Patent Publication Number: US-H2010-H

Title: Double cusp gyro gun

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to the generation of electron beams for use in microwave generators and, more particularly, to the generation of gyrating electron beams in a controllable manner particularly suited for use in a wide range of gyro-amplifiers and gyro-oscillators. 
     2. Description of the Prior Art 
     Gyro-amplifiers and gyro-oscillators, which are commonly referred to as gyrotrons, require an electron beam that is different from that which is normally employed in linear microwave tubes, such as klystrons and traveling-wave tubes. In general, and as is known in the art, in gyrotrons microwave energy is extracted from the beam rotational energy through electron orbital phase bunching resulting from resonant interaction between the electron gyration and the transverse component of the electromagnetic waves contained in the interaction circuit, sometimes referred to as cyclotron resonant maser instability. To maximize this resonant interaction process and enhance the efficiency of the gyrotron, it is necessary for the bem forming system, also known as gyrotron gun or gyro-gun, to accomplish the following three factors: (a) form the gyrating electron beam with a large transverse-to-axial velocity ratio, α=v ⊥ /v z  typically between one and two; (b) achieve and control the axial velocity, v z , so as to have a low velocity spread in order to provide phase bunching stability; and (c) place the electron&#39;s beam guiding center, r g , at the peak of the wave transverse electric field. The attainment of these three factors for all gyrotron device applications has not been accomplished by a single gyro-gun because of certain limitations. 
     First, the desired factors of the transverse-to-axial velocity ratio, α=v ⊥ /v z , and the desired position of the electron&#39;s beam guiding center, r g , primarily determine the electron orbital parameter which is different for various gyrotron applications. The selection of these desired factors in a gyro-gun to satisfy a gyrotron device requiring a particular orbit, such as, a small-orbit (non-axis encircling), may not be suitable when the same gyrotron gun is used for another application requiring a different type of orbit, such as, a large-orbit (axis-encircling). 
     Second, the desired parameter of controlling the axial velocity v z  spread is primarily of importance to the interaction circuit located at the output of the gyrotron gun and which circuit extracts microwave energy from the kinetic energy of the gyrating electron. The axial velocity spread is determined, in part, by the cathode of the gyrotron gun and the operation of the cathode. One approach to control the axial velocity v z  spread is to reduce the cathode&#39;s annulus width which, in turn, has the disadvantage of creating higher cathode loading. Another approach is to increase the cathode&#39;s mean radius which, in turn, has the disadvantage of increasing the overall size of the gyrotron gun which may not be desired for some applications. 
     FIRST PROBLEM 
     In relation to the first problem, several approaches, dictated by the parametric requirements in the beam-wave interaction region, have been used to provide for a desired small-orbit or large-orbit gyrotron beam. Although gyrotron guns designed for a particular parametric requirement serve well their intended function, once built employing existing beam-forming techniques, the gyrotron gun is often difficult to adjust in order to accommodate parameter changes that may arise from time to time. Various beam-forming devices determined by parametric requirements that have been developed prior to 1981 are well documented and summarized in a detailed report by Baird and Attard entitled “Gyrotron Gun Study Report” of the Naval Research Laboratory (NRL) Report TR-3-476 (1981). Each of the approaches prior to 1981 is suitable for use as a beam-forming system for a specific gyrotron device, depending upon the type of beam parameters required. For instance, the gyrotron gun, magnetic injection gun (MIG), originally conceived in the early 1960&#39;s, has been continuously used until the present time as a gyrotron beam-forming system and is particularly suited for small-orbit applications, but is not suited as a gyrotron beam-forming system having large-orbit applications. For a large-orbit gyrotron applications, a modified version of a magnetically shielded, space-charged limited Pierce gun (known in the art) has been proposed and is described by G. P. Scheitrum; R. S. Symons; and R. B. True, in the technical article entitled “Low Velocity Spread Axis Encircling Electron Beam Forming System,” documented in the Technical Digest of Electron Devices Meeting, pp 743-746 (1989). Accordingly, although various beam-forming techniques are known to accommodate both small and large-orbit gyrotron devices, no one technique is known to accommodate both the small and large-orbit applications. 
     SECOND PROBLEM 
     In relation to the second problem, a primary cause of axial velocity v z  spread in gyrotron devices is due to the fact that electrons emitted from the cathode of the gyrotron gun at different radial positions enclose different amounts of magnetic flux, commonly referred to as canonical angular momentum spread. As previously mentioned, several approaches are known to reduce the axial velocity v z  spread and one of which is to reduce the cathode&#39;s annulus width. This is not however very practical, since this reduction creates a higher cathode loading factor, which has a tendency to overburden the cathode and, thereby, degrade its operational life characteristic. Another approach is to increase the cathode&#39;s mean radius. While this approach reduces velocity spread, it is accomplished at the expense of increasing the overall size of the gyrotron gun which may not be desired for some applications. An approach is to reduce the axial magnetic field on the surface of the cathode. An adaptation of this approach is to use a magnetic envelope and a magnetic center post as proposed by Chow and Pantell in the technical article “The Cyclotron Resonance Backward Wave Oscillator,” documented in the proceedings of the IEEE, Vol. 48, pp. 1865-1867 (1980). In this technique, the center post carries the magnetic flux, while the magnetic envelope reduces the axial magnetic field on the cathode structure to virtually zero. However, a problem with this technique is that the magnetic center post is at essentially the same potential as that of the cathode; hence, practical implementations of this technique are prone to arcing between the center post and the anode due to large potential differences at their proximity. Moreover, this approach does not permit the flexibility of varying the beam canonical angular momentum spread to actively control the beam velocity spread for different applications of the gyrotron gun. 
