Abstract:
A superconducting gravitational wave senser includes a toroid-like torque body having first and second diametrically opposed mass objects to provide a bi-pole mass distribution about its Z-axis for torque perturbations by gravitational waves. The torque body includes superconducting material that produces a magnetic field when perturbed; the field indicative a gravitation wave.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims the benefit of U.S. Provisional Patent Application 62/177,912 filed Mar. 27, 2015 by the applicants herein and entitled “Superconducting Antenna For Gravitational Wave Detection”, the disclosure of which is incorporated herein by reference. 
     
    
     BACKGROUND 
       [0002]    Gravitational waves, first postulated by Einstein, have been detected by the Laser Interferometer Gravitational-Wave Observatory (LIGO). The LIGO detector detects the difference in the path length of the two arms of a interferometer detector using the principles of interferometry. 
         [0003]    Optical interferometric devices, such as LIGO, cannot provide the benefit of practically infinite coherence time, while, by contrast, the current in a superconducting ring, though in a metastable state, can theoretically flow indefinitely. Thermodynamic noise cannot degrade the phase coherence of a Bose-Einstein Condensate (BEC) or a Cooper-Pair Condensate (CPC). Current noise in a superconductor is consequent to the fluctuation of the Condensate wave function. This noise will be strongly reduced by the unique property of BECs to restore the nominal phase and amplitude values of their quantum wave function, thus making the coherence time infinitely long. 
         [0004]    The density of photons in a laser beam is Poisson distributed and therefore fluctuates even for a beam of nominally constant power which determines the signal-to-noise ratio (SNR). By raising the power of the laser, the signal-to-noise ratio can be improved, although increased laser power introduces other noise sources. Considering noise, superconductors have single-particle excitations (unpaired electrons and Cooper Pairs) separated by an energy gap from the CPC. These excitations generate thermodynamic noise. Charge neutrality couples the motion of CPC and single-particle excitations. However, at sufficiently low temperatures, the number of single-particle excitations (either electrons or holes) is exponentially small because of the energy gap and the perturbing effects on the CPC become negligible. Low noise associated with superconducting devices is an invaluable asset when dealing with small signals induced by gravitational waves. 
         [0005]    In contrast to the LIGO interferometer configuration, the present invention converts the gravitational waves into rotational motion using a low-noise superconducting torque body based on Cooper-Pair Condensates in superconductor materials; CPCs are related to Bose-Einstein Condensates (BECs) that are considered low-noise entities. 
       SUMMARY 
       [0006]    A superconducting sensor system suitable for gravitational wave detection includes a gravitational wave sensing structure having a bi-pole mass distribution about it Z-axis. The gravitational sensing structure is ‘floated’ in a cryogenic liquid, usually liquid helium, so that the gravitational sensing structure is free to rotate about its Z-axis in response to successive gravitational waves. Because of the nature of the bi-pole mass distribution, the successive gravitational waves torque the sensing structure in one direction and then the other direction abut its Z-axis. The sensing structure includes an integrally formed superconducting loop or is attached to a superconducting loop cooled below its critical transition temperature T c  by the liquid helium so that Cooper-Pairs are formed with the lattice atoms being ionized to provide a positively charged lattice points. As the superconducting loop is torqued in a direction about its Z-axis, the rotary displacement of the positive lattice ions generates a magnetic field that is indicative of the gravitational wave. 
