Abstract:
An electrical system having an underlying structure resembling the double helix most commonly associated with DNA may be used to produce useful electromagnetic fields for various applications.

Description:
FIELD OF THE INVENTION 
       [0001]    The invention relates to bodies structured as helically wound runners around which one or more conductive wires may be wound, electrical devices and/or systems configured to include such bodies, and the manufacture of such bodies and/or such electrical devices and/or systems. The invention also relates to methods of operation of these devices and systems, and applications thereof. 
       BACKGROUND OF THE INVENTION 
       [0002]    It is known that spirally wound electrical conductors may exhibit certain electromagnetic properties and/or generate particular electromagnetic fields. For example, it is known that an electromagnetic coil may act as an inductor and/or part of a transformer, and has many established useful applications in electrical circuits. An electromagnetic coil may be used to exploit the electromagnetic field that is created when, e.g., an active current source is operatively coupled to both ends of the coil. 
       SUMMARY 
       [0003]    One aspect of the invention relates to an electrical system comprising a body and one or more conductive wires. The body may include two intertwined helically wound runners. A first runner is coupled to the second runner by struts. The body is arranged in a toroidal shape. The one or more conductive wires may be spirally wound to form a coil around at least part of one runner of the body. 
         [0004]    One aspect of the invention relates to an electrical system comprising a body and two conductive wires. The body may include two intertwined helically wound runners. A first runner is coupled to a second runner by struts that substantially do not conduct electricity between the first runner and the second runner. The body is arranged in a toroidal shape having a centroid. The first conductive wire is spirally wound using a first predetermined winding around at least part of the first runner of the body such that the first conductive wire is arranged in a helical shape having an axis that coincides with the first runner. The second conductive wire is spirally wound using a second predetermined winding around at least part of the second runner of the body such that the second conductive wire is arranged in a helical shape having an axis that coincides with the second runner. The first runner includes two leads configured to be electrically coupled to a current source to receive a first current such that an electromagnetic field is created. The second runner includes two leads configured to be electrically coupled to the current source to receive a second current such that the electromagnetic field is modified. 
         [0005]    These and other objects, features, and characteristics of the present disclosure, as well as the methods of operation and functions of the related components of structure and the combination of parts and economies of manufacture, will become more apparent upon consideration of the following description and the appended claims with reference to the accompanying drawings, all of which form a part of this specification, wherein like reference numerals designate corresponding parts in the various figures. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a definition of the any limits. As used in the specification and in the claims, the singular form of “a”, “an”, and “the” include plural referents unless the context clearly dictates otherwise. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0006]      FIG. 1  illustrates a side view of an exemplary body including two intertwined helically wound runners, coupled by struts. 
           [0007]      FIG. 2  illustrates an isometric view of an exemplary body including two intertwined helically wound runners, coupled by struts. 
           [0008]      FIG. 3  illustrates a top-down view of an exemplary body including two intertwined helically wound runners sharing the same circular axis, both runners coupled by struts. 
           [0009]      FIG. 4  illustrates an isometric view of an exemplary body including two intertwined helically wound runners sharing the same circular axis, both runners coupled by struts. 
           [0010]      FIG. 5  illustrates a top-down view of an exemplary body including two intertwined helically wound runners sharing the same circular axis and having wire guides, both runners coupled by struts. 
           [0011]      FIG. 6  illustrates an isometric view of an exemplary body including two intertwined helically wound runners sharing the same circular axis and having wire guides, both runner coupled by struts. 
           [0012]      FIG. 7  illustrates a top-down view of an exemplary body including two intertwined helically wound runners sharing the same elliptical axis, both runner coupled by struts. 
           [0013]      FIG. 8  illustrates a top-down view of an exemplary body including two intertwined helically wound runners sharing the same circular axis, both runners coupled by struts and having conductive wires spirally wound therearound. 
           [0014]      FIG. 9  illustrates a top-down view of an exemplary body including two intertwined helically wound runners sharing the same circular axis, both runner coupled by struts and having a wire spirally wound around both runners of the body. 
