SYSTEMS AND PROCESSES FOR PRODUCING RELATIVELY UNIFORM TRANSVERSE IRRADIATION FIELDS OF CHARGED-PARTICLE BEAMS

Abstract

The hybrid beam emittance uniformization system includes a charged particle beam generator for emitting a plurality of charged particles, a quadrupole magnet positioned relatively inline with the charged particle beam generator, and an adjustable aperture quadrupole positioned inline with the charged particle beam generator, wherein the combination of the quadrupole magnet and the adjustable aperture quadrupole concentrate the plurality of charged particles emitted by the charged particle beam generator into a relatively uniform square beam having a relatively uniform flux density all throughout a target area positioned a target distance from the charge particle beam generator.

Claims

1. An adjustable aperture quadrupole, comprising: a first charge plate having a first charge; a second charge plate having a second charge and positioned generally opposite the first charge plate and offset therefrom by an adjustable distance; a charged particle transfer chamber positioned between the opposing first and second charge plates and having a size and shape for facilitating transfer of charged particles through the adjustable aperture quadrupole within a magnetic field formed through interaction of the first charge of the first charge plate and the second charge of the second charge plate, the characteristics of the magnetic field being responsive to the adjustable distance between the first charge plate and the second charge plate; and an adjuster coupled to at least one of the first charge plate or the second charge plate for selectively setting the adjustable distance between the first charge plate and the second charge plate to define the magnetic field within the charged particle transfer chamber through which charged particles travel.

2. The adjustable aperture quadrupole of claim 1, including a support frame comprising a generally box-like structure having a rectangular cross-section, the adjuster generally suspending the first charge plate, the second charge plate, and the charged particle transfer chamber relative to the support frame.

3. The adjustable aperture quadrupole of claim 2, wherein the adjuster couples to the support frame about a pivot formed at a terminating end of an outwardly extending support.

4. The adjustable aperture quadrupole of claim 3, wherein the outwardly extending support comprises a pair of triangular-shaped brackets downwardly extending from a vertical support of the support frame.

5. The adjustable aperture quadrupole of claim 2, wherein the adjuster pivots relative to the support frame.

6. The adjustable aperture quadrupole of claim 1, wherein the adjuster includes a piston positionable between a retracted position and an extended position, wherein the adjustable distance is relatively smaller when the piston is in the retracted position relative to when the piston is in the extended position.

7. The adjustable aperture quadrupole of claim 6, including at least one linkage including a support bar extending from the piston and terminating in an eyelet pivotally coupled to a yoke-based pivot rod.

8. The adjustable aperture quadrupole of claim 1, wherein the charged particle transfer chamber includes a deflectable vacuum sealed housing responsive to movement of the adjuster.

9. The adjustable aperture quadrupole of claim 8, wherein the deflectable vacuum sealed housing simultaneously couples to each of the first and second charge plates, whereby defection thereof causes relative movement of each of the first and second charge plates.

10. The adjustable aperture quadrupole of claim 8, wherein the deflectable vacuum sealed housing includes an adjustable height and an adjustable width.

11. The adjustable aperture quadrupole of claim 1, wherein the first and second charge plates include at least a pair of coils having a rib extending at least partially into an offset spatially offsetting the respective pair of coils.

12. The adjustable aperture quadrupole of claim 11, wherein the first and second charge plates include respective first and second yokes positioned stationary relative to the respective pair of coils.

13. The adjustable aperture quadrupole of claim 11, wherein the first and second charge plates include respective first and second pole faces generally outwardly extending from each side of the respective pair of coils.

14. The adjustable aperture quadrupole of claim 13, wherein each of the first and second pole faces include an inwardly presented inner fillet proximate the respective pair of coils for creating positive higher order modes.

15. The adjustable aperture quadrupole of claim 13, wherein each of the first and second pole faces include an outwardly presented fillet distal the respective pair of coils for creating negative higher order modes.

16. The adjustable aperture quadrupole of claim 13, wherein each of the first and second pole faces comprise a shape generating an octupole moment in the absence of a current source.

17. The adjustable aperture quadrupole of claim 1, wherein the charged particle transfer chamber includes a pair of zero charge sides formed generally orthogonal relative to each of the first and second charge plates.

18. The adjustable aperture quadrupole of claim 17, wherein the zero charge sides selectively move relative to the first and second charge plates.