     OBJECTS OF THE INVENTION 
     Accordingly, one object of the present invention, the double cusp gyro-gun, is to provide a gyrotron gun and a method of use thereof that have the flexibility of actively controlling the axial velocity v z  spread so as to accommodate different applications of the gyrotron gun. 
     Another object of the present invention is to provide a gyrotron gun and a method of use thereof that actively control the gyrating electron&#39;s beam transverse-to-axial velocity, α=V ⊥ /v z , as well as the position of the electron&#39;s beam guiding center, r g , so as to allow the gyrotron gun to be used for both small and large orbiting applications. 
     A still further object of the present invention is to provide a gyrotron gun and a method of use thereof that provide the flexibility for independently and simultaneously controlling the gyrating electron beam transverse-axial velocity ratio, α=V ⊥ v z ; the position of the electron&#39;s beam guiding center, r g ; as well as the spread of the axial velocity, v z . 
     SUMMARY OF THE INVENTION 
     The invention is directed to a gyrotron gun that is operated to independently and simultaneously control a gyrating electron beam transverse-to-axial velocity ratio, α=v ⊥ v z ; the position of the electron&#39;s beam guiding center, r g ; as well as the spread of the axial velocity v z , thereby, allowing the gyrotron gun to be used for large-orbit, small-orbit and even linear-beam modes of operation. 
     The gyrotron gun generates and forms a beam of electrons manifesting electron gyrating around a guiding center and having rotational energy. This is so that efficient phase bunching will result from a resonant interaction between the electron gyration and transverse component of the electromagnetic wave in the ensuing beam-wave interaction circuit. The gyrotron gun comprises first, second and third field coils and first and second means for establishing an abrupt change in a magnetic field. The field coils and the devices for establishing an abrupt change are arranged to form three regions. The field coils are operated so that each supply a predetermined strength of an axial magnetic field to allow for the control of the gyrating electron beam transverse-to-axial velocity ratio, α=V ⊥ /v z ; the position of the electrons beam guiding center r g ; and the spread of the axial velocity, v z , so that the gyrotron gun can be used for small and large-orbit and even linear-beam modes of operation. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and other objects, features and advantages of the present invention, as well as the invention itself, will become better understood by reference to the following detailed description when considered in connection with the accompanying drawings, wherein like reference numerals designate identical or corresponding plots throughout the several views, and wherein: 
     FIG. 1 is a schematic illustrating an arrangement of the interrelated elements of the present invention; 
     FIG. 2 illustrates a plot of the magnetic profile of the present invention; 
     FIG. 3 is composed of FIGS.  3 (A), (B), and (C), wherein FIGS.  3 (A) and  3 (B) each illustrates a plot useful in the understanding in the large-orbit operation of the gyrotron gun of the present invention which is generally illustrated in FIG.  3 (C); 
     FIG. 4 is composed of FIGS.  4 (A), (B), and (C), wherein FIGS.  4 (A) and  4 (B) each illustrates a plot useful in the understanding of the small-orbit operation of the gyrotron gun of the present invention which is generally illustrated in FIG.  4 (C); 
     FIG. 5 is composed of FIGS.  5 (A), (B), and (C), wherein FIGS.  5 (A) and  5 (B) each illustrates a plot useful in the understanding of the linear-mode operation of the gyrotron gun of the present invention which is generally illustrated in FIG.  5 (C); 
     FIG. 6 is composed of FIGS.  6 (A), and (B), each of which illustrates a plot related to the axial velocity, v z , spread associated with the large-orbit operation of the gyrotron gun of the present invention; 
     FIG. 7 is composed of FIGS.  7 (A), (B), and (C), each of which illustrates a plot related to the axial velocity, v z , spread associated with the small-orbit operation of the gyrotron gun of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring now to the drawings, FIG. 1 illustrates an arrangement of elements of a gyrotron gun  10  having a centerline  12 . The gyrotron gun  10  is preferably circular so that the arrangement of the elements of FIG. 1 is actually also below the centerline  12 . 
     The gyrotron gun  10  generates gyrating electron beams in a controllable manner suitable for a wide range of applications. The gyrotron gun  10  has a predetermined operating period, sometimes referred to as a gyro-period, with a corresponding predetermined wavelength. The gyrotron device  10  may also be referred to herein as a double-cusp gyro gun  10 . The gyrotron device  10  generates and forms a beam of electrons manifesting electron gyrating around a guiding center and having rotational energy. This is so that efficient phase bunching will result from a resonant interaction between electron gyration and a transverse component of electromagnetic waves contained in the ensuing beam-wave interaction circuit  50 . The resonant interaction is determined by three factors which are: ( 1 ) the transverse-to-axial velocity ratio, α=v ⊥ /v z , of the gyrating electron beam; ( 2 ) the position of the electron&#39;s beam guiding center, r g , and ( 3 ) the spread of the axial velocity v z  of the electron beam. The gyrotron device  10  of FIG. 1 comprises a plurality of elements each having a reference number all of which are given in Table 1. 
     