         [0007]    This magnetic field generated by the rotation of the lattice ions is detected either by 1) a SQUID detector or SQUID detector complex which is positioned suitable to detect the magnetic field, or 2) using the magnetic field to generate a current in a pick up coil which is then detected by a SQUID detector or SQUID complex detector. 
         [0008]    The superconducting magnetic field sense loop has a current induced therein by the magnetic filed and is connect to or associated with a SQUID detector or SQUID detector complex to provide an output signal representative of the detected gravitational waves. 
         [0009]    The gravitational wave sensing structure is suitable for use as a gravitational wave detector and, differently configured, can serve as a gravimeter function, a gravity gradiometer function, rate-of-turn transducer function, and an accelerometer function. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWING 
         [0010]      FIG. 1  is an elevational view, in partial cross-section, of the organization of a gravitational wave sensing structure; 
           [0011]      FIG. 2  is a detail of a torque body component shown in  FIG. 1 ; 
           [0012]      FIG. 3  is a side elevational view, in partial cross-section view of the torque body shown in  FIGS. 1 and 2 ; 
           [0013]      FIG. 4  is a detail of a torque body variant; 
           [0014]      FIG. 5  is side elevation, in partial cross-section view of the torque body shown in  FIG. 4 ; 
           [0015]      FIG. 6  is a view of a “barbell” structure having a mass at each end superposed over a gravity wave representation such that a counterclockwise torque is applied thereto; 
           [0016]      FIG. 7  is a view of the “barbell” structure of  FIG. 6  superposed over a successive gravity wave representation such that a clockwise torque is applied thereto; 
           [0017]      FIG. 8  represents an arrangement for calibrating the position of the torque body; 
           [0018]      FIG. 9  illustrates a gravitational wave depiction superimposed over a torque body for a first portion of a gravitational wave; 
           [0019]      FIG. 10  illustrates a gravitational wave depiction superimposed aver a torque body for a second portion of a gravitational wave; 
           [0020]      FIG. 11  illustrates a variant of the gravitational wave sensing structure having a bearing structure associated with the torque body; 
           [0021]      FIG. 12  illustrates a further variant of the gravitational wave sensing structure having a taut-band suspension associated with the torque body; 
           [0022]      FIG. 13  illustrates four distributed mass objects subject to first portion of a gravitational wave; 
           [0023]      FIG. 14  illustrates the four distributed mass object subject to a second portion of a gravitational wave; 
           [0024]      FIGS. 15 and 16  illustrate, in exaggerated form, respective resilient loop deformations corresponding to  FIGS. 13 and 14 ; 
           [0025]      FIG. 17  represents a rectangular torque body having mass portions A and B at opposite diagonal corners; and 
           [0026]      FIG. 18  represents the mass distribution of  FIG. 17  in terms of distributed mass objects. 
       