19. The adjustable aperture quadrupole of claim 1, wherein the charged particle transfer chamber includes a width and a height relatively larger than a height and a width of a charged particle beam.

20. The adjustable aperture quadrupole of claim 19, wherein a first-order focusing field includes wherein the height comprises approximately 5 cm and the width comprises approximately 30 cm, thereby forming a relatively rectangular-shaped uniform beam having a Cartesian width of approximately 15 cm when a charged particle beam passes therethrough.

21. The adjustable aperture quadrupole of claim 1, wherein the charged particle transfer chamber comprises a wall thickness of approximately 3 mm.

22. The adjustable aperture quadrupole of claim 1, wherein a transverse width of the charged particle transfer chamber comprises approximately 2 of a Gaussian beam size.

23. The adjustable aperture quadrupole of claim 1, wherein the adjustable charged particle transfer chamber comprises a vacuum chamber for reducing particle loss.

24. The adjustable aperture quadrupole of claim 1, wherein the first charge comprises the same charge as the second charge.

25. A hybrid beam emittance uniformization system, comprising: a charged particle beam generator for emitting a plurality of charged particles; a quadrupole magnet positioned relatively inline with the charged particle beam generator; and an adjustable aperture quadrupole positioned inline with the charged particle beam generator, the combination of the quadrupole magnet and the adjustable aperture quadrupole concentrating the plurality of charged particles emitted by the charged particle beam generator into a relatively uniform square beam having a relatively uniform flux density at a target area positioned a target distance from the charge particle beam generator.

26. The system of claim 25, including a second quadrupole magnet positioned inline with the charged particle beam generator and a second adjustable aperture quadrupole inline with the charged particle beam generator and positioned downstream from the second quadrupole magnet.

27. The system of claim 26, wherein the second quadrupole magnet is generally offset from the adjustable aperture quadrupole by approximately 45 degrees and generally axially aligned with the first quadrupole magnet.

28. The system of claim 26, wherein the second adjustable aperture quadrupole is generally offset from the second quadrupole magnet and turned approximately 45 degrees into a general vertical orientation offset by approximately 90 degrees from the adjustable aperture quadrupole.

29. The system of claim 25, wherein the relatively uniform square beam includes a relatively uniform transverse distribution.

30. The system of claim 25, wherein the adjustable aperture quadrupole includes a rectangular-shaped vacuum chamber.

31. The system of claim 25, including wherein each of the quadrupole magnet and the adjustable aperture quadrupole focus one dimension of the plurality of charged particles at a time.

32. The system of claim 25, wherein the quadrupole magnet includes a first order focusing moment and the adjustable aperture quadrupole includes a second higher order folding moment.

33. The system of claim 25, wherein the adjustable aperture quadrupole is positioned downstream of the charged particle beam generator and the quadrupole magnet and generally offset therefrom by approximately 45 degrees.

34. The system of claim 25, wherein the relatively uniform square beam includes a y-axis distribution of approximately 0.2 meters and an x-axis distribution of approximately 0.2 meters.

35. The system of claim 25, wherein the quadrupole magnet includes a maximum field gradient of 0.79 T/m.

36. A process for producing a relatively uniform transverse irradiation field of a charged-particle beam, comprising the steps of: emitting a charged particle beam with a beam generator; sizing the charged particle beam with a quadrupole magnet for passage through an adjustable aperture quadrupole; and transforming the charged particle beam with the adjustable aperture quadrupole into a transverse charged particle beam having a relatively square distribution and a relatively uniform density.

37. The process of claim 36, including the step of adding an octupole moment with the adjustable aperture quadrupole.

38. The process of claim 37, wherein the octupole moment comprises a positive octupole moment or a negative octupole moment.

39. The process of claim 36, including the step of desensitizing a peak intensity of the charged particle beam with a second adjustable aperture quadrupole.

40. The process of claim 36, wherein the quadrupole magnet includes a first order focusing moment and the adjustable aperture quadrupole imparts a high order folding moment to attain the transverse charged particle beam.

41. The process of claim 36, including the step of shaping magnetic scalar potential equipotential with a pair of pole faces integrated into the adjustable aperture quadrupole.

42. The process of claim 41, including the step of exciting a higher order field with the pair of pole faces.

43. The process of claim 42, including the step of changing the higher order field while generally maintaining a quadrupole strength.

44. The process of claim 43, including performing the changing step in real-time.

45. The process of claim 36, including the step of passing the charged particle beam through the adjustable aperture quadrupole with relatively lossless transmission.

46. The process of claim 36, including the step of folding a Gaussian transverse beam distribution with a positive octupole moment.

47. The process of claim 36, including the step of fine tuning a transverse beamline of the charged particle beam.

48. The process of claim 36, including the step of changing an excitation current and scaling the field amplitude.

49. A process for adjusting a field component strength of a quadrupole, comprising the steps of: disposing a first charge plate having a first charge relative to a second charge plate having a second charge generally positioned opposite thereof; and adjusting an offset distance between the first charge plate and the second charge plate, thereby simultaneously altering a magnetic field in an adjustable channel having a size and shape for controlled passage of a charged particle beam therethrough.

50. The process of claim 49, including the step of independently controlling a field component strength by shifting at least one of a first pole face associated with the first charge plate or a second pole face associated with the second charge plate, wherein shifting displaces the first and second pole faces relative to one another about a symmetry plane.

51. The process of claim 49, including the step of generating an electrical current through at least one coil in each of the first and second charge plates to generate the respective first and second charges.

52. The process of claim 51, wherein the at least one coil includes an upper coil residing within an upper charge plate and a lower coil residing within a lower charge plate.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The accompanying drawings illustrate the invention. In such drawings:

[0047] FIG. 1 is a schematic view of a dipole field formed by a dipole magnet;

[0048] FIG. 2 is a schematic view of a quadrupole field;

[0049] FIG. 3 is a perspective schematic view of a quadrupole magnet having a pair of positive quadrupole rods and a pair of negative quadrupole rods for focusing charged particles from a charged particle beam source to a target area along a length thereof;

[0050] FIG. 4 a schematic view of a octupole magnet having end facing alternating magnetic poles arranged in an octagonal relationship;

[0051] FIG. 5 is a perspective view of the octupole magnet illustrated with respect to FIG. 4;

[0052] FIG. 6 is a diagrammatic view of an idealized Gaussian intensity distribution;

[0053] FIG. 7 is a diagrammatic view of an idealized plateau intensity distribution;

[0054] FIG. 8 is a scatter plot illustrating a relative distribution of charged particle emittance in a general elliptical shape, with relatively heavier concentrations at a darker center and relatively lower concentrations along a relatively lighter periphery;

[0055] FIG. 9 is a perspective view of one embodiment of a Panofsky quadrupole magnet;

[0056] FIG. 10 is an end view of an alternatively-shaped rectangular-faced Panofsky quadrupole magnet, further illustrating current directions and a relatively wide channel;

[0057] FIG. 11 is a perspective view of one embodiment of a hybrid beam emittance uniformization system as disclosed herein, for producing a relatively more uniform beamline through deployment of a normal quadrupole and a adjustable aperture quadrupole;

[0058] FIG. 12 is a perspective view of the adjustable aperture quadrupole;

[0059] FIG. 13 is a cross-sectional view of the adjustable aperture quadrupole taken about the line 13-13 of FIG. 12;

[0060] FIG. 14 is a schematic illustrating an end view of the adjustable aperture quadrupole, including only an upper charge plate and a lower charge plate;

[0061] FIG. 15 is a perspective view of a pair of pole faces having inner fillets for creating positive higher order modes;

[0062] FIG. 16 is a perspective view of a pair of pole faces having outer fillets for creating negative higher order modes;

[0063] FIG. 17 is a plot illustrating an on-axis field magnitude in a positive displacement region as a function of a high order pole face vertical offset; and