       
         
           
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 REFERENCE NO. 
                 ELEMENT 
               
               
                   
               
             
            
               
                 14 
                 Cathode 
               
               
                 16 
                 Anode 
               
               
                 18 
                 Vacuum Envelope 
               
               
                 20 
                 Electron Tunnel 
               
               
                 22 
                 Entrance Section of Electron 
               
               
                   
                 Tunnel 20 
               
               
                 24 
                 Intermediate Section of 
               
               
                   
                 Electron Tunnel 20 
               
               
                 26 
                 Exit Section of Electron 
               
               
                   
                 Tunnel 20 
               
               
                 28 
                 First Field Coil 
               
               
                 30 
                 Second Field Coil 
               
               
                 32 
                 Third Field Coil 
               
               
                 34 
                 First Cusp Member 
               
               
                 36 
                 Second Cusp Member 
               
               
                 38 
                 First Bucking Coil 
               
               
                 40 
                 Second Bucking Coil 
               
               
                 42 
                 Electron Beam 
               
               
                   
               
            
           
         
       
     
     The cathode  14  is preferably of a thermionic type or any other electron emitting type and also preferably has an annular shape. As is known, the thermionic cathode  14 , when subjected to a relatively high-voltage pulse  44 , generated from a conventional power modulator  46  and present at the entrance section  22 , allows the extraction therefrom of an electron beam  42  which is accelerated toward a higher potential anode  16 , also located in the entrance section  22 . The electron beam  42  moves along the full length of an electron tunnel  20  and is extracted from the exit section  26  thereof, as shown by arrow  48 , into a beam-wave interaction circuit  50 , known in the art. The beam-wave interaction circuit  50  converts the kinetic energy of the electron beam  42  into microwave energy. 
     Also as is known in the art, and as is shown in FIG. 1, the anode  16  (preferably of an annular shape) is offset from the cathode  14  and protrusions  52  and  54  are interposed therebetween allowing the electron beam  42  attracted to the anode  16  to be diverted away therefrom and directed toward the intermediate section  24 . 
     The vacuum envelope  18 , illustrated by a cross-hatch representation in FIG. 1, forms the electron tunnel  20  having the entrance section  22 , the intermediate section  24  having first and second portions  24 A and  24 B, and the exit section  26 . The vacuum envelope  18  is preferably formed of a non-magnetic metallic material and arranged in a manner known in the art. 
     The first, second and third field coils  28 ,  30 , and  32 , respectively, are preferably formed of a metallic material, known in the art, and are arranged so that the first field coil  28  is situated near the entrance section  22  and the second and third field coils  30  and  32  are situated at the intermediate section  24 . The field coils  28 ,  30  and  32 , as well as the bucking coils  38  and  40 , are indicated in FIG. 1 with an X symbol. 
     The first and second cusp devices  34  and  36  preferably comprise a high permeability material, such as soft iron. The term “cusp” is known in the art and is meant to represent that the device provides for an abrupt change in a magnetic field as the magnetic field passes through the cusp device. The arrangement of the cusp devices  34  and  36 , relative to the field coils  28 ,  30  and  32 , provide for three different operating regions which are of particular importance to the present invention. 
