Abstract:
A small superconducting undulator with a period less than 1 cm, referred to here as a “super-mini” undulator. The embodiment of the super-mini encompasses of two coils wound bifilarly around a pair of bobbins in a racetrack configuration, such that the currents in adjacent coil segments run antiparallel to each other. If such coils are arranged alongside each other, separated only by a small gap on the order of a couple of millimeters, a spatially alternating magnetic field is produced that makes a passing electron beam undulate and emit undulator radiation. The wound bobbins are mounted within a frame and combined with upper and lower pole pieces to close gap between the wire coils.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    Not applicable 
       STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    Not applicable 
       SEQUENCE LISTING OR PROGRAM 
       [0003]    Not applicable 
       BACKGROUND OF THE INVENTION 
       [0004]    The field of short-period superconducting undulators, called “super-mini undulators”, represents an exciting emerging field with great potential to increase the photon energy of synchrotrons and FELs. Super-minis are tightly wound superconducting coils that create a spatially alternating field with a small gap that makes a passing electron beam undulate and emit undulator radiation. The photon energy is much higher than that of conventional undulators at the same electron energy, owing to the short period length. Similarly, a particular photon energy requires a much smaller electron energy, providing considerable cost savings of accelerator operation and construction. 
         [0005]    The development of superconducting mini-undulators started in the early 1990s with work at Brookhaven National Laboratory (BNL) (Ben-Zvi et al.,  Nucl. Instrum. Methods, A  297, 301, 1990) and Karlsruhe Institute of Technology (KIT) (Moser et al. German Patent P 41 01 094.9-33, Jan. 16, 1991). In 1998, KIT demonstrated the first photon production with a super-mini with a period length of 3.9 mm (Hezel et al.,  J. Synchrotron Rad.  5, 448, 1998; Hezel et al.,  Free Electron Lasers  1999, J. Feldhaus, H. Weise, eds., pp. 11-103, North Holland, 2000). This super-mini consisted of two coils wound bi-filarly in analogy to a solenoid. In the basic set-up of two coils in close proximity, planar and elliptical superconducting mini-undulators were built for the ANKA storage ring (Casalbuoni et al.,  Phys. Rev. ST Accel. Beam,  9, 010702, 2006; Bernhard et al.,  Proceedings of EPAC  2004, Lucerne, Switzerland, July 2004) The next step towards the most basic geometry was achieved by proposing the single-coil superconducting mini-undulator (Moser and Diao, PCT Application PCT/SG2009/000338, Sep. 14, 2009; Moser, Krevet and Holzapfel, German Patent Application p 41 01 094.9-33, Jan. 16, 1991; Diao and Moser,  Horizons in World Physics Volume  267, D. Matteri, L. Futino, eds., pp. 321-332, Nova Science Publishers, Hauppauge, N.Y., USA, 2010). 
         [0006]    If such coils are arranged alongside each other, separated only by a small gap of the order of a couple of millimeters, a spatially alternating magnetic field is produced that makes a passing electron beam undulate and emit undulator radiation. The advantageous properties of the super-mini undulator can be revealed through consideration of the following three formulas: 
         [0000]    
       
         
           
             
               
                 
                   λ 
                   = 
                   
                     
                       
                         λ 
                         u 
                       
                       
                         2 
                          
                         
                             
                         
                          
                         n 
                          
                         
                             
                         
                          
                         
                           γ 
                           2 
                         
                       
                     
                      
                     
                       ( 
                       
                         1 
                         + 
                         
                           
                             K 
                             2 
                           
                           2 
                         
                         + 
                         
                           
                             ( 
                             γϑ 
                             ) 
                           
                           2 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   K 
                   = 
                   
                     0.934 
                      
                     
                         
                     
                      
                     
                       
                         B 
                         0 
                       
                        
                       
                         [ 
                         T 
                         ] 
                       
                     
                      
                     
                       
                         λ 
                         u 
                       
                        
                       
                         [ 
                         cm 
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           P 
                            
                           
                             [ 
                             W 
                             ] 
                           
                         
                         = 
                           
                          
                         
                           6.33 
                            
                           
                               
                           
                            
                           
                             
                               E 
                               2 
                             
                              
                             
                               [ 
                               
                                 G 
                                  
                                 
                                     