[0064] FIG. 18 is a plot illustrating a transverse distribution density at the end of the uniformization beamline on top of a proposed target shape according to one embodiment of the hybrid beam emittance uniformization system disclosed herein.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0065] As shown in the exemplary drawings for purposes of illustration, the present invention for a hybrid beam emittance uniformization system for producing relatively uniform transverse irradiation fields of charged-particle beams is generally illustrated in FIG. 11 with respect to reference numeral 102, which includes an adjustable aperture quadrupole 104, as disclosed herein and illustrated in more detail with respect to FIGS. 11-13, and expands on the concepts disclosed in U.S. Appl. No. 62/567,108, the contents of which are herein incorporated by reference in its entirety. As illustrated in FIG. 11, the hybrid beam emittance uniformization system 102 as disclosed herein is able to create a relatively uniform transverse distribution through use of an adjustable aperture quadrupole 104 in combination with a standard quadrupole magnet 34. In the embodiment illustrated in FIG. 11, a first standard quadrupole magnet 34 is positioned in line along a beam tube 106 in a first orientation generally offset by approximately 45 degrees relative to a following first vertically oriented adjustable aperture quadrupole 104. Moreover, in the embodiment illustrated in FIG. 11, the beam tube 106 travels through the first adjustable aperture quadrupole 104 and into a second quadrupole magnet 34 generally offset from the first adjustable aperture quadrupole 104 by approximately 45 degrees such that the first and second quadrupole magnets 34, 34 are generally axially aligned. The beam tube 106 then continues from the second quadrupole magnet 34 into a second adjustable aperture quadrupole 104 generally offset from the second quadrupole magnet 34 and turned by approximately 45 degrees into a general vertical orientation offset by approximately 90 degrees from the first adjustable aperture quadrupole 104. To this end, charged particles that pass through the waistline of each of the progressively positioned first quadrupole magnet 34, first adjustable aperture quadrupole 104, second quadrupole magnet 34, and second adjustable aperture quadrupole 104, exit the hybrid beam emittance uniformization system 102 having a desired uniform transverse distribution, such as illustrated with respect to FIG. 18, as discussed in more detail below.

[0066] Moreover, the hybrid beam emittance uniformization system 102 mentioned above provides enhanced uniform transverse beam densities by transforming the Gaussian transverse spatial distribution emanating from a standard accelerator source using higher order fields to more efficiently fold over the wings of the Gaussian distribution towards the center of the beam. While the fold over concept has been demonstrated with separate quadrupole and octupole magnets, as briefly discussed above, the hybrid beam emittance uniformization system 102 disclosed herein further utilizes a modified version of the Panofsky-style magnets in the form of the adjustable aperture quadrupole 104 to achieve an unexpectedly more consistent beam distribution in the target area. Thus, the hybrid beam emittance uniformization system 102 is able to achieve higher order fields by altering the outer pole faces of the nominally quadrupole geometry as illustrated, e.g., with respect to FIG. 11, to create a more uniform density beam. Essentially, the hybrid beam emittance uniformization system 102 has a first order focusing moment as well as a higher order folding moment. In this respect, a generally elongated channel is well suited for beams with large aspect ratios and also provides the flexibility to straightforwardly add the octupole component, due to freedom of design in the extreme ends of the magnet in the dimension where the beam is large.

[0067] The adjustable aperture quadrupole 104 is more specifically illustrated in FIG. 12 and the cross-sectional view of FIG. 13 and includes box-like structure having an outer supportive frame 108 that includes, from a front plan view, a pair of generally elongated upper and lower horizontal supports 110, 110 that intersect a pair of relatively shorter left and right vertical supports 112, 112. Each of the horizontal supports 110, 110 and the vertical supports 112, 112 frame a generally rectangular cross-section as best illustrated in FIGS. 13 and 14 configured for pass through of a charged particle beam as disclosed herein. The outer supportive frame 108 further includes a pair of rearward upper horizontal supports 114 and a pair of rearward lower horizontal supports 116 that essentially couple to a reciprocal pair of the horizontal supports 110, 110 and a pair of the vertical supports 112, 112 forming a similar rectangular cross-section toward a rear side 118 of the adjustable aperture quadrupole 104.

[0068] As illustrated more specifically in the cross-sectional view of FIG. 13, each of the rearward upper horizontal supports 114 of the adjustable aperture quadrupole 104 includes a pair of triangular-shaped supports 120 downwardly extending from about a mid-point thereof. Each of the downwardly extending triangular supports 120 include a circular aperture 122 to generally support and suspend a support rod 124 (FIG. 12) therebetween. The distance between each of the downwardly extending triangular supports 120 accommodates an eyelet 126 extending from one end of a linkage 128 that couples to a piston 130 at an opposite end thereof. The piston 130 then couples to an interiorly located secondary linkage 132 having a similar eyelet 134 that couples to a yoke-based pivot rod 136. In this respect, the triangular supports 120 cooperate with the linkage 128, the piston 130, and the secondary linkage 132 to generally suspend a vacuum chamber 138 from the outer supportive frame 108.