     The first cusp device  34  is interposed between the first and second field coils  28  and  30 , respectively. The second cusp device  36  is interposed between the second and third field coils  30  and  32 , respectively. The first field coil  28  and the first cusp device  34  establish a first operating region  56 . Further, the first cusp device  34  and the second cusp device  36 , both in combination with the second field coil  30 , establish a second operating region  58 . Further, the second cusp device  36  and the third field coil  32  establish a third operating region  60 . The first ( 56 ), second ( 58 ), and third ( 60 ) operating regions are respectively herein termed the diode region  56 , the double-cusp region  58 , and the adiabatic compression region  60 . The first cusp device  34  and the second cusp device  36  are spaced apart, as shown in FIG. 1, from each other by a distance  62  which preferably corresponds to one-half of the operating gryo-period of the gyrotron device  10 . 
     The first and second bucking coils  38  and  40  are supplied with opposite currents and are located near, but preferably behind, the cathode  14 , as shown in FIG. 1, so as to reduce or even cancel the axial magnetic field on the cathode surface in a manner as to be further described hereinafter with reference to FIGS. 6 and 7. 
     The parameters of the electron beam  42  formed and generated by the gyrotron gun  10  are controlled by the field strength of the axial magnetic fields applied to the regions  56 ,  58  and  60  by way of the first, second and third field coils  28 ,  30  and  32 , respectively. The operation of the gyrotron device  10  is primarily determined by a magnetic profile  64 , which may be further described with reference to FIG.  2 . 
     FIG. 2 illustrates the magnetic profile  64  of the electron beam  42  as it passes through and is developed therein by the diode, double-cusp and adiabatic compression regions  56 ,  58  and  60 , respectively, and propagates to the tip  66  of the exit section  26 , whereby the kinetic energy of the electron beam  42  is extracted by the beam-wave interaction circuit  50  to provide microwave energy therefrom. FIG. 2 has a horizontal axis, given by the quantity, z, representative of the axial position of the electron beam  42  as it moves along the gyrotron device  10 , as generally illustrated in FIG.  1 . Further, FIG. 2 has a vertical axis represented by the quantity B z  (Z) which is the average axial magnetic field enclosed by the electron beam  42 . 
     The magnetic profile  64  comprises a first section  64 A, a second section  64 B, and a third section  64 C, respectively, associated with regions  56 ,  58  and  60 , and respectively represented by the quantities f 1 B 0 , f 2 B 0  and B 0  and B f =f m B 0 , wherein the quantities B 0  and B f =f m B 0  are present at the initial and terminal portions, respectively, of the third section  64 C. The cusp devices  34  and  36  (see FIG. 1) impart a rotation to the electron beam  42  which impartations are generally illustrated in FIG. 2 by ramping portions  64 D and  64 E respectively. 
     In general, the usage of the first and second cusp devices  34  and  36 , the selection of the quantities f 1 B 0 , f 2 B 0 , B 0  and f m B 0 , determined by the operation of the first, second and third field coils  28 ,  30  and  32  respectively, as well as the operation of the bucking coils  38  and  40 , provide for independent and simultaneous control of the three factors: ( 1 ) the transverse-to-axial velocity ratio, α=v ⊥ /v z ; ( 2 ) the position of the electron&#39;s beam guiding center, r g ; and ( 3 ) the axial velocity spread, all of which three factors have been previously discussed in the “Background” section. The operation and method of the present invention provide the capability to optimize the energy conversion in the beam-wave interaction circuit  50  without modifying the mechanical features of the double cusp gyro gun  10 . More particularly, once the physical features, composition and arrangement of the elements of the double-cusp gyro gun  10  are selected, they do not need to be changed, but rather only the amount of current applied to the field coils  28 ,  30  and  32  and bucking coils  38  and  40  need to be adjusted to control the operating parameters of the double-cusp gyro gun  10 . Thus, problems and limitations associated with prior art beam-forming practices, discussed in the “Background” section, are avoided. 
     The trajectory of the electrons forming beam  42 , after extraction from the cathode  14 , is dictated primarily by the magnetic field profile  64 , via Lorentz force. Evaluation of such a trajectory is based on an idealized theoretical model which employs the principle of canonical angular momentum conservation. The canonical angular momentum, P θ , of an electron charge q, mass m and energy γ, at radius r, axial position z, and angular velocity v θ  may be represented by expression 1 given below: 
     
