Patent Publication Number: US-8525447-B2

Title: Compact cold, weak-focusing, superconducting cyclotron

Description:
BACKGROUND 
     A cyclotron for accelerating ions (charged particles) in an outward spiral using an electric field impulse from a pair of electrodes and a magnet structure is disclosed in U.S. Pat. No. 1,948,384 (inventor: Ernest O. Lawrence, patent issued: 1934). Lawrence&#39;s accelerator design is now generally referred to as a “classical” cyclotron, wherein the electrodes provide a fixed acceleration frequency, and the magnetic field decreases with increasing radius, providing “weak focusing” for maintaining the vertical phase stability of the orbiting ions. 
     Modern cyclotrons are primarily of a class known as “isochronous” cyclotrons, wherein the acceleration frequency provided by the electrodes is likewise fixed, though the magnetic field increases with increasing radius to compensate for relativity; and an axial restoring force is applied during ion acceleration via an azimuthally varying magnetic field component derived from contoured iron pole pieces having a sector periodicity. Most isochronous cyclotrons use resistive magnet technology and operate at magnetic field levels from 1-3 Tesla. Some isochronous cyclotrons use superconducting magnet technology, in which superconducting coils magnetize warm iron poles that provide the guide and focusing fields required for acceleration. These superconducting isochronous cyclotrons operate at field levels from 3-5T. The present inventor worked on the first superconducting cyclotron project in the early 1980s at Michigan State University. 
     Cyclotrons of another class are known as synchrocyclotrons. Unlike classical cyclotrons or isochronous cyclotrons, the acceleration frequency in a synchrocyclotron decreases as the ion spirals outward. Also unlike isochronous cyclotrons, though like classical cyclotrons, the magnetic field in a synchrocyclotron decreases with increasing radius. The present inventor recently invented a high-field synchrocyclotron (described in U.S. Pat. Nos. 7,541,905 B2 and 7,696,847 B2) for proton beam radiotherapy and other clinical applications. Embodiments of this synchrocyclotron have warm iron poles and cold superconducting coils, like the existing superconducting isochronous cyclotrons, but maintain beam focusing during acceleration in a different manner that scales to higher fields and can accordingly operate with a field of, for example, about 9 Tesla. 
     SUMMARY 
     A compact, cold, weak-focusing, superconducting cyclotron is described herein. Various embodiments of the apparatus and methods for its construction and use may include some or all of the elements, features and steps described below. 
     The compact, cold, weak-focusing, superconducting cyclotron can include at least two superconducting coils on opposite sides of a median acceleration plane. A magnetic yoke surrounds the coils and contains an acceleration chamber. The magnetic yoke is in thermal contact with the thermal link from a cryogenic refrigerator and with the superconducting coils, and the median acceleration plane extends through the acceleration chamber. 
     During operation of the cyclotron, an ion is introduced into the median acceleration plane at an inner radius. A radiofrequency voltage from a radiofrequency voltage source is applied to a pair of electrodes mounted inside the magnetic yoke to accelerate the ion in an expanding orbit across the median acceleration plane. The superconducting coils and the magnetic yoke are cooled by the cryogenic refrigerator to a temperature no greater than the superconducting transition temperature of the superconducting coils. A voltage is supplied to the cooled superconducting coils to generate a superconducting current in the superconducting coils that produces a magnetic field in the median acceleration plane from the superconducting coils and from the yoke; and the accelerated ion is extracted from the acceleration chamber when it reaches an outer radius. 
     The cyclotron can be of a classical design, building on the original weak-focusing cyclotron of E. O. Lawrence, which has fixed frequency (like the isochronous cyclotron) and a simple magnetic circuit (like the synchrocyclotron). To make the classical cyclotron scale to high fields, the entire magnet (yoke and coils) can be cooled to cryogenic temperatures during operation, while space and clearances are preserved for warm acceleration components to reside inside the magnetic yoke. This cold-iron, weak-focusing cyclotron can be scaled to such high fields with reduced size to enable its use as a portable cyclotron device. Such cyclotrons may be restricted to energies of less than 25 MeV for protons, but most cyclotrons built for applications are in this energy range, and there exists a number of industrial and defense applications that would be enabled for practical use by the existence of such a cyclotron. 
     The compact, cold, weak-focusing, superconducting cyclotron can include a simple cylindrical cryostat with a slotted warm penetration through the mid-section of the cyclotron. The cold components inside the cyclotron may be cooled via any number of manners, for example, directly by mechanical cryogenic refrigeration, by a thermo-siphon circuit employing a mechanical cooler, by continuous supply of liquid cryogens, or by a static charge of pool boiling cryogens. The operating temperature of the cyclotron can be from 4K to 80K and may be dictated by the superconductor selected for the coils. 