[0069] In an alternative embodiment, the adjustable aperture quadrupole 104 may include a reciprocal set of upwardly extending triangular supports 140 (FIG. 12) coupled to each of the rearward lower horizontal supports 116 to provide additional support for the vacuum chamber 138 relative to the outer supportive frame 108. To this end, the upwardly extending triangular supports 140 may include a comparable aperture 122, support rod 124, eyelet 126, linkage 128, piston 130, and secondary linkage 132 for select pivoted coupling with a similar yoke-based pivot rod 136 of the vacuum chamber 138, in accordance with the embodiments disclosed above with respect to the downwardly extending triangular supports 120. The downwardly extending triangular supports 120 and the upwardly extending triangular supports 140 may cooperate to provide enhanced support and suspension of the vacuum chamber 138 from the outer supportive frame 108, in accordance with the embodiments disclosed herein.

[0070] As discussed above, conventional Panofsky quadrupoles, such as the one illustrated with respect to FIG. 9, include a series of alternating charged plates (e.g., the positive charge plates 92 and the negative charge plates 94) in a relatively fixed position relative to one another. As such, this effectively fixes the size of the aperture or channel 96 formed thereby.

[0071] One aspect of the adjustable aperture quadrupole 104 as disclosed herein is that it includes an adjustable aperture or channel 142 that may change in size (e.g., height, width, and/or shape) depending on the desired application. More specifically, as best illustrated in FIG. 13, the adjustable aperture quadrupole 104 generally includes an upper charge plate 144 and a lower charge plate 146 vertically movable relative to one another through extension and/or attraction of each of the pistons 130, i.e., the the pistons 130 effectively act is a vacuum chamber adjustment. More specifically in this respect, extension of each of the pistons 130 toward an interior of the adjustable aperture quadrupole 104 generally causes pivoting movement of the eyelets 134 about each of the rods 136. In turn, a vacuum chamber housing 148 deflects the upper charge plate 144 upwardly simultaneously while deflecting the lower charge plate 146 downwardly, thereby increasing a vertical gap 150 therebetween. As illustrated in FIG. 13, the vacuum chamber housing 148 includes outwardly extending vacuum chamber ribs 152 that extend at least partially into a relatively small offset 154 separating a plurality of coils 156 that generate electrical current therein to effectively magnetize the upper charge plate 144 and the lower charge plate 146. In this respect, an upper main yoke 158 and a lower main yoke 160 remain respectfully stationary relative to each of the coils 156 and the vacuum chamber housing 148 along with the outwardly extending vacuum chamber ribs 152 at least partially residing within the offsets 154 between each of the coils 156 (e.g., racetrack coils able to provide field excitation). Conversely, to decrease the vertical gap 150, each of the pistons 130 may retract the respective secondary linkages 132, thereby causing each of the eyelets 134 to again pivot about the respective pivot rods 136. Here, the vacuum chamber housing 148 deflects inwardly, thereby closing the vertical gap 150 between each of the upper charge plate 144 and the lower charge plate 146. The adjustable aperture quadrupole 104 may also include a fine traverse magnet adjustment knob 162, as illustrated in FIG. 13.

[0072] To this end, one difference between the adjustable aperture quadrupole 104 as disclosed herein and that of a conventional Panofsky quadrupole is the fact that the adjustable aperture quadrupole 104 includes only two charge plates for operation, i.e., the upper charge plate 144 and the lower charge plate 146. The adjustable aperture quadrupole 104 does not include or require the use of side charge plates, such as the negatively charged plates 94 illustrated in FIG. 9 with respect to the Panofsky quadrupole magnet 90. As such, because the upper charge plate 144 and the lower charge plate 146 are not fixed relative to one another (e.g., by the negatively charged plates 94), this allows relative offset positioning of the upper charge plate 144 relative to the lower charge plate 146 to vary the vertical gap 150 therebetween, as needed and/or desired, including in real-time. This may be particularly useful to fine tune the transverse beamline for specific (sensitive) applications such as silicon ingot exfoliation.