       
           P   θ   =γmrv   θ   −qrA   θ ( r,z )  (1) 
       
     
     The term P θ  represent a conserved quantity in an azimuthally symmetric system. The vector potential, A θ (rz), for the total magnetic field profile  64 , may be estimated by expression 2 given below: 
     
       
           A   θ ( r,z )=½ rB   z ( z )  (2) 
       
     
     where B z  (z) is the average axial magnetic field enclosed by an electron forming part of the electron beam  42 . With the quantity ω c2 ≡(qB z )/(γm), the canonical angular momentum may be represented by expression 3 given below which is treated as a conserved quantity throughout the entire gyrotron device  10 : 
       P   θ =(γ m )[ rv   θ −½ r   2 ω cz ( z )]  (3) 
     As previously mentioned with reference to FIG. 2, the first cusp device&#39;s  34  transition field imparts an angular velocity to the electron beam  42 , via the v z ×B r  Lorentz force term, hence, initiating cyclotron motion within the double-cusp region  58 . From conservation of the canonical angular momentum, it can be shown that the electron perpendicular velocity in the double-cusp region  58  may be represented by expression 4 given below: 
     
       
           v   ⊥1+ =½(1 −f   1 ) f   2 ω co   r   1   (4) 
       
     
     where r 1  is assumed to be the electron radial position at the cathode  14  and also at the first cusp device  34 ; f 1  and f 2  are the axial magnetic field quantities respectively related to the diode region  56  and the double cusp region  58 , and ω co  is the electron angular cyclotron frequency at the start of the adiabatic compression region  60 . More particularly, with reference to FIG. 2, the quantities f 1  and f 2  are respectively included in sections  64 A and  64 B of magnetic profile  64  and the quantity ω co  is included in the peak of the ramp portion  64 E of the magnetic profile  64 . It should be pointed out that the electron perpendicular motion immediately after the first cusp device  34  is primarily azimuthal, since the electron motion has assumed to be paraxial in the diode region  56 . Based on this assumption, the electron position at the second cusp device  36  where the electron radial velocity vanishes may be represented by the expression 5 given below: 
     
       
           r   2   =f   1   r   1   (5) 
       
     
     As previously mentioned, the distance  62  (see FIG. 1) between the two cusp devices  34  and  36  is preferably and precisely one-half of a gyro-period. For such a preferred distance  62 , the electron motion in the double-cusp region  58  is that of a small-orbit (non-axis encircling) gyration wherein its guiding center may be represented by expression 6 given below: 
     
       
           r   g1+ =½(1 +f   1 ) r   1   (6) 
       