     The entire magnet, including coils, poles, the return-path iron yoke, trim coils, permanent magnets, shaped ferromagnetic pole surfaces, and fringe-field canceling coils or materials can be mounted on a single simple thermal support, installed in a cryostat and held at the operating temperature of the superconducting coils. The cyclotron accelerator structure (e.g., the ion source and the electrodes) can be entirely within the external warm central slot in the cryostat and can therefore be both thermally and mechanically isolated from the cold superconducting magnet. This design is believed to represent a fundamentally new electromechanical structure for a cyclotron of any type. The magnet here is designed to provide the required acceleration and focusing fields in the warm slot for the operation of weak-focusing, fixed-frequency cyclotron acceleration of all positive ion species at 25 MeV or less. 
     Because there is no gap between the yoke and the coils, there is no need for a separate mechanical support structure for the coils to mitigate the large decentering forces that are encountered at high field in the existing superconducting cyclotrons, and decentering forces can be uniquely eliminated. The cold magnet materials of the magnetic yoke can be used simultaneously to shape the field and to structurally support the superconducting coils, further reducing the complexity and increasing the intrinsic safety of the cyclotron. Moreover, with all of the magnet contained inside the cryostat, the external fringe field may be cancelled without adversely affecting the acceleration field, either by cancellation superconducting coils or by cancellation superconducting surfaces affixed to intermediate temperature shields within the cryostat. 
     The cyclotron designs, described herein, can offer a number of additional advantages both over existing superconducting isochronous cyclotrons and over existing superconducting synchrocyclotrons, which are already more compact and less expensive than conventional equivalents. For example, the magnet structure can be simplified because there is no need for separate support structures to maintain the force balance between constituents of the magnetic circuit, which can reduce overall cost, improve overall safety, and reduce the need for space and active protection systems to manage the external magnetic field. Additionally, the cyclotrons can produce a high magnetic field (e.g., about 8 Tesla) without a need for a complex variable-frequency acceleration system, since the classical design of these cyclotrons can operate on a fixed acceleration frequency. Accordingly, the cyclotrons of this disclosure can be used in mobile contexts and in smaller confines. 
     Preliminary studies suggest that these cyclotrons can offer a factor of 100 or more reduction in size over conventional cyclotrons at these energies, and these cyclotrons accordingly can be portably utilized in a widely distributed manner, including at remote field locations, as well as at ports and airports, for aerial and submarine reconnaissance, and for explosive and nuclear threat detection. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a sectioned view of an embodiment of a compact, cold, weak-focusing, superconducting cyclotron, without showing a custom-engineered profile on the inner surfaces of the poles. 
         FIG. 2  is a perspective view of the cyclotron of  FIG. 1 . 
         FIG. 3  is a side sectional view of an embodiment of the compact, cold, weak-focusing, superconducting cyclotron with a series of cryostats and a cryogenic refrigerator. 
         FIG. 4  is a partially sectioned view of an embodiment of a beam chamber within an inner cryostat inside the acceleration chamber between the poles. 
         FIG. 5  is a sectional view of an embodiment of a magnetic coil and surrounding structure in the magnetic yoke. 
         FIG. 6  is a sectional view of an embodiment of the yoke and the coils showing a custom inner pole profile. 
         FIG. 7  is a sectional view of a magnet structure, wherein the poles of the yoke have the pole profile of  FIG. 6  as well as magnetic tabs for providing magnetic field compensation at the vacuum feed-through port. 
         FIGS. 8-10  provide views of a first embodiment of the magnetic tab that is positioned along the outside of the pole wing. 
         FIGS. 11-15  provide views of a second embodiment of the magnetic tab that is positioned along the outside of the pole wing and also wraps around the inner surface of the pole wing. 
         FIG. 16  is a top sectional view of an embodiment of the compact, cold, weak-focusing, superconducting cyclotron. 
     
    
    
     In the accompanying drawings, like reference characters refer to the same or similar parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating particular principles, discussed below. 
     DETAILED DESCRIPTION 
     The foregoing and other features and advantages of various aspects of the invention(s) will be apparent from the following, more-particular description of various concepts and specific embodiments within the broader bounds of the invention(s). Various aspects of the subject matter introduced above and discussed in greater detail below may be implemented in any of numerous ways, as the subject matter is not limited to any particular manner of implementation. Examples of specific implementations and applications are provided primarily for illustrative purposes. 
     Unless otherwise defined, used or characterized herein, terms that are used herein (including technical and scientific terms) are to be interpreted as having a meaning that is consistent with their accepted meaning in the context of the relevant art and are not to be interpreted in an idealized or overly formal sense unless expressly so defined herein. For example, if a particular composition is referenced, the composition may be substantially, though not perfectly pure, as practical and imperfect realities may apply; e.g., the potential presence of at least trace impurities (e.g., at less than 1 or 2% by weight or volume) can be understood as being within the scope of the description; likewise, if a particular shape is referenced, the shape is intended to include imperfect variations from ideal shapes, e.g., due to machining tolerances. 
     Spatially relative terms, such as “above,” “upper,” “beneath,” “below,” “lower,” and the like, may be used herein for ease of description to describe the relationship of one element to another element, as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the apparatus in use or operation in addition to the orientation depicted in the figures. For example, if the apparatus in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the exemplary term, “above,” may encompass both an orientation of above and below. The apparatus may be otherwise oriented (e.g., rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. 
