although detailed illustrative embodiments are disclosed herein , other suitable structures and machines for practicing the invention may be employed and will be apparent to persons of ordinary skill in the art . consequently , specific structural and functional details disclosed herein are representative only ; they describe the preferred embodiments of the invention . in the following detailed description , like reference numerals will be used to refer to like or corresponding elements in the different figures of the drawings . referring to fig1 there is shown a complex extended interaction structure 10 with integral coupling and bunching section according to one embodiment of the present invention . in one embodiment the integral coupling and bunching section can be a coaxial waveguide section 11 . a coaxial waveguide is one having an inner conductor and an outer conductor . an electron beam 12 traverses the interaction structure through an electron beam channel 13 . the electron beam 12 enters the interaction structure 10 and passes across a first gap 14 of a first doubly re - entrant buncher cavity 16 . a doubly re - entrant cavity is one in which two sets of metallic boundaries extending into its interior . the electron beam 12 then passes through the coaxial waