Waveguide for a particle accelerator

Abstract

Waveguide cells with a spiral cavity are disclosed. The waveguide cell has a central axis and a cavity with a cross section whose rotational position around the central axis varies along the central axis. Methods of determining the shape of a waveguide cell are also disclosed.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to waveguides, in particular waveguides for particle accelerators, to methods of designing waveguides, and to particle accelerators comprising waveguides. The present disclosure also relates to waveguide cells for waveguides. BACKGROUND

[0002] Particle accelerators are used to accelerate charged particles to high speeds.

[0003] Linear accelerators, in particular linear accelerators for medical use, accelerate charged particles, such as electrons, along an acceleration path through a waveguide to a relative speed. The waveguide has a plurality of resonant cavities arranged along the acceleration path. Radio frequency (RF) electromagnetic waves (described herein as RF energy, which refers to the energy in the electromagnetic waves) are applied to the waveguide, which provides an oscillating electric field in each cavity. This field accelerates the electrons.

[0004] The RF energy applied to the waveguide is used to accelerate the electrons along the acceleration path. There are factors that limit the amount of RF energy that can be applied to the waveguide. For example, there is a point of failure. SUMMARY

[0005] Various aspects and features of the present invention are described in the appended claims.

[0006] According to a first aspect, a helical waveguide cell is provided. A helical waveguide consists of helical waveguide cells, which comprise a helical cavity. A waveguide consists of resonant cavities, each of which can also be referred to as a waveguide cell. A waveguide comprising a helical cavity is provided, as well as a waveguide cell comprising a helical cavity.

[0007] Optionally, the waveguide cell further comprises a central axis and a cavity having a transverse cross-section, the rotational position of which around the axis varies along the axis. The transverse cross-section is non-circular. A transverse cross-section can be referred to as a fixed transverse cross-section, given that the shape of the transverse cross-section does not vary along the length of the cell, but the rotational position of the shape of the transverse cross-section varies along the length of the cell. The transverse cross-section of the waveguide cell is a shape that is constant along the length of the cell, only its rotational position varies along the length of the cell. Each transverse cross-section of the helical waveguide cell of the present invention is rotationally symmetric to each other. The central axis of the helical waveguide cell is the acceleration axis along which the electrons travel, and can be denoted by the z-axis. The length of the waveguide cell is the distance of one cell along the acceleration axis. The transverse cross-section is used to define the transverse cross-section in a plane orthogonal to the central axis denoted as the x / y-plane (if z is defined as the central axis). The cavity can comprise a non-circular transverse cross-section that spirally rotates around the central axis along the axis. The cavity can be referred to as a helical cavity.

[0008] Optionally, the waveguide unit further comprises a transverse cross-section that helically rotates along the length of the unit. The rotational position of the transverse cross-section shape varies along the length of the unit, the variation in rotational position being continuous. The motion of each unit along the longitudinal length of the unit (in the z-direction) corresponds to a rotation of the transverse cross-section of the unit about the central axis. The rate of rotation (amount of rotation per length) can or can not be constant. Optionally, the rate of rotation is fixed / constant.

[0009] Optionally, the transverse cross-section helically rotates 180 degrees along the length of the unit. That is, the rotational position of the transverse cross-section varies by 180 degrees along the length of the unit. The overall twist angle of the transverse cross-section is 180 degrees.

[0010] Optionally, the transverse cross-section rotates at a fixed rate of rotation along the length of the unit. The fixed rate of rotation along the length of the unit can be referred to as a twist rate, which can be defined in units of rad / m or deg / m.

[0011] Optionally, the twist rate is π / L, where L is the length of one cell. A constant twist rate of π / L along the length of the unit results in the transverse cross-section rotating 180 degrees along the length of the unit.

[0012] The length of one cell L remains constant as it is fixed between the conventional cell and the helical cell counterpart. The length of the unit L is the period length, and the length L can be repeated multiple times to form a waveguide comprising a series of units. The length of the waveguide unit is the distance of one unit or cell along the acceleration axis.

[0013] Optionally, the waveguide unit further comprises a longitudinal cross-section in a first plane and a longitudinal cross-section in a second plane, the longitudinal cross-sections being the same shape that are out of phase relative to each other.

[0014] Optionally, the waveguide unit further comprises a longitudinal section at a first angle and a longitudinal section of the waveguide unit at a second angle orthogonal to the first angle, both longitudinal sections being 180 degrees out of phase with each other. In other words, the longitudinal sections in a first plane and a second plane orthogonal to the first plane are the same shape translated half a period. The longitudinal sections can be in any plane containing the central axis (z-axis). That is, the longitudinal sections can be y / z plane or x / z plane, but also other planes taken at any angle around the z-axis. The x / z plane is equivalent to a plane taken at 0 or 180 degrees around the z-axis. The y / z plane is equivalent to a plane taken at 90 or 270 degrees around the z-axis. A longitudinal section at a first angle around the z-axis means a 2D plane taken from the 3D cavity / waveguide unit at the first angle. This can be referred to as a longitudinal section in a first plane. A longitudinal section at a second angle around the z-axis means a 2D plane taken from the 3D cavity / waveguide unit at the second angle. This can be referred to as a longitudinal section in a second plane. The two longitudinal sections at the two angles define different cells of the same periodic structure, the cells being shifted by one half period with respect to each other, thus being 180 degrees out of phase with each other. Thus, the two longitudinal section unit cells have a constant area contained within the shape they define as well as the same period length L.

[0015] Optionally, the spiral cavity has a known (non-spiral) cavity counterpart produced by known techniques. The spiral cavity is derived from the shape of the known counterpart cavity. Similarly, the spiral waveguide has a known (non-spiral) waveguide. In some planes, the longitudinal sections of the spiral waveguide (cell) have the shape of the longitudinal sections of the counterpart waveguide (cell).

[0016] Optionally, the waveguide unit further comprises a fixed non-circular transverse section derived from a 2D shape having a membrane and an equator, and wherein the longitudinal section of the unit observed at a first angle is a membrane-to-membrane unit cell and observed at a second angle orthogonal to the first angle is an equator-to-equator unit cell. The equator-to-equator unit cell starts at a wide point of the cavity (equator), then narrows at a narrow point (membrane), then ends at a wide point (equator). The cavity unit cell can also be defined as a membrane-to-membrane starting at a narrow point (membrane), then widening to a widest part (equator), then ending at a narrow point (membrane). The equator-to-equator unit cell and the membrane-to-membrane unit cell are 180 degrees out of phase with each other.

[0017] Optionally, the waveguide unit further comprises a non-circular transverse cross-section that is helically rotated 180 degrees along the length of the unit. Helically rotating refers to extruding back a polar 2D cross-section in the z-axis of a Cartesian coordinate system with a twist rate. The twist rate can be L / π. Over a length L, the two-dimensional polar shape is continuously twisted 180 degrees to generate a 3D shape. The two-dimensional polar transverse cross-section is gradually rotated around the z-axis in a continuous manner along the length of the axis to "scan out" the shape of the cavity. The two-dimensional polar transverse cross-section is the transverse cross-section of the waveguide unit. The twist rate π / L is a fixed rate of rotation along the length L of the unit, which can be defined in rad / m or deg / m. The length of the unit L is a period length, and the length L can be repeated multiple times to form a waveguide comprising a series of units.

[0018] According to an aspect, there is provided a waveguide comprising a series of units. The waveguide can comprise helical resonant cavities, each of which can also be referred to as a waveguide unit.

[0019] Optionally, the waveguide further comprises a longitudinal cross-section in a first plane at a first angle to the periodic structure, and wherein the longitudinal cross-section in a second plane orthogonal to the first plane has the periodic structure 180 degrees out of phase with respect to the first plane. The two transverse cross-sections at the two angles define different boundaries of the same periodic structure, which are offset by half a period with respect to each other, and thus 180 degrees out of phase with each other.

[0020] According to an aspect, there is provided a method of determining a 3D shape of a waveguide unit, the method comprising: identifying a Cartesian 2D cross-section; helically rotating the transverse cross-section around a central axis along a length of the unit to generate a 3D shape; outputting the 3D shape. The Cartesian 2D cross-section comprises an equator and a membrane. The Cartesian 2D cross-section is a longitudinal cross-section of a cavity, for example a cross-section of a standard cavity manufactured using known techniques. The shape can be taken from or derived from a table of known cavity shapes. The generated 3D shape can be considered a "helical cavity" in that the 3D shape defines a resonant cavity, and is generated by helical rotation around the z-axis.

[0021] Optionally, the waveguide unit has a length L, and identifying a 2D cross-section comprises: identifying a Cartesian 2D cross-section of the unit in Cartesian coordinates; and generating a polar 2D cross-section in polar coordinates by converting the 2D Cartesian cross-section into polar coordinates, the theta direction being defined as between 0 and L / 2π; and wherein helically rotating the polar coordinate 2D cross-section around a central axis along a length of the unit to generate a 3D shape comprises: extruding back the 2D polar coordinate shape in the z-axis of a Cartesian coordinate system with a twist rate of π / L. The period length L of the unit is fixed, and the geometry of the longitudinal cross-section is converted from Cartesian coordinates to cylindrical coordinates in the r and theta plane.