[0073] Additionally, the adjustable aperture quadrupole 104 may include a respective upper pole face 166 and a lower pole face 168 that vary in geometric shape to attain a desired higher order mode. Here, e.g., the pole faces 166, 168 generally outwardly extend from each of the coils 156 (e.g., generally illustrated as a single block in FIGS. 15 and 16). More specifically, in the embodiment illustrated in FIG. 15, the poles faces 166, 168 include a generally block-shaped geometric shape with an inner fillet 170 inwardly presented and adjacent each of the coils 156. In this embodiment, the pole faces 166, 168 having the inner fillet 170 create positive higher order modes. Alternatively, FIG. 16 illustrates an alternative embodiment wherein each of the upper pole face 166 and the lower pole face 168 include a respective set of outer fillets 172 upwardly presented yet distal the coils 156. In this embodiment, each of the pole faces 166, 168 create negative higher order modes. Of course, other configurations as may be known in the art may be used in connection with each of the upper pole face 166 and the lower pole face 168.

[0074] In one embodiment, the adjustable aperture quadrupole 104 may start with a simple first-order focusing field having the vertical gap 150 of approximately 5 cm and a horizontal gap 164 (FIG. 13) of approximately 30 cm. This setting produces a relatively square-shaped uniform beam having a Cartesian width of approximately 15 cm when a charged particle beam is passed therethrough to a target (e.g., an exfoliation surface of a silicon workpiece). In this embodiment, the rectangular aperture supported by the upper main yoke 158 and the lower main yoke 160 may include, in one embodiment, wherein the vacuum chamber housing 148 includes a wall thickness of approximately 3 mm.

[0075] Generally, in one embodiment during operation, the vertical gap 150 and the horizontal gap 164 may be greater than the width of the charged particle beam to sustain the quadrupole field throughout the adjustable channel 142. Although, to create a strong enough higher-order field component, the transverse width may be reduced to about 2 of the Gaussian beam size. Outside of this limit, the pole faces 166, 168 may be shaped to create an octupole moment, and unlike a standard Panofsky quadrupole geometry, no current sources may be present. The pole faces 166, 168 may shape the magnetic scalar potential equipotentials such that higher order modes are excited. The nominal mirror symmetry of the hybrid beam emittance uniformization system 102 may assure that any even order multi poles are nonexistent.

[0076] The choice to create a positive octupole moment (i.e., a rising field) or a negative octupole moment (i.e., a falling field) with the shaped pole faces 166, 168 may depend on several considerations. First, the shape of the adjustable channel 142 must allow the charged particle beam to pass through without significant losses. A positive higher order octupole requires that the pole faces 166, 168 reduce the effective size of the adjustable channel 142 so that the vacuum chamber housing 148 terminates a distance far enough away from a mid-plane of the charged particle beam path. A negative multipole does not have this limitation, as the effective bore size increases as a function of offset.

[0077] A second consideration that has an impact on beamline design is where the effective octupole focus is located. A positive octupole moment leads to folding that creates a uniform distribution when the beam is converging, which means the uniform distribution will be before the waist created by the quadrupole component (e.g., quadrupole magnets 34, 34 in FIG. 11), as the hybrid beam emittance uniformization system 102 is generally focusing the dimension of the octupole action. The converse of having a negative higher order multipole is also true, i.e., the uniform distribution point is after the corresponding waist. For purposes of silicon ingot exfoliation, such as those processes disclosed in U.S. Pat. Nos. 9,499,921 and 9,404,198, the contents of which are herein incorporated by reference in their entireties, the beam should go through the waist at least once for the desired folding to happen to attain the desired transverse dimensions illustrated, e.g., as illustrated in FIG. 18.

[0078] Another consideration applies to tuning the strengths of the different multipole orders. The adjustable aperture quadrupole 104 may include two ways to systematically change the structure of the fields. Changing the excitation current may scale the field amplitude. If the high order pole tips generated by the coils 156 are movable relative to the inner pole, e.g., such as by way of changing the vertical gap 150 with the pistons 130, they can change the higher order fields while minimally changing the quadrupole strength. This adds a beamline design consideration as it may be advantageous to create a charged particle beam transport having nominally strong quadrupole gradients such that there is a wide tuning range for the higher order moments as there is more physical room for adjustment.

[0079] FIG. 17 illustrates a series of field maps 174 modeled using a 3D static magnetic field solver in Ansoft Electronics Desktop Suite (Ansoft Software) with respect to the adjustable aperture quadrupole 104 having the outer fillets 172 for creating negative higher order modes. In this embodiment, the upper main yokes 158, 160 were modeled as low carbon 1010 steel to take into account any saturation issues. Meshing was automatically refined by the Ansoft Software to account for edges and the curvature of the pole faces 166, 168 which were designed based on equipotential solutions to the 2D Laplacian in polar coordinates:

.sub.n(,)=.sup.nsin(n) Equation 8

.sub.n(,)=.sup.nsin(n) Equation 9

[0080] Here, Equation 8 represents a positive n-th order and Equation 9 represents a negative n-th order.

[0081] A pole profile was created using the equipotential lines for an n=3 moment with a radius on the scale of the beam size. The pole shape was then translated to meet conveniently with the edge of the Panofsky region. A translation of this type creates a spectrum of higher order odd n terms, which does not have notable negative consequences towards the folding goal of the magnet.

[0082] The strength of the field can be altered by changing the current density in the excitation coils 156. A standard conservative maximum current density recommended for air-cooled coils is 1.5 A/mm.sup.2 and that the field is linear with current density even when exceeding this limit. Any possible saturation effects, localized or otherwise, may not be an issue in the nominal operating regime.

[0083] The higher order field component strength can be controlled independently of the overall scale factor by shifting the outer pole faces 166, 168 toward or away from the symmetry plane of the magnet. The field profile results due to this shifting are illustrated in the field maps 174 in FIG. 17.

[0084] Referring back to FIG. 11, each of the pair of adjustable aperture quadrupoles 104, 104 and the quadrupole magnets 34, 34 were used in a simulated beamline to create a square of uniform density for illustrative purposes. Here, the first quadrupole magnet 34 is used to defocus the beam vertically such that the beam is sized properly for the adjustable aperture quadrupole 104 at the location of the focal point in the horizontal direction. The adjustable aperture quadrupole 104 is placed at this location and provides a weak, negative octupole kick with an effective focal length to match the location of ideal transverse beam size after the initial waist of the quadrupole magnet 34. The second quadrupole magnet 34 ensures that the vertical beam waist is located at the correct location of the horizontally acting adjustable aperture quadrupole 104, as determined by the focal length of the first quadrupole 34. The octupole kick of the second adjustable aperture quadrupole 104 may be positive and much stronger than the first as the focal length is much shorter. A chart 176 illustrating a y-axis distribution 178 and an x-axis distribution 180 of the charged particles is illustrated in FIG. 18.

[0085] In this simulation, the respective y-axis field strength 182 and the x-axis field strength 184 are not perfectly optimized as optimization with field maps is difficult and tedious. Regardless, the strengths 182, 184 are systematic enough and within range of an ideal field strength 186. Thus, the simulated strengths of magnets needed for this beamline are attainable using conventional techniques. The quadrupole magnets 34, 34 require a maximum field gradient of 0.79 T/m; and the adjustable aperture quadrupoles 104, 104 require a current density about 30 percent lower than the limit imposed by using air cooled coils, thus giving an ample safety margin.

[0086] Current models of the quadrupole magnets 34, 34 and the adjustable aperture quadrupoles 104, 104 can roughly predict the weight of the beamline elements. The current design of the adjustable aperture quadrupoles 104, 104 suggests a weight around 400-600 lbs, not including mounting hardware. The 10 in. bore quadrupoles have yet to be fully optimized for size but they are expected to weigh around 1,000-1,500 lbs, not including mounting hardware.

[0087] Inclusion of the vacuum chamber 142 is designed to reduce particle loss, which may be important for overall efficiency and minimizing heating effects due to particle collisions. Losses in the first adjustable aperture quadrupole 104 are generally nonexistent because the beam remains Gaussian during transport through the quadrupole 104 due to peak particle densities in the center. Once the charged particle beam reaches the second adjustable aperture quadrupole 104, its peak desensitizes on the edges of the distribution. In this case, the vacuum chamber 138 is enlarged as much as possible to accommodate the new distribution. This prevents the vacuum chamber 138 from having a simple rectangular shape without significantly reducing the strength of the higher order moments as one must reduce the size of the adjustable channel 142 as a function of the axis offset. The resulting transverse shape of one embodiment of the vacuum chamber 138 is illustrated in FIG. 14.

[0088] In general, the hybrid beam emittance uniformization system 102 incorporating a combined set of standard quadrupole-octupoles and the adjustable aperture quadrupoles 104, 104 provides consistency with needed functionality of the nonlinear beam optics for transforming a Gaussian profile beam to a uniform square at, e.g., a target area.

[0089] Although several embodiments have been described in detail for purposes of illustration, various modifications may be made without departing from the scope and spirit of the invention. Accordingly, the invention is not to be limited, except as by the appended claims.