Wiring of assemblies and methods of forming channels in wiring assemblies

A conductor assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, comprising:

• a conductor having a spiral configuration, positioned along a path in a cylindrical plane and which extends along an axis central to the cylindrical plane, positions along the path varying in azimuthal angle, θn, where:
• the azimuthal angle of each position is measurable in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis,
• the configuration comprises a continuous series of connected turns, Tn, for which n is an integer ranging from one to N, each turn, Tn, including a first arc and a first straight segment, the configuration including a spacing between at least one turn, Tn, and an adjacent turn Tn+1 or Tn−1, and
• for a given value of n:
• (i) a spacing between one of the straight segments in a turn Tn and an adjacent straight segment in an adjoining turn Tn+1 or Tn−1 in the cylindrical plane is determined according to the relationship
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• /
• 2
• N
• where positions between which the spacing exists are defined by the azimuthal angle, n, or
• (ii) a spacing between one of the arcs in a turn Tn and an adjacent arc in an adjoining turn Tn+1 or Tn−1 in the cylindrical plane is determined according to the relationship
• F
• 
• (
• x
• )
• *
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• /
• 2
• N
• ,
• where m is an integer greater than zero, x is a position along the axis and F(x) varies in value along the arc from zero to one, and positions between which the spacing exists are defined by the azimuthal angle, θn.

A conductor assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, comprising:

• a body having a first channel formed therein defining a first path extending along a first cylindrical plane and along a direction parallel to an axis central to the cylindrical plane, where the first channel is in a configuration comprising a continuous series of connected turns, GTj, providing a first spiral pattern, where:
• the azimuthal angle of each position is measured in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis,
• the configuration comprises a continuous series of connected turns, GTj, for which j is an integer ranging from one to N,
• each turn, GTj, includes a first arc, a second arc and first and second straight segments connected to one another by the first arc,
• the second arc connects the turn, GTj to an adjoining turn, GTj+1 or GTj−1,
• for a given value of n, each of the first and second straight segments in the turn GTj is spaced apart from an adjacent straight segment in an adjoining turn GTj+1 or GTj−1, and
• for each straight segment in each turn, GTj, the azimuthal angle, θn, defines a sufficient number of positions according to the relationship
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• /
• 2
• N
• where m is an integer greater than zero, that all positions along a majority of the length of each straight segment in each turn, GTj, conform to
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• /
• 2
• N
• .

A method for constructing a conductor assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, comprising:

• providing a conductor having a spiral configuration, positioned along a path in a first cylindrical plane, which conductor extends along an axis central to the cylindrical plane, positions along the path varying in azimuthal angle where:
• the azimuthal angle of each position is measured in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis,
• the configuration comprises a first plurality of N turns, Tn, connected to one another in a continuous series in the first cylindrical plane, each turn, Tn, including first and second coil ends which are each a portion of a turn not parallel with the axis,
• for a given value of n, each of the turns Tn is spaced apart from an adjacent straight segment in an adjoining turn Tn+1 or Tn−1, and
• for each turn, Tn, a sufficient number of positions along a majority of the length of the turn are in accord with the relationship
• F
• 
• (
• x
• )
• *
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• /
• 2
• N
• ,
• where m is an integer greater than zero, x is a position along the axis and F(x) varies in value along the coil ends between zero and one, such that all positions along a majority of the length of each turn, Tn, conform to
• F
• 
• (
• x
• )
• *
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• /
• 2
• N
• .

A length of conductor extending in a continuous spiral pattern in a first cylindrical plane extending along a central axis to create a saddle coil shape, the pattern comprising N turns, Tn, with each turn having a fixed position in the same cylindrical plane, each turn including a pair of straight segments parallel to one another, the straight segments arranged in spaced-apart relation as a function of azimuthal angle, θn, about the axis, according to

• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• /
• 2
• N
• where m is an integer greater than zero and the azimuthal angle, θn, of each position along each straight segment is measured in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis.

A method of forming a conductor assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, comprising:

• (i) defining a series of closed conductor paths, n, where n ranges from 1 to N, all of the closed paths residing in one cylindrical plane positioned about an axis in accord with the relationship
• F
• 
• (
• x
• )
• *
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• /
• 2
• N
• ,
• where m is an integer value greater than one;
• θ is the azimuthal angle of each position measured in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis, said relationship providing a suitable approximation for an ideal current density distribution according to cos(mθ);
• x is a position along the axis;
• and F(x) is a shape function which varies in value from zero to one;
• and
• (ii) a set of conductive winding turns is created by modifying the contours of the closed conductor paths with respect to the axial direction, x, to transform the closed shapes into a set of open shapes which each connect to another open shape to create a spiral configuration which departs from the ideal current density distribution.

