Waveguide for a particle accelerator

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.

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.