     Further still, in this disclosure, when an element is referred to as being “on,” “connected to” or “coupled to” another element, it may be directly on, connected or coupled to the other element or intervening elements may be present unless otherwise specified. 
     The terminology used herein is for the purpose of describing particular embodiments and is not intended to be limiting of exemplary embodiments. As used herein, the singular forms, “a,” “an” and “the,” are intended to include the plural forms as well, unless the context clearly indicates otherwise. Additionally, the terms, “includes,” “including,” “comprises” and “comprising,” specify the presence of the stated elements or steps but do not preclude the presence or addition of one or more other elements or steps. 
     In general terms, cyclotrons are members of the circular class of particle accelerators. The beam theory of circular particle accelerators is well-developed, based upon the concepts of equilibrium orbits and betatron oscillations around equilibrium orbits. The principle of equilibrium orbits (EOs) can be described as follows:
         a charged ion of given momentum captured by a magnetic field will transcribe an orbit;   closed orbits represent the equilibrium condition for the given charge, momentum and energy of the ion;   the field can be analyzed for its ability to carry a smooth set of equilibrium orbits; and   acceleration can be viewed as a transition from one equilibrium orbit to another.
 
Meanwhile, the weak-focusing principle of perturbation theory can be described as follows:
   the particles oscillate about a mean trajectory (also known as the central ray);   oscillation frequencies (v r , v z ) characterize motion in the radial (r) and axial (z) directions, respectively;   the magnet field is decomposed into coordinate field components and a field index (n); and v r =√{square root over (1−n)}, while v z =√{square root over (n)}; and   resonances between particle oscillations and the magnetic field components, particularly field error terms, determine acceleration stability and losses.       

     The weak-focusing field index parameter, n, noted above, is defined as follows: 
               n   =       -     r   B       ⁢       ⅆ   B       ⅆ   r           ,         
where r is the radius of the ion from the central axis  16 , as shown in the sectioned illustration of a compact cyclotron in  FIG. 1 ; and B is the magnitude of the axial magnetic field at that radius. The weak-focusing field index parameter, n, is in the range from zero to one across the entirety of the section of the median acceleration plane (shown in  FIG. 3 ) within the acceleration chamber  46  over which the ions are accelerated (with the possible exception of the central region of the chamber proximate the central axis  16 , where the ions are introduced and where the radius is nearly zero) to enable the successful acceleration of ions to full energy in a cyclotron in which the field generated by the coils dominates the field index. In particular, a restoring force is provided during acceleration to keep the ions oscillating with stability about the mean trajectory. One can show that this axial restoring force exists when n&gt;0, and this condition requires that dB/dr&lt;0 since B&gt;0 and r&gt;0. The cyclotron has a field that decreases with radius to match the field index required for acceleration.
 
     The magnet structure  10 , as shown in  FIGS. 1 and 2 , includes a magnetic yoke  20  with a pair of poles  38  and  40  and a return yoke  36  that define an acceleration chamber  46  with a median acceleration plane  18  for ion acceleration. As shown in  FIG. 3 , the magnet structure  10  is supported and spaced by structural spacers  82  formed of an insulating composition, such as an epoxy-glass composite, and contained within an outer cryostat  66  (formed, e.g., of stainless steel or low-carbon steel and providing a vacuum barrier within the contained volume) and a thermal shield  80  (formed, e.g., of copper or aluminum). A compression spring  88  holds the 80K thermal shield  80  and magnet structure  10  in compression. 
     A pair of magnetic coils  12  and  14  (i.e., coils that can generate a magnetic field) are contained in and in contact with the yoke  20  (i.e., without being fully separated by a cryostat or by free space) such that the yoke  20  provides support for and is in thermal contact with the magnetic coils  12  and  14 . Consequently, the magnetic coils  12  and  14  are not subject to decentering forces, and there is no need for tension links to keep the magnetic coils  12  and  14  centered. 
     As shown in  FIG. 5 , each coil  12 / 14  is covered by a ground wrap additional outer layer of epoxy-glass composite  90  and a thermal overwrap of tape-foil sheets  92  formed, e.g., of copper or aluminum. The thermal overwrap  92  is in thermal contact with both the low-temperature conductive link  58  for cryogenic cooling and with the pole  38 / 40  and return yoke  36 , though contact with between the thermal overwrap  92  and the pole  38 / 40  and return yoke  36  may or may not be over the entire surface of the overwrap  92  (e.g., direct- or indirect-contact may be only at a limited number of contact areas on the adjacent surfaces). Characterization of the low-temperature conductive link  58  and the yoke  20  being in “thermal contact” means that there is direct contact between the conductive link  58  and the yoke or that there is physical contact through one or more thermally conductive intervening materials [e.g., having a thermal conductivity of at least about 1 W/(m·K)], such as a thermally conductive filler material of suitable differential thermal contraction that can be mounted between and flush with the thermal overwrap  92  and the low-temperature conductive link  58  to accommodate differences in thermal expansion between these components with cooling and warming of the magnet structure. 
