implemented as well. 
       FIG.  24 A  is a diagram illustrating an exemplary embodiment of a sinusoidal cross-sectional profile of a protruding portion of a coil element of a multi-piece corrugated waveguide as described herein. As shown in  FIG.  24 A , a coil element  2400  can include a base portion  2405  and a protruding portion  2425  extending from the base portion  2405 . The base portion  2405  can include a height  2410 , a width  2415 , and a back surface  2420 . Although the base portion  2405  is shown with a rectangular-shaped profile, additional base portion profile shapes can be implemented. Similarly, although the back surface  2420  is shown as a flat-shaped back surface, additional back surface shapes or profiles can be implemented. In some embodiments, the height  2410  can include a height 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. 
     As shown in  FIG.  24 A , the coil element  2400  can include a protruding portion  2425  extending from the base portion  2405 . The protruding portion  2425  can include a symmetrically-shaped sinusoidal profile as shown in  FIG.  24 A , although other shaped sinusoidal profiles can be implemented. In some embodiments, the protruding portion  2425  can have an angular profile, such as a triangular-shaped profile. In some embodiments, multiple protruding portions  2425  can extend from the base portion and each of the protruding portions can have the same or different profile shapes. The protruding portion  2425  can include a height  2430 , an offset  2435 , and a width  2440 . In some embodiments, protruding portion  2425  can be arranged between two offsets  2435 . 
     In some embodiments, the height  2430  can include a height of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, or 0.6 mm - 1.0 mm. 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  2430  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. 
     In some embodiments, the offset  2435  can include an offset of 0.05 mm - 0.1 mm, 0.075 mm - 0.15 mm, 0.1 mm - 0.15 mm, 0.125 mm - 0.175 mm, 0.15 mm - 0.2 mm, 0.175 - 0.25 mm, 0.2 mm - 0.4 mm, 0.3 - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, or 0.6 mm - 1.0 mm. In some embodiments, the offset can be greater than 1.0 mm or less than 0.2 mm. Other offsets are possible. In some embodiments, the offset  2435  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. In some embodiments, the offset  2435  can be the same on either side of the protruding portion  2425 . In some embodiments, the offset  2435  on one side of the protruding portion  2425  can be different than an offset  2435  on an opposite side of the protruding portion  2425 . 
     In some embodiments, the width  2440  can include a width of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, 0.6 mm - 0.8 mm, 0.7 mm - 0.9, or 0.8 mm -1.0 mm. In some embodiments, the width can be greater than 1.0 mm or less than 0.2 mm. Other widths are possible. In some embodiments, the width  2440  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. 
       FIG.  24 B  is a diagram illustrating an exemplary embodiment of a plurality of coil elements, each coil element including a sinusoidal cross-sectional profile of a protruding portion as described herein. As shown in  FIG.  24 B , a plurality of coil elements  2445  can be formed such that each coil element (e.g., coil elements  2400 A- 2400 C) has the same cross-sectional profile and dimensions as described in relation to the coil element shown in  FIG.  24 A . 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 dimensioned to be a ⅙ of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the space  2450  can be a ⅙ of a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. As further shown in  FIG.  24 B , the plurality of coil elements  2445  can include a pitch  2455 . The pitch  2455  can be dimensioned to be a ⅓ of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the pitch  2455  can be a ⅓ of a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. Other dimensions can be implemented as well. 
       FIG.  25 A  is a diagram illustrating an exemplary embodiment of a protruding portion of a coil element including multiple cross-sectional profiles as described herein. As shown in  FIG.  25 A , a coil element  2500  can include a base portion  2505  and a protruding portion  2525  extending from the base portion  2505 . The base portion  2505  can include a height  2510 , a width  2515 , and a back surface  2520 . Although the base portion  2505  is shown with a rectangular-shaped profile, additional base portion profile shapes can be implemented. Similarly, although the back surface  2520  is shown as a flat-shaped back surface, additional back surface shapes or profiles can be implemented. In some embodiments, the height  2510  and/or the back surface  2520  can include a height of 0.2 mm - 0.4 mm, 0.3 mm - 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. 