                                 
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                               ] 
                             
                           
                            
                           
                             I 
                              
                             
                               [ 
                               A 
                               ] 
                             
                           
                            
                           
                             
                               B 
                               0 
                               2 
                             
                              
                             
                               [ 
                               T 
                               ] 
                             
                           
                            
                           
                             L 
                              
                             
                               [ 
                               cm 
                               ] 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           7.26 
                            
                           
                               
                           
                            
                           
                             
                               E 
                               2 
                             
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                               [ 
                               
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                             I 
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                               A 
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                             N 
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                            
                           
                             
                               K 
                               2 
                             
                             
                               
                                 λ 
                                 u 
                               
                                
                               
                                 [ 
                                 cm 
                                 ] 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0007]    Eq. 1 describes the wavelength of undulator photons, λ, in terms of the undulator period length, λ u , the harmonic number, n, which can be take on odd integer values of 1, 3, 5, 7, and so on, the relativistic Lorentz factor of the electron beam passing through the undulator, γ, the emission angle, θ, which is zero in the average direction of electron propagation, and the so-called wiggler/undulator parameter K. 
         [0008]    Eq. 2 describes the wiggler/undulator parameter, K, which is a linear function of the peak magnetic field, B 0 . 
         [0009]    Eq. 3 describes the total power emitted from a planar undulator, P, where I is the electron beam current, L=N u λ u , is the total undulator length, and N u  is the number of undulator periods. 
         [0010]    It can be seen immediately that the wavelength of the emitted photons is linearly proportional to the period length at constant K. To keep K constant when λ u , is reduced, the peak magnetic field must increase, which is why superconducting coils are necessary. An increase of the magnetic field while keeping the electron energy, the beam current, and the undulator length constant also increases the total power delivered by the undulator. Moreover, reducing the undulator period while keeping the electron energy, beam current, number of periods, and K constant, also raises the total power. We also see that tuning the photon wavelength, which is typically achieved by varying K, can be achieved by varying the peak magnetic field, which is directly controlled by the current through the superconducting coil. 
         [0011]    The benefits of exploiting these parameters are substantial cost savings, as it represents the ultimate in size reduction conceivable for a superconducting undulator. The device described herein uses only one coil instead of the standard two coils used in modern superconducting undulators (Kim et al., Proc. 2003 Particle Accelerator Conference, p. 1020, IEEE Catalog Number: 03CH374). Consequently, the size, weight, and cost of the proposed device can be reduced by a factor of two. All other advantages of superconducting mini-undulators including short period, high peak magnetic field, and facile tunability by means of the varying the current through the superconductor are preserved. 
       SUMMARY OF THE INVENTION 
       [0012]    This device utilizes a single superconducting wire that is wound bifilarly around two bobbins in unique winding pattern that facilitates a very short period. The wire is initially wrapped under tension in a “racetrack” formation. The bobbins are first wound in one direction filling every other groove alternating top and bottom. After the first set of grooves are filled, the wire is reversed and the remaining grooves are filled. This produces a set of wire segments in which the currents run in opposite directions on the top and bottom of the bobbins to produce the undulating field. The wires are wound in such a way that within a single turn, a wire segment in the top groove returns on the adjacent groove on the bottom. 