[0022] Optionally, identifying the 2D cross-section comprises: identifying a periodic Cartesian 2D cross-section of the cell, wherein the periodic Cartesian 2D cross-section defines a periodic function f(z); and wherein spirally rotating the cross-section along the length of the cell about the central axis to generate the 3D shape comprises: transforming the periodic function f(z) into a new function F(0) in a helical coordinate system, converting the z values according to the twist rate p / L, and the 0 values are in the range of 0 to L / 2p. The helical rotation is achieved by mapping the Cartesian coordinate system onto a helical coordinate system. The periodic function f(z) represents the conventional cavity shape along the acceleration axis (central axis), i.e. the z direction. The function f(z) is periodic in terms of the cavity / cell length L along the z axis. The function f(z) can define a conventional longitudinal cross-section spanning multiple cells. The Cartesian function f(z) is transformed into a new function F(0) in a helical coordinate system, converting the z values according to the twist rate p / L, and thus the 0 values are in the range of 0 to L / 2p. The 0 values are defined by the values of the f(z) function, as these values are converted in the F(0) frame.

[0023] Optionally, the method further comprises including a Cartesian 2D cross-section of the cell including an equator and a septum, and wherein a longitudinal cross-section of the cell viewed from a first angle is a septum-to-septum unit cell, and a longitudinal cross-section of the cell viewed from a second angle orthogonal to the first angle is an equator-to-equator unit cell. The equator-to-equator cell and the septum-to-septum cell are 180 degrees out of phase with each other.

[0024] Optionally, the method further comprises simulating an electric field generated when radio frequency energy is applied to a waveguide including a cell having a 3D shape using Maxwell solver computational software. Radio frequency (RF) electromagnetic waves can be described as RF energy, which refers to the energy in electromagnetic waves. The RF energy can be simulated into the waveguide to provide an oscillating electric field in each cavity.

[0025] Optionally, the method further comprises identifying a maximum field. The maximum magnetic field can be a maximum electric field, a magnetic field, or both. The maximum field can be found for the surface of the cavity.

[0026] Optionally, the method further comprises simulating an electric field generated when radio frequency energy is applied to a waveguide including a cell having a shape with a 2D Cartesian cross-section swept out about a central axis; identifying a maximum surface field in the simulation; comparing the maximum surface field to the first maximum field; solving Maxwell’s equations with computational software. The cell having a shape with a 2D Cartesian cross-section swept out about a central axis is a cavity according to known techniques, wherein there is no helical rotation. Comparing the maximum surface field to the first maximum field comprises comparing the maximum field of the cavity produced with known techniques to its helical counterpart.

[0027] Optionally, the method further comprises a Cartesian 2D cross-section, which is a longitudinal cross-section of the known cavity shape, and wherein the known cavity shape comprises one of the following shapes: pillbox shape, elliptical shape, Ichiro shape or Tesla shape. Standard waveguides known in the art can comprise standard cavity shapes, such as pillbox shape, elliptical shape, Ichiro shape or Tesla shape.

[0028] Optionally, the method further comprises manufacturing a waveguide having a 3D shape. The waveguide can comprise a spiral of resonant cavities, each resonant cavity can also be referred to as a waveguide cell.

[0029] According to an aspect, there is provided a method of determining a shape of a 3D waveguide cell having a length L, comprising: identifying a periodic Cartesian 2D cross-section of the cell, wherein the periodic Cartesian 2D cross-section defines a periodic function f(z); transforming the periodic function f(z) into a new function F(0) in a spiral coordinate system, wherein the z value is transformed by a twist rate of π / L and the 0 value is in the range of 0 to L / 2π; and outputting the shape.

[0030] According to an aspect, there is provided a waveguide manufactured by the method of another aspect.

[0031] According to an aspect, there is provided a waveguide cell as shown in any one of the Figures 6 to 9 of the present application.

[0032] According to an aspect, there is provided a particle accelerator comprising the waveguide as described above. According to an aspect, there is provided a linear accelerator comprising the waveguide as described above. According to an aspect, there is provided a radiotherapy device comprising a linear accelerator having the waveguide as described above.

[0033] According to an aspect, there is provided a waveguide cell having a central axis and a cavity having a cross-section, the rotational position of the cross-section around the central axis varying along the central axis. BRIEF DESCRIPTION OF DRAWINGS

[0034] The specific embodiments will be described below, by way of example only, and with reference to the drawings in which:

[0035] Figure 1 A linear accelerator for use in radiotherapy is shown;

[0036] Figure 2 A portion of a waveguide for a particle accelerator is shown;

[0037] Figure 3 Conventional generation of waveguide cavity shapes is shown;

[0038] Figure 4a and Figure 4bA field map is shown formed by applying RF energy to a known waveguide;

[0039] Figure 5 A method of determining a waveguide shape according to the present disclosure is shown;

[0040] Figure 6 A helical cavity according to the present invention is shown;

[0041] Figure 7 A field map is shown formed by applying RF energy analogously to a helical cavity of the present disclosure;

[0042] Figure 8 A plurality of cavities according to the present disclosure is shown; and

[0043] Figure 9 Fabrication of a waveguide including a helical cavity according to the present disclosure is shown. DETAILED DESCRIPTION

[0044] The present invention provides a waveguide cell shape referred to as a "helical cell" or "helical cavity", and provides a method for producing a helical cell from a known cavity shape of the art. The helical cavity is a resonant cavity, the helical shape of which is produced by a continuous rotation of a 2D cross-section in the z-axis, where the rate of rotation can be considered a constant twist rate (rad / m), and where the 2D cross-section is derived from a known cavity shape. The helical waveguide of the present invention has field cancellation properties. When comparing the helical cavity to its known cavity counterpart, the helical cavity can reduce surface fields, reduce surface fields at the iris, prevent RF breakdown at the cavity surface, and improve the acceleration gradient of the beam production.

[0045] Figure 1

[0046] In radiation therapy, radiation is delivered to a patient to destroy unhealthy tissue and cells, such as cancerous tumors. A treatment plan is created to determine the amount of radiation (dose) to be applied to the patient. For a variety of reasons, it is desirable to deliver the required radiation to the patient in as short a time as possible. Faster radiation therapy will reduce the overall treatment time, thereby reducing discomfort and inconvenience to the patient. This will also increase the number of patients that can be treated per day.

[0047] One way to reduce treatment time is to increase the dose rate (amount of radiation applied per second). It is desirable to reduce the treatment time for the patient in order to make the patient's experience as comfortable as possible. Additionally, the patient can move during treatment, and such movement will present problems and be difficult during treatment. Reducing treatment time can also minimize the impact of patient movement on the treatment.

[0048] In Figure 1The diagram shows a high-level overview of a linear accelerator. The linear accelerator 110 includes an electron source 112, a waveguide 114, and a target 116. Electrons are emitted from an electron gun and accelerated along an acceleration path 118 aligned with the central axis of the waveguide. A magnet is used to bend the electron beam and strike the target 116 to generate an X-ray beam 120. The X-ray beam 120 is used to treat patients.

[0049] Radio frequency (RF) source 122 (e.g., magnetron) generates radio frequency (RF) waves. The RF source is coupled to a waveguide and configured to pulse RF waves into the waveguide.

[0050] The electron source 112 may be an electron gun. The electron source is configured to inject electrons into the waveguide 114. The waveguide 114 includes a plurality of interconnected accelerating cavities (not shown), wherein the accelerating cavities form a channel through which the electron beam passes. Injecting electrons into the waveguide 114 is synchronized with pumping radio frequency waves into the waveguide 114.

[0051] The radio frequency source 122, electron source 112, and waveguide 114 are designed and operated as follows: when electrons propagate along the acceleration path 118 through waveguide 114, the radio frequency wave accelerates the electrons to very high energies. The waveguide is designed to generate an appropriate electric field pattern that accelerates the electrons propagating through waveguide 114.

[0052] Figure 1 The present invention describes waveguides and linear accelerators used in radiotherapy equipment. However, the waveguides described herein can be used in particle accelerators of systems other than radiotherapy equipment. This disclosure is not limited to waveguides used in particle accelerators for radiotherapy equipment.

[0053] Figure 2 The image shows a waveguide used in a particle accelerator. This is a cross-sectional view, or "longitudinal section," along the waveguide's longitudinal axis. This waveguide can be used for, for example... Figure 1 The example shown is a linear accelerator, but it can also be used in other accelerators (e.g., curved accelerators such as cyclotrons or synchrotrons). The examples and discussion below concern the acceleration of electrons, but waveguides can be used to accelerate any charged particle, and therefore can be used to accelerate any charged particle. For example, the techniques described herein can be used to accelerate protons, positrons, and ions.

[0054] Figure 2 A brief description of a known waveguide

[0055] Figure 2A portion of a known waveguide is shown. The waveguide is a periodic structure, comprising waveguide cells, the cells having cavities. In other words, the waveguide consists of resonant cavities, each of which can also be referred to as a waveguide cell. Two cavities 210 in a sequence of connected cavities are shown. Each cavity is connected by an iris 214 along a central axis 212. Although a typical waveguide will have many more cavities, only two complete cavities are shown in Figure 2 The exact number will vary depending on the design criteria of the accelerator. Each cavity is defined in the form of a groove in a surrounding outer shell of electrically conductive material, typically copper. The central axis can be referred to herein as the acceleration axis, central axis or z-axis.