     The low-temperature conductive link  58 , in turn, is thermally coupled with a cryocooler thermal link  37  (shown in  FIGS. 1 and 2 ), which, in turn, is thermally coupled with the cryocooler  26  (shown in  FIG. 3 ). Accordingly, the thermal overwrap  92  provides thermal contact among the cryocooler  26 , the yoke  20  and the coils  12  and  14 . 
     Finally, a filler material of suitable differential thermal contraction can be mounted between and flush with the thermal overwrap  92  and the low-temperature conductive link  58  to accommodate differences in thermal expansion between these components with cooling and warming of the magnet structure. 
     The magnetic coils  12  and  14  surround the acceleration chamber  46  (as shown in  FIG. 1 ), which contains the beam chamber  64 , on opposite sides of the median acceleration plane  18  (see  FIG. 3 ) and serve to directly generate extremely high magnetic fields in the median acceleration plane  18 . When activated via an applied voltage, the magnetic coils  12  and  14  further magnetize the yoke  20  so that the yoke  20  also produces a magnetic field, which can be viewed as being distinct from the field directly generated by the magnetic coils  12  and  14 . 
     The magnetic coils  12  and  14  are symmetrically arranged about a central axis  16  equidistant above and below the acceleration plane  18  in which the ions are accelerated. The magnetic coils  12  and  14  are separated by a sufficient distance to allow for at least one RF acceleration electrode  48  and a surrounding super-insulation layer  30  to extend there between in the acceleration chamber  46 . Each coil  12 / 14  includes a continuous path of conductor material that is superconducting at the designed operating temperature, generally in the range of 4-30K, but also may be operated below 2K, where additional superconducting performance and margin is available. Where the cyclotron is to be operated at higher temperatures, superconductors such as bismuth strontium calcium copper oxide (BSCCO), yttrium barium copper oxide (YBCO) or MgB 2  can be used. 
     The outer radius of each coil is about 1.2 times the outer radius reached by the ions before the ions are extracted. For a magnetic field greater than 6 T, ions accelerated to 10 MeV are extracted at a radius of about 7 cm, while ions accelerated to 25 MeV are extracted at a radius of about 11 cm. Accordingly, a compact cold cyclotron of this disclosure designed to produce a 10-MeV beam can have an outer coil radius of about 8.4 cm, while a compact cold cyclotron of this disclosure designed to produce a 25-MeV beam can have an outer coil radius of about 13.2 cm. 
     The magnetic coils  12  and  14  comprise superconductor cable or cable-in-channel conductor with individual cable strands having a diameter of 0.6 mm and wound to provide a current carrying capacity of, e.g., between 2 million to 3 million total amps-turns. In one embodiment, where each strand has a superconducting current-carrying capacity of 2,000 amperes, 1,500 windings of the strand are provided in the coil to provide a capacity of 3 million amps-turns in the coil. In general, the coil can be designed with as many windings as are needed to produce the number of amps-turns needed for a desired magnetic field level without exceeding the critical current carrying capacity of the superconducting strand. The superconducting material can be a low-temperature superconductor, such as niobium titanium (NbTi), niobium tin (Nb 3 Sn), or niobium aluminum (Nb 3 Al); in particular embodiments, the superconducting material is a type II superconductor—in particular, Nb 3 Sn having a type A15 crystal structure. High-temperature superconductors, such as Ba 2 Sr 2 Ca 1 Cu 2 O 8 , Ba 2 Sr 2 Ca 2 Cu 3 O 10 , MgB 2  or YBa 2 Cu 3 O 7-x , can also be used. 
     The coils can be formed directly from cables of superconductors or cable-in-channel conductors. In the case of niobium tin, unreacted strands of niobium and tin (in a 3:1 molar ratio) may also be wound into cables. The cables are then heated to a temperature of about 650° C. to react the niobium and tin to form Nb 3 Sn. The Nb 3 Sn cables are then soldered into a U-shaped copper channel to form a composite conductor. The copper channel provides mechanical support, thermal stability during quench; and a conductive pathway for the current when the superconducting material is normal (i.e., not superconducting). The composite conductor is then wrapped in glass fibers and then wound in an outward overlay. Strip heaters formed, e.g., of stainless steel can also be inserted between wound layers of the composite conductor to provide for rapid heating when the magnet is quenched and also to provide for temperature balancing across the radial cross-section of the coil after a quench has occurred, to minimize thermal and mechanical stresses that may damage the coils. After winding, a vacuum is applied, and the wound composite conductor structure is impregnated with epoxy to form a fiber/epoxy composite filler in the final coil structure. The resultant epoxy-glass composite in which the wound composite conductor is embedded provides electrical insulation and mechanical rigidity. Features of these magnetic coils and their construction are further described and illustrated in U.S. Pat. No. 7,696,847 B2 and in U.S. Patent Application Publication No. 2010/0148895 A1. 
