Method for forming saddle coil and other conductor assemblies

1. 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.

2. 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, T n , connected to one another in a continuous series in the first cylindrical plane, each turn, T n , 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 T n is spaced apart from an adjacent turn T n+1 or T n−1 , and

for at least one turn, T n , 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.

3. 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, T n , connected to one another in a continuous series in the first cylindrical plane, each turn, T n , 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 T n is spaced apart from an adjacent turn T n+1 or T n−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.

4. The method of claim 3 wherein, for at least one turn, T n , 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.

5. The method of claim 4 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 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.

6. The method of claim 5 wherein multipole content which would otherwise be present in a field generated by the spiral configuration because of path segments which deviate from ideal channel path segments, relative to a multipole field which would theoretically be generated by a configuration having an ideal cos(mθ) current distribution, is reduced by applying a numerical optimization technique which modifies the shapes of turns to more closely conform the field generated by the spiral configuration to the multipole field which would theoretically be generated by a configuration having an ideal cos(mθ) current distribution.