[0056] In the following description, the term "longitudinal cross-section" is used to define a cross-section in any plane that passes through the central axis. "Transverse cross-section" is used to define a cross-section in a plane that is perpendicular to the central axis. The longitudinal centre of an object is the half along the longitudinal axis of the object. For example, the longitudinal centre of a cavity is the half plane along the central axis of the cavity. The longitudinal centre can also be referred to as the equator of the cavity. In the following description, the z-axis is defined as the median axis or central axis. Thus, a longitudinal cross-section can be described as a y / z plane or an x / z plane. A longitudinal cross-section is taken in a plane that contains the central axis (z-axis). This cross-section is described by an x / y plane, which is a plane that is orthogonal to the z-axis.

[0057] A longitudinal cross-section can be in any plane that contains the central axis (z-axis). That is, a longitudinal cross-section can be a y / z plane or an x / z plane, but can also be other planes that are taken at any angle around the z-axis. An x / z plane is equivalent to a plane that is taken at an angle of 0 degrees or 180 degrees around the z-axis. For example, it can be a longitudinal cross-section taken from the "side". A y / z plane is equivalent to a plane that is taken at an angle of 90 degrees or 270 degrees around the z-axis. For example, it can be a longitudinal cross-section taken from above or below the waveguide.

[0058] Each cavity 210 has an iris 214 connected to the preceding cavity in the sequence, and has an iris 214 connected to the next cell in the sequence. The irises and optical cavities are centred on the central axis. In use, the central axis defines the electron acceleration path along which electrons travel as they are accelerated through the waveguide. Overall, the cavities and irises are axisymmetric around the central axis, forming a circular torus, i.e. a three-dimensional shape formed by sweeping a two-dimensional shape around an axis. In some waveguides, a "nosecone" is formed on each end of the iris, which lengthens the iris along the central axis to protrude into the cavity. However, as Figure 2 shown, some waveguides do not include a nosecone.

[0059] The cavities are fabricated by welding the individual segments of conductive material together at the junctions. The junctions of the individual segments are typically in the "equator" of the cavity, which is the longitudinal center of the cavity. The equator is typically the widest point of the cavity, where width refers to the y-axis. Additionally, the plane at the equator is a plane of symmetry. Each cavity 210 is composed of two independent segments that abut at the central equator. Each segment has two equators 218 that define the leftmost and rightmost edges of the segment. In Figure 2 One segment is shown in the shaded portion in the middle. Adjacent segments establish a unit, which is repeated to form the waveguide. The shaded segment is an example of an equator-to-equator unit or a wide-narrow-wide (WNW) structure. The WNW shape starts at a wide point (equator 218), then narrows at the iris 214, then ends at a wide point (equator 218). The cavity unit can also be defined as an iris-to-iris or narrow-wide-narrow (NWN) structure. The NWN cavity shape starts at a narrow point (iris), then widens to an equator, then ends at a narrow point (iris). Typically, the cavity is described as having two irises. Some cavities are fabricated using segments that have junctions elsewhere in the waveguide.

[0060] The waveguide is a periodic structure, which includes waveguide units, the units having cavities. A unit refers to a waveguide segment having a cavity of conductive material, i.e., a portion of the waveguide having a cavity. The structure of the waveguide varies with a particular frequency or periodicity along its length, e.g., the width of the waveguide varies along its length between iris features and equator features, and thus, a particular phase of the structural variation frequency or periodicity can be defined at a particular point along the length of the waveguide. The iris-to-iris and equator-to-equator unit cells can be considered to be perfectly out of phase with each other. The iris-to-iris and equator-to-equator unit cells define two separate starting points from which the cavity shape is defined. The unit cells can be described as periodic structures. The equator is halfway between the irises, and in this way, the iris-to-iris and equator-to-equator unit cells are offset by half a period with respect to each other. In terms of the periodic difference between the forms, the iris-to-iris and equator-to-equator can be considered to be 180 degrees out of phase with each other. Thus, the iris-to-iris and equator-to-equator unit cells have a constant area contained within the shape they define as well as the same period length L. There is an infinite number of alternative unit cells that can be used to describe the same cavity shape, each using a different starting point along the shape. The iris-to-iris and equator-to-equator unit cells are the most frequently used unit cells and are referred to herein.

[0061] The electromagnetic field introduced into the waveguide over time can be simulated by applying a model of a radio frequency wave to the waveguide. In turn, this can be used to simulate the effect of the electromagnetic field on an electron or a plurality of electrons injected at one end of the waveguide. The acceleration of the electrons along the acceleration path, the velocity of the electrons at the distal end of the waveguide (the end opposite the electron gun), and the proportion of electrons that reach the distal end of the waveguide when some of the electrons are laterally deflected from the acceleration path can also be determined. In medical applications, this information can be used to determine the dose of radiation produced by the waveguide. The electromagnetic field simulation is typically determined by numerical methods, for example, by numerical calculation software capable of solving Maxwell's equations.

[0062] Figure 3 - how to determine a brief description of a known waveguide shape

[0063] Figure 3 A conventionally generated waveguide with a "pill box" cavity shape according to known techniques is shown. Although Figure 3 The pill box shape is shown, but the method is equally applicable to any known standard cavity shape. The waveguide comprises repeating pillared-to-pillared units. First, a longitudinal profile 310 of the cavity unit is determined, which is a two-dimensional shape that can be used to define the waveguide shape. The longitudinal profile is in a plane intersecting the central (acceleration) axis; for example, the x / z plane or the y / z plane. The two-dimensional shape is the profile of the cavity defined by the acceleration axis. That is, the acceleration axis forms the outermost lower edge of the two-dimensional shape.

[0064] In the example of Figure 3 The longitudinal profile 310 defines a conventional pill box cavity for an equator-to-equator unit. As will be appreciated by those skilled in the art, there are many known cavity shapes with corresponding longitudinal profiles. The two-dimensional longitudinal profile 310 is then scanned around the z-axis to form a hollow three-dimensional shape 312, which represents a three-dimensional cavity defined as an equator-to-equator unit. Thus, the three-dimensional shape 312 is axisymmetric or rotationally symmetric about the central axis (z-axis). For any cross-section of the waveguide taken through the x / y plane, the radially outermost surface of the inner waveguide cavity will form a circle.

[0065] The three-dimensional cavity in equator-to-equator form can be fabricated as one segment (e.g. Figure 2 the shaded segment in) and a series of aligned segments to produce a series of pillared-to-pillared cavities. The three-dimensional unit in equator-to-equator form can be processed into its pillared-to-pillared form 314. The three-dimensional cavity of the pillared-to-pillared form 314 can also be found by using the two-dimensional longitudinal profile defined for the cavity of the pillared-to-pillared form. The three-dimensional shape in the equator-to-equator or pillared-to-pillared form 314 can be repeated adjacently to form the waveguide shape. Figure 3 The equator 324 and the pillaring 322 are shown in

[0066] In any transverse cross-section of the waveguide or three-dimensional shape, taken through the x / y plane, the radially outermost surface of the internal waveguide cavity will form a circle. The cross-section of the channel formed by the cavity and the diaphragm at any one point is circular or formed from multiple circles. The waveguide is toroidal. It will be appreciated that the easiest imagined shape that has an infinite order of rotational symmetry about a central axis (z-axis) is a circle. Any shape that has an infinite order of rotational symmetry about a point includes a circle or multiple circles with their centres at that point. Figure 2 and Figure 3 As shown, the known waveguide has an infinite order of rotational symmetry about the central axis (z-axis). To help understanding, it should be noted that the easiest imagined shape that also has an infinite order of rotational symmetry is a circle. Any shape that has an infinite order of rotational symmetry about a point includes a circle or multiple circles with their centres at that point.

[0067] Axial symmetry is also evident in the longitudinal cross-section of the cavity. The longitudinal cross-section in any plane containing the central axis is the same, regardless of the angle of the plane. That is, the longitudinal cross-section of the cavity does not change when rotated about the central axis. The longitudinal cross-section in the y / z plane is the same as the longitudinal cross-section in the x / z plane and as the longitudinal cross-section in any plane therebetween.

[0068] If the three-dimensional shape is viewed at a longitudinal cross-section at a first angle about the z-axis, nominally rotated 0 degrees about the z-axis, then the diaphragm-to-diaphragm unit RF unit is obtained. If the three-dimensional shape with the longitudinal cross-section is viewed at a second angle about the z-axis (a second angle orthogonal to the first angle, rotated 90 degrees relative to the z-axis), then the diaphragm-to-diaphragm unit RF unit is obtained. The cross-sections at the first and second angles are identical. Indeed, the longitudinal cross-section taken at any angle relative to the z-axis is identical. Equivalently, if a cross-section is taken through the three-dimensional shape at a central point (i.e. at y = 0) through the x / z plane, then the first cross-section 316 is produced. If a cross-section is taken through the three-dimensional shape at a central point (i.e. at x = 0) through the y / z plane, then the second cross-section 318 is produced. Due to the symmetry about the central axis (z-axis), the two cross-sections through the y / z plane and the x / z plane are identical. Thus, there is rotational symmetry about the z-axis.

[0069] The cross-sections 316, 318 are analogous to the cavity cross-sections shown in Figure 2 . Figure 2 represents a conventional "pillbox" type cavity shape, Figure 3 also represents a conventional pillbox type cavity shape. The equator 324 and diaphragm 322 are labelled for the cross-sections 316 and 318.