     With the high magnetic fields, the magnet structure can be made exceptionally small. In one embodiment, the outer radius of the magnetic yoke  20  is about two times the radius, r, from the central axis  16  to the inner edge of the magnetic coils  12  and  14 , while the height of the magnetic yoke  20  (measured parallel to the central axis  16 ) is about three times the radius, r. 
     Together, the magnetic coils  12  and  14  and the yoke  20  generate a combined field, e.g., of about 8 Tesla in the median acceleration plane  18 . The magnetic coils  12  and  14  generate a majority of the magnetic field in the median acceleration plane, e.g., at least about 3 Tesla or more when a voltage is applied thereto to initiate and maintain a continuous electric current flow through the magnetic coils  12  and  14 . The yoke  20  is magnetized by the field generated by the magnetic coils  12  and  14  and can contribute up to about another 2.5 Tesla to the magnetic field generated in the chamber for ion acceleration. 
     Both of the magnetic field components (i.e., both the field component generated directly from the coils  12  and  14  and the field component generated by the magnetized yoke  20 ) pass through the median acceleration plane  18  approximately orthogonal to the median acceleration plane  18 . The magnetic field generated by the fully magnetized yoke  20  at the median acceleration plane  18  in the chamber, however, is much smaller than the magnetic field generated directly by the magnetic coils  12  and  14  at the median acceleration plane  18 . The magnet structure  10  is configured (by shaping the inner surfaces  42  of poles  38  and  40  or by providing additional magnetic coils to produce an opposing magnetic field in the acceleration chamber  46  or by a combination thereof) to shape the magnetic field along the median acceleration plane  18  so that the magnetic field decreases with increasing radius from the central axis  16  to the radius at which ions are extracted in the acceleration chamber  46  to enable classical-cyclotron ion acceleration. An embodiment of the tapered inner pole surfaces  42  with four stages (A, B, C and D) for shaping the magnetic field in the median acceleration plane is shown in  FIG. 6 , which is further discussed, infra. 
     The magnet structure  10  is also designed to provide weak focusing and phase stability in the acceleration of charged particles (ions) in the acceleration chamber  46 . Weak focusing maintains the charged particles in space while they accelerate in an outward spiral through the magnetic field. Phase stability ensures that the charged particles gain sufficient energy to maintain the desired acceleration in the chamber. Specifically, more voltage than is needed to maintain ion acceleration is provided at all times via an electrically conductive conduit  68  to the high-voltage electrode  48  in a beam chamber  64  inside the acceleration chamber  46 ; and the yoke  20  is configured to provide adequate space in the acceleration chamber  46  for the beam chamber  64  and for the electrode  48 . Where one electrode  48  is used, a ground (which may be referred to as a “dummy dee”) is positioned at 180° relative to the electrode  48 . In alternative embodiments, two electrodes (spaced 180° apart about the central axis  16 , with grounds spaced at 90° C. from the electrodes) can be used. The use of two electrodes can produce higher gain per turn of the orbiting ion and better centering of the ion&#39;s orbit, reducing oscillation and producing a better beam quality. 
     During operation, the superconducting magnetic coils  12  and  14  can be maintained in a “dry” condition (i.e., not immersed in liquid refrigerant); rather, the magnetic coils  12  and  14  can be cooled to a temperature below the superconductor&#39;s critical temperature (e.g., as much as 5K below the critical temperature, or in some cases, less than 1K below the critical temperature) by one or more cryogenic refrigerators  26  (cryocoolers). When the magnetic coils  12  and  14  are cooled to cryogenic temperatures (e.g., in a range from 4K to 30K, depending on the composition), the yoke  20  is likewise cooled to approximately the same temperature due to the thermal contact among the cryocooler  26 , the magnetic coils  12  and  14  and the yoke  20 . 
     The cryocooler  26  can utilize compressed helium in a Gifford-McMahon refrigeration cycle or can be of a pulse-tube cryocooler design with a higher-temperature first stage  84  and a lower-temperature second stage  86 . The lower-temperature second stage  86  of the cryocooler  26  can be operated at about 4.5 K and is thermally coupled via thermal links  37  and  58  with low-temperature-superconductor (e.g., NbTi) current leads  59  (shown in  FIG. 16 ) that include wires that connect with opposite ends of the composite conductors in the superconducting magnetic coils  12  and  14  and with a voltage source to drive electric current through the coils  12  and  14 . The cryocooler  26  can cool each low-temperature conductive link  58  and coil  12 / 14  to a temperature (e.g., about 4.5 K) at which the conductor in each coil is superconducting. Alternatively, where a higher-temperature superconductor is used, the second stage  86  of the cryocooler  26  can be operated at, e.g., 4-30 K. Accordingly, each coil  12 / 14  can be maintained in a dry condition (i.e., not immersed in liquid helium or other liquid refrigerant) during operation. 