           [0015]      FIGS. 10A-D  illustrate various different windings to spirally wind one or more wires around a runner in accordance with exemplary embodiments. 
           [0016]      FIG. 11  illustrates a winding that spirally winds a wire around a runner and around struts in accordance with exemplary embodiments. 
       
    
    
     DETAILED DESCRIPTION 
       [0017]      FIG. 1  illustrates a side view of an exemplary body  15 . Body  15  may include two or more intertwined helically wound runners—runner  16  and runner  17 . Runner  16  and runner  17  may be coupled by struts  18 . Body  15  includes two ends—end  20  and end  21 —disposed at opposite sides of body  15 . Runners  16  and/or  17  may be arranged in the shape of a three-dimensional curve similar to or substantially the same as a helix. A helix may be characterized by the fact that a tangent line at any point along the curve has a constant angle with a (fixed) line called the axis. The pitch of a helix may be the width of one 360 degree helix turn (a.k.a. revolution), e.g. measured parallel to the axis of the helix. Intertwined helically wound runners may share the same axis, be congruent, and/or differ by a translation along the axis, e.g. measuring half the pitch. The two runners shown in  FIG. 1  may share the same axis  22 , extending horizontally for approximately three complete revolutions. The length of body  15 , as measured along axis  22  from end  20  to end  21 , may thus be approximately three times the length of pitch  23 . A helical shape may have constant pitch, constant radius (measured in the plane perpendicular to the axis), constant torsion, constant curvature, constant ratio of curvature to torsion, and/or a straight axis. In  FIG. 1 , the radius of body  15  may be half of diameter  24 . It is noted that the shape of body  15  resembles the general shape of DNA. 
         [0018]    The shape of the cross-section of a runner may include one or more of a circle, an oval, a square, a triangle, a rectangle, an angular shape, a polygon, and/or other shapes. The width and height of the cross-section of a runner may be limited to a maximum of half the pitch for practical purposes. The shape and/or size of the cross-section of a runner may change along the length of the runner. The relation of the width of a runner to the pitch of the helical shape may define a characteristic measurement/feature of body  15 . This relation may be constant along the length of body  15 , e.g. from end  20  to end  21 . In  FIG. 1 , the shape of cross-section of runner  16  and runner  17  may be a rectangle that is approximately three times wider than it is tall. Furthermore, the width of runner  16  or runner  17  may be approximately 1/13 th  of the pitch of said runner of body  15 . As a result, runner  17  of body  15  resembles a ribbon having an inner surface  25  (facing axis  22  of the helical shape) and an outer surface  26  (facing the opposite way as inner surface  25 ). Runner  16  of body  15  resembles a ribbon having an inner surface  27  (facing axis  22  of the helical shape) and an outer surface  28  (facing the opposite way as inner surface  27 ). Note that embodiments of this disclosure are not intended to be limited by any of the given examples. 
         [0019]    Struts  18  coupling the runner  16  and runner  17  may be substantially straight, curved, the shape of an arc, twisted, and/or other shapes. In  FIG. 1 , struts  18  may be substantially straight. Struts  18  may be arranged substantially perpendicular to axis  22 , and/or substantially parallel to others of struts  18 . The shape of a cross-section of a strut may include one or more of a circle, an oval, a square, a triangle, a rectangle, an angular shape, a polygon, and/or other shapes. The shape and/or size of the cross-section of one of struts  18  may change along the length of the strut. In  FIG. 1 , the shape of the cross-section of struts  18  may be a circle. In  FIG. 1 , all or most struts may have substantially the same length. The number of struts per revolution may not be constant. In  FIG. 1 , body  15  includes approximately 10 struts per complete revolution of a runner. As shown in  FIG. 1 , the diameter of each strut may be smaller than the width of a runner as measured e.g. at inner surface  25  of runner  17  at the point of engagement  19  with one of struts  18 . The diameter of one strut may not be constant. The diameters of multiple adjacent struts may not be the same. 