         [0013]    The bobbins are machined with grooves to accept and secure the wire segments. The bobbins can be machined to accept multiple turns per groove. The grooves are separated by several millimeters and the entire longitudinal length of the embodiment described herein is 100 mm. The length can easily be extrapolated to any desired length. The wound bobbins are then mounted between two end plates that are designed to facilitate the relative horizontal positions of the bobbins. 
         [0014]    Upper and lower pole pieces are designed to receive the wire coil segments and must be placed in sync with the bobbins in order to maintain tension throughout the entire superconducting wire coil, and allow gradual movement of the bobbins through contact with curved relief regions. The racetrack configuration reaches its final configuration by moving the upper and lower pole pieces closer together along the vertical axis while the mounted bobbins are brought closer together along the horizontal axis. This is performed while these components are constrained between the two end plates. After the transformation is complete, the final gap between the upper pole piece and lower pole piece should be on the order of millimeters. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]    The invention as described herein with references to subsequent drawings, contains similar reference characters intended to designate like elements throughout the depictions and several views of the depictions. It is understood that in some cases, various aspects and views of the invention may be exaggerated or blown up (enlarged) in order to facilitate a common understanding of the invention and its associated parts. 
           [0016]      FIG. 1  shows the overall cryostat design. 
           [0017]      FIG. 2  shows a cross-sectional view of the winding of the superconducting (SC) wire around two bobbins in a racetrack winding configuration. 
           [0018]      FIG. 3  shows a bobbin under construction. 
           [0019]      FIG. 4  is a depiction of the wound bobbins mounted in between the front and rear end plates. 
           [0020]      FIG. 5  is a depiction of the grooves of a pole piece. 
           [0021]      FIG. 6  is a depiction of the winding frame with mounted pole piece. 
           [0022]      FIG. 7  is a graphical plot of the spool vs. pole movement. 
           [0023]      FIG. 8  is a depiction of the 1 meter device concept. 
           [0024]      FIG. 9  is the wire path within the super-mini undulator. 
           [0025]      FIG. 10  is the finished assembly. 
           [0026]      FIG. 11  shows the vertical test facility assembly (view 1). 
           [0027]      FIG. 12  shows the vertical test facility assembly (view 2). 
           [0028]      FIG. 13  shows the vertical test facility assembly (view 3). 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0029]    Provided herein is a detailed description of one embodiment of the invention. It is to be understood, however, that the present invention may be embodied with various dimensions. Therefore, specific details enclosed herein are not to be interpreted as limiting, but rather as a basis for the claims and as a representative basis for teaching one skilled in the art to employ the present invention in virtually any appropriately detailed system, structure, or manner. 
         [0030]      FIG. 1  shows the overall cryostat design that ADC plans to construct. The outside of a cryostat vessel  24  consists of thermal buffer operation/safety  14  and  16 , a safety pop-off valve  15 , a gate valve  18 , a beam gate valve  23 , and current leads  25 . It contains a cold mass with a support structure, radiation shields, wherein the cold mass temperature is maintained by cryocoolers  17 ,  19 ,  22 , and  26 , connected to the outside of the cryostat vessel  24 . A vacuum within the vessel  24  is maintained by a turbo/roughing pump  20  and ion pump  21 . The old mass includes a superconducting (SC) magnet, a liquid helium (LHe) vessel with piping, and a cold beam chamber with thermal links to the cryocoolers. Cold mass is structurally supported by a base frame. LHe flows from the LHe vessel into the SC magnet cores and returns into the LHe vessel. The vapor is then re-condensed into liquid in the vessel  24 . 
         [0031]    We have foreseen four cryocoolers  17 ,  19 ,  22 , and  26 , but have also added a helium fill/vent turret which would not be needed for a fully cryogen-free design. On the other hand, we could plan for a volume in which we condense gaseous helium (GHe) to LHe as a better buffer for quenches and power load. This would avoid the cool-down and filling procedure with LHe, but would offer a larger heat capacity for transient heat load peaks. We plan to add a safety valve burst disk at the smaller turret on top of the cylindrical cryostat vessel  24 . 
         [0032]    The super-mini undulator involves a single SC wire  28  that is wrapped around two identical bobbins  27  each about 50 mm in diameter. The wire  28  is initially wrapped under tension in a “racetrack” formation as shown in  FIG. 2 . 
         [0033]    The bobbins  27  are machined with grooves to accept wires that are rectangular. The bobbins, however, could also be machined to accept wires of different shapes. In this embodiment, the wire  28  is wound around both bobbins with 4 turns per groove. The two end section grooves have only have 3 turns per groove.  FIG. 3  shows an actual bobbin in which the end sections show a stepped groove  29  in which one wire segment  30  would be replaced by the material of the bobbin. 