     The warmer first stage  84  of the cryocooler  26  can be operated at a temperature of, e.g., 40-80 K and can be thermally coupled with a thermal shield  80  that is accordingly cooled to, e.g., about 40-80 K to provide an intermediate-temperature barrier between the magnet structure  10  and the cryostat  66 , which can be at room temperature (e.g., at about 300 K). The volume defined by the cryostat  66  can be evacuated via a vacuum pump (not shown) to provide a high vacuum therein and thereby limit convection heat transfer between the cryostat  66 , the intermediate thermal shield  80  and the magnet structure  10 . The cryostat  66 , thermal shield  80  and the magnet structure  10  are each spaced apart from each other an amount that minimizes conductive heat transfer and structurally supported by insulating spacers  82  (formed, e.g., of an epoxy-glass composite). 
     Use of the dry cryocooler  26  allows for operation of the cyclotron away from sources of cryogenic cooling fluid, such as in isolated treatment rooms or on moving platforms. Where a pair of cryocoolers  26  are provided permit, the cyclotron can continue operation even if one of the cryocoolers fails. 
     The magnetic yoke  20  comprises a ferromagnetic structure that provides a magnetic circuit that carries the magnetic flux generated by the superconducting coils  12  and  14  to the acceleration chamber  46 . The magnetic circuit through the magnetic yoke  20  also provides field shaping for weak focusing of ions in the acceleration chamber  46 . The magnetic circuit also enhances the magnetic field levels in the acceleration chamber  46  by containing most of the magnetic flux in the outer part of the magnetic circuit. The magnetic yoke  20  can be formed of low-carbon steel, and it surrounds the coils  12  and  14  and an inner super-insulation layer  30  (shown in  FIG. 4  and formed, e.g., of aluminized mylar and paper) that surrounds the beam chamber  64 . Pure iron may be too weak and may possess an elastic modulus that is too low; consequently, the iron can be doped with a sufficient quantity of carbon and other elements to provide adequate strength or to render it less stiff while retaining the desired magnetic levels. The magnetic yoke  20  circumscribes the same segment of the central axis  16  that is circumscribed by the coils  12  and  14  and the super-insulation layer  30 . 
     The magnetic yoke  20  further includes a pair of poles  38  and  40  exhibiting approximate mirror symmetry across the median acceleration plane  18 . The poles  38  and  40  are joined at the perimeter of the magnetic yoke  20  by a return yoke  36 . The magnetic yoke  20  exhibits approximate rotational symmetry about the central axis  16 , except allowing for discrete ports (such as the beam-extraction passage  60  and the vacuum feed-through port  100 ) and other discrete features at particular locations, as described or illustrated elsewhere herein, and except providing a saddle-like contour with additional magnetic tabs  96  (shown in  FIGS. 7-15  and formed, e.g., of iron) at the vacuum feed-through port  100  (shown in  FIG. 16 ), to narrow the pole separation gap at the feed-through port  100  and thereby balance less iron in the yoke  20  where a void is created by the feed-through port  100 . In alternative embodiments, the magnetic tabs  96  are incorporated into a continuous belt that wraps around the perimeter of the yoke  20 . 
     A first embodiment of the tab  96  is in the form of a curved strip, as shown in  FIGS. 8-10 ;  FIGS. 8 and 9  respectively provide views (relative to the orientation of  FIG. 7 ) from the top and side, while  FIG. 10  provides a perspective view of a tab  96 . A second embodiment of the tab  96 , this time in the form of a curved strip, as in the first embodiment, though also including a tapered cover section  97  that extends over the surface of the pole wing  98  that faces inward toward the median acceleration plane  18 . In this embodiment, the height of the tapered cover section  97  progressively narrows across the surface of the pole wing  98  as the distance to the central axis  16  decreases. Relative to the orientation of the lower pole  38 , the tab  96  with the tapered cover section  97  is shown from the side in  FIG. 11 , from the central axis  16  in  FIG. 12 , from the top and bottom respectively from  FIGS. 14 and 15 , while a perspective view of this embodiment of the tab  96  is provided in  FIG. 13 . 
     The poles  38  and  40  have tapered inner surfaces  42 , shown in  FIG. 6 , that jointly define a pole gap between the poles  38  and  40  and across the acceleration chamber  46 . The profiles of the tapered inner surfaces  42  are a function of the position of the coils  12  and  14  and as a function of distance from the central axis  16  such that the distance from the median acceleration plane  18  is greatest (e.g., 3.5 cm) at stage B, between opposing surfaces  42 , where expansion of this pole gap provides for sufficient weak focusing and phase stability of the accelerated ions. 
     The distance of the inner pole surface  42  from the median acceleration plane  18  is at a median of, e.g., 2.5 cm both immediately adjacent the central axis at stage A and beyond stage B at stage C. This distance narrows to, e.g., 0.8 cm at the pole wings  94  in stage D, to provide for weak focusing against the deleterious effects of the strong superconducting coils, while properly positioning the full energy beam near the pole edge for extraction. In this embodiment, the near surfaces of coils  12  and  14  at stage E are spaced 3.5 cm above/below the median acceleration plane  18 . In alternative embodiments, the stages A-D are not discrete and instead are tapered to provide a continuous smooth slope transitioning from one stage to the next. In another alternative design, more or fewer than four stages are provided across the inner pole surfaces  42 . 