         [0020]    Runner  16 , runner  17  and/or struts  18  may be manufactured from one or more of plastic, plastic plated with metals including copper, nickel, iron, soft iron, nickel alloys, and/or other metals and alloys, and/or other materials. In some embodiments, runner  16 , runner  17  and struts  18  are manufactured from non-conductive material. Runner  16 , runner  17 , and struts  18  may be manufactured from different materials. Runner  16 , runner  17 , and struts  18  may be manufactured through integral construction or formed separately prior to being assembled. 
         [0021]      FIG. 2  illustrates an isometric view of an exemplary body  15  including two intertwined helically wound runners—runner  16  and runner  17 —coupled by struts  18 . Body  15  is shown here with axis  22  of both helically wound runners extending vertically. 
         [0022]      FIG. 3  illustrates a top-down view of an exemplary body  35  including two intertwined helically wound runners—runner  36  and runner  37 —sharing the same circular axis  42 , both runners coupled by struts  38 . The resulting shape of body  35  may be referred to as toroidal. Body  35  may be formed the same as or similar to body  15 , though comprising more revolutions, by arranging the body in a planar circular shape and joining both ends—end  20  and end  21  in FIG.  1 —together. The preceding statement is not intended to limit the (process of) manufacture of bodies similar to or substantially the same as body  35  in any way. Note that the shape of the cross-section of both runner  36  and runner  37  in  FIG. 3  may be circular, whereas it may be rectangular for body  15  in  FIGS. 1 and 2 . 
         [0023]    Referring to  FIG. 3 , the diameter  44  of the circular axis of body  35 , as well as the number of complete revolutions per runner required to completely extend along the entire circular axis  42  may be characteristic measurements/features of body  35 . For example, as shown in  FIG. 3 , runner  36  and runner  37  of body  35  may require approximately eight complete revolutions around circular axis  42  to completely extend along the entire circular axis  42  of body  35 , or some other number of rotations. 
         [0024]    Note that one or more struts  38  of body  35  in  FIG. 3  include a center-strut element  39 , which is lacking from struts  18  of body  15 . Center-strut element  39  may be associated with a particular strut of body  35 . The shape of the cross section of a center-strut element may include one or more of a circle, an oval, a square, a triangle, a rectangle, an angular shape, a polygon, and/or other shapes. The shape and/or size of the cross-section of one of center-strut elements  39  may change along the length of center-strut element  39 . One or more struts  38  of body  35  may include a center-strut element  39 , which may have a different shape than a center-strut element  39  of another one of struts  38 . In  FIG. 3 , the shape of the cross-section of center-strut element  39  may be circular, such that center-strut element  39  may have a cylindrical shape, in which the axis of the cylindrical shape of a given center-strut element  39  may coincide with the associated strut  38 . In  FIG. 3 , struts  38  include center-strut element  39 , having substantially the same shape. A center-strut element may enhance structural integrity and/or serve other purposes. 
         [0025]      FIG. 4  illustrates an isometric view of an exemplary body  35  including two intertwined helically wound runners—runner  36  and runner  37 —sharing the same circular axis, both runners coupled by struts  38 . Note that, as in  FIG. 3 , the struts of body  35  in  FIG. 4  may include a center-strut element  39 , which may be lacking from struts  18  of body  15 . 
         [0026]      FIG. 5  illustrates a top-down view of an exemplary body  55  including two intertwined helically wound runners—runner  57  and runner  58 —sharing the same circular axis  62  and having wire guides  56 , both runners coupled by struts  59 . Though the shape of the cross-section of runner  57  and runner  58  in  FIG. 5  may be circular, a runner may still have an inner surface (the half of the surface of a runner for which normal vectors are directed approximately inward toward body  55 ) and an outer surface (the half of the surface of a runner for which normal vectors are directed approximately outward, away from body  55 ). Any part of runner  57  or runner  58  may include wire guides  56 . Wire guides  56  may include grooves, notches, protrusions, slots, and/or other structural elements disposed on and/or in runner  57  or runner  58  and configured to guide a wire along at least a part of the surface of runner  57  or runner  58 , generally in a direction substantially perpendicular to the direction of runner  57  or runner  58  at the point of engagement between one of wire guides  56  and runner  57  or runner  58 . 
