Waveguide for a particle accelerator
Disclosed herein is a waveguide cell having a helical cavity. The waveguide cell has a central axis and a cavity having a transverse cross section whose rotational position about the central axis varies along the central axis. There is also disclosed a method a determining the shape of a waveguide cell.
1. A waveguide cell comprising:
a helical cavity; and
a central axis, wherein the helical cavity includes a transverse cross section whose rotational position about the central axis varies along the central axis, wherein a longitudinal cross section of the waveguide cell in a first plane and a longitudinal cross section of the waveguide cell in a second plane, orthogonal to the first plane, are a same shape 180 degrees out of phase relative to each other, wherein the transverse cross section is a polar coordinates conversion of an iris-to-iris 2D cartesian cell shape, and wherein the longitudinal cross section of the waveguide cell viewed in a first plane is the iris-to-iris 2D cartesian cell shape, and wherein the longitudinal cross section of the waveguide cell viewed in a second plane, orthogonal to the first plane is an equator-to-equator 2D cartesian cell shape.
2. The waveguide cell of claim 1 , wherein the transverse cross section is continuously helically rotated along a length of the waveguide cell.
3. The waveguide cell of claim 2 , wherein the transverse cross section is rotated at a fixed rotation rate along the length of the waveguide cell.
4. The waveguide cell of claim 2 , wherein the transverse cross section is helically rotated along the length of the waveguide cell through at least 180 degrees.
5. The waveguide cell of claim 1 , in combination with one or more additional waveguide cells in a series arrangement.
6. The waveguide cell of claim 1 , wherein the longitudinal cross section in the first plane has a periodic structure, and wherein the longitudinal cross section in the second plane has the periodic structure 180 degrees out of phase relative to the first plane.
7. A method of generating a three-dimensional (3D) shape of a waveguide cell, the method comprising:
identifying a two-dimensional (2D) cross section of the waveguide cell, wherein identifying a 2D cross section comprises:
identifying a Cartesian 2D cross section of the waveguide cell in Cartesian coordinates; and
generating a polar 2D cross section in polar coordinates by converting the 2D Cartesian cross section into polar coordinates defining a θ direction between 0 and L/2π;
helically rotating the (2D) cross section around a central axis along a length (L) of the waveguide cell to generate a 3D shape, wherein helically rotating the 2D cross section around the central axis along the length of the cell to generate a 3D shape comprises:
extruding the 2D polar coordinates shape back in a z axis of the Cartesian coordinate system with a twist rate of π/L; and
outputting the 3D shape.
8. The method of claim 7 wherein helically rotating the cross section comprises rotating the cross section along the length of the waveguide cell through 180 degrees.
9. The method of claim 7 , wherein identifying a 2D cross section comprises:
identifying a periodic Cartesian 2D cross section of the waveguide cell, wherein the periodic Cartesian 2D cross section defines a periodic function f(z);
and wherein helically rotating the cross section around the central axis along the length of the waveguide cell to generate a 3D shape comprises:
transforming the periodic function f(z) into a new function F(θ) in a helical coordinate system, wherein one or more z values are converted by a twist rate π/L and a value of θ ranges from 0 to L/2π.
10. The method of claim 7 , wherein the Cartesian 2D cross section of the cell comprises an iris-to-iris cell shape, and wherein a longitudinal cross section of the waveguide cell in a first plane is the iris-to-iris Cartesian cell shape, and in a second plane, orthogonal to the first plane, is an equator-to-equator Cartesian cell shape.
11. The method of claim 10 , wherein the Cartesian 2D cross section is the longitudinal cross section of a known cavity shape and wherein the known cavity shape comprises one of:
a pillbox shape, an elliptical shape, an Ichiro shape or a Tesla shape.
12. A linear accelerator comprising:
a waveguide, the waveguide including:
a waveguide cell, the waveguide cell including:
a central axis; and
a helical cavity, wherein the helical cavity includes a transverse cross section, wherein a rotational position of the transverse cross section about the central axis varies along the central axis, wherein a longitudinal cross section of the waveguide cell in a first plane and a longitudinal cross section of the waveguide cell in a second plane, orthogonal to the first plane, are a same shape 180 degrees out of phase relative to each other, wherein the transverse cross section is a polar coordinates conversion of an iris-to-iris 2D cartesian cell shape, and wherein the longitudinal cross section of the waveguide cell viewed in a first plane is the iris-to-iris 2D cartesian cell shape, and wherein the longitudinal cross section of the waveguide cell viewed in a second plane, orthogonal to the first plane, is an equator-to-equator 2D cartesian cell shape.
13. The linear accelerator of claim 12 , wherein the transverse cross section is continuously helically rotated along a length of the waveguide cell.
14. The linear accelerator of claim 13 , wherein the transverse cross section is rotated at a fixed rate of rotation along the length of the waveguide cell, and wherein the transverse cross section is helically rotated along the length of the waveguide cell through 180 degrees.