     Stages A, B, C and D radially extend along the median acceleration plane  18  from the central axis  16  across substantially equal distances, wherein each of A, B, C, and D extends across about one quarter of the distance from the central axis  16  to the inner surface of the coils  12 / 14  (or slightly less than one quarter to accommodate the passage along the central axis for insertion of the ion source). For example, where the radius from the central axis  16  to the inner radius of the coils  12 / 14  is 10 cm, each stage radially extends across a distance of about 2.5 cm parallel to the median acceleration plane. In this embodiment, the stages are discrete, though in alternative embodiments, the stages can be sloped and tapered, providing smooth transitions between stages on the pole surfaces. 
     This pole geometry can be used for a broad range of acceleration operations, with energy levels for the accelerated particles ranging, for example, at any level from 3.5 MeV to 25 MeV. The pole profile thus described has several acceleration functions, namely, ion guiding at low energy in the center of the machine, capture into stable acceleration paths, acceleration, axial and radial focusing, beam quality, beam loss minimization, attainment of the final desired energy and intensity, and the positioning of the final beam location for extraction. In particular, the simultaneous attainment of weak focusing and acceleration phase stability is achieved. 
     The magnetic yoke  20  also provides at least one radial passage, such as the vacuum feed-through port  100  (shown in  FIG. 16 ), and sufficient clearance for insertion into the acceleration chamber  46  of a resonator structure including the radiofrequency (RF) accelerator electrode  48 , which is formed of a conductive metal. The accelerator electrode  48  includes a pair of flat semi-circular parallel plates that are oriented parallel to and above and below the acceleration plane  18  inside the acceleration chamber  46  (as described and illustrated in U.S. Pat. Nos. 4,641,057 and 7,696,847). Ions can be generated by an internal ion source  50  positioned proximate the central axis  16  or can be provided by an external ion source via an ion-injection structure. An example of an internal ion source  50  can be, for example, a heated cathode coupled to a voltage source and proximate to a source of hydrogen gas. 
     The accelerator electrode  48  is coupled via an electrically conductive pathway with a radiofrequency voltage source that generates a fixed-frequency oscillating electric field to accelerate emitted ions from the ion source  50  in an expanding spiral orbit in the acceleration chamber  46 . In particular embodiments, wherein the cyclotron operates in a synchrocyclotron mode, the radiofrequency voltage source can be set by a radiofrequency rotating capacitor to provide variable frequency such that the frequency of the electric field decreases as the ion spirals outward in the median acceleration plane. 
     Inside the acceleration chamber  46 , the beam chamber  64  and the dee electrode  48  reside inside the inner super-insulation structure  30 , as shown in  FIG. 4 , that provides thermal insulation between the electrode  48 , which emits heat, and the cryogenically cooled magnetic yoke  20 . The electrode  48  can accordingly operate at a temperature at least 40K higher than the temperature of the magnetic yoke  20  and the superconducting coils  12  and  14 . The illustration of  FIG. 4  is split, wherein an inside section showing the dee electrode  48  is provided to the left of the central axis  16  and an outside view of the ground (dummy dee)  76 , including an inner face  77  and an outer electrical ground plate  79  (in the form, e.g., of a copper liner) is provided to the right of the central axis  16 . 
     The acceleration-system beam chamber  64  and dee electrode  48  can be sized, for example, to produce a 20-MeV proton beam (charge=1, mass=1) at an acceleration voltage, V o , of less than 20 kV. The beam chamber  64  can define a cylindrical volume having, e.g., a height of 3 cm and a diameter of 16 cm. The ferromagnetic iron poles and return yoke are designed as a split structure to facilitate assembly and maintenance; the yoke has an outer radius of about twice the radius, r p , of the poles from the central axis  16  to the coils  12 / 14  (e.g., about 20 cm, where r p  is 10 cm) or less, a total height of about 3r p  (e.g., about 30 cm, where r p  is 10 cm), and a total mass less than 2 tons ( ˜ 2000 kg). 
     Accelerated in the magnetic field generated by the magnetic coils  12 ,  14  and the magnetic yoke  20 , ions have an average trajectory in the form of a spiral orbit  74  expanding along a radius, r, from the central axis  16 . The ions also undergo small orthogonal oscillations around this average trajectory. These small oscillations about the average radius are known as betatron oscillations, and they define particular characteristics of accelerating ions. 
     Upper and lower pole wings  98  sharpen the magnetic field edge for extraction by moving the characteristic orbit resonance, which sets the final obtainable energy closer to the pole edge. The upper and lower pole wings  98  additionally serve to shield the internal acceleration field from the strong split coil pair  12  and  14 . Regenerative ion extraction or self-extraction can be accommodated by providing additional localized pieces of ferromagnetic upper and lower iron tips to be placed circumferentially around the face of the upper and lower pole wings  98  to establish a sufficient localized non-axi-symmetric edge field. 