     
     At the second cusp device  36 , the radial magnetic field thereat imparts an additional velocity thrust on the electron beam (see FIG. 2, in particular, ramp portion  64 E). As further seen in FIG. 2, the field strength at the exit of the double-cusp region  58  is B 0  which is illustrated near the termination of the ramp portion  64 E which corresponds to the second cusp device  36  transition region of the profile  64 . Upon leaving the transition region of the second cusp device  36 , the perpendicular velocity may be represented by expression 7 given below: 
       V   ⊥2+ =½( f   1   −f   2 )ω co   r   1   (7) 
     The guiding center region at the beginning of the adiabatic compression region  60  may be represented by expression 8 given below:                      r     g2   +                  =       r   2     -       V     ⊥     2   +           ω   co                                  =       1   /   2          (       f   1     +     f   2       )          r   1                                       (   8   )                         
     It should be noted, and as will be further discussed hereinafter with reference to FIGS. 6 and 7, that for a particular case wherein f 1 =−f 2 , there is no beam guiding center spread. The ratio of the perpendicular velocity to axial velocity is found from energy conservation and may be represented by expression 9 given below:                α     2   +       =         v     ⊥     2   +             [       v   o   2     -     v     ⊥   2            +   2       ]       1   /   2              
                     
                =       [         1   /   4            (       f   1     -     f   2       )     2            ω   2     co          r   1   2           v   o   2     -       1   /   4            (       f   1     -     f   2       )     2          ω   co   2          r   1   2           ]       1   /   2                 (   9   )                         
     where v o  is the electron velocity at the exit of the diode region  56 . 
     From expressions (7) and (8) it may be shown that by properly selecting the magnetic field profiles, in particular the quantities f 1  and f 2 , a wide variety of beam configurations can be generated and are shown in Table 2. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 QUANTITIES f 1  AND f 2  OF 
                   
               
               
                   
                 MAGNETIC FIELD PROFILE 64 
                 BEAM CONFIGURATION 
               
               
                   
                   
               
             
            
               
                   
                 (f 1  = f 2 ) 
                 Linear Beam 
               
               
                   
                 (|f 1 | = −|f 2 |) 
                 Large-Orbit 
               
               
                   
                 (f 1  ≠ f 2 ) 
                 Small-Orbit 
               
               
                   
                   
               
            
           
         
       