A method for constructing a conductor assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, comprising:

• providing a conductor having a spiral configuration, positioned along a path in a first cylindrical plane, which conductor extends along an axis central to the cylindrical plane, positions along the path varying in azimuthal angle where:
• the azimuthal angle of each position is measured in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis,
• the configuration comprises a first plurality of N turns, Tn, connected to one another in a continuous series in the first cylindrical plane, each turn, Tn, including first and second coil ends which are each a portion of a turn not parallel with the axis,
• for a given value of n, each of the turns Tn is spaced apart from an adjacent turn Tn+1 or Tn−1, and
• for at least one turn, Tn, the positions along a majority of the length of the turn are in accord with the relationship
• F
• 
• (
• x
• )
• *
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• /
• 2
• N
• ,
• where m is an integer greater than zero, x is a position along the axis and F(x) varies in value along the coil ends between zero and one, and
• wherein multipole content which would otherwise be present in a field generated by the spiral configuration, relative to a pure multipole field of order m, which would theoretically be generated by a configuration having an ideal cos(nθ) current distribution, is reduced by applying a numerical optimization technique which modifies the shapes of turns to more closely conform the field pattern generated by the spiral configuration to the pure multipole field of order m.

A method for constructing a conductor assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, a channel in the assembly having a spiral configuration for a multipole field configuration of order m, the method comprising:

• inserting multiple layers of the conductor in the channel to conform each layer of the conductor to the spiral configuration, with each layer of the conductor positioned along a path in a different one of multiple concentric cylindrical planes, which paths extend along an axis central to the cylindrical planes, positions along the paths varying in azimuthal angle, where:
• the azimuthal angle of each position is measurable in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis,
• each layer in the configuration comprises a plurality of N turns, Tn, connected to one another in a continuous series in the first cylindrical plane, each turn, Tn, including first and second coil ends which are each a portion of a turn not parallel with the axis, and
• for a given value of n, each of the turns Tn is spaced apart from an adjacent turn Tn+1 or Tn−1;
• and
• defining paths in the channel for straight portions of the channel or for curved portions of the channel which result in path segments which deviate from ideal channel path segments into which one or more segments of conductor turns in one or more conductor layers are placed.

A configuration for a conductive winding of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, comprising:

• a conductor having a spiral positioned along a path in a first cylindrical plane, which conductor extends along an axis central to the cylindrical plane, positions along the path varying in azimuthal angle where:
• each turn, Tn, includes a first arc, a second arc and first and second straight segments
• the azimuthal angle of each position is measured in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis,
• a first turn Tn and a second turn Tn+1 or Tn−1 adjoin one another in the series and are spaced apart from one another,
• a first segment of the conductor in the first turn and a second segment of the conductor in the second turn Tn+1 or Tn−1 each follow a path in accord with
• F
• 
• (
• x
• )
• *
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• 2
• N
• where m is an integer greater than zero, x is a position along the axis and F(x) varies in value along the coil ends between zero and one, and
• the conductor further comprises a third segment which does not follow a path in accord with
• F
• 
• (
• x
• )
• *
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• 2
• N
• ,
• the third segment providing electrical connection between the first and second segments.

A channel configuration for a conductive winding of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, comprising:

• a spiral channel formed in a body comprising a continuous series of connected channel turns, GTn, positioned along a path in a first cylindrical plane, which channel extends along an axis central to the cylindrical plane, positions along the path varying in azimuthal angle where:
• each turn, GTn, includes a first arc, a second arc and first and second straight segments the azimuthal angle of each position is measured in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis,
• a first turn GTn and a second turn GTn+1 or GTn−1 adjoin one another in the series,
• a first segment of the channel in the first turn GTn and a second segment of the channel in the second turn GTn+1 or GTn−1 each follow a path in accord with
• F
• 
• (
• x
• )
• *
• sin
• 
• (
• m
• *
• θ
• n
• )
• -
• n
• -
• 1
• 2
• N
• ,
• where m is an integer greater than zero, x is a position along the axis and F(x) varies in value along each of the arcs between zero and one, and
• the channel further comprises a third segment which does not follow a path in accord with
• F
• 
• (
• x
• )
• *
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• 2
• N
• ,
• the third segment providing a path for a conductive segment to provide electrical connection between conductor in the first and second segments.

