Patent Number: 044255063
Section: description

DETAILED DESCRIPTION OF THE INVENTION FIG. 1 shows an x-ray therapy machine 10 incorporating a magnetic deflection system 13. The therapy machine 10 comprises a generally C-shaped rotatable gantry 14, rotatable about an axis of revolution 16 in the horizontal direction. The gantry 14 is supported from the floor 18 via a pedestal 20 having a trunnion 22 for rotatably supporting the gantry 14. The gantry 14 includes a pair of generally horizontally directed parallel arms 24 and 26. A linear electron accelerator 27 communicating with quadrupole 28 is housed within arm 26 and a magnetic deflection system 11 and target 29 are disposed at the outer end of the horizontal arm 26 for projecting a beam of x-rays between the outer end of the arm 26 and an x-ray absorbing element 30 carried at the outer end of the other horizontal arm 24. The patient 32 is supported from couch 34 in the lobe of the x-rays issuing from target 28 or theraputic treatment. Turning now to FIGS. 2 and 3, a pole cap 50 of the polepiece of the invention is shown. A step 52 divides pole cap 50 into regions 54 and 56, the pole cap 50 in region 56 having a greater thickness than region 54 by the height h of the step 52. Consequently, the magnet comprising pole cap 50 and 50' is characterized by a relatively narrow gap of width d in the region 56 and a relatively wide gap (d+2h width) in the region 54. Accordingly, the magnet comprises a constant uniform region 54 of relatively low magnetic field and another constant uniform region 56 of relatively high magnetic field. Excitation of the magnet is accomplished by supplying current to axially separated coil structure halves 58 and 58' each disposed about respective outer poles 60 and 60' to which the pole caps 50 and 50' are affixed. The magnetic return path is provided by yoke 62. Trim coils 64 and 64' provide a vernier to adjustment of the field ratio in the regions 54 and 56. A vacuum envelope 67 is placed between the poles of the magnet and communicates with microwave linear accelerator cavity 68 through quadrupole Q. As discussed below, another important design parameter is the angle of incidence of the trajectory with respect to the field at the entrance of the deflector. The control of the fringing field to maintain the desired position and orientation of the outer virtual field boundary 69 with respect to the entrance region is accomplished with field clamp 66 displaced from the pole caps by aluminum spacer 66'. In similar fashion, the location of the exit field boundary and orientation is controlled by suitable shape and position of the field clamp 66 in this region. An interior virtual field boundary 55 may be defined with respect to step 52 by appropriate curvature of the stepped surfaces 53 and 53'. This curvature compensates for the behavior of the magnetic field as saturation is approached and controls the fringing field in this region. Such shaping is well known in the art. Neither field boundary 69 nor 55 constitutes well defined locii and each is therefore termed "virtual" in accord with convention. A parameter is associated with each virtual field boundary to characterize the fringing field behavior in the transition region from one magnetic field region to another. Thus a parameter K.sub.1 is a single parameter description of the smooth transition of the field from the entrance drift space l.sub.1 to region 54 along a selected trajectory, as for example, central orbit P.sub.0 (and between region 54 and the exit drift space l.sub.2 in similar fashion). The fringing field parameter K.sub.2 describes similar behavior between magnetic field regions 54 and 56. It is conventional in the discussion of dipole magnetic optical elements for the z axis of the coordinate system to be chosen tangent to a reference trajectory with origin z=0 at the entrance plane and z=1 at the exit plane. (The entrance and exit planes are, in general, spaced apart from the magnetic field boundaries by drift spaces as indicated and should not be identified with any field boundary). The x axis is selected as the displacement axis in the plane of deflection of the bending plane. The y axis then lies in the transverse direction to the bending plane. The y axis direction is conventionally called "vertical" and the x axis, "horizontal". In the plane of deflection, a central orbital axis labeled P.sub.0 is described by a particle of reference momentum arrow P.sub.0. It is desired that displaced trajectories C.sub.x and C.sub.y having initial trajectories parallel to P.sub.0 (in the bending plane and transverse thereto, respectively), produces