Accelerator for coherent bosons
BACKGROUND OF THE INVENTION 
     (i) Field of the Invention 
     This invention relates to an accelerator for coherent bosons. 
     (ii) Prior Art 
     Traditionally, accelerators are constructed for accelerating charged particles such as electrons, photons and ions. The energy range is in the MeV range for Van der Graff accelerators, up to TeV (=10 12  eV) for the largest proton accelerator at Fermi National Laboratory, Batavia, Ill., U.S.A. The size of an accelerator increases with energy, for example from a 10 meter tall Van der Graff accelerator to kilometer diameter synchrotrons. 
     BRIEF DESCRIPTION OF THE INVENTION 
     According to the present invention there is provided a method of accelerating first bosons comprising colliding those bosons with second energetic coherent bosons to cause the first bosons to form an energetic coherent boson beam. 
     The invention also provides a particle accelerator for accelerating first bosons comprising means for generating second energetic coherent bosons and directing those to collide with the first bosons and cause these to form an energetic coherent boson beam. 
     By the present invention it is possible to generate a high energy coherent boson beam without using large structures. 
    
    
     BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS 
     The invention is further described by way of example only with reference to the accompanying drawings in which: 
     FIG. 1 is a Feynman diagram useful in describing the invention; and 
     FIG. 2 is a diagram of an apparatus constructed in accordance with the invention. 
    
    
     DETAILED DESCRIPTION 
     The physical mechanism underlying the invention is described in U.S. Ser. No. 035,734 incorporated herein by reference. Using the scattering of coherent laser light with matter at very low temperature, such as Helium II (a superfluid) at below 2.1° K., the reaction is: ##EQU1## with n.sub.γ coherent photons with momentum k from a powerful laser shining on m coherent helium atoms. The m coherent helium atoms will gain energy from the impact of the laser-light and change their momentum from p to p&#39;. The photons will be scattered into N different clusters each with m coherent photons with mN=n.sub.γ. The N clusters of coherent photons in general have different momentum=k 1  &#39;,k 2  &#39;, k n  &#39;. The transition rate for equation 1 can be calculated from n.sub.γ --order perturbation theory in quantum field theory to be approximately: ##EQU2## For each coherent beam with n particles, there is associated a factor n!. The first n! is for the initial coherent photon beam. The next factorial (m!) 2  is for the m initial and final state coherent helium atoms. For N clusters of coherent photons each with m photons in the final state, there is the factor (m!) n . In the final state there are n.sub.γ  photons distributed into N different clusters with m photons each. The combinational factor is 
     
         n.sub.γ !/(N!).sup.m m! 
    
     Since it is coherent scattering, the combinational occurs in the amplitude, and there is a square to the combinational factor. The probability and transition rate of one photon scattering off one helium atom are denoted by P 2  and w and η is the inverse of the total number of states available from phase space considerations alone in the final state. Equation 1 can be recast to be: 
     
         w.sub.1 =z.sup.ny w                                        (equation 3) 
    
     with ##EQU3## where σ is the cross section of photon helium elastic scattering (˜10 -26  cm 2  for photon with 1 eV energy), ω the angular frequency of the incoming photon, T the interaction time, V the normalization volume, e is the exponential number, and m is the number of first bosons. 
     The critical condition is then z=1, because of the large value of n.sub.γ. For Z&lt;1, the transition rate w is negligible and for Z≧1 the transit ratio w is very large. It is equivalent to the scattering of two macroscopic objects. It occurs with certainty and not with probability. 
     The helium atoms gain enormous energy. The quantum mechanical Feynman diagram is shown in FIG. 2. The origin of such process is quantum mechanical but the result is a classical phenomenum. 
     The energy transfer between photons and helium atoms may be estimated. The mass of a helium atom (m He  ˜3.7 GeV) is considerably larger than the energy of a photon (˜1 eV) from a laser. The photon essentially loses very little energy. It may be imagined to be like bouncing off a brick wall. If it bounces backwards, the helium mass gains a momentum ΔP˜2k, where k is momentum of the photon. For bouncing N photons, the helium atom gains 
     