         [0034]    In the prototype, the grooves are separated by 7 mm and the entire length of the prototype is 100 mm. The bobbins are first wound bifilarly in one direction filling every other groove alternating top and bottom. After the first set of grooves are filled, the wire is reversed and the remaining grooves are filled. This produces a set of wire segments in which the currents run in opposite directions on the top and bottom of the bobbins to produce the undulating field. The wires are parallel between the spools but must crossover each other on the outside of the bobbin in order to fill alternating grooves. The wires are wound in such a way that within a single turn, a wire segment in the top groove returns on the adjacent groove on the bottom. The bobbins are entirely wound in the forward direction first and then the reverse. 
         [0035]    Four turns are made on each full groove before moving to the next “forward” groove skipping a “reverse” groove. The wire is reversed at a turning nut before the reverse grooves are filled. One can see that providing a separate and distinct groove that supports the wire all the way around the outside of the spool is a difficult task. Grooves must be cut in an “S” pattern on a curved surface at varying depths. Initial attempts at producing a point-to-point (P-P) tool path that a computer numerical control (CNC) machine could execute were dropped in favor of a smooth outer spool surface. 
         [0036]    The forward wires are wound and then potted with epoxy before winding the reverse wires which are also potted in epoxy to maintain wire position in bobbin grooves. This is a compromise that would be corrected by devising a mathematical model that would then generate the P-P tool path. Once this is done, modifications to a standard CNC milling machine would be necessary to include the extra axes needed to deal with the curved surface and varying depths. 
         [0037]      FIG. 4  shows a mounting structure to support the wound bobbins, in which the bobbins  27  and wire  28  are sandwiched between a front end plate  33  and a rear end plate  38 . The windings  34  must be held under tension. The parts associated include the spool  30 , drive spindle  31 , guide  32 , front end plate ( 20 ), mounted SC wire  35 , right bobbin  36 , left bobbin  37 . 
         [0038]    Studies have shown that superconducting wire does not typically fail to super-conduct until the tension is such that the copper surrounding the superconducting fiber matrix yields. Nonetheless, the winding mechanism includes a tension monitor. 
         [0039]    Once the bobbins have been wound and the outside potted, pole pieces made of vanadium permendur are mounted above and below the bobbins on the same winding frame. The poles have a base  39  that supports pole grooves  42  and pole crowns  43  to accept the SC wire segments as shown in  FIG. 5 . The groove bottoms are slightly crowned in the center while the top of the groove is flat. The poles are designed this way in order to gently assist the wire segments into their respective grooves during transformation by means of the transformation grooves  41  at each end of the pole grooves  42 . The poles must be placed in sync with the bobbins in order to maintain tension throughout the entire SC wire, and allow gradual movement of the bobbins through contact with curved bobbin relief regions  40 . 
         [0040]    The racetrack configuration is “transformed” into the final configuration by moving the upper pole piece  46  and lower pole piece  45  closer together along the vertical axis while the mounted bobbins  47  are brought closer together along the horizontal axis. This is performed while these components are constrained between the front end plate  33  and rear end plate  38 . After the transformation is complete, the final gap between the upper pole piece and lower pole piece should be about 2 mm. The winding frame with the pole pieces mounted is shown in  FIG. 6 . Transformation screws  44  on either end of the bobbins and pole pieces are used to manually reduce the gap between the bobbins and pole pieces during transformation. One can also see the direction reversing nuts  48  at one end of one of the bobbins, along with a guide bar  49 , guide slot  50 , and stiffener  51  for controlling the position of the upper pole piece  46 . This winding process is manual for this prototype but would be automated for a longitudinally longer device. 
         [0041]    As the pole pieces are brought together, the bobbins must also move closer together to maintain the same tension on the wires. A plot of the bobbin movement vs. pole movement is shown in  FIG. 7 . One can see the relationship is non-linear. Note that care must be exercised during this transformation to ensure that undue tension is not produced in the wire. Once the desired positions of the pole pieces are reached, the necessary gap end caps are placed to maintain the gap between the pole pieces. 