a like displacement at the exit of the deflector. A trajectory that enters this system at an angle .beta..sub.i to the field boundary exits at an angle .beta..sub.f. In the present discussed embodiment it is desired that .beta..sub.i =.beta..sub.f =.beta.. The trajectory is characterized by a radius of curvature .rho..sub.1 in the region 54 of the magnet due to magnetic field B.sub.1. In the region 56, the corresponding radius of curvature is .rho..sub.2 due to the magnetic field B.sub.2. The notation .rho..sub.0,1 (see FIG. 2) refers to the radius of curvature of the reference trajectory P.sub.0 in the low field region. The line determined by the respective centers for radii of curvature .rho..sub.0, 1 and .rho..sub.0, 2 intersects the virtual field boundary 55 determining the angle of incidence .beta..sub.2 to region 56 (incoming) and from symmetry the angle of incidence through field boundary 55 as the trajectory again enters region 4. For simplicity, the 0 subscript will be deleted. The deflection angle in the bending plane in the region 54 (incoming) is .alpha..sub.1 and again an angle .alpha..sub.1 in the outgoing trajectory portion of the same field region 54. In the high field region 56 the particle is deflected through a total angle 2.alpha..sub.2 for a total deflection angle .chi.=2(.alpha..sub.1 +.alpha..sub.2) through the deflection system. It is a necessary and sufficient condition for an achromatic deflection element that momentum dispersive trajectory d.sub.x (initial central trajectory direction, having a magnitude of P.sub.0 +.DELTA.P) is dispersed and brought to parallelism with the central trajectory P.sub.0 at the midpoint deflection angle .alpha..sub.1 +.alpha..sub.2, that is, at the symmetry plane. Further, the trajectory of particles initially displaced from, and parallel with trajectory P.sub.0 (in the bending plane) are focused to a cross-over with trajectory P.sub.0 at the symmetry plane. These trajectories are known in the art as "cosine-like" and designated C.sub.x, where the subscript refers to the bending plane. Trajectories of particles initially diverging from trajectory P.sub.0 (in the bending plane) at the entrance plane of the magnet are shown in FIG. 2. These trajectories are known in the art as "sine-like" and are labeled as S.sub.x in the bending plane. The condition of maximum dispersion and parallel-to-point focussing occurs at the symmetry plane and therefore defining slits 72 are located in this plane to limit the range of momentum, angular divergence accepted by the system. In common with similar systems, these slits 72, which are secondary sources of radiation, are remote from the target and shielded by the polepieces of the magnet. In the present invention, the gap is narrower in precisely this region, wherefore the greater mass of the polepieces 50 and 50' more effectively shield the environment from slit radiation. Trajectories C.sub.y and S.sub.y refer to cosine-like and sine-like trajectories in the vertical (y-z) plane. It is therefore required to obtain the relationship of the radii of curvature .rho..sub.1 and .rho..sub.2 and therefore, the magnetic fields B.sub.1 and B.sub.2 for the parameters of .alpha..sub.1 and .alpha..sub.2, P.sub.0, and the field extension parameters K.sub.1 and K.sub.2 of the virtual field boundaries subject to the condition of zero angular divergence in the bending plane of the momentum dispersive trajectory at the symmetry plane, e.g., (.differential.d.sub.x /.differential..sub.8)=0 for deflection angle .chi./2. From this condition, imposed at the symmetry plane, it can be shown that d.sub.x and its divergence, d.sub.x' ' will vanish at the exit of the magnet. In a simple analytical treatment of the problem, transfer matrices through the system are written for the incoming trajectory through region 54, proceeding to the incoming portion of region 56 to the symmetry plane, and then outgoing from region 56 to the boundary with region 54 and again outgoing through region 54. These matrices for the bending plane are written as the matrix product of the transfer matrices corresponding to propagation of the beam through the four regions 54.sub.o, 56.sub.o, 56.sub.i, 54.sub.i as shown in FIG. 4 ##EQU1## where c.sub.1, s.sub.1, c.sub.2, s.sub.2, are a short notation for respectively, cosine .alpha. and sine .alpha. in the respective low (1) and high (2) field regions and .beta. here stands for tam .beta.. The variables .rho..sub.1 and .rho..sub.2 refer to radii of curvature in the respective regions 1 and 2 corresponding to regions 54 and 56. The C.sub.i and S.sub.i parameters are conventionally expressed