[0070] Simulation and breakdown

[0071] To perform the simulations, software is typically used in which two-dimensional measurements of the waveguide are input into the software, i.e. the longitudinal profile of a cavity unit cell (e.g. 310) is input into the software to create a 2D axisymmetric framework for a full 3D model. Based on the full 3D model of the waveguide, the time-varying electric field produced by the radio frequency waves exerted on the waveguide is simulated. The waveguide can then be built based on this model of the waveguide. Alternatively, the above process can be used to model the electric field of an existing waveguide by inputting the dimensions of the waveguide. Typically, these simulations are always performed in two dimensions only. Traditionally, waveguides and cavities / mirrors within waveguides are initially made to be axisymmetric (formed by scanning a two-dimensional shape around a central axis).

[0072] When RF energy is applied to the waveguide, an electric field is produced in the waveguide; in the material of the waveguide and in the cavities. The electric field is non-uniform within the waveguide. A surface electric field is formed on the surface of the cavities. Regions with high surface electric field are more likely to cause electrical breakdown.

[0073] Breakdown is caused by the combination of large surface electric fields and magnetic fields, and is a complex phenomenon that depends on many conditional factors in addition to the driving fields. These factors include field emission, multi-step operation, gas breakdown, and surface heating. During breakdown, the number of electrons reaching the target is typically reduced. In some cases, the number of electrons reaching the target is zero. Formulas derived empirically (e.g. the Kilpatrick breakdown limit for conducting accelerating structures) can predict to some extent whether RF breakdown will occur:

[0074]

[0075] where E Smax is the maximum surface field (MV / m) and f is the frequency of the RF wave (GHz). If the surface field is greater than the Kilpatrick breakdown limit, there is a high probability of RF breakdown at that location. The Kilpatrick limit provides a rough estimate, as the mechanism of RF breakdown depends on many conditional factors.

[0076] Therefore, waveguides for radiotherapy are designed for stability to avoid breakdown, which is a trade-off of as high a field as possible within the accelerating structure to provide either:

[0077] 1. high dose rate (according to beam loading, transfer of energy from the RF field to the beam itself, by putting more input beam current into the steerer (from the particle source) and raising the RF field to accelerate additional particles to the same energy and thus increase the final dose rate)

[0078] 2. high energy (according to beam loading, transfer of energy from the RF field to the beam itself, by having more field to increase the total gradient of the accelerating field seen by the particles, and accelerating them to a higher final energy).

[0079] Thus, for either of the above cases, it is desirable to increase the RF energy that can be applied to the cell before breakdown occurs.

[0080] Figure 4a and Figure 4b A field plot showing the electric field intensity generated in the cavity when RF energy is applied to a known axisymmetric waveguide (e.g. Figure 2 The waveguide) is shown. The input RF frequency for the simulation was calculated at 1.3 GHz.

[0081] Figure 4a A longitudinal cross-section of the waveguide cavity (a cross-section taken along the z-axis) is shown, Figure 4b A perspective view of the entire cavity is shown. The shape of the cavity is a conventional “Ichiro” shape.

[0082] The intensity is shown as a gray scale plot, where the strongest (i.e. highest density) electric field is black, the weakest (i.e. lowest density) field is white, and the field intensities in between are shown in shades of gray. The highest field (shown in black) is on the surface of the iris and on the nosecone, as indicated by reference numeral 410. There is also a high field along the acceleration path in the center of the cavity. The lowest field (shown in white) is through the center of the iris along the acceleration path, and at the radial edges of the cavity around the central plane, indicated by reference numeral 412.

[0083] The point of peak surface field (i.e. this highest electric field) is on the surface of the iris. This is also the point of the surface of the cavity closest to the acceleration path. The high field means that breakdown is likely to occur at this location.

[0084] The present disclosure provides waveguides with reduced breakdown potential and methods of manufacturing waveguides.

[0085] In the present disclosure, a spiral cavity is provided to reduce the surface field and prevent RF breakdown. A waveguide including a spiral-shaped cavity can reduce the maximum surface field. An exemplary method for determining the spiral shape of the waveguide cavity is provided below.

[0086] As explained above, a typical cavity is generated using a two-dimensional Cartesian shape (a longitudinal profile) and scanning the two-dimensional shape around a central axis (z-axis in a cylindrical coordinate system). This creates an axisymmetric waveguide, and is shown in Figure 3 According to the present disclosure, a new cavity shape is generated by reconsidering the two-dimensional shape scanned around the central axis and how the scanning of the two-dimensional shape around the central axis is performed.

[0087] Reference is now made to Figure 5 , Figure 5 A method according to the present disclosure is described. Reference is also made to Figure 6 , Figure 6 A spiral cavity of the present invention is described.

[0088] Figure 5 - method of creating a spiral cavity

[0089] In the first step, the shape of the transverse cross-section of the waveguide, which is helically rotating around the central axis, is identified. This method is described in steps 510 to 520.

[0090] The method begins at step 510. In step 510, the two-dimensional shape of the cell in Cartesian coordinates is identified. The Cartesian two-dimensional cross-section includes the equator and the diaphragm. This shape is a longitudinal cross-section of the cavity, such as the cross-section of a standard cavity formed using known techniques. This shape can be taken from or derived from a table of known cavity shapes. Figure 8 The document describes nine known cavity shapes. These shapes can be known shapes of conventional waveguides used for transformation.

[0091] For example, this shape is a two-dimensional cross-section of a known standard waveguide's periodic structure, similar to... Figure 2 or Figure 3 See 316 and 318. Each cavity, in sheet-to-sheet form, has a periodic length L (for repeating acceleration structures), two sheets, and an equator.

[0092] A two-dimensional Cartesian shape can be a longitudinal section of a known diaphragm-to-diaphragm cavity. Similarly, a two-dimensional Cartesian shape can be a longitudinal section of a known equator-to-equator cavity that includes two equators and a diaphragm. Figure 5 Any unit can be used in the method because the cavity shape is equivalent for both sheet-to-sheet and equator-to-equator units.

[0093] Figure 6 The longitudinal section of a diaphragm-to-diaphragm cavity waveguide is shown. Figure 6 The diaphragm-to-diaphragm longitudinal section selected in step 510 is shown. This shape is identical to the longitudinal profile 310 of the reflection along the z-axis. However, the described shape is a two-dimensional longitudinal section of the periodic structure of the waveguide cavity. Figure 3 Similarly, in Figure 6 The membrane is marked 322 and the equator 324.

[0094] At step 520, the Cartesian two-dimensional cross-section of step 510 is converted to polar coordinates (r, θ) with the direction θ defined between 0 and L / 2π to generate a polar cross-section. The period length of the cell L (length of the final waveguide cell) is fixed, and the geometry of the longitudinal cross-section is converted from Cartesian coordinates to a cylindrical coordinate system in the r and θ plane. The direction θ is then defined between 0 and L / 2π in terms of this geometry. Step 520 can be performed for any known cavity shape Cartesian two-dimensional cross-section. Converting the Cartesian two-dimensional cross-section to polar coordinates at step 520 is equivalent to mapping the shape onto the r and θ plane. The r and θ plane can be seen on a polar coordinate graph. Converting polar coordinates follows the normal equations:

[0095]

[0096] θ = tan-1(y / x) [3]

[0097] The resulting two-dimensional shape, i.e., the polar cross-section in polar coordinates, is generated. The z-axis (i.e., the central axis) is in the middle of the two-dimensional polar shape. The polar two-dimensional cross-section has no z-component. The shape has 2-fold rotational symmetry around the z-axis.

[0098] For a pillbox cavity shape as shown in Figure 6 , the two-dimensional longitudinal cross-section is converted to polar coordinates via equation [2] and equation [3] (and plotted on a polar coordinate graph) to form a polar two-dimensional cross-section 610. It is in accordance with step 520 of Figure 5 The z-axis (i.e., the central axis 670) is in the middle of the polar two-dimensional cross-section 610. The polar two-dimensional cross-section has no z-component. The shape has 2-fold rotational symmetry around the z-axis.

[0099] At step 530, the two-dimensional polar cross-section of step 520 is helically rotated along the length of the cell around the central axis to generate a hollow 3D shape. The polar two-dimensional cross-section is extruded with a twist rate of π / L on the z-axis of the Cartesian coordinate system. Over a length L, the two-dimensional polar shape is continuously twisted a total of 180 degrees to generate the 3D shape. The twist rate π / L is a fixed rate of rotation along the length of the cell L, which can be defined in units of rad / m or deg / m. In other implementations, different twist rates can be envisioned, however, the twist rate of π / L provides field cancellation.

[0100] The two-dimensional polar cross-section is gradually rotated around the z-axis in a continuous manner along the length of the axis to "sweep out" the shape of the cavity. This means a "spiral rotation" of the shape around the axis. A 180 degree rotation over the length L results in the three-dimensional shape of the cavity. The spiral rotation is along the length L (a constant), but can also be achieved by a variation as a continuous function or as a step function. Since the cross-section of the cavity (the two-dimensional polar shape) has a two-degree order of rotational symmetry around the central axis, a 180 degree rotation of the shape over the cell length means that the transverse cross-section of the cavity is the same at the beginning of the cavity and at the end of the cavity (along the z-axis). In this way, multiple cavities can be positioned end-to-end to produce a waveguide.