         [0027]    In  FIG. 5 , one of wire guides  56  of runner  58  may include a protrusion disposed on the outer surface of runner  58 , arranged such that wire guide  56  may guide a wire arranged in a helical shape around runner  58 , wherein the helical shape has an axis that coincides with runner  58 . Such a wire, as any wire listed in any figure included in this description, may be insulated, uninsulated, or partially insulated and partially uninsulated. As shown in  FIG. 5 , wire guides  56  may be disposed in an intermittent pattern rather than a continuous pattern, e.g. such that no protrusion is disposed on the surface of runner  57  or runner  58  approximately nearest to (or directly opposite to) one of points of engagement  63  between runner  57  or runner  58  and of one struts  59 . The number of wire guides per complete revolution of a runner and/or the number of wire guides between adjacent struts may be characteristic measurements/features of body  55 . The size, shape, position, and/or pattern of disposition of wire guides  56  may be characteristic measurements/features of body  55 . 
         [0028]      FIG. 6  illustrates an isometric view of an exemplary body  55  including two intertwined helically wound runners—runner  57  and runner  58 —sharing the same circular axis and having wire guides  56 , both runners coupled by struts  59 . 
         [0029]      FIG. 7  illustrates a top-down view of an exemplary body  75  including two intertwined helically wound runners—runner  76  and runner  77 —sharing the same elliptical axis  78 , both runner coupled by struts  79 . A body including two (or more) intertwined helically wound runners sharing the same axis may be arranged in any planar shape, including a circle, an oval, a triangle, a square, a rectangle, an angular shape, a polygon, and/or other planar shapes. Alternatively, and/or simultaneously, such a body may be arranged in a three-dimensional curve (a.k.a. space curve). In  FIG. 7 , body  75  may be formed from a body similar to body  15 , though comprising more revolutions, by arranging the body in a planar elliptical shape and joining both ends—end  20  and end  21  in FIG.  1 —together. The preceding statement is not intended to limit the (process of) manufacture of bodies similar to or substantially the same as body  75  in any way. 
         [0030]      FIG. 8  illustrates a top-down view of an exemplary body  85  including two intertwined helically wound runners—runner  88  and runner  89 —sharing the same circular axis, coupled by struts  90  and having conductive wires—wire  86  and wire  87 —spirally wound therearound to form coils. Wire  86  and wire  87 , as any wire listed in any figure included in this description, may be insulated, uninsulated, or partially insulated and partially uninsulated. The shape of body  85  may be similar to the shape of body  35  in  FIG. 3 . Runner  88  and runner  89  of body  85  may form cores around which wire  86  and wire  87  are spirally wound, respectively. As such, wire  86  and wire  87  may be arranged in a helical shape having axes that coincide with runner  88  and runner  89 , respectively. As shown in  FIG. 8 , wire  86  and  87  may be wound such that they go around any of struts  90  of body  85  and/or around any points of engagement between one of struts  90  and one of runners  88  and  89 . The number of wire turns per complete revolution of a runner and/or the number of wire turns between adjacent struts may be characteristic measurements/features of body  85 . In  FIG. 8 , wire  86  and wire  87  may be arranged to make approximately five turns between adjacent struts associated with runner  88  and runner  89 , respectively, and/or some other number of turns. The windings of wire  86  and wire  87  around runner  88  and runner  89 , respectively, are exemplary windings and are not intended to be limiting in any way. Different types of windings are contemplated. Using multiple conductive wires per runner is contemplated. 