     
     The present invention also provides a means to control independently the beam guiding center r g , and the transverse-to-axial α=v ⊥ /v z  via selecting the sum, f 1 +f 2 , and the difference, f 1 −f 2 , of quantities of diode region  56  and of double-cusp region  58 . 
     Finally, after the adiabatic compression region  60  alters the axial field strength from B 0  to B f =f m B 0 , the guiding center r g  sometimes referred to as r gf , and transverse-to-axial velocity ratio α, sometimes referred to as α f , at the tip  66  (see FIG. 2) of the gyrotation device  10  as it enters the beam-wave interaction circuit  50  may be respectively represented by expressions 10 and 11 given below:                r   gf     =         1     f   m     1   /   2              r     g2   +         =           f   1     +     f   2         2        f   m     1   /   2                r   1                 (   10   )                 α   f     =         [           (     α     2   +       )     2          f   m         1   +       (     1   -     f   m       )            (     α     2   +       )     2           ]       1   /   2       =       [         1   /   4              f   m     -   1            (       f   1     -     f   2       )       2          ω   cf   2          r   1   2           v   0   2     -       1   /   4              f   m     -   1            (       f   1     -     f   2       )       2          ω   cf   2          r   1   2           ]       1   /   2                 (   11   )                         
     where ω cf  is the angular cyclotron frequency at the r f  interaction region of the beam-wave interaction circuit  50 . 
     In addition to the relationships given by the expressions 10 and 11 for terms normally referred to as r g  and α, for a gyrotron gun  10  satisfying the requirements that the distance  62  between the two cusp devices  34  and  36  (see FIG. 1) being one-half of a gyro-period in length, the gyrotron device  10  further has interrelationship between the quantities f 2  and f m . That is, the ratio f 2 /f m  is determined by both f 2 B 0  (half gyro-period criterion), and f m B 0  (interaction circuit  50  requirement). Consequently, for a given value of the parameter B f , it is possible to adjust the guiding center, r g , and the transverse-to-axial velocity ratio, α, independently by adjusting the quantities f 1  and f 2 . More particularly, the employment of the double-cusp region  58  in the gyrotron gun  10  permits the independent control over the parameters (α, r g , and B) in a relatively simple manner by means of selecting and adjusting the quantities f 1 , f 2 , and f m , hence, achieving more flexibility with less complexity as compared to prior art beam-forming apparatuses. 
     It is important to emphasize, however, that the necessity that the radial velocity vanish (see expression (5)) at the second cusp device  36  (hence, the half-gyro-period length criterion discussed for distance  62 ) is not really needed for small-orbit operations of the gyrotron gun  10 . However, for linear and large-orbit operations of the gyrotron gun  10 , it is desired that the radial velocity be zero (see expression (5)) at the second cusp device  36  so as to ensure that beam ripple (scalloping) is minimized. 
     It should now be appreciated that the practice of the present invention provides for a gyrotron gun  10  employing a first and second cusp devices  34  and  36 , respectively, that allow for the ability to provide independent and simultaneous control of the quantities of expressions  10  and  11 , that is, guiding center r g  and transverse-to-axial velocity ratio α respectively. Furthermore, it should be appreciated that the control of the guiding center r g  and transverse-to-axial velocity ratio α is accomplished simply by varying the magnetic field profile  64  shown in FIG.  2  and is done so without modifying or altering any physical features of the gyrotron gun  10 . 
     In the practice of the present invention, a beam optic simulation study was performed. In the study, the mechanical features of the gyrotron gun  10  remain fixed and only the magnetic field profile  64  was varied to affect various final beam parameters that allowed the gyrotron gun  10  to provide small and large-orbits and linear beam modes of operation. The magnetic field profiles were obtained from a magnetic design code, POISSON, by specifying the currents for the electric field coils  28 ,  30  and  32 , and the bucking coils  38  and  40  all shown in FIG.  1 . The POISSON is a well-known magnetic design code developed by Los Alamos National Laboratories. The magnetic field profiles obtained from the POISSON magnetic design were used as inputs to a MAGIC code to perform beam optics simulation. The MAGIC code is a self-consistent, two-and-one-half dimensional, particle-in-cell code developed by Mission Research Corporation and is known in the art. The study performed for the gyrotron device  10  resulted in different beam types exemplified by three beam optic cases shown in FIGS. 3,  4  and  5  and respectively representative of a large-orbit operation, a small-orbit operation, and a linear beam mode of operation. 