[0101] Steps 520 and 530 provide a method for converting a conventional cavity shape into a spiral cavity shape. In one example, steps 520 and 530 can be performed by mapping a Cartesian coordinate system onto a spiral coordinate system. First, define a periodic function f(z) in Cartesian coordinates, f(z) represents the conventional cavity shape in the z-direction (the conventional cavity shape according to step 510). The function f(z) is periodic with respect to the cavity / cell length L along the z-axis (the central axis). The function f(z) can define a conventional longitudinal cross-section spanning multiple cells. Then transform the Cartesian function f(z) into a new function F(0) in a spiral coordinate system, the z values are transformed according to the twist rate p / L, so the 0 values are in the range 0 to L / 2p. The 0 values are defined by the values of the f(z) function, as these values are transformed in the F(0) frame, which can be written as:

[0102]

[0103] At step 540, output the three-dimensional shape from step 530. The 3D shape is the result of the spiral rotation around the z-axis. Equivalently, the 3D shape is the result of extruding along the z-axis.

[0104] A waveguide having a cavity with the three-dimensional shape is then manufactured. The manufacturing method is discussed in more detail below.

[0105] Figure 6 - Physical description of the spiral cavity

[0106] Figure 6 A waveguide having a cavity is shown, the cavity having a shape resulting from the method using Figure 5 . Figure 6 A polar two-dimensional cross-section 610 is shown, rotated in a spiral around the z-axis, forming a three-dimensional cavity shape 620. The two-dimensional polar cross-section is gradually rotated around the z-axis in a continuous manner along the length of the axis to sweep out the shape of the cavity. Equivalently, the two-dimensional polar cross-section is extruded backwards along the z-axis to form the three-dimensional cavity shape 620.

[0107] The 3D shape generated by steps 510 to 540 can be considered a “spiral cavity” because the 3D shape defines a resonant cavity and is produced by a helical rotation about the z-axis. The waveguide that includes the spiral cavity can be considered a “spiral waveguide”. Each spiral cavity and spiral waveguide has a known (non-spiral) cavity and waveguide counterpart. For example, the spiral cavity has a known cavity counterpart 314, which corresponds to an axisymmetric cavity having a longitudinal profile equivalent to the Cartesian 2D cross-section used to derive the spiral shape.

[0108] For the 3D shape (spiral cavity) output at step 540, any two-dimensional transverse cross-section perpendicular to the z-axis (i.e., within the x / y plane) is identical to the polar two-dimensional shape of step 520, albeit rotated to varying degrees about the z-axis.

[0109] However, an asymmetry has been introduced in the corresponding x and y longitudinal cross-sections taken along the z-axis. In this way, the axial symmetry of the cavity is broken. This is the so-called helical rotation along the length L (a constant). By way of Figure 5 The spiral cavity produced by the method of

[0110] For the 3D shape (spiral cavity) output at step 540, its transverse cross-sections (which are equivalent to the polar 2D cross-sections produced at step 520) are continuously helically rotated about the central axis along the length of the cell. The rotational position of the transverse cross-section shape varies along the length of the cell, and the variation in rotational position is continuous. The transverse cross-section is rotated at a fixed rate of rotation along the length of the cell. The fixed rate of rotation along the length of the cell can be referred to as the twist rate, which can be defined in units of rad / m or degrees / m. In the method of the present disclosure, the twist rate is defined as π / L, where L is the length of one cavity (as explained above, the length L is fixed in the relationship between the conventional cavity and the spiral cavity). The twist rate of π / L provides a 180-degree rotation along the length of the cell. Figure 5

[0111] In the waveguide, the longitudinal cross-sections correspond to the two-dimensional Cartesian shape from which the polar transverse cross-sections are derived. That is, since the 2D polar transverse cross-sections are helically rotated 180 degrees about the z-axis over the length of the cell, the waveguide cell with longitudinal cross-sections in the first longitudinal plane has a two-dimensional Cartesian shape from which the method starts. This is the same longitudinal cross-section as produced using the known method described above in Figure 3 Therefore, at one angle of rotation about the z-axis, the longitudinal cross-section of the spiral cell 630 is identical to the longitudinal cross-section of the membrane-to-membrane (NWN) of the axisymmetric cell (at any angle).​

[0112] At a second angle of rotation about the z-axis orthogonal to the first angle of rotation, the longitudinal cross-section of the helical cell is identical to the cross-section of an equator-to-equator (WNW) axisymmetric cell. In other words, this configuration is such that a membrane-to-membrane cell RF cell is obtained at the 0-degree cross-section (with respect to the z-axis) and an equator-to-equator cell RF cell is obtained at the 90-degree cross-section (with respect to the z-axis).

[0113] Likewise, the final helical twist shape must yield a membrane-to-membrane cell RF cell (2D Cartesian cell shape) at a cross-section taken along the central axis through the x / z plane (i.e. y = 0) and an equator-to-equator cell RF cell (2D Cartesian cell shape) at a cross-section taken along the central axis through the y / z plane (i.e. x = 0). The x / z plane and the y / z plane are a first plane and a second plane orthogonal to each other.

[0114] A longitudinal cross-section can be taken through the helical waveguide cell, where the longitudinal cross-section at a first angle about the central axis is a membrane-to-membrane cell when the first angle is orthogonal to the second angle, and the longitudinal cross-section at a second angle about the central axis is an equator-to-equator cell. The two longitudinal cross-sections taken at these two orthogonal angles can be considered to be 180 degrees out of phase. This can be seen by way of example helical cavity.

[0115] This structure of the waveguide gives rise to field cancellation properties.

[0116] In Figure 6 these conditions for field cancellation properties are shown, the final helical twist shape observed at 180 degrees of rotation with respect to the z-axis reproduces in Cartesian coordinates the same cross-sections as the helical cavity observed at 0 degrees of rotation with respect to the z-axis. The cross-section observed at 0 degrees is shown by 650, while the cross-section observed at 180 degrees is shown by 650. This configuration is such that a membrane-to-membrane cell RF cell is obtained at the 0-degree cross-section (with respect to the z-axis) and an equator-to-equator cell RF cell is obtained at the 90-degree cross-section (with respect to the z-axis). Equivalently, the final helical twist shape at a longitudinal cross-section taken through the x / z plane (i.e. y = 0) yields a membrane-to-membrane cell RF cell 650 and at a longitudinal cross-section taken through the y / z plane (i.e. x = 0) yields an equator-to-equator cell RF cell 640.

[0117] When the helical cavity is compared to its standard counterpart, the helical cavity can reduce the surface field, reduce the surface field at the membrane, and improve the acceleration gradient of the beam produced by its respective waveguide. The standard counterpart is a known (non-helical) cavity, which is the starting point for producing the helical form.

[0118] As explained above, if a longitudinal section of the helical cavity is taken at 0 degrees about the z-axis, a particular profile results, at 90 degrees another profile results, and at 180 degrees another profile results. In other words, there is a periodicity in the phase distribution similar to the membrane-to- membrane or equator-to-equator features described above for the length of a conventionally known waveguide within a particular longitudinal section. However, in the waveguide disclosed herein, the phase can be defined at a particular point of rotation about the longitudinal section. The first section (membrane-to-membrane form) and the second section (equator-to-equator form) can be considered to be the same shape but 180 degrees out of phase (completely or exactly out of phase) with each other. This is the condition for the helical cavity to have field cancellation properties. A longitudinal section can be taken at any angle about the z-axis and will result in a section that can be considered to be the same shape as the section that is just partially out of phase. Any cross section taken about the z-axis will have a constant area since the shape is translated and not changed. The sections all have the same area contained within the shape.

[0119] A waveguide, which can be referred to as a helical waveguide, is also provided. The helical waveguide can be manufactured using the method of Figure 5 The helical waveguide consists of a helical waveguide unit, which includes a helical cavity. The helical cavity is a cavity that includes a fixed non-circular transverse cross section whose rotational position about a central axis varies along the central axis, such as 620. The central axis of the helical waveguide unit is the axis of acceleration along which the electrons travel. The helical waveguide can define a longitudinal section in a first plane at a first angle, the waveguide and the longitudinal section being periodic structures. A longitudinal section can also be defined in a second plane, the second plane being orthogonal to the first plane and the periodic structures being 180 degrees out of phase with respect to the first plane.

[0120] For example, the helical cavity can form a helical waveguide unit having a central axis 660. The helical waveguide can consist of a helical waveguide unit having a helical cavity. The cavity has a fixed non-circular transverse cross section whose rotational position about a central axis varies along the central axis. The helical waveguide consisting of the cavity can define a longitudinal section in a first plane at a first angle, the waveguide and the longitudinal section being periodic structures. A longitudinal section can also be defined in a second plane, the second plane being orthogonal to the first plane and the periodic structures being 180 degrees out of phase with respect to the first plane.

[0121] At step 540, and optionally at step 550, any waveguide designed according to the method of Figure 5 is manufactured. Figure 9 A helical cavity to be manufactured is shown. The waveguide generated in this way has a cavity that varies as a function of twist, the twist about the z-axis described above.