         [0031]    Wire  86  may include two leads—lead  86   a  and lead  86   b . Wire  87  may include two leads—lead  87   a  and lead  87   b . Wire  86  and wire  87  may be conductive. Body  85  may be used in an electrical system having one or more power sources and/or current sources arranged such that electrical coupling with one or both of wire  86  and wire  87  may be established, e.g. through coupling with lead  86   a  and  86   b  of wire  86  and through coupling with lead  87   a  and  87   b  of wire  87 . The current supplied to wire  86  may be a direct current or an alternating current. The current supplied to wire  87  may be a direct current or an alternating current. The currents supplied to wire  86  and wire  87  may flow in the same direction or the opposite direction. For alternating currents, operating frequencies ranging from 0 Hz to 100 GHz are contemplated. The operating frequencies for wire  86  and wire  87  may be the same or different. Other electrical operating characteristics of current supplied to wire  86  and wire  87 , such as phase, may be the same or different. The electrical system may be used to exploit the electromagnetic field that is created when electrical power is supplied to one or more wires of body  85 . 
         [0032]    Some embodiments of an electrical system including a body similar to or substantially the same as body  85  in  FIG. 8 , thus including wire  86  and wire  87 , may be configured to have a current in wire  86  flowing in the opposite direction as the current in wire  87 . In some embodiments the current supplied to one wire may be a direct current, whereas the current supplied to another wire may be an alternating current. 
         [0033]      FIG. 9  illustrates a top-down view of an exemplary body  95  including two intertwined helically wound runners—runner  97  and runner  98 —sharing the same circular axis, both runner coupled by struts and having a wire  96  spirally wound around both runners of body  95 . Wire  96 , as any wire listed in any figure included in this description, may be insulated, uninsulated, or partially insulated and partially uninsulated. Wire  96  may include two leads—lead  86   a  and lead  86   b . The resulting shape of body  95  with wire  96  may be referred to as a helicoidal shape. Wire  96  may be conductive. Body  95  may be used in an electrical system having a power source and/or a current source arranged such that electrical coupling with wire  96 , e.g. through leads  96   a  and  96   b , may be established. The electrical power supplied to wire  96  may include a direct current or an alternating current. Operating frequencies for an alternating current flowing through wire  96  are contemplated to range from 0 Hz to 100 GHz. The electrical system may be used to exploit the electromagnetic field that is created when electrical power is supplied to wire  96  of body  95 . 
         [0034]      FIGS. 10A-D  illustrate various different windings to spirally wind one or more wires around a runner in accordance with exemplary embodiments. As depicted in  FIGS. 10A-D , various different windings are illustrated for a runner  88 , which may be similar to or substantially the same as runner  88  depicted in  FIG. 8 . As depicted in  FIGS. 10A-D , the side view of runner  88  may appear to indicate that runner  88  is shaped in a straight line, from runner end  88   a  on the left to runner end  88   b  on the right in each of the  FIGS. 10A-D . This is merely for illustrative purposes and is not intended to be limiting in any way. The shape of runner  88  may have any of the shapes described herein for runners, including a helically wound runner that is arranged in a toroidal shape such that the ultimate runner end  88   a  may meet and/or coincide with the ultimate runner end  88   b . The use of runner  88  is not intended to be limiting in any way. The various windings described herein may be applied to any runner described herein, and thus be included in any body described herein. 
         [0035]      FIG. 10A  illustrates a bifilar winding of wire  11  around runner  88 . Wire  11  has two leads, labeled a and b. 
         [0036]      FIG. 10B  illustrates a winding of wire  12  and wire  13  around runner  88 . Wire  12  has two leads, labeled a and c. Wire  13  has two leads, labeled b and d. The winding depicted in  FIG. 10B  may correspond to different types of coils around runner  88 , and/or different directions for currents running through wire  12  and wire  13 , and thus different resulting electromagnetic fields once the one or more windings in  FIG. 10B  are used in electrical systems described herein. Different types of coils may correspond to different connections between the leads of wire  12  and wire  13 . For example, by connecting lead c of wire  12  to lead d of wire  13 , the windings depicted in  FIG. 10B  form a bifilar coil around runner  88  that is similar the bifilar coil depicted in  FIG. 10A . Referring to  FIG. 10B , all permutations of coupling the leads of wire  12  and the leads of wire  13  are contemplated. 