A configuration for a conductive winding of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, comprising:

• a conductor having a spiral shape comprising turns, Tn, positioned along a path in a first cylindrical plane, and at least a second continuous series of connected turns positioned along a path in a second cylindrical plane, which conductor extends along an axis central to the cylindrical plane, positions along the path varying in azimuthal angle where:
• each turn includes a first arc, a second arc and first and second straight segments,
• the azimuthal angle of each position is measured in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis,
• a first segment of the conductor in a first turn in the first continuous series in the first cylindrical plane and a second segment of the conductor in the second continuous series in the second cylindrical plane each follow a path in accord with
• F
• 
• (
• x
• )
• *
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• 2
• N
• ,
• where m is an integer greater than zero, x is a position along the axis and F(x) varies in value along the coil ends between zero and one, and
• the conductor further comprises a third segment which does not follow a path in accord with
• F
• 
• (
• x
• )
• *
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• 2
• N
• ,
• the third segment providing electrical connection between the first and second segments.

A channel configuration for a conductive winding of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, comprising:

• a spiral channel formed in a body comprising a first continuous series of connected channel turns positioned along a path in a first cylindrical plane, and at least a second continuous series of connected channel turns positioned along a path in a second cylindrical plane, which channel extends along an axis central to the cylindrical plane, positions along the path varying in azimuthal angle where:
• each channel turn includes a first arc, a second arc and first and second straight segments
• the azimuthal angle of each position is measured in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis,
• a first segment of the channel in a first turn in the first continuous series in the first cylindrical plane and a second segment of the channel in the second continuous series in the second cylindrical plane each follow a path in accord with
• F
• 
• (
• x
• )
• *
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• 2
• N
• ,
• where m is an integer greater than zero, x is a position along the axis and F(x) varies in value along the coil ends between zero and one, and
• the channel further comprises a third segment which does not follow a path in accord with
• F
• 
• (
• x
• )
• *
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• 2
• N
• ,
• the third segment providing a path for a conductive segment to provide electrical connection between conductor in the first and second segments.

A method of fabricating a spiral winding structure, comprising:

• defining a spiral shaped channel about an axis in a body to provide a path, the channel comprising a series of N spaced apart and connected channel turns Tn (n=1 to N), each channel turn having a first arc, a second arc and first and second straight segments, where spacings between adjoining turns in the series are in accord with
• F
• 
• (
• x
• )
• *
• sin
• 
• (
• m
• *
• θ
• n
• )
• =
• n
• -
• 1
• 2
• N
• ,
• along the majority of each channel turn;
• and
• conforming a conductive material to the path of the spiral shaped channel, wherein:
• m is an integer greater than zero,
• θn is an angle measured in a plane orthogonal to the axis and relative to a reference point in the plane orthogonal to the axis,
• x is a position along the axis, and
• F(x) varies in value along each arc between zero and one.

A structure comprising at least first and second layers positioned in place about one another and two or more conductor portions, each conductor portion positioned along a different one of the layers, the first of the conductor portions in a first cylindrical plane centered about an axis and the second of the conductor portions in a second cylindrical plane also centered about the axis, with the second plane a greater distance from the axis than the first cylindrical plane, wherein at least the first and second conductor portions are segments in a continuous conductive path extending from along the first of the layers to along at least the second of the layers, the conductive path arranged so that when conducting current a magnetic field can be generated or so that when, in the presence of a changing magnetic field, a voltage is induced, the first and second conductor portions each having a spiral configuration positioned along the path in one of the cylindrical planes, which conductor portions each extend along the axis, positions along the path varying in azimuthal angle where:

• the azimuthal angle of each position is measurable in a plane orthogonal to the axis and relative to a reference point in a plane orthogonal to the axis,
• each conductor portion comprises a continuous series of connected turns, Tn, for which n is an integer ranging from one to N,
• each turn, Tn, includes a first arc, a second arc and first and second straight segments connected to one another by the first arc,
• the second arc connects the turn, Tn, to an adjoining turn, Tn+1 or Tn−1.

A method of securing multiple layers of conductor in a single channel, comprising:

• forming a channel having a spiral configuration comprising a series of channel turns with the channel having a restricted opening of a first dimension smaller than a thickness dimension of the conductor;
• pushing a first portion of the conductor through the restricted channel opening with application of a force so that the channel receives the conductor to create a first level of conductor turns in the channel turns;
• and
• pushing a second portion of the conductor through the restricted channel opening with application of a force so that the channel receives the conductor to create a second level of conductor turns in the channel turns.

A method of forming a channel with a restricted opening that secures multiple layers of conductor in a single channel, comprising:

• forming a channel having a spiral configuration comprising a series of channel turns with the channel having a restricted opening of a first dimension smaller than a thickness dimension of the conductor by providing a first cut to a body to create an initial opening and at least a portion of the channel with the initial opening having a first width and a portion of the interior of the channel also having the first width;
• covering the initial opening with a layer of removable material;
• and
• providing a second cut to create the restricted opening through the layer of removable material, the restricted opening having a second width smaller than the first width.