     As shown in  FIG.  25 A , the coil element  2500  can include multiple protruding portions  2525  extending from the base portion  2505 . The protruding portions  2525  can each include a rectangular-shaped profile as shown in  FIG.  25 A , although other profile shapes can be implemented. In some embodiments, each of the multiple protruding portions  2525  can include the same shaped profile as shown in  FIG.  25 A . In some embodiments, one or more of the protruding portions  2525  can include a profile that is shaped differently from the profile shape of other protruding portions  2525 . The protruding portions  2525  can include a height  2530 , a width  2535 , an offset  2540 , and a combined protruding portion width  2545 . In some embodiments, the height  2530  can include a height of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, or 0.6 mm - 1.0 mm. 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  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. In some embodiments, the height  2530  can be the same or different for adjacent or non-adjacent protruding portions  2525 . 
     In some embodiments, the width  2535  can include a width of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, 0.6 mm - 0.8 mm, 0.7 mm - 0.9, or 0.8 mm -1.0 mm. In some embodiments, the width can be greater than 1.0 mm or less than 0.2 mm. Other widths are possible. In some embodiments, the width  2535  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. In some embodiments, the width  2535  can be the same or different for adjacent or non-adjacent protruding portions  2525 . 
     In some embodiments, the offset  2540  can include an offset of 0.05 - 0.1 mm, 0.075 -0.15 mm, 0.1 mm - 0.15 mm, 0.125 mm - 0.175 mm, 0.15 mm - 0.2 mm, 0.175 mm - 0.25 mm, 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, or 0.6 mm - 1.0 mm. In some embodiments, the offset can be greater than 1.0 mm or less than 0.2 mm. Other offsets are possible. In some embodiments, the offset  2540  can include a tolerance range, such as +/-0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. In some embodiments, the offset  2540  can be the same on either side of the protruding portion  2525 . In some embodiments, the offset  2540  on one side of the protruding portion  2525  can be different than an offset  2540  on an opposite side of a protruding portion  2525 . In some embodiments, the offset  2540  can be the same or different with respect to non-adjacent protruding portions  2525 . 
     In some embodiments, the combined protruding portion width  2545  can include a width of 0.2 mm - 0.4 mm, 0.3 mm - 0.5 mm, 0.4 mm - 0.6 mm, 0.5 mm - 0.7 mm, 0.6 mm - 0.8 mm, 0.7 mm - 0.9, 0.8 mm - 1.0 mm, 0.9 mm - 2.0 mm, 1.5 mm - 3.0 mm, 2.5 mm - 5.0 mm, 4.0 mm - 8.0 mm, 6.0 mm - 10.0 mm, 8.0 mm - 15.0 mm, or 10.0 mm - 20.0 mm. In some embodiments, the width can be greater than 20 mm or less than 0.2 mm. Other combined protruding portion widths are possible. In some embodiments, the combined protruding portion width  2545  can include a tolerance range, such as +/- 0.010 mm, +/- 0.020 mm, +/- 0.030 mm, +/- 0.040 mm, or +/- 0.050 mm, although other tolerance ranges are possible. 
       FIG.  25 B  is a diagram illustrating an exemplary embodiment of a plurality of coil elements, each coil element including a protruding portion having multiple cross-sectional profiles as described herein. As shown in  FIG.  25 B , a plurality of coil elements  2550  can be formed such that each coil element (e.g., coil elements  2500 A- 2500 C) has the same cross-sectional profile and dimensions as described in relation to the coil element shown in  FIG.  25 A . The plurality of coil elements  2550  can include a space  2555  between adjacent protruding portions  2525  of adjacent coil elements. In some embodiments the space  2555  can be dimensioned to be a ⅙ of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the space  2555  can be a ⅙ of a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. As further shown in  FIG.  25 B , the plurality of coil elements  2550  can include a pitch  2560 . The pitch  2560  can be dimensioned to be a ⅓ of a wavelength of an electromagnetic wave provided through the MCG described herein. For example, the pitch  2560  can be a ⅓ of a wavelength of a millimeter electromagnetic wave injected into the borehole of a well. Other dimensions can be implemented as well. The coil elements  2550  can be axially fixed inside an outer tube of the MCG described herein by bolts or utilizing an immediate part to connect them together and/or to the outer tube of the MCG described herein. 