         [0037]      FIG. 10C  illustrates a caduceus winding of wire  12  and wire  13  around runner  88 . Wire  12  has two leads, labeled a and c. Wire  13  has two leads, labeled b and d. The winding depicted in  FIG. 10C  may correspond to different types of coils around runner  88 , and/or different directions for currents running through wire  12  and wire  13 , and thus different resulting electromagnetic fields once the one or more windings in  FIG. 10C  are used in electrical systems described herein. Different types of coils may correspond to different connections between the leads of wire  12  and wire  13 . For example, by connecting lead c of wire  12  to lead d of wire  13 , the windings depicted in  FIG. 10C  form a caduceus coil around runner  88 . All permutations of coupling the leads of wire  12  and the leads of wire  13  are contemplated, as well as all directions for currents running through wire  12  and wire  13 . 
         [0038]      FIG. 10D  illustrates a double bifilar winding of wire  12  and wire  13  around runner  88 . Wire  12  has two leads, labeled a and b. Wire  13  has two leads, labeled c and d. Though the windings of wire  12  and wire  13  are depicted in  FIG. 10D  as being wound from runner end  88   a  to runner end  88   b , this is not intended to be limiting in any way. It is contemplated that wire  12  and wire  13  are wound in different directions around runner  88 . For example, when runner  88  is arranged in a toroidal shape, wire  12  and wire  13  may be wound clockwise and counter-clockwise. By way of non-limiting example (and not depicted in  FIG. 10D ), leads c and d of wire  13  may be disposed near runner end  88   b  such that wire  13  is wound from runner end  88   b  to runner end  88   a.    
         [0039]    The winding of wire  12  in  FIG. 10D  may be similar to the bifilar winding of wire  11  depicted in  FIG. 10A . Referring to  FIG. 10D , the winding of wire  13  may be similar to the bifilar winding of wire  11  depicted in  FIG. 10A . Referring to  FIG. 10D , the windings depicted in  FIG. 10D  may correspond to different types of coils around runner  88 , and thus different resulting electromagnetic fields once the one or more windings in  FIG. 10D  are used in electrical systems described herein. Different types of coils may correspond to different connections between the leads of wire  12  and wire  13 . All permutations of coupling the leads of wire  12  and the leads of wire  13  are contemplated, as well as all directions for currents running through wire  12  and wire  13 . Additional windings include an Ayrton-Perry winding, a trifilar winding, windings of braided wires, windings around a runner and (part of) one or more struts, and/or other types of windings. 
         [0040]    In some embodiments, a wire may be wound around a particular runner from a first strut to a second adjacent strut (such that these and other struts connect the particular runner to a second runner), subsequently wound around one of the struts, e.g. from the particular runner down to the center of a strut, before proceeding back up to the particular runner to continue being wound around the particular runner in the same direction towards a third strut that is adjacent to the second strut, and so on. In other words, the wire may be alternately wound around a segment of the particular runner between (adjacent) struts and around a strut, for all or part of the body that includes the runner. Additionally, a second wire may be similarly wound around the second runner and around the same struts that connect the particular runner to the second runner. By winding the second wire up to the center of a strut (or up to the winding of the wire carried by the particular runner described above), the second wire may stay clear of the wire carried by the particular runner. When winding wires around both runners and the connecting struts, the direction of the wires wound around the struts may be the same or opposite. 