         ΔP˜Nk                                          (equation 5) 
    
     where the factor 2 is dropped for an estimate of the order of magnitude for a nonrelativistic helium atom in the final state, its energy is given by ##EQU4## For relativistic helium atoms in the final state, each helium atom has energy ##EQU5## The larger N is, the higher is the energy that the helium atoms gain. Since N=n.sub.γ /m, one could increase N by increasing the total energy of each laser pulse or by reducing the number m of the coherent helium atom. FIG. 2 illustrates an experimental setup which will produce an energetic coherent beam of helium atoms. 
     The helium gas is cooled by liquid helium to low temperatures at high pressure, say one atmospheric pressure. Then the cooled helium gas is allowed to expand through a nozzle 12 into a low pressure chamber 14. During the expansion phase, the helium gas will cool down and helium clusters will be formed. At below 2.1° K., the helium clusters 13 will contain coherent Particles. The number of atoms in a cluster may range from two to thousands, depending, inter alia, on the nozzle size, initial pressure and temperature. When coherent helium clusters are formed, laser light 15 is shone on them from a laser 16. The clusters are accelerated by the impact of the coherent light to form a high energy coherent beam 17 of helium atoms. As shown, the expansion chamber 14 may be formed as part of a vacuum chamber 20, having an inlet 21 at an end opposite the expansion chamber for inlet of the helium gas into a pre-chamber 23. From the pre-chamber 23, the gas Passes through the nozzle 12, formed an opening in a transverse divider wall 29 across chamber 20, and thence into the expansion chamber. Skimmers 31 are shown adjacent nozzle 12 in chamber 14 to direct the emergent clusters of helium. The laser 16 is arranged to direct the light 15 tranversely across the path of the clusters in chamber 14. the light 15 may be introduced through a suitable window 25 of the chamber 14. 
     The energetic coherent helium beam is exited from the chamber 14 via a side outlet in chamber 14 opposite window 25. Suitable ports 37, 39 may be provided in chamber 14 for pumping out of helium to maintain a low pressure in the chamber 14. 
     Table 1 tabulates the energies of the final coherent beam from different initial conditions. the total energy of a laser pulse ranges from 10 -6  Joule to 10 3  Joule. The size of the cluster is assumed to be m=10 3 . For one thousand clusters under the influence of one laser light pulse, then m=10 6 . The energy E He  that the helium atom in a coherent cluster beam attains ranges from E He  =100 keV to 10 19  eV. The highest energy 10 19  eV is seven orders of magnitude higher than the highest energy (TeV) obtained in the aforementioned proton accelerator at Fermi National Laboratory. A currently proposed Superconducting Super Collider (SSC) will have a diameter of 60 miles with a maximum energy of 20 TeV. It is difficult to envisage considerable improvement over the SCC by using any conventional accelerating mechanism. However the new mechanism above described is capable of achieving a higher energy. Furthermore the size of this new accelerator may be measured in meters and not in kilometers. Correspondingly, the cost may be several orders of magnitude less than the proposed costs of SSC. 
     