       FIGS.  26 A- 26 C  are diagrams illustrating an exemplary embodiment of a multi-piece corrugated waveguide formed from two (2) nested coil springs as described herein. As shown in  FIG.  26 A , a first coil spring  2605  can be inserted into a second coil spring  2610  by rotating the first coil spring  2605  into the second coil spring  2610  such that the coil elements of each coil spring become threaded together as shown in the assembled 2-piece coil spring  2615  shown in  FIG.  26 B .  FIG.  26 C  shows a cross-sectional view of the 2-piece coil spring  2615 . 
       FIG.  27    is a diagram illustrating an exemplary embodiment of the multi-piece corrugated waveguide of  FIG.  26 C . As shown in  FIG.  27   , detail A of  FIG.  26 C  is shown to illustrate the two coil springs nested together to create a profile of corrugation features corresponding to the diameter and pitch of the first coil spring  2605  and the second coil spring  2610 . The first coil spring  2605  can have an inner diameter  2705  that is greater than the inner diameter  2710  of the second coil spring  2610 . In some embodiments, the first coil spring  2605  can be coated with a first material, such as a dielectric or ferromagnetic material. The second coil spring  2610  can be coated with a second material, such as a conductive material. 
     Some implementations of the current subject matter can provide a multi-piece corrugated waveguide suitable for use with electromagnetic wave transmission. For example, some implementations of the current subject matter can enable formation and use of a corrugated waveguide suitable for drilling a borehole of a well using millimeter electromagnetic waves in a variety of transmission modes, such as HE11 mode. Some implementations of the multi-piece configuration of the corrugated waveguide described herein can reduce the complexity of manufacturing such apparatuses by providing corrugated waveguide features via a coil spring that can be inserted into a tube, instead of machining the corrugation features within long lengths of tube. As a result, some implementations of the MCG described herein can be manufactured at higher precision tolerances than forming the corrugated features via machining, tapping, or boring, which can leave machined material inside the waveguide and reduce electromagnetic transmissivity. Additionally, coating or plating components of the MCG can be more readily performed because insulative, dielectric, or conductive materials can be applied to individual components during manufacturing instead of coating or plating long lengths of tube with insulative, dielectric or conductive materials after corrugation features have been machined into the long tube lengths. 
     Certain exemplary embodiments have been described to provide an overall understanding of the principles of the structure, function, manufacture, and use of the systems, devices, and methods disclosed herein. One or more examples of these embodiments have been illustrated in the accompanying drawings. Those skilled in the art will understand that the systems, devices, and methods specifically described herein and illustrated in the accompanying drawings are non-limiting exemplary embodiments and that the scope of the present invention is defined solely by the claims. The features illustrated or described in connection with one exemplary embodiment may be combined with the features of other embodiments. Such modifications and variations are intended to be included within the scope of the present invention. Further, in the present disclosure, like-named components of the embodiments generally have similar features, and thus within a particular embodiment each feature of each like-named component is not necessarily fully elaborated upon. 
     Approximating language, as used herein throughout the specification and claims, may be applied to modify any quantitative representation that could permissibly vary without resulting in a change in the basic function to which it is related. Accordingly, a value modified by a term or terms, such as “about,” “approximately,” and “substantially,” are not to be limited to the precise value specified. In at least some instances, the approximating language may correspond to the precision of an instrument for measuring the value. Here and throughout the specification and claims, range limitations may be combined and/or interchanged, such ranges are identified and include all the sub-ranges contained therein unless context or language indicates otherwise. 
     One skilled in the art will appreciate further features and advantages of the invention based on the above-described embodiments. Accordingly, the present application is not to be limited by what has been particularly shown and described, except as indicated by the appended claims. All publications and references cited herein are expressly incorporated by reference in their entirety.