    
    
     DESCRIPTION 
       [0027]    A currently preferred embodiment of a gravitational wave sensor is shown in cross-section in  FIG. 1  and is designated therein by the reference character  20 . As shown, the gravitational wave sensor  20  includes a container  22  having a quantity of liquid helium  24  therein with the surface of the liquid helium indicated at  26 . Liquid helium is preferred as it does not support electron flow below its critical transition temperature T c  and can be considered an dielectric. Because liquid helium has a relatively low density (0.125 gm/cm 3 ), a buoyancy control device  30  provides buoyant support for the various structures described below. The buoyancy control device  30  takes the form of an enclosed chamber or plenum having a volume sufficiently large to provide buoyant support for a torque body  32  having mass objects A 1  and A 2  thereon and a magnetic-field sense loop  34 . The interior of the buoyance control device  20  can be evacuated  61  can be filled with an inert gas. 
         [0028]    The annular or toroidally shaped torque body  32 , described more fully below, floats at or near the surface  26  of the liquid helium  24 . A superconducting magnetic-field sense loop  34  is mounted above the torque body  32  and is spaced apart by a gap so that the torque body  32  can rotate about its Z axis relative to the magnetic-field sense loop  34 . The magnetic-field sense loop  34  is coupled to or integrated with a SQUID detector  36  (or a multi-SQUID array), for example, by being placed in a sensing relationship adjacent to the magnetic-field sense loop  34  or placed in series circuit therewith, to provide a signal output indicative of the sensed magnetic field and, consequently, indicative of the gravitational perturbation. Since SQUID detectors typically have a sensing loop with Josephson junctions, a modified SQUID detector can have a sensing loop with Josephson junctions as the magnetic-field sense loop  34 . 
         [0029]    A cover  38  is provided to close the container  22  to prevent the liquid helium from climbing the walls thereof and flowing out of container  22 . 
         [0030]    As represented by the reference character  40 , the entire gravitational wave sensor  20  is enclosed within a shielding containment that shields the gravitational wave sensor  20  from external magnetic, electrostatic, and electrical fields. The containment  40  is preferably fabricated from mu-metal or a functionally similar material. Additionally, the gravitational wave sensor  20  is isolated from mechanical vibration, and insulated against changes in the environmental temperature. 
         [0031]    The organization shown in  FIG. 1  is well-suited for sensing gravitational waves that are or at least resemble sinusoidal wave patterns so that the toque-body  32  experiences successive torques and a counter-torques about its Z axis Az-Az with successive alternations of the gravity wave, as explained below in relationship to  FIGS. 6 and 7 . 
         [0032]    The organization of  FIG. 1  uses a torque body  32  that is not inherently self-centering or self-aligning. As indicated at  42 , it is preferred that the mass of the torque body  32  be distributed to prevent or minimize any portion thereof causing a “tipping” misalignment that could provide an uneven gap between the torque body  32  and the magnetic field sensing loop  34 . Since the torque body  32  is buoyant, adding or removing liquid helium can control the gap spacing between the torque body  32  and the magnetic-field sense loop  34 . The distance the torque body extends above the surface  26  of the liquid helium can be controlled by controlling the volume of the buoyance control device  30 . 
         [0033]    While the torque body  32  has been shown as floating in liquid helium so part of the torque body  32  is above the surface  26  thereof partial or total submersion of the torque body  32  is acceptable. 
         [0034]    There may be circumstances in with the torque body  32  drifts from its preferred aligned position for a variety of reasons. In this case and as shown in  FIG. 8 , a plurality of near-field mass objects, M 1 , M 2 , M 3 , can be positioned about the gravitational wave sensor  20 ; the respective positions thereof are adjusted to bias the torque body  32  toward and to its preferred alignment. 
         [0035]    As shown in the top view of  FIG. 2  and the side view of  FIG. 3 , the torque body  32  can be divided into four equi-angular segments (90°) with two opposite segments having, respectively, a mass object A 1  and A 2  attached or secured thereto to provide a bi-pole mass arrangement. 
         [0036]    In  FIGS. 6 and 7 , the mass object A 1  and the mass object A 2  are represented as spheres at the opposite ends of a connecting bar (a “barbell” configuration).  FIGS. 6 and 7  also show respective “+” type gravitational waves superimposed over the barbell structural organization. The gravitational wavefronts include curved-line representations with directional arrows in opposite directions in different quadrants. In  FIG. 6 , the superposed gravitational wave will tend to torque the connected mass objects A 1  and A 2  counterclockwise while in  FIG. 7 , the superposed gravitational wave will tend to torque the connected mass objects A 1  and A 2  clockwise. 