         [0042]    For the prototype, the process of moving the pole pieces and bobbins is a simple but tedious process which requires that an operator manually turns the eight controlling screws in a pattern by a specific amount and then measures the effect with a depth gauge. For a 1 meter device as depicted in a transparent view in  FIG. 8 , it would be helpful to make this process more automated. A completed 1 meter device encompasses, but is not limited to, the following components: power connections  39 , a thermal buffer operation/safety  53 , a vessel safety valve  54 , a thermal buffer operation/safety  55 , liquid nitrogen shielding  56 , a gate valve  57 , 20K shielding  58 , a plurality of cryocoolers  59  and  62 , a turbo/roughing pump  60 , an ion pump  61 , a gate valve  64 , and an RF beam funnel  65 . The completed undulator  66  is housed within a vacuum chamber  67 . The electron beamline  63  is depicted passing through the undulator  66 . 
         [0043]    Once the device is fully transformed, the wound wire will take the shape shown in  FIG. 9 , which depicts the cross-section of the wire path as it passes between the right bobbin  36 , left bobbin  37 , and under the upper pole piece  68 . This figure only shows the upper half, but the lower half is a mirror image. The position in which the wire meets the transformation groove  41  is also shown. 
         [0044]    After transformation, sides are added to hold the bobbins and pole pieces together. The finished assembly is shown in  FIG. 10 . This figure depicts previously mentioned components, including right bobbin  36 , left bobbin  37 , pole base  39 , transformation screws  44  and lower pole piece  45 . Connection points are added for copper bus bars on either end of the bobbins. 
         [0045]      FIGS. 11 ,  12  and  13  illustrate a vertical test facility (VTF), which is required to verify the superconducting current density and magnetic field produced by the super-mini undulator. The VTF encompasses a Dewar  74 , power rods  71 , pre-cooling power rod vacuum sleeves  75 , heat shield baffles  72 , and the prototype super-mini undulator  73 . The undulator is structurally supported by the Dewar lid  70  by the power rods that supply a current on the order of 1000 amps to the superconducting coil. Since it is supported from the Dewar lid, it is possible to get accurate magnetic field readings from a Hall sensor, which is fed down the center baffle support rod  76 . The Hall sensor  78  should be placed inside of the gap of the transformed wire coil in the superconducting undulator  77 . The position of the Hall sensor can be controlled using a linear positioning slide  69 . An ADC DS400-200, for example, could be used for this purpose. 
         [0046]    The VTF consists of a liquid helium Dewar  74  within which the super-mini undulator  73  is immersed. This Dewar is pre-cooled with liquid nitrogen, as are the copper bus bars. The copper bus bars, however, create a significant heat leak and must be pre-cooled to reduce the temperature differential between the LHe bath and the outside ambient temperature. The copper bus bars must be quite large (1.125 inches in diameter in this embodiment) to carry the required current density. 
         [0047]    A power supply with 1000 amps at 10 volts is suggested. The LHe level is monitored with a level detector as is the temperature of the undulator. A quench protection circuit is provided to shut down the power supply in the event of a quench. If a quench occurs, the power supply is quickly shut down allowing a high current freewheeling diode to shunt any high voltage spikes caused by the collapsing field around the supply, thereby protecting the output circuitry. 
         [0048]    Encapsulated Hall probes are too thick to fit within the wire coil gap. Therefore, the field should be measured with a cryogenic, bare, Hall probe that is approximately 0.7 mm thick. The Hall probe is attached to a support rod  76  that moves up and down within a central tube. Guidance for the Hall probe is provided inside the tube. The tube is then attached to a framework that is also attached to the end of the undulator. Heat shield baffles  72  are attached to the central tube. Similar but smaller baffles are attached to the copper bus bars to take advantage of the cold He gas at the top of the Dewar  74 . 
         [0049]    An ADC stage, at room temperature, is located above the top cap of the Dewar  74 . The stage connects to the central rod and moves the Hall probe up and down while keeping track of the probes position with an encoder. The Hall probe must be able to travel 5 periods beyond each end to attain a reasonable zero field. The expected field has been predicted to be 1.1 T using RADIA calculations. On the lid the linear positioning slide  69  is placed to supply a 300 mm linear displacement for the hall probe. This allows for a data collection of magnetic flux changes generated by the superconducting undulator. 
         [0050]    The embodiment described herein currently supports a 7 mm period, K factor of 0.72, gap of 2 mm, 10 periods with 4 end periods. This would produce a field of 1.1 T with an expected current density of 1000 A/mm 2 . The overall length of the prototype device is 100 mm. However, one of ordinary skill in the art of undulator design would be able to extrapolate the device length based on the design considerations disclosed herein. 
         [0051]    It is to be understood that the embodiment disclosed herein is not indented to limit the scope of the invention to a particular form set forth. On the contrary, it is intended to cover such alternatives, modifications, and equivalents as may be included within the spirit and scope of the invention as defined by the claims.