                       TABLE 1                                                     
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Energy of helium for different kinds of laser pulse                       
          No. of                                                          
Total energy of                                                           
          photons                                                         
laser pulse (J)                                                           
          n.sub.γ                                                   
                   N               E.sub.He                               
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10.sup.-6 J                                                               
          10.sup.13                                                       
                   m = 10.sup.6                                           
                             10.sup.7                                     
                                     100 keV                              
                   = 10.sup.3                                             
                             10.sup.10                                    
                                     10 GeV                               
10.sup.-3 J                                                               
          10.sup.16                                                       
                   m = 10.sup.6                                           
                             10.sup.10                                    
                                     10 Gev                               
                   = 10.sup.3                                             
                             10.sup.13                                    
                                     10 TeV                               
1 J       10.sup.19                                                       
                   m = 10.sup.6                                           
                             10.sup.13                                    
                                     10 TeV                               
                   = 10.sup.3                                             
                             10.sup.16                                    
                                     10.sup.4 TeV                         
10.sup.3 J                                                                
          10.sup.22                                                       
                   m = 10.sup.6                                           
                             10.sup.16                                    
                                     10.sup.4 TeV                         
                   = 10.sup.3                                             
                             10.sup.19                                    
                                     10.sup.7 TeV                         
1 J       10.sup.19                                                       
                   m = 3 × 10.sup.14, 3 × 10.sup.4            
                                   0.1 eV                                 
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     Table 2 lists the difference between conventional accelerators and the present accelerator for coherent beams. 
     A high energy coherent boson accelerator can only have a small number of particles. However, for investigating high energy phenomena this presents no problem because the hadron- hadron scattering cross-section will be increased by at least (m!) 2  with one factor m! coming from each of the two colliding high energy coherent beams. 
     For coherent beams, the outcoming beam is not confined to the high energy region at all. If the number m of coherent helium atoms is increased, it is possible to have a low energy coherent beam. 
     
                       TABLE 2                                                     
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Different characteristics as between conventional                         
accelerators and coherent boson accelerators                              
             Conventional Coherent Boson                                  
Characteristics                                                           
             Accelerator  Accelerator                                     
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(1) Range of Energy                                                       
                 10.sup.6 ˜ 10.sup.13 eV                            
                              0.1 eV 10.sup.19 ev                         
(2) Flux         10.sup.10 per bunch                                      
                              m = 10.sup.3 per cluster                    
                              or more for low                             
                              energy                                      
(3) Accelerating Electric Field                                           
                              Momentum transfer                           
    Mechanism                 from scattering                             
                              among coherent                              
                              particles                                   
(4) Accelerating Continuous   One shot                                    
    Mode         Acceleration                                             
short distance                                                            
long distance                                                             
    (&lt;μm)                                                              
                 (10 m 10 km)                                             
(7) hadron-hadron                                                         
                 σ ˜ 10.sup.-26 cm.sup.2                      
                              at least (m!).sup.2 σ                 
    cross section                                                         
                 small        or larger                                   
    (σ)                                                             
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     In the last column of Table 1 it is noted that for m=10 14  one may have E He  0.1 eV, a very low energy coherent helium beam. Low energy beams are useful in investigating molecular and atomic physics. 
     Typical numerical values associated with the experimental set up as shown in FIG. 2 are now described. The volume of a helium cluster V He  is given by ##EQU6## The value of the volume V for the photon pulse V is given by 
     
         V=L.A 
    
     where one chooses the cross section area A and the length of the photon pulse L to be 
     A=1 mm×1 mm 
     L=30 cm 
     for a laser pulse with bandwidth 1 GHz. 
     so ##EQU7## where T is about the order of magnitude of the life time of the virtual state of the helium atom excited by one photon. Choose ##EQU8## Therefore, 
     
         P.sub.1 η˜4×10.sup.-22 
    
     For a light pulse of 10 -7  Joule, one has n=10 12  and for a cluster m=10 3 . Therefore, the critical value ##EQU9## is greater than one. If the laser pulse energy is higher, Z remains bigger than one. When Z&gt;1, the coherent helium will be accelerated by the impact of the laser pulse. 
     It is possible to accelerate coherent bosons from a CW (continuous wave) laser. A CW laser emits continuous light which is divided into a series of coherent light pulses, defined by its coherence length. From the accelerated bosons beam&#39;s point of view it has received a series of accelerations from a series of coherent light pulses. 
     It is also possible to accelerate a coherent boson beam by more than one laser. A series of lasers can be placed along the path of the beam and be timed to fire when the coherent beam passes each of the lasers. 
     A specific example of coherent helium clusters has been given. In principle, any coherent bosons or boson may be accelerated. For example, the cluster could be made up of deuterium at low temperature so long as the critical condition z≧1 is satisfied for that particular scattering process. Another example is that the coherent bosons may be the electron pairs called Cooper pairs in superconducting materials. The cluster may then be made up of superconducting materials.