[0122] After step 540, Figure 5The method may optionally include simulating an electric field to identify the maximum field before fabricating the 3D shape in step 550. Figure 5 These steps are not described in the method. The simulation of the electric field generated when radio frequency energy is applied to a waveguide comprising units with a 3D shape can be performed using Maxwell's solver software, although other simulations are also possible. Simulations can also be performed on cavities with a two-dimensional Cartesian cross-sectional shape scanned around a central axis (and...). Figure 3 Similar known waveguide counterparts perform simulated electric fields generated when radio frequency energy is applied to the waveguide. Based on these simulations, the maximum surface field can be identified. The maximum surface field of a conventional waveguide can be compared to that of an equivalent helical waveguide.

[0123] Each helical cavity has a corresponding (non-helical) cavity produced by a known technique, the known cavity counterpart being the starting point for producing the helical form. Each known cavity can have a helical counterpart.

[0124] Figure 7 - field in a solenoid

[0125] Figure 7 A simulated surface electric field is shown for an exemplary helical cavity 712, which is achieved through... Figure 5 The method produces it, and therefore it is essentially similar to a cavity. The original two-dimensional profile received at step 510 for generating the spiral shape is a shape similar to Ichiro's. Figure 7 The known shape of the Ichiro cavity is depicted. The longitudinal section (section taken along the z-axis) of the waveguide cavity 710 is also depicted.

[0126] and Figure 4a and Figure 4b Similarly, the intensities are represented as a grayscale image, where the strongest (i.e., highest density) electric field is black, the weakest (i.e., lowest density) field is white, and the field intensities in between are shown in grayscale. The longitudinal section of the waveguide cavity 710 also contains vector arrows representing the electric fields, which are colored according to the grayscale image.

[0127] It can be seen that, with Figure 4a Compared to the standard unit in, Figure 7 The maximum field ratio in the spiral unit is significantly reduced. This means that the strongest electric field is along the acceleration path and relative to... Figure 4a The peak intensity point shown has shifted. Figure 7 In the spiral cavity 712, the peak field point is not on the diaphragm surface; the surface of diaphragm 410 is no longer black in the figure. Figure 4b Compared to its standard counterpart, the surface field intensity ratio in the Ichiro spiral cavity 712 is reduced. Figure 4b The standard counterpart is the known (non-helical) cavity, which is the starting point for generating the helical cavity 712 form.

[0128]

[0129] Table 1: Results of simulated comparison between known waveguide shape and helical counterpart according to the present disclosure

[0130] In addition to Figure 7 the results of Table 1 show the results of a simulated comparison between the known waveguide Ichiro shape and its helical counterpart according to the present disclosure. The simulated input RF frequency was calculated at 10.9 GHz for both the conventional and helical waveguide shapes. The visual results of this simulation are described in Figure 7 as the helical waveguide cell, the visual simulation of the conventional waveguide cell calculated at 10.9 GHz is not shown. The conventional Ichiro shape waveguide and the helical Ichiro shape cavity waveguide have six quantities listed in Table 1: average acceleration gradient (Eac(average)), maximum surface electric field (Esurf(max)), Kilpatrick limit, quality factor (Q-factor), shunt impedance (R), and R / Q value.

[0131] Table 1 shows a slight decrease in R / Q, shunt impedance, and Q-factor for the helical Ichiro shape cavity waveguide, however, for the same simulated stored power (1 J energy in this case), the maximum surface field is greatly reduced and the acceleration gradient is increased. Comparable to Figure 7 the results of Table 1 show a reduction in surface electric field, the electric field has been moved along the acceleration path.

[0132] The method of the present invention provides a cavity optimized in such a way that the strongest electric and magnetic intensities exist only in the path of the accelerated beam, while the fields on all surface structures are either absent (have been cancelled) or have been minimized to a level far below the breakdown threshold. Such a system will have a high acceleration gradient and a high quality beam production. We note that among all possible cell shapes, the above method can only be applied to the non-recoverable cavity shapes (otherwise, an unmanufacturable shape will be obtained, i.e. a shape that is geometrically twisted on itself and self-intersecting).

[0133] Degradation modes (high and low order modes)

[0134] In any accelerating structure, in addition to the desired fundamental mode, other electromagnetic modes can be excited. These are called higher order modes (HOMs) or lower order modes (LOMs). HOMs and LOMs will establish additional electric and magnetic field variations on top and above the desired accelerating electric field. If these variations have a non-trivial component at the acceleration path, they will have an impact on the beam. HOMs and LOMs have undesirable effects on the electron beam. For example, if a higher order mode has an electric field component aligned with the electric field component of the fundamental mode (E zIf the field varies within a single cell, and can cause beam dispersion.

[0135] HOMs and LOMs with electric fields extending in different directions (E x and E y ) on the edges towards the cavity will induce lateral forces for deflecting the beam sideways and off the accelerator axis. It is therefore important to ensure that such higher order modes are suppressed, particularly in applications that rely on a stable and uniform beam.

[0136] The energy in the higher order modes does not accelerate the charged particles, so the higher order modes result in energy being wasted from the rf field. Eliminating the HOMs and / or LOMs provides more efficient guiding, where all the energy applied to the guiding is used in the fundamental field (which extends along the middle straight line of the cavity and away from the edges).

[0137] The helical structure provides field cancellation properties, as Figure 7 illustrated, whereby the degenerate fields (lower order modes (LOMs) and higher order modes (HOMs)) that are typically found in conventional accelerating equivalents are destructively superimposed together due to the rotational twist of the structure. This results in a reduction in the field in the regions, such that the field is only concentrated in the regions of the rotating volume, such as the axes and centre of the side lobes of the structure. In Figure 7 the helical structure, a region of zero values just above the iris can be clearly observed, as opposed to what is seen in conventional accelerating structures as Figure 4a or Figure 4b illustrated. The LOMs and HOMs of the helical structure are significantly different compared to conventional accelerating equivalents, the result of which is that the resulting dispersion properties are also different, and with cavity optimisation, this structure can also be used to potentially minimise other problems and effects caused by such degenerate modes (such as the problem of trapped modes), resulting in a more efficient RF accelerating structure.

[0138] Figure 8 Nine different known cavities (cells) are depicted by known longitudinal sections (1). The known waveguides include Figure 8 the known cavities (cells). The known longitudinal sections (1) are longitudinal sections of the known waveguide cells. At step 510 of the method Figure 5 each known longitudinal section can be used. The known longitudinal sections are Cartesian two-dimensional sections that include the equator and the iris. Each longitudinal section is similar to the longitudinal sections seen in Figure 2 or 316, 318 seen in Figure 3 . Each cavity in iris-to-iris form has a periodic length L (for a repeating accelerating structure), two irises and an equator.

[0139] It has four standard cavity shapes and five standard cavity shape variants. The four standard cavity shapes are: spherical, elliptical, Ichiro, and Tesla shapes. The shapes can be known shapes used in conventional waveguides, which have transformations in the form of variants. The five standard cavity shape variants are: spherical shape variant 1, spherical shape variant 2, spherical shape variant 3, spherical shape variant 4, and elliptical shape variant.

[0140] For each known cavity (unit) longitudinal section, Figure 8 The transverse section of its corresponding helical cavity (unit) is also shown. The transverse section of the helical cavity is a polar coordinate transformation of the longitudinal section of the standard cavity, where, according to... Figure 5 The method of this disclosure has converted a known cavity into its helical cavity counterpart. A helical cavity (unit) for each known cavity shape is provided in... Figure 8 As shown in the figure, according to Figure 5 Each spiral unit is generated using this method.

[0141] Those skilled in the art will understand that other shapes can also be used to fabricate waveguides according to this disclosure.

[0142] As explained above, the helical cavity has a longitudinal section in a first plane and a longitudinal section in a second plane orthogonal to the first plane, the longitudinal sections in the second plane having the same shape but out of phase by 180 degrees (perfectly out of phase). This provides field cancellation properties.

[0143] For example, the longitudinal section of the cell observed in the first plane can be a diaphragm-to-diaphragm 2D Cartesian cell shape, while the cell observed in the second plane orthogonal to the first plane can be an equator-to-equator 2D Cartesian cell shape.

[0144] Figure 8 Two longitudinal sections are depicted for each of the nine depicted helical cavity shapes. A first longitudinal section is taken at a first position (the x / z plane at y=0) through each 3D helical unit, and a second longitudinal section is taken at a second position (the y / z plane at x=0) through each 3D helical unit. The first and second planes are orthogonal to each other. Figure 8 Each of the nine helical waveguide units depicted exhibits field cancellation characteristics because diaphragm-to-diaphragm RF units (2D Cartesian unit shape) are obtained at the first plane, and equatorial-to-equatorial RF units (2D Cartesian unit shape) are obtained at the second plane. Equivalently, for each of the nine helical cavities, diaphragm-to-diaphragm RF units (2D Cartesian unit shape) are obtained at the 0-degree cross-section (relative to the z-axis), and equatorial-to-equatorial RF units (2D Cartesian unit shape) are obtained at the 90-degree cross-section (relative to the z-axis).Figure 8 It can be seen that the longitudinal cross-section of the helical cell through the second plane (the y / z plane) is an equator-to-equator equator until its shape is identical to the known waveguide cell longitudinal cross-section.

