Generating highly uniform electromagnetic field characteristics
First Claim
Patent Images
1. An apparatus for generating an electromagnetic field having a region of homogeneity of a characteristic of said electromagnetic field, said apparatus comprising:
- a central axis of said apparatus; and
at least eight conductive pathways disposed about and substantially parallel to said central axis, azimuthal locations, current or charge magnitudes, and distances from said central axis of said conductive pathways being substantially defined by;
solutions to one or more equations selected from the group consisting of ##EQU11## where N is a number of conductive pathways per quadrant, φ
n are the azimuthal locations of said conductive pathways, Rn are the distances from said central axis of said conductive pathways, In are the current or charge magnitudes, w is selected from the group consisting of 0 and 0.5, J is an integer equal to 2(N+w)-1, C is a collection of J equations to be solved, all identical except that running index j changes from 1 to J from equation to equation, Σ
is a sum of N terms in each equation over index n, m is an integer greater than 0, and either not all current or charge magnitudes are substantially equal in absolute value or not all distances from said central axis are substantially equal;
wherein said characteristic comprises a characteristic selected from the group consisting of rate of rotation, field magnitude, radial gradient, and higher order radial derivatives of field magnitude.
0 Assignments
0 Petitions
Accused Products
Abstract
An apparatus and method for generating homogenous electromagnetic fields within a volume. The homogeneity provided may be for magnetic and/or electric fields, and for field magnitude, radial gradient, or higher order radial derivative. The invention comprises conductive pathways oriented mirror symmetrically about a desired region of homogeneity. A corresponding apparatus and method is provided for substantially canceling the electromagnetic field outside of the apparatus, comprising a second set of conductive pathways placed outside the first set.
41 Citations
8 Claims
-
1. An apparatus for generating an electromagnetic field having a region of homogeneity of a characteristic of said electromagnetic field, said apparatus comprising:
-
a central axis of said apparatus; and at least eight conductive pathways disposed about and substantially parallel to said central axis, azimuthal locations, current or charge magnitudes, and distances from said central axis of said conductive pathways being substantially defined by;
solutions to one or more equations selected from the group consisting of ##EQU11## where N is a number of conductive pathways per quadrant, φ
n are the azimuthal locations of said conductive pathways, Rn are the distances from said central axis of said conductive pathways, In are the current or charge magnitudes, w is selected from the group consisting of 0 and 0.5, J is an integer equal to 2(N+w)-1, C is a collection of J equations to be solved, all identical except that running index j changes from 1 to J from equation to equation, Σ
is a sum of N terms in each equation over index n, m is an integer greater than 0, and either not all current or charge magnitudes are substantially equal in absolute value or not all distances from said central axis are substantially equal;wherein said characteristic comprises a characteristic selected from the group consisting of rate of rotation, field magnitude, radial gradient, and higher order radial derivatives of field magnitude. - View Dependent Claims (2)
-
-
3. A method for generating an electromagnetic field having a region of homogeneity of a characteristic of the electromagnetic field, the method comprising the steps of:
-
a) establishing a central axis; b) situating at least eight conductive pathways disposed about and substantially parallel to the central axis, azimuthal locations, current or charge magnitudes, and distances from the central axis of the conductive pathways being substantially defined by;
solutions to one or more equations selected from the group consisting of ##EQU12## where N is a number of conductive pathways per quadrant, φ
n are the azimuthal locations of said conductive pathways, Rn are the distances from said central axis of said conductive pathways, In are the current or charge magnitudes, w is selected from the group consisting of 0 and 0.5, J is an integer equal to 2(N+w)-1, C is a collection of J equations to be solved, all identical except that running index j changes from 1 to J from equation to equation, Σ
is a sum of N terms in each equation over index n, m is an integer greater than 0, and either not all current or charge magnitudes are substantially equal in absolute value or not all distances from said central axis are substantially equal; andc) generating the electromagnetic field comprising a region of homogeneity of a characteristic selected from the group consisting of rate of rotation, field magnitude, radial gradient, and higher order radial derivatives of field magnitude. - View Dependent Claims (4)
-
-
5. An apparatus for generating an electromagnetic field having a region of homogeneity of a characteristic of said electromagnetic field, said apparatus comprising:
-
a central axis of said apparatus; shield means at a uniform radius Rs from said central axis; and at least four conductive pathways disposed about and substantially parallel to said central axis, azimuthal locations, current or charge magnitudes, and distances from said central axis of said conductive pathways being substantially defined by;
solutions to one or more equations selected from the group consisting of ##EQU13## where N is a number of conductive pathways per quadrant, φ
n are the azimuthal locations of said conductive pathways, Rn are the distances from said central axis of said conductive pathways, In are the current or charge magnitudes, w is selected from the group consisting of 0 and 0.5, J is an integer equal to 2(N+w)-1, C is a collection of J equations to be solved, all identical except that running index j changes from 1 to J from equation to equation, Σ
is a sum of N terms in each equation over index n, and m is an integer greater than 0;wherein said characteristic comprises a characteristic selected from the group consisting of rate of rotation, field magnitude, radial gradient, and higher order radial derivatives of field magnitude. - View Dependent Claims (6)
-
-
7. A method for generating an electromagnetic field having a region of homogeneity of a characteristic of the electromagnetic field, the method comprising the steps of:
-
a) establishing a central axis; b) locating a shield at a uniform radius Rs from the central axis; c) situating at least four conductive pathways disposed about and substantially parallel to the central axis, azimuthal locations, current or charge magnitudes, and distances from the central axis of the conductive pathways being substantially defined by;
solutions to one or more equations selected from the group consisting of ##EQU14## where N is a number of conductive pathways per quadrant, φ
n are the azimuthal locations of the conductive pathways, Rn are the distances from the Central axis of the conductive pathways, In are the current or charge magnitudes, w is selected from the group consisting of 0 and 0.5, J is an integer equal to 2(N+w)-1, C is a collection of J equations to be solved, all identical except that running index j changes from 1 to J from equation to equation, Σ
is a sum of N terms in each equation over index n, and m is an integer greater than 0; andd) generating the electromagnetic field comprising a region of homogeneity of a characteristic selected from the group consisting of rate of rotation, field magnitude, radial gradient, and higher order radial derivatives of field magnitude. - View Dependent Claims (8)
-
Specification