         [0037]    The mass objects A 1  and A 2  are preferably fabricated from high-density materials, such as tungsten or gold (each 19.3 g/cm3), depleted uranium (19 gm/cm3), or lead (11.4 g/cm3). The particular material chosen for mass objects A 1  and A 2  has a higher specific density then the material between the A 1  and A 2  sectors so the torque body  32  approximates the mass-distribution of the “barbell” shown in  FIGS. 6 and 7 . 
         [0038]    While a toroid shape is presently preferred, other shapes are not excluded including the discoidal shape  32 - 1  shown in  FIGS. 4 and 5  in which the mass objects A 1  and A 2  are embedded near the peripheral edge of the discoid. 
         [0039]    In the currently preferred embodiment, the torque body  32  serves as a carrier for the mass objects A 1  and A 2  and as a magnetic field generator responsive to rotations caused by the interaction with the alternating gravitational waves. To this end, the torque body  32  is fabricated from a superconductor, such as tin (Sn). When the superconductor is cooled below its critical transition temperature T c  the electrons form Cooper Pairs. As a consequence, the atoms at the lattice points are ionized and have a positive charge as schematically illustrated by the “+” signs in the cross-sectional view of  FIG. 3 . While the lattice ions are immobile relative one another in their respective lattice positions, displacement of the lattice will induce a magnetic field, as explained more fully below. 
         [0040]    The torque body  32 , as described above, serves as a carrier for the mass bodies A 1  and A 2  and as a magnetic field generator by virtue its fabrication using a superconductor. As can appreciated, two separate structures can also be used. For example, a torque body with its mass objects can be fabricated from a glass, polysilicon, fused quartz, ceramic, or similar electrically and magnetically inert material. A separate superconducting magnetic field generator can then be affixed to the torque body to generate a magnetic field in response to displacement of both connected structures caused by interaction with a gravitational wave. 
         [0041]    In  FIG. 1 , the superconducting magnetic field sense loop  34  is supported above the torque body  32  and separated by a gap. The magnetic field sense loop  34  is preferably fabricated from a substrate, such as glass, polysilicon, fused quartz, ceramic, or similar electrically and magnetically inert material, with an exterior surface having a superconductor material layer, such as tin, deposited or otherwise formed thereon or applied thereto. While a superconductor can be used to fabricate the magnetic field sense loop  34  in its entirely, superconduction is a “skin” effect that conducts within the London penetration depth λ d . Thus, the surface of any substrate used to fabricate the magnetic field sense loop  34  is provided with a superconductor layer thicker than the London penetration depth λ d ; suitable superconductors include tin (Sn) and lead (Pb). The superconductor layer can be applied, for example, by chemical vapor deposition, plasma vapor deposition, sputtering, atomic layer deposition, or by any suitable process used for applying or depositing thin layers. 
         [0042]    Since superconduction is a “skin” effect, the responsiveness of the magnetic field sense loop  34  can be increased by increasing the surface area of the magnetic field sense loop  34 . As shown in  FIG. 1 , the exterior surface of the magnetic field sense loop  34  includes radially outward extending triangular projections that serve to increase the surface area. 
         [0043]    While the surface-area enhancement of  FIG. 1  is preferred, the use of a smooth-surface magnetic field sense loop  34  is not precluded. 
         [0044]    In operation, the gravitational wave sensor  20  of  FIGS. 1, 2, and 3  is exposed to periodic gravitational waves, for example, from the Crab nebula. As the wave transits through the sensor  20  (as represented in  FIGS. 9 and 10 ), the torque body  32  will experience a successive counterclockwise and clockwise torques to, in turn, cause small counterclockwise and clockwise rotations of the torque body  32  with the displacement of the positive ions of the lattice generating a magnetic field for sensing by the magnetic field sense loop  34 . 
         [0045]    The magnetic field provided by the torque body  32  can be directly measured by a single SQUID detector  36 , a plurality of SQUID detectors, or, as shown in  FIG. 1 , induced into the enhanced surface-area superconducting magnetic-field sense loop  34  for sensing by a SQUID detector  38  or by a plurality of SQUID detectors. As mentioned above, SQUID detectors typically have a sensing loop with Josephson junctions, a modified SQUID detector can have a sensing loop with Josephson junctions as the magnetic-field sense loop  34 . 
         [0046]    In the description above, the torque body  32  has been described as an annular or toroidal structure. Other types of configurations are equally suitable, including, for example, the discoidal configuration of  FIGS. 4 and 5  showing a torque body variant  32 - 1 . 