[0145] The longitudinal cross-section of the helical cavity (“helical longitudinal cross-section”) has the same shape as the longitudinal cross-section of the standard corresponding cavity from which the helical cavity is derived (“known waveguide cell longitudinal cross-section”). Depending on the angle of the plane of the helical longitudinal cross-section, the helical longitudinal cross-section corresponds to the known waveguide cell longitudinal cross-section at different points along the length of the known waveguide cavity. That is, the helical longitudinal cross-section is the known waveguide cell longitudinal cross-section translated by a certain amount along the length of the cell. As the angle of the plane of the helical longitudinal cross-section changes around the z-axis, the amount of translation of the known waveguide cell longitudinal cross-section changes. Cross-sections are the cell shapes taken from different points along the length of the cell. Observing the helical longitudinal cross-section in a plane that is continuously rotated around the z-axis corresponds to the known waveguide cell cross-sections that are continuously translated along the z-axis. Rotating the helical longitudinal cross-section by 90 degrees around the z-axis corresponds to translating the known waveguide cell longitudinal cross-section by half the length of the cell along the z-axis.

[0146] Figure 9 - manufacturing options

[0147] Figure 9 Helical cavities 910 of the present disclosure and two corresponding three-dimensional shapes that can be used to manufacture waveguides comprising the helical cavities 910 are depicted. Figure 9 Two shapes 920, 930 are shown that correspond to two different methods of manufacturing waveguides comprising the helical cavities 910. This manufacturing method can be used in step 550 of Figure 5 The manufacturing shapes can be designed or imported into CAD software. The helical cavities can be manufactured as waveguides for use in linear accelerators and / or radiation therapy devices.

[0148] Traditionally, each cavity is manufactured from a conductive metal such as copper, and then the cavities are stacked adjacent to one another to form the waveguide. The cavities can be joined together at the joining portions by brazing or welding. The joining portions of the segments are typically in the equator of the cavities.

[0149] Some helical cavities of the present disclosure, such as 910, can be manufactured using traditional methods. For example, 920 is a single cavity that can be manufactured repeatedly, and the single pieces can be welded together at the joining portions to form the waveguide. By Figure 5The method of generating the helical cavity 910 is that the Cartesian two-dimensional cross-section identified at step 510 is an Ichiro shape. For the helical cavity 910, the simplest repeating unit to fabricate is the shape 920, which is half the length of the helical cavity 910. As defined previously, the length of the cavity refers to its distance along the central axis (z-axis). The shape 920 is the shape that is actually “printed” into the part. To form one helical cavity 910, two parts of the shape 920 can be stacked at 90 degrees to each other. Of course, to form a waveguide, for example, many parts of the shape 920 can be stacked at 90 degrees to each other, requiring many cavities to form the waveguide. Other waveguides according to the present disclosure that include helical cavities can be fabricated in a similar manner using half helical cavities as the repeating unit. Alternatively, for other waveguides according to the present disclosure that include helical cavities, the entire helical cavities can be used as the repeating unit to fabricate these waveguides. The choice of repeating unit depends on which repeating unit is easiest to fabricate and which repeating unit is easiest to join to form the waveguide.

[0150] Alternatively, the cavities can be fabricated into waveguides using a split or “subway sandwich” technique. In this technique, multiple cavities are virtually presented, for example, in CAD software. The multiple cavities can form a portion of a waveguide, or in some cases can form an entire waveguide. A waveguide segment is cut along an acceleration axis, which is equivalent to cutting through a longitudinal plane (e.g., the y / z plane or the x / z plane) to form two halves. The two halves are fabricated into two parts, which are “sandwiched together” to form the waveguide segment. The two halves are “sandwiched together” by welding. This process can be repeated for the number of waveguide segments that form an entire waveguide. The waveguide segments can be joined together by welding to form the entire waveguide.

[0151] The present disclosure also relates to methods of fabricating waveguides of the present disclosure.

[0152] Some helical cavities of the present disclosure can be fabricated using the subway sandwich method. In particular, for more complex geometries, the subway sandwich technique can be easier and more successful to implement than traditional methods. For example, in Figure 9 One half of a waveguide segment 930 for the subway sandwich fabrication technique is depicted in FIG. 9B, but the other half of the waveguide segment is not shown. Figure 9 The halves depicted in FIG. 9B are fabricated into one part, while the corresponding other halves are fabricated into a second separate part. The two halves are sandwiched together by welding to form the waveguide segment. Multiple waveguide segments are fabricated in this manner, which are welded together to form an entire waveguide. The helical cavity fabrication shape 930 is derived from the helical cavity 910 generated by the method of FIG. 9A. Figure 5 The two half cavities of the helical cavity 910 include the waveguide segment 930.

[0153] The cavities in the waveguide can vary in shape, and the waveguide fabrication can involve slight changes to the shape of the cavities depending on their location in the waveguide. For example, the cavities near the electron gun can be used for bunching of the electrons, and can be shorter in length compared to the cavities near the heavy metal target for acceleration.

[0154] Advantages

[0155] The waveguide designed according to the present disclosure, the dimensions of the waveguide are not limited by the scan that creates a two-dimensional model around the central axis. Rather, a three-dimensional model of the waveguide is created, where the dimensions of the cavities vary around the axis. Thus, the transverse cross-section of the acceleration channel at one point is not circular or annular. This is a fundamental difference from the waveguides included in the prior art.

[0156] The spiral waveguide of the present invention has field cancellation properties. When comparing the spiral cavity to its known counterpart, the spiral cavity can reduce the surface field, reduce the surface field at the diaphragm and improve the acceleration gradient of the beam production of its respective waveguide. As explained above, high electric fields at the cavity surface can cause RF breakdown at these locations. An empirically derived formula, such as the Kilpatrick breakdown limit, can predict to some extent whether RF breakdown will occur. If the surface field is greater than the Kilpatrick breakdown limit, there is a high probability of RF breakdown at that location. The Kilpatrick limit provides an estimate, as the mechanism of RF breakdown depends on many factors, such as field emission, multi-step operation, gas breakdown, and surface heating.

[0157] When the Kilpatrick limit test is applied to the spiral cavity of the present disclosure, the surface field is approximately the same as the limit that predicts that there will be no RF breakdown at these locations. Alternatively, if the surface field is reduced below the threshold for RF breakdown, the input RF frequency can be safely increased without causing RF breakdown. Increasing the applied RF energy increases the strength of the field throughout the waveguide, including the field on the acceleration path. Thus, more energy can be delivered to the electrons, the x-ray beam can have higher energy, and patient treatment time can be reduced.

[0158] Referring to Table 1, the Kilpatrick limit for both the traditional Ichiro shaped waveguide and the spiral Ichiro shaped cavity waveguide is 643 (MV / m) as the input frequency is the same for both (10.9 GHz). For the traditional waveguide, the maximum electric field is 865 MV / m, which is higher than the Kilpatrick limit (643 MV / m), which means that at this frequency there will be RF breakdown and the traditional waveguide will not be able to operate at this frequency level. However, for the spiral waveguide, the maximum electric field is 645 MV / m, which is approximately equal to the Kilpatrick limit (643 MV / m), which means that there is no RF breakdown at this frequency level.

[0159] The location of the maximum surface field in an accelerating structure (either normally conducting or superconducting) is typically found on the membrane of the cell as this is where the surface field is most concentrated due to the geometry and the way the field interacts with the surface. However, in alternative designs, such as the spiral geometry presented in the present disclosure, the maximum surface field can be greatly reduced in these regions which are shifted to new locations. The field generated in the cavity can be minimized at all or some locations other than along the acceleration path. Whether the maximum surface field is localized to a point or spans the entire surface, results in a structure that can generate a higher acceleration gradient. An exemplary increase in the acceleration gradient of the spiral cavity waveguide compared to its traditional counterpart can be seen in Table 1.

[0160] Another factor that affects breakdown is surface roughness. A smoother surface is less likely to cause breakdown than a rough surface. That is, increased roughness of the cavity edges increases the likelihood of breakdown. The membrane is the most difficult part of the cavity to machine to a high smoothness. By shifting the point of peak field away from the surface or by reducing the field at the membrane, a rough surface cavity can be used without causing breakdown. Alternatively or additionally, a higher accelerating field can be used without causing breakdown.

[0161] Shifting the field away from the membrane means that the level of smoothness and uniformity at the nosecone or membrane can be reduced while maintaining the acceleration capability and efficiency of the waveguide. Again, this is because the effect of having a spiral cavity waveguide is that the highest intensity part of the electric field is reduced at the surface. As the membrane is difficult to manufacture and particularly difficult to smooth, this can reduce the cost of manufacturing the waveguide without reducing the dose rate that can be achieved by the waveguide.

[0162] Other advantages are that if the field is reduced at the surface, the cells can be welded together in the plane in which the acceleration path lies. This means that, in order to manufacture the waveguide, it is possible to use, for example, Figure 9The depicted metrology sandwich method of welding two opposing halves together forms a number of cavities at once. This technique is currently not possible without precise positioning of the two halves, because if there is a surface field, the cavities and slight misalignments will have a huge impact on the electric field generated in the waveguide.

[0163] As explained above, the spiral cavity provides a field cancellation property, as Figure 7 As shown, due to the rotational twist of the structure, the degenerate fields (low order modes (LOM) and high order modes (HOM)) that are normally found in conventional accelerating equivalent cavities have been destructively added together. This results in a reduction of the field in the region, such that the field is only concentrated in the regions of the rotation body, e.g. the axis of the structure and the center of the side lobes. In Figure 7 In the spiral structure of Figure 4a and Figure 4b shown) are observed. The LOM and HOM of the spiral structure differ significantly compared to the conventional accelerating equivalent, the result of which is that the resulting dispersion properties are also different, and using this structure that results in a more efficient RF accelerating structure, the other issues and effects caused by this degenerate mode (e.g. the problem of trapped modes) can also be potentially minimized with cavity optimization.