as displacements with respect to the reference trajectory. Equation 1 can be reduced to yield, in the bending plane ##EQU2## The matrix element R.sub.11 expresses a coefficient describing the relative spatial displacement of the C.sub.x trajectory. The R.sub.12 element describes the relative displacement of S.sub.x. In similar fashion, the element R.sub.21 element describes the relative angular divergence of C.sub.x and the element R.sub.22 the relative angular divergence of the S.sub.x trajectory. Matrix elements R.sub.13 and R.sub.23 describes the displacement in the bending plane of the momentum dispersive trajectory d.sub.x (which was initially congruent with the central trajectory at the object plane) and R.sub.23 describes its divergence. Several conditions are operative to simplify the optics: (a) the apparatus maps incoming parallel trajectories to outgoing parallel trajectories at the entrance and exit planes respectively, which follows from the matrix element R.sub.21 =0; (b) the deflection magnet having no dependence upon the sense of the trajectory from which it follows that R.sub.22 =R.sub.11 ; (as is also apparent from consideration of the symmetry of the system); (c) the determinant of the matrix is identically 1 by Liouville's theorem. It follows from conditions (b) and (c) that R.sub.11 ==-1. The bottom row of the matrix describes the momentum in either plane. These elements are identically 0,0 and 1 because there is not net gain or loss in beam energy (momentum magnitude) in traversing any static magnet system. For an achromatic system, the dispersion displacement term R.sub.13 and its divergence, R.sub.23 must be 0. As expressed above, the condition on R.sub.23 at the symmetry plane is developed analytically to yield a relationship among certain design parameters of the system. As a result thereof one obtains the expression ##EQU3## which can be solved to yield the condition ##EQU4## Following conventional procedure the corresponding vertical plane matrices for the same regions 54 (incoming), 56 (incoming), 56 (outgoing), and 54 (outgoing) may be written and reduced to obtain the matrix equation for transverse plane propagation through the system. EQU y(1)=R.sub.y y(0) where 1 is the z coordinate location of the exit plane for the entrance plane, z=0. A principal design constraint is the realization of a parallel to parallel focusing in this plane is to be contrasted with the deflection plane where the corresponding condition follows from the geometry of the magnet. Thus far the transfer matrices R.sub.x and R.sub.y describe the transfer functions which operate on the inward directed momentum vector P(z.sub.1) at the field boundary 69 to produce outgoing momentum vector P(z.sub.2) at the field boundary 69 after transit of the magnet. In the preferred embodiment, drift spaces l.sub.1 and l.sub.2 are included as entrance and exit drift spaces, respectively. Drift matrices of the form ##EQU5## operate on the R.sub.x,y matrices which both exhibit the form of equation 2, e.g., ##EQU6## and it is observed that the magnet transfer matrix has the form of an equivalent drift space. Thus, the transformation through the total system with drift spaces l.sub.1 and l.sub.2 will yield total transfer matrices for the bending and transverse planes given by ##EQU7## where the minus sign refers to the matrix R.sub.x.sbsb..tau. and the plus sign refers to R.sub.y.sbsb..tau.. the lengths L.sub.x and L.sub.y are the distances from the exit plane to the projected crossovers of the S.sub.x and S.sub.y trajectories. Turning now to FIG. 5, the general situation is shown wherein the waist in the bending or radial plane and the waist in the transverse plane are achieved at different positions on the z axis. Thus, in one plane the beam envelope is converging while diverging in another plane. Previously, a plurality of quadrupole elements would be arranged to bring these waists into coincidence at a common location z. In the present invention, the condition d.sub.x '=0 and C.sub.y =0 are satisfied at the symmetry plane with the result that d.sub.x =0 at the field exit boundary. Moreover, it follows from this that C.sub.x characterizes parallel to parallel transformation through the magnet in the bending plane. In the transverse plane parallel to parallel transformation is imposed on the design. Consequently, the matrix describing either transverse or bending plane exhibits the form as given above. The effect of the quadrupole singlet at the entrance of the system takes the form ##EQU8## where s.sub.q may be identified with the (variable) quadrupole focal length. The waist of the beam is attained from expressions of the form EQU .vertline.x(.sub.1).vertline..sup.2 =.vertline.C.sub.x X.sub.