     FIG. 3 is composed of FIGS.  3 (A), (B) and (C), wherein FIGS. 3A and 3B respectively illustrates the beam perpendicular γβ p  and axial momenta γβ z , normalized by the speed of light as a function of axial distance. A gyrotron gun  10  is generally illustrated in FIG.  3 (C), but without the placement of the field coils  28 ,  30  and  32  thereon. FIGS.  3 (A), (B) and (C) are all interrelated to the diode region  56 , double-cusp region  58 , and the adiabatic compression region  60  (shown above FIG.  3 (A)) and the interrelationship thereof is shown by the use of dimensional lines  68  and  70 . FIG. 3 shows a beam perpendicular momentum plot  72  (FIG.  3 (A), an axial momentum plot  74  (FIG.  3 (B)) and a beam trajectory  76  (FIG.  3 (C)), all corresponding to the usage of the gyrotron gun  10  for a large-orbit operation, where the resulting beam trajectory  76  is rotated around the gyrotron axis  12  (axis encircling). The large-orbit operation of FIG. 3 was accomplished by the use of a 60 kV, 4.4-A electron beam, which was also used in the operations illustrated in FIGS. 4 and 5. 
     FIG. 4 is similar to FIG.  3  and illustrates a plot  78  of the beam perpendicular momentum quantity γβ p  (FIG.  4 (A)), a plot  80  of the axial momentum quantity γβ z  (FIG.  4 (B)) and a beam projectory  82  (FIG.  4 (C)), all related to the small-orbit operation of the gyrotron gun  10 . As is known in the art, for a small-orbit operation, the electrons comprising electron beam  42  of FIG. 1 are rotated around and off-axis from its guiding center r g . 
     FIG. 5 is similar to both FIGS. 3 and 4 and illustrates a plot  84  of the beam perpendicular momentum quantity γβ p  (FIG.  5 (A)), a plot  86  of the axial momentum quantity γβ z  (FIG.  5 (B)), and a beam projectory  88  (FIG.  5 (C)), all related to a linear-beam mode of operation of the gyrotron gun  10 . The linear-beam operation is one in which the beam is non-rotating. It should be noted in FIG.  5 (A) that the perpendicular momentum γβ p  essentially vanishes after the second cusp device  36  (not shown) that separates the double-cusp region  58  from adiabatic compression region  60 . 
     It should now be appreciated that the practice of the present invention provides for a gyrotron gun  10  wherein the quantities given in Table 2 may be selected so as to provide for a small-orbit, large-orbit or linear modes of operation. 
     As mentioned in the “Background” section, the energy conversion efficiency of the beam-wave interaction circuit  50  is dependent upon the beam velocity spread. As further discussed in the “Background” section, various approaches were used to control the beam velocity spread, but none yielded complete success. The present invention accomplishes such control by the use of the bucking coils  38  and  40 . More particularly, the bucking coils  38  and  40  are supplied with opposite currents and preferably located behind the cathode  14  so as to reduce or even cancel the axial magnetic field on the surface of the cathode  14  and, hence, the canonical angular momentum spread. This technique permits the active control of the beam velocity spread and also avoids potential arcing problems discussed in the “Background” section. Further, this technique provides the gyrotron gun  10  with the ability to operate in the large and small-orbit modes of operation which may be further described with reference to FIGS. 6 and 7 illustrating results that were obtained from the aforementioned particle simulation study, already described with reference to FIGS. 3,  4  and  5 . 
     FIG. 6 is composed of FIGS.  6 (A) and  6 (B) both of which show the electron beam  42  normalized in axial momentum vs axial distance for two separate large-orbit simulations, similar to each other except for the amount of canonical angular momentum P θ  spread. FIG.  6 (A) illustrates the normalized axial momentum γβ z  shown by plot  90 , wherein the bucking coils  38  and  40  are completely activated (no P θ  spread). Conversely, FIG.  6 (B) illustrates the normalized axial momentum γβ z  shown by plot  92  resulting from the bucking coils  38  and  40  being turned-off, thereby, providing for an axial velocity spread of 11.2% at α=1.83. The large velocity spread indicates that the P θ  quantity is one of the main contributors that cause for velocity spread in large-orbit beams. 
     FIG. 7 is composed of FIGS.  7 (A), (B) and (C) all related to small-orbit operations of gyrotron device  10 . FIG.  7 (A), (B) and (C) respectively illustrates plots  94 ,  96  and  98 , wherein, respectively, the bucking coils  38  and  40  are fully turned on, the bucking coils  38  and  40  are partially turned on, and the bucking coils  38  and  40  are turned off. The plot  94  indicates a final velocity spread of 3.9% at α=1.4, the plot  96  indicates a final velocity spread of 1.6% at α=1.35, and the plot  98  indicates a final velocity spread of 14.5% at α=1.2. A comparison between plots  94 ,  96  and  98  reveals that the gyrotron device  10 , in particular, the bucking coils  38  and  40  act as a means for controlling the velocity spread related to the small-orbit beam operation, and also that this velocity spread may be advantageously adjusted for various applications by the practice of this invention. 
     It should now be appreciated that the practice of the present invention provides for a means for controlling the axial velocity v z  spread, the gyrating electron transverse-to-axial velocity ratio α, as well as the electron beam guiding center, r g . These factors are controlled by the diode region  56 , the double-cusp region  58 , and the adiabatic compression region  60  carrying an adjustable and predetermined magnetic profile  64 . 
     It should therefore readily be understood that many modifications and variations of the present invention are possible within the purview of the claimed invention. It is, therefore, to be understood that, within the scope of the appended claims, the invention may be practiced otherwise than as specifically described.