     In operation, a voltage (e.g., sufficient to generate 2,000 A of current in the embodiment with 1,500 windings in the coil, described above) can be applied to each coil  12 / 14  via the current lead in conductive link  58  to generate a magnetic field of, for example, at least 8 Tesla within the acceleration chamber  46  when the coils are at 4.5 K. In other embodiments, a greater number of coil windings can be provided, and the current can be reduced. The magnetic field includes a contribution of up to about 2.5 Tesla from the fully magnetized iron poles  38  and  40 ; the remainder of the magnetic field is produced by the coils  12  and  14 . 
     This magnet structure  10  serves to generate a magnetic field sufficient for ion acceleration. Pulses of ions can be generated by the ion source, e.g., by applying a voltage pulse to a heated cathode to cause electrons to be discharged from the cathode into hydrogen gas; wherein, protons are emitted when the electrons collide with the hydrogen molecules. Though the acceleration chamber  46  is evacuated to a vacuum pressure of, e.g., less than  10   —3  atmosphere, hydrogen is admitted and regulated in an amount that enables maintenance of the low pressure, while still providing a sufficient number of molecules for production of a sufficient number of protons. As alternatives to protons, other ions with a heavier mass, such as deuterons or alpha particles all the way up to much heavier ions, such as uranium, can be accelerated with these apparatus and methods; in operation, the frequency of the electric field can be decreased for heavier elements. During operation, the electrode  48  and other components inside the inner cryostat can be at a relatively warm temperature (e.g., around 300K or at least 40K higher than the temperature of the magnetic yoke  20  and superconducting coils  12  and  14 ). 
     In this embodiment, the voltage source (e.g., a high-frequency oscillating circuit) maintains an alternating or oscillating potential difference of, e.g., 20,000 Volts across the plates of the RF accelerator electrode  48 . The electric field generated by the RF accelerator electrodes  48  has a fixed frequency (e.g., 140 MHz) matching that of the cyclotron orbital frequency of the proton ion to be accelerated. The electric field produced by the electrode  48  produces a focusing action that keeps the ions traveling approximately in the central part of the region of the interior of the plates, and the electric-field impulses provided by the electrode  48  to the ions cumulatively increase the speed of the emitted and orbiting ions. As the ions are thereby accelerated in their orbit, the ions spiral outward from the central axis  16  in successive revolutions in resonance or synchronicity with the oscillations in the electric fields. 
     Specifically, the electrode  48  has a charge opposite that of the orbiting ion when the ion is away from the electrode  48  to draw the ion in its arched path toward the electrode  48  via an opposite-charge attraction. The electrode  48  is provided with a charge of the same sign as that of the ion when the ion is passing between its plates to send the ion back away in its orbit via a same-charge repulsion; and the cycle is repeated. Under the influence of the strong magnetic field at right angles to its path, the ion is directed in a spiraling path through the electrode  48  and the ground  76 . As the ion gradually spirals outward, the velocity of the ion increases proportionally to the increase in radius of its orbit, until the ion eventually reaches an outer radius  70  at which it is magnetically deflected by a magnetic deflector system (e.g., in the form of iron tips positioned about the perimeter of the acceleration chamber  46 ) into a collector channel to allow the ion to deviate outwardly from the magnetic field and to be withdrawn from the cyclotron (in the form of a pulsed beam) into a linear beam-extraction passage  60  extending from the acceleration chamber  46  through the return yoke  36  toward, e.g., an external target. 
     In describing embodiments of the invention, specific terminology is used for the sake of clarity. For the purpose of description, specific terms are intended to at least include technical and functional equivalents that operate in a similar manner to accomplish a similar result. Additionally, in some instances where a particular embodiment of the invention includes a plurality of system elements or method steps, those elements or steps may be replaced with a single element or step; likewise, a single element or step may be replaced with a plurality of elements or steps that serve the same purpose. Further, where parameters for various properties are specified herein for embodiments of the invention, those parameters can be adjusted up or down by 1/100 th , 1/50 th , 1/20 th , 1/10 th , ⅕ th , ⅓ rd , ½, ¾ th , etc. (or up by a factor of 2, 5, 10, etc.), or by rounded-off approximations thereof, unless otherwise specified. Moreover, while this invention has been shown and described with references to particular embodiments thereof, those skilled in the art will understand that various substitutions and alterations in form and details may be made therein without departing from the scope of the invention. Further still, other aspects, functions and advantages are also within the scope of the invention; and all embodiments of the invention need not necessarily achieve all of the advantages or possess all of the characteristics described above. Additionally, steps, elements and features discussed herein in connection with one embodiment can likewise be used in conjunction with other embodiments. The contents of references, including reference texts, journal articles, patents, patent applications, etc., cited throughout the text are hereby incorporated by reference in their entirety; and appropriate components, steps, and characterizations from these references optionally may or may not be included in embodiments of this invention. Still further, the components and steps identified in the Background section are integral to this disclosure and can be used in conjunction with or substituted for components and steps described elsewhere in the disclosure within the scope of the invention. In method claims, where stages are recited in a particular order—with or without sequenced prefacing characters added for ease of reference—the stages are not to be interpreted as being temporally limited to the order in which they are recited unless otherwise specified or implied by the terms and phrasing.