         [0047]    In general, two types of gravitational wave signals relevant to the device described herein are known: pulsed of shorter duration and perhaps greater magnitude wave (like those that LIGO reported detecting) and periodic (continuing for months or years, but of lower magnitude for likely known sources). In the following calculations, a periodic source is assumed and is likely to detect gravitational radiation of the magnitude expected from the Crab Pulsar. 
         [0048]    A variant of the gravitational wave sensor  20  is shown in the detail view of  FIG. 11 . As shown, a support disc  46  is attached to the underside of the torque body  32  and includes a downwardly opening cup bearing  42  that sits atop a upstanding post  40 . The tip of the post  40  is received within the cup bearing  42  with sufficient clearance to allow some lateral movement of the torque body ( 28  or  28 - 1 ); the buoyancy of the torque body is adjusted so that the post  40  does not support the weight of the torque body ( 28  or  28 - 1 ). The arrangement of  FIG. 11  effectively locates the torque body in the preferred position. 
         [0049]    A further variant of the gravitational wave sensor  20  is shown in cross-section in  FIG. 12 . In the organization of  FIG. 12 , the torque body  32  is supported by an axially aligned “taut-band” suspension using narrow-band metal ribbons  50  and  52  to maintain the axial alignment. If desired, each band can be subject to an axial counter-twisting that tends to hold the torque body  32  in place. While the descriptor “taut” implies a tensioned band, any tensioning sufficient to prevent small up/down movements of the torque body  32  is acceptable. 
         [0050]    In general, two types of gravitational wave signals are relevant to the device described herein: pulsed gravitational waves of shorter duration and perhaps greater magnitude (like those that LIGO reported detecting) and periodic gravitational waves (continuing for months or years, but of lower magnitude for likely known sources). In the following calculations, a periodic source is assumed and, as indicated, gravitational waves radiation of the magnitude expected from the Crab Pulsar is detectable. 
         [0051]    Assuming a gravitational wave of strain h=h o  Sin (ωt) propagates perpendicular to the plane of the detector, where h 0  is the strain amplitude, it will adiabatically impart to and retrieve a kinetic energy from the quadrapolar mass distribution discussed below. The kinetic energy of the rotation is: 
         [0000]        E   kin   =m   tot ( Lωh   o ) 2 /2 
         [0052]    where m tot  is the total mass of the torque body. This kinetic energy, or at least a part thereof, is converted into a current in the pickup coil. 
         [0053]      FIGS. 13 and 14  illustrate four equal mass objects distributed about a center point. During the first half-period of a gravitational wave, the x-components of the gravitational wave forces tend to pull the two horizontal mass objects apart and pull the two vertical mass objects together as indicated by the arrows and the dotted-line representations. The same pattern, but with all forces and resulting motions reversed, occurs in the end half-period as illustrated in  FIG. 14 . 
         [0054]      FIGS. 15 and 16  correspond to  FIGS. 13 and 14  and represent, respectively and in highly exaggerated form, a resilient loop undergoing the stretch-and-squeeze and successive squeeze-and-stretch forces. This succession of stretch-end-squeeze effect followed by a squeeze-and-stretch is characteristic of gravitational waves. 
         [0055]      FIG. 17  presents a rectangular torque body having a mass object A in the lower left and upper right corners and a mass object B at it lower right and upper left corners.  FIG. 17  shows four equivalent mass objects and indicates that mass objects A are substantially more massive than mass objects B. 
         [0056]    Let p A  and p B  be the densities of the materials A and B respectively. If p A =p B  then all forms would effectively cancel and there would be no torque. However, in the case p A &gt;p B  the torque body rotates around its center of mass. 
         [0057]    Ions in the lattice of a superconducting material will move with the torque body, while the Cooper pairs will partially stay in rest. As a result, a magnetic flux will be generated by the rotating loop. A superconducting magnetic field sense loop suspended in a plane parallel to torque body and secured to stay at rest and mechanically detached from the moving system will experience an opposite current therein because the sum of the two fluxes is quantized and adds to zero (fluxoid quantization). 
         [0058]    Calculations of the current: For simplicity, the mass of the moving superconductor loop is considered to be negligibly small compared to the mass of the torque body, and to simplify further, assume the case where p A &gt;&gt;p B . Then the linear velocity of rotation of the loop of radius L in response to The gravitational wave 
         [0000]    
       