A method of manufacturing a conductive winding of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, comprising:

• creating in a portion of a body a spiral channel which accommodates two or more layers of conductor for positioning therein, one layer over another layer, the channel including a series of connected channel turns formed in a portion of a body, the turns positioned along a path so that the channel extends along an axis, the channel having a depth extending in a radial direction with respect to the axis to contain the two or more layers, the channel including a series of shaped repository openings along walls of the channel, each repository opening positioned a different radial distance from the axis to provide a series of repository positions, with one or more of the repository positions positioned over another one of the repository positions, wherein each repository opening is of a dimension smaller than a thickness dimension of the conductor to restrict passage of the conductor into an adjoining repository position such that a force must be applied to push the conductor through the repository opening and into the repository position;
• and
• sequentially passing segments of the conductor through one or more of the repository openings to place each segment in one repository position to create a multi-level helical winding path in a single groove.

A wiring assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, comprising:

• a series of spaced-apart spiral configurations of conductor with each configuration positioned in a different one of multiple cylindrical planes each centered about a common axis, each spiral configuration comprising a plurality of conductor turns, wherein the conductor includes
• (i) segments positioned to provide turn-to-turn transitions which connect turns in each plane to form a multi-turn helical geometry in each plane;
• and
• (ii) segments positioned out of the cylindrical planes to conductively connect pairs of spiral configurations of conductor in the adjoining cylindrical planes to form one continuous multi-level winding configuration.

A method of forming a superconductor in a channel having a spiral path comprising:

• placing chemical precursor materials for synthesizing the superconductor in a tube;
• positioning the tube with the chemical precursor materials inside of the tube in the channel;
• and
• chemically reacting the precursor materials in the tube after the tube is placed in the groove to synthesize the superconductor in situ.

A method for fabricating a superconducting assembly which forms superconducting material in situ during fabrication of a winding configuration, the assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, the method comprising:

• mixing precursor materials for synthesizing the superconducting material in stoichiometric proportions
• creating, in a support structure, a plurality of channels each positioned along a different cylindrical plane but centered about a common axis, each channel comprising multiple helically shaped turns connected to one another;
• placing the mixed precursor materials in each of the channels;
• and
• reacting the mixed precursor materials in each of the channels to synthesize the superconductor in the channels.

A method for fabricating a superconducting assembly which forms superconducting material in situ during fabrication of a winding configuration, the assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, the method comprising:

• mixing precursor materials for synthesizing the superconducting material in stoichiometric proportions;
• creating, in a support structure, a plurality of ports each positioned along a different cylindrical plane but centered about a common axis, each channel comprising multiple helically shaped turns connected to one another;
• placing the mixed precursor materials in each of the channels by causing the mixed precursor materials to flow into each port with a carrier liquid;
• allowing the carrier liquid to evaporate so that the precursor materials build up along walls of the ports;
• and
• heating the support structure to chemically synthesize the superconductor material in the ports.

A method for fabricating a superconducting assembly which forms superconducting material in situ during fabrication of a winding configuration, the assembly of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, the method comprising:

• forming an open channel in a support structure
• sequentially forming in the channel (i) a metal layer along a channel wall, (ii) a barrier layer over the metal layer, and a first mixture of precursor materials in stoichiometric proportions over the barrier layer;
• and
• heating the precursor materials to chemically synthesize a first layer of superconductor material in the channel.

A configuration for a superconducting winding of the type which, when conducting current, generates a magnetic field or which, in the presence of a changing magnetic field, induces a voltage, comprising:

• a spiral channel which accommodates two or more layers of the superconductor material for positioning therein, one layer over another layer, the channel including a series of connected channel turns formed in a portion of the body, the turns positioned along a path so that the channel extends along an axis, the channel having a depth extending in a radial direction with respect to the axis to contain the two or more layers, the channel including a series of shaped repository openings along walls of the channel, each repository opening positioned a different radial distance from the axis to provide a series of repository positions, with one or more of the repository positions positioned over another one of the repository positions, wherein each repository opening is of a dimension smaller than a thickness dimension of the conductor to be passed therethrough to restrict passage of each conductor into an adjoining repository position such that a force must be applied to push the conductor through the repository opening and into the repository position, the configuration including
• (i) a first segment of copper conductor positioned in a first repository position closest to the axis;
• (ii) a first barrier layer formed on a surface of the copper conductor;
• (iii) a first mixture of precursor material for synthesizing the superconductor material in a second repository position over the first repository position;
• (iv) an insulative space over the second repository position;
• (v) a second segment of copper conductor positioned in a third repository position positioned over the second repository position;
• (vi) a second barrier layer formed on a surface of the second segment of copper conductor;
• (viii) a second mixture of precursor material for synthesizing the superconductor material in a fourth repository position over the third repository position;
• and
• (ix) an insulative layer over the fourth repository position.