(o).vertline..sup.2 +.vertline.S.sub.x X'.sub.(o) .vertline..sup.2 EQU .vertline.y.sub.(1) .vertline..sup.2 =C.sub.y y.sub.(o) .vertline..sup.2 +.vertline.S.sub.y Y'.sub.(o) .vertline..sup.2 It is noted that S.sub.x and S.sub.y are unaffected by the quadrupole inasmuch as these trajectories exhibit zero amplitude, by definition, at z=0. The displacement of trajectories C.sub.y and C.sub.x are of opposite side. If the range l.sub.1 +l.sub.2 has been properly selected the focal length of the quadrupole can be adjusted to bring the radial waist and transverse waist into coincidence. The matrix equations EQU X.sub.(1) =R.sub.x.sbsb..tau. X.sub.(o) EQU y.sub.(1) =R.sub.y.sbsb..tau. y.sub.(o) which describe the total system including drift spaces in the vertical and bending planes are most conveniently solved by suitable magnetic optics programs, such as, for example, the code TRANSPORT, the use of which is described in SLAC Report 91 available from Reports Distribution Office, Stanford Linear Accelerator Center, P.O. Box 4349, Stanford, CA 94305. The TRANSPORT code is employed to search for a consistent set of parameters: subject to selected input parameters, .rho..sub.1, the radius of curvature of P.sub.0 in region 54, .rho..sub.1 /.rho..sub.2, the relative radius of curvature of P.sub.0 in region 54 to the radius of curvature in region 56, .beta..sub.1, the angular incidence of trajectory P.sub.0 on virtual field boundary, .alpha..sub.2, the angular rotation of the central trajectory P.sub.0 in the high field region which also determines .beta..sub.2 the angle of incidence of P.sub.0 on the interior virtual field boundary, .alpha..sub.1, the rotation of the reference trajectory in the low field region, subject to the selected input parameters as follows: K.sub.1, the parameter of the virtual field boundary between the low field region and the external field free regions, K.sub.2 /K.sub.1, the relative parameter describing the virtual interior field boundary between the high field and low field regions, For the preferred embodiment symmetry has been imposed, e.g., .chi.=2(.alpha..sub.1 +.alpha..sub.2). In one representative set of design parameters for 270.degree. electron deflection, the desired mean electron energy is variable between 6 Mev and 40.5 Mev. First order achromatic conditions are required over this range. The angle of incidence .beta. for entrance and exit portions of the trajectory is 45.degree. and the outer virtual field boundary 69 is located at z=10 cm relative to the entrance collimator (z=0) aperture. The central trajectory rotates through an angle .alpha..sub.1 of 41.5.degree. under the influence of a magnetic field B.sub.1 of 4.17 kilogauss and intercepts the interior virtual field boundary 55 at z=33.5 cm at an angle .beta..sub.2 =90.degree.-.alpha..sub.2 of 31/2.degree. to reach the symmetry plane at z=37.4 cm and continued rotation through the angle .alpha..sub.2 (93.5.degree.) under the influence of magnetic field B.sub.2 of 15.90 kilogauss. The trajectory is symmetric within the magnetic field boundaries and the target is located at beyond the outer virtual field boundary. At the entrance collimator the beam envelope is 2.5 mm in diameter exhibiting (semi cone angle) divergence properties in both planes of 2.4 mr. The geometry of the magnet assures a parallel to parallel with deflection plane transformation. The condition that d.sub.x '=0 at the symmetry plane provides momentum independence. The parallel to parallel condition in the transverse plane is therefore a constraint. The bend angles .alpha..sub.1 and .alpha..sub.2 and the ratio of field intensities are varied to obtain the desired design parameter set. It has been found that a first order achromatic deflection system for a deflection angle of 270.degree. can be achieved with a variety of field ratios (B.sub.1 /B.sub.2) as shown from equation 3. Further, absolute values of corresponding matrix elements for both the horizontal and vertical planes can be obtained which are very nearly the same, yielding an image beam spot which is symmetric. One of ordinary skill in the art will recognize that other deflection angles may be accommodated by deflection systems similarly constructed. Moreover the interior field boundary may take the form of a desired curve if desired. Accordingly, the foregoing description of the invention is to be regarded as exemplary only and not to be considered in a limiting sense; thus, the actual scope of this invention is indicated by reference to the appended claims.