[0164] In general, a waveguide comprising a spiral cavity is provided, the shape of which advantageously reduces the surface field.

[0165] Variants

[0166] Throughout this disclosure, reference is made to the reduction of the surface field, in particular the electric field. However, the reduction of the surface field can equally refer to the reduction of the magnetic field according to the present invention. For simplicity, the magnetic field is not shown.

[0167] Once the waveguide has been produced, the waveguide can be "tuned" to try to reduce asymmetries in the field generated in the waveguide. This can be achieved by measuring the electric field generated in the waveguide when the radio frequency energy is applied, introducing a dent into the waveguide, and then taking another measurement of the electric field to determine whether the asymmetries have been reduced. The overall goal of the known tuning is to reduce the asymmetries on the plate to align the optimal path taken by the electron.

[0168] There are multiple waveguide adjustment methods. The first method is to use adjustment dimples or posts at the equatorial position at 0 or 90 degree cross section locations (relative to the z-axis), which introduces volume changes and frequency shifts, and this can be applied to any of the spiral cavities of the present disclosure. If the structure has a sufficiently thin diaphragm section, such as seen in the Ichiro shape, the length of the cell can be adjusted by pulling the diaphragm using a specialized tool at the 0 or 90 degree cross section locations, which adjusts the twist of the cell, and has a large phase impact and a small frequency shift impact. Dielectric loading of the structure with RF absorbers (such as SiC) at the 0 or 90 degree cross section locations can introduce frequency shifts. Precision machining of the structure can be performed so that the structure does not need adjustment after brazing (if this is the preferred manufacturing method) or according to older manufacturing techniques such as electroforming (and removal of the inner mold by dissolution in acid or by growing the surface on a pre-existing mold).

[0169] The modes within the spiral cavity can be considered hybrid modes, rather than pure transverse electric (TE) or transverse magnetic (TM) modes as seen in conventional RF cavities. The frequency obtained in the spiral cavity can be higher than its conventional counterpart when using the same geometrical input, and this needs to be compensated by a slight increase in the cavity height. The height of the spiral cavity can be increased by trial and error until the RF frequencies of the spiral cavity and the conventional cavity match. It is not always necessary to reproduce the same frequency in the spiral cavity as its conventional counterpart. In fact, one advantage of the present invention is to provide a system in which a higher frequency RF can be safely used without experiencing breakdown.

[0170] Thus, the above method can include an additional step of adjusting the height of the spiral cavity. This is done after step 540 in the method of Figure 5 The time-varying electric field produced by applying a radio frequency wave to the waveguide is simulated. The RF frequency produced in the spiral cell is compared to the RF frequency induced when RF energy is applied to a standard waveguide (an axisymmetric waveguide with a longitudinal cross section equal to the axisymmetric waveguide of the cavity of 2D Cartesian shape in step 510 of the method). The frequency in the spiral cavity is compared to the frequency in the conventional cavity. If the frequencies are different or not within a threshold of each other, the height of the spiral cavity is increased to produce a modified spiral cavity shape. The time-varying electric field produced by applying the RF wave to the modified spiral cavity is simulated. The frequency in the modified spiral cavity is compared to the frequency in the conventional cavity. If the frequencies do not match, the spiral cavity shape is again modified and the method is repeated. If the frequencies match or are within a threshold of each other, the spiral shape is output as the final shape.

[0171] So far, the acceleration of the electrons is about the axis acceleration, but it is also possible to support a deflection mode generated in the solenoid cavity for acceleration. The deflection mode has a different application to the axis acceleration. The axis acceleration can be used in a linear accelerator for a radiotherapy device, and the deflection mode can be used for particle separation and time beam diagnostics. If the ratio of the length of the equator to the height is kept below a certain ratio for any of the described solenoid cavities, the axis acceleration is obtained. At a certain point, beyond this ratio (i.e. if the cavity is made very long), then the field cancellation of the solenoid cavity results in a deflection mode instead of an axis acceleration mode. The deflection mode results in a complex machine acceleration structure. This configuration can be manufactured using the deflection mode for these types of shapes only by the subway sandwich method, similar to Figure 9 930. The beam tube can be placed along the axis for a deflection mode cavity without causing too much disturbance to the system (i.e. the field cancellation will still occur).

[0172] The solenoidal waveguide of the present invention comprising a solenoidal waveguide cell (solenoid cavity) can be used in a standing wave configuration or in a travelling wave configuration. The solenoidal waveguide can also be applied to high and low beta cavity structures. Any type of charged particle can be accelerated in the solenoidal waveguide, such as electrons, protons or ions (carbon or other).

[0173] In addition to providing waveguide cells and waveguides according to the above description, the present disclosure also relates to a particle accelerator comprising the disclosed waveguides, and to a linear accelerator comprising the disclosed waveguides. A radiotherapy device comprising the linear accelerator is also disclosed.

[0174] A method of manufacturing the waveguides described herein is also disclosed.

[0175] Definitions

[0176] Axial asymmetry

[0177] In the asymmetric waveguide according to the present disclosure, the walls that define the cavity edge do not maintain a constant distance to the central axis in a rotation about the central axis. That is, the cross-section of the acceleration cavity at a given point is not circular. The radius that defines the distance from the wall to the central axis is not constant around the central axis; rather, it varies through a rotation about the central axis. In other words, the order of rotational symmetry of the cross-section of the acceleration channel around the central axis is not infinite; it is discrete.

[0178] The waveguides described above can be used in a particle accelerator. The particle accelerator can be a linear accelerator. The linear accelerator can be used in a radiotherapy device.

[0179] The waveguide is fabricated by fabricating a series of cavities interconnected along a central axis to form an acceleration channel. In one particular embodiment, fabricating a series of cavities includes fabricating a plurality of segments of material that define a portion of at least one cavity; and joining the segments to form the series of interconnected cavities. The material can be any electrically conductive material, and in particular embodiments is copper. The segments are joined together by brazing or welding. The fabricated waveguide can have any of the characteristics or dimensions of the waveguides of the present disclosure as described above.

[0180] Also provided are waveguides fabricated using the disclosed methods.

[0181] Acceleration cavity

[0182] An acceleration cavity is a cavity through which an acceleration path passes.

[0183] Additional components inserted into the acceleration channel, such as couplers that protrude into the acceleration path, do not affect the shape of the acceleration channel or acceleration cavity. The acceleration cavity and the shape of the acceleration cavity are intended to represent the shape of the volume of the channel through which the acceleration path of the electron passes.

[0184] Features of the various aspects described above can be combined in any suitable manner. It will be appreciated that the above descriptions are merely specific embodiments of aspects and that many modifications and changes can be made within the scope of those skilled in the art, which is not to be regarded as limiting. The scope of the application should be determined by reasonable interpretation of the appended claims.

Claims

1. A method of determining a 3D shape of a waveguide cell, the method comprising: identifying a 2D cross-section; spiral ly rotating the 2D cross-section along a length of the cell about a central axis to generate a 3D shape; and outputting the 3D shape; wherein the waveguide cell has a length L, and the identifying a 2D cross-section comprises: identifying a Cartesian 2D cross-section of the cell in Cartesian coordinates; and generating a polar 2D cross-section in polar coordinates by converting the Cartesian 2D cross-section into polar coordinates, the direction theta being defined to be between 0 and L / 2pi; the spiral ly rotating the 2D cross-section along a length of the cell about a central axis to generate a 3D shape comprises: extruding the 2D polar coordinate shape backwards on the z-axis of the Cartesian coordinate system with a twist rate of pi / L. spiral ly rotating the 2D cross-section comprises: rotating the 2D cross-section 180 degrees along the length of the cell.

2. The method of claim 1, wherein, the identifying a 2D cross-section comprises: identifying a periodic Cartesian 2D cross-section of the cell, wherein the periodic Cartesian 2D cross-section defines a periodic function f(z); and 3. The method of claim 1, wherein, the spiral ly rotating the 2D cross-section along a length of the cell about a central axis to generate a 3D shape comprises: transforming the periodic function f(z) into a new function F(theta) in a spiral coordinate system, wherein the z values are transformed by a twist rate of pi / L, and the theta values are in the range of 0 to L / 2pi. the Cartesian 2D cross-section of the cell comprises a diaphragm-to-diaphragm cell shape, and wherein a longitudinal cross-section of the cell in a first plane is the diaphragm-to-diaphragm Cartesian cell shape, and a longitudinal cross-section of the cell in a second plane orthogonal to the first plane is an equator-to-equator Cartesian cell shape.

4. The method of claim 1, wherein, the Cartesian 2D cross-section is a 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.

5. The method of any one of claims 1 to 4, wherein, manufacturing a waveguide having the 3D shape.

6. The method of any one of claims 1 to 4, further comprising:

7. A waveguide manufactured by the method of any one of claims 1 to 6.

8. A linear accelerator comprising the waveguide of claim 7.

9. A radiotherapy device comprising the linear accelerator of claim 8. ​

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