         [0041]    By way of illustration,  FIG. 11  illustrates a winding that spirally winds wire  87  around runner  88  and around struts  91  and  92  in accordance with exemplary embodiments, as described above. Only a segment of runner  88  and runner  89  is depicted in  FIG. 11 , as indicated by the dashed continuation lines. The number of revolutions between struts in  FIG. 11  is exemplary and not intended to be limiting in any way. The number of revolutions around a strut in  FIG. 11  is exemplary and not intended to be limiting in any way. The number or fraction of struts  90  used to wind wire  87  around as depicted in  FIG. 11  is exemplary and not intended to be limiting in any way. For example, wire  87  may be wound around every strut that is included in a body. As depicted in  FIG. 11 , wire  87  is wound up to the approximate center of struts  91  and  92 . Note that a second wire may be similarly wound around runner  89  and down to the approximate center of struts  91  and  92 , and/or other struts in struts  90  (this is not depicted in  FIG. 11 ), as described above. 
         [0042]    Any of the bodies and windings shown in  FIGS. 1-10  and/or described herein may be used in an electrical system. Conductive wires may be spirally wound around one or more runners, one or more struts, and/or any combination thereof to produce electrical systems having specific electromagnetic properties when electrical power is supplied to one or more of the conductive wires. These conductive wires may be insulated, uninsulated, or partially insulated and partially uninsulated. A (magnetic) core may be disposed in the space between multiple runners, such that the runners helically wound around the (magnetic) core. Alternatively, and/or simultaneously, relative to any body described herein, a (magnetic) core may be moved along a straight line, along any curve of the body, along a strut, along a runner, along any axis of the body, or along any surface of the body, in any three-dimensional relation to the body. For example, a magnet may be moved along a line perpendicular to the planar shape of body  85 , in the center of the circular axis of body  85 , a.k.a. through the “donut-hole.” 
         [0043]    In some embodiments, electrical systems as described herein may include one or more resistive elements that are electrically coupled to one or more conductive wires that form a coil. By way of non-limiting example, a resistive element may be a resistor. The electrical characteristics of the one or more resistive elements may be chosen such that the impedance of the one or more conductive wires combined with the impedance of the one or more resistive elements substantially matches a predetermined value. 
         [0044]    In some embodiments, the predetermined value for impedance matching substantially may be the nominal impedance of a current source. By way of non-limiting example, an electrical system using body  85 , as depicted in  FIG. 8 , and having bifilar windings, as depicted in  FIG. 10A , around both runners such that conductive wire  86  is electrically coupled to conductive wire  87 , may have a particular exemplary nominal impedance. One or more resistive elements may be electrically coupled to conductive wire  86  and/or conductive wire  87  such that the combined nominal impedance matches a predetermined value, such as, e.g., 4 ohms, 8 ohms, 16 ohms, 32 ohms, 100 ohms, 600 ohms, and/or another predetermined value. For example, the particular exemplary impedance may be 4.7 ohms. A 3.3 ohm resistor may be added serially to this electrical system, such that this electrical system now matches an 8 ohms impedance of a current source. 
         [0045]    Applications for any of the electrical systems described herein may include affecting growth and/or growth rate of plants and/or other organisms. Applications for any of the electrical systems described herein may include therapeutic applications. Applications for any of the electrical systems described herein may include energy production, conversion, and/or transformation. Applications for any of the electrical systems described herein may include ATP production, transfer, and/or processing. 
         [0046]    In some embodiments, an electrical system including any of the bodies and windings shown in  FIGS. 1-10  may be used as a component in an electrical circuit, performing one or more functions and/or applications including a (tunable) inductor, a (Tesla) coil, a transformer, a transducer, a transistor, a resistor, a solenoid, a stator for an electrical motor, an electromagnet, an electromagnetic pulse generator, an electromagnetic actuator, an energy conversion device, a position servomechanism, a generator, a stepping motor, a DC motor, a (contact-free) linear drive, an axial flux device, a measurement device for magnetic permeability, a dipole magnet, and a device to alter electron and/or particle trajectory. 
         [0047]    Although the invention has been described in detail for the purpose of illustration based on what is currently considered to be the most practical and preferred embodiments, it is to be understood that such detail is solely for that purpose and that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover modifications and equivalent arrangements that are within the spirit and scope of the appended claims. For example, it is to be understood that the present invention contemplates that, to the extent possible, one or more features of any embodiment can be combined with one or more features of any other embodiment.