         
           
             v 
             ∼ 
             
               
                 d 
                  
                 
                     
                 
                  
                 L 
               
               dt 
             
             ∼ 
             
               L 
                
               
                 dh 
                 dt 
               
             
             ∼ 
             
               L 
                
               
                   
               
                
               ω 
                
               
                   
               
                
               
                 h 
                 0 
               
             
           
         
       
     
         [0059]    relative to a laboratory reference system. In this laboratory reference system, the Cooper pairs stay partially (because of the magnetic field of the rotating ions) at rest relative to the lattive ions of the solid torque body, and the ions of the superconductor material move and constitute a current. Correspondingly, for an observer moving with the ions, the Cooper pairs move through the loop and constitute a current. Assume that the diameter d of the superconducting wire is less than the London penetration depth λ L  of the superconductor: λ L . This ensures that the superconducting current density j is approximately constant within the wire cross section (so that the Meissner effect does not preclude the motion of charges in the bulk of the wire). Thus, the current I=I Cos ωt will have amplitude: 
         [0000]      I 0 ˜jd 2 ˜enLh 0 d 2  
 
         [0060]    Substituting from the values from Table 1 the current amplitude equals I 0 ˜10 −7  electrons per second which is approximately 10 −26  Amperes. 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
             
             
               
                   
                 n ~10 30  meter 3   
                 d ~10 −7  meter 
                 L ~10 meter 
               
               
                   
                 ω ~10 2  second −1   
                 h 0  ~10 −26   
               
               
                   
                   
               
             
          
         
       
     
         [0061]    A current I in a loop with the radius R creates a magnetic field B, which at a distance α from the loop axis in the plane of the loop is equal to 
         [0000]    
       
         
           
             
               
                 
                   
                     B 
                      
                     
                       ( 
                       α 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           μ 
                           0 
                         
                          
                         I 
                       
                       
                         2 
                          
                         
                             
                         
                          
                         
                           π 
                            
                           
                             ( 
                             
                               R 
                               + 
                               α 
                             
                             ) 
                           
                         
                       
                     
                      
                     
                       { 
                       
                         
                           K 
                            
                           
                             ( 
                             
                               k 
                               0 
                             
                             ) 
                           
                         
                         + 
                         
                           
                             
                               R 
                               + 
                               α 
                             
                             
                               R 
                               - 
                               α 
                             
                           
                            
                           
                             E 
                              
                             
                               ( 
                               
                                 k 
                                 0 
                               
                               ) 
                             
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 and 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     k 
                     0 
                   
                   = 
                   
                     2 
                      
                     
                       
                         
                           R 
                            
                           
                               
                           
                            
                           α 
                         
                       
                       
                         R 
                         + 
                         α 
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
           
         
       
     
         [0000]    where K(k) and E(k) ere complete elliptic functions of the first and second kind. Integrating this, the total flux in the loop: 
         [0000]    
       
         
           
             
               Φ 
               = 
               
                 
                   2 
                    
                   
                       
                   
                    
                   π 
                    
                   
                     
                       ∫ 
                       0 
                       R 
                     
                      
                     
                       
                         B 
                          
                         
                           ( 
                           α 
                           ) 
                         
                       
                        
                       α 
                        
                       
                           
                       
                        
                       d 
                        
                       
                           
                       
                        
                       α 
                     
                   
                 
                 ∼ 
                 
                   
                     10 
                     
                       - 
                       4 
                     
                   
                    
                   Weber 
                 
               
             
             , 
           
         
       
     
         [0000]    for R=L=10 meter, and I=1 Ampere. In the case of current amplitude 10˜10 −26  Ampere, the flux will be φ˜10 −+ Weber or, in terms of the magnetic flux quantum, 
         [0000]    
       
         
           
             
               ϕ 
               0 
             
             = 
             
               
                 h 
                 
                   2 
                    
                   
                       
                   
                    
                   e 
                 
               
               ∼ 
               
                 
                   207 
                   · 
                   
                     10 
                     
                       - 
                       15 
                     
                   
                 
                  
                 Weber 
               
             
           
         
       
     
         [0000]    where h is Planks constant, and a is the charge of the electron, resulting in 
         [0000]      φ=10 −15  φ 0 Weber
 
         [0000]    this flux is cancelled by a flux of equal value due to oppositely directed current induced in the second, non-moving, loop. The latter current could be measured by coupling it via flux transformer to a SQUID pick-up loop using standard methods of superconducting electronics. A principal requirement follows from the sensitivity of contemporary SQUIDs, that routinely achieve a noise floor δφ˜10 −6 φ 0 Hz 1/2  at 4.2K. 
         [0062]    Better results can be expected at much lower temperatures. However, it is clear that the current should be much larger than I 0 ˜10 −26  Ampere to observe sources producing h 0 ˜10 −26  (such as the Crab Nebula). 
         [0063]    Another way off enhancing the current is to use a wire with a greater diameter than the London depth d&gt;&gt;λ L  and further enhanced with a corrugated surface as shown in  FIGS. 1 and 3 . In this case, the current will flow in the surface layer within the London thickness in a direct analogy with the physics of London&#39;s momentum), but the effective cross section will be larger. Then the flux will be greater by 
         [0000]    
       
         
           
             
               η 
                
               
                   
               
                
               d 
             
             
               λ 
               L 
             
           
         
       
     
         [0000]    where η&gt;&gt;1 is a factor due to the corrugation. If η˜10 2  and d˜1 cm the fly generated in the primary loop is φ˜10 −8 φ 0  and the signal will be above the noise floor of the SQUID for an observation time t=104 seconds (less than a day). 
         [0064]    Correspondingly, the current amplitude in the case of corrugated surface is I 0 ˜10 −19  Ampere. 
         [0065]    In addition to the above-mentioned noise of signal-registering electronics, other noise factors should be taken into amount. In particular, intrinsic thermodynamic noise (of Johnson-Nyquist origin) generated by electron-hole excitations is inevitable in superconductors. This noise contribution can be modeled via a finite resistor attached in parallel to the superconducting current lead. Then the average noise: 
         [0000]                  I   noise           =[4( k   B   T/R   n ] 1/2    
         [0000]    where k B  is Boltzmann constant, T is the temperature in Kelvin, δv is the bandwidth, and R n , is the resistance of the normal component of the superconductor. 
         [0000]        R   n =(ρ L/S )exp(Δ/( k   B   T )
 
         [0066]    where ρ is the resistivity of normal electrons in a superconductor (not to be confused with the previous rho used for density), S is the wire cross-section, and Δ=Δ(T) is the BCS gap in the spectrum of unpaired excitation. For a single loop with d˜λ L  adopting ρ˜1 micro ohm cm, Δ˜10 MeV (superconductors with even larger gap values are readily available), and operational temperature T˜4K we have from (5): R n ˜10 20  Ohm. Substituting this into Eq. (4) and choosing, as above, dυ˜=1/t˜10 −8  Hz yielding I noise ˜10 −25  Amperes. Though this is larger than the signal (the current I 0 ˜10 −25  Ampere in a single loop), for N loops the noise increases as N1/2, while the signal increases as N. Thus, at N&gt;100 the signal becomes greater than thermodynamic noise, and the low limit of N (˜10 5 ) is set by the noise floor of superconducting electronics considered above. 
         [0067]    The case of corrugated wires can be analyzed in a similar manner. In this case the optimum cross-section is S˜ηdλ L , so that the normal resistance of the corrugated path 
         [0000]                R noise   corr           ˜10 13  Ohm
 
         [0000]    Accordingly, the average current noise of the corrugated path 
         [0000]                I noise   corr           ˜10 −21  Ampere
 
         [0000]    which is orders of magnitude smaller than the value of signal current 
         [0000]                I 0   corr           ˜10 −19 Ampere
 
         [0068]    As will be apparent to those skilled in the art, various changes and modifications may be made to the illustrated embodiment of the present invention without departing from the spirit and scope of the invention as determined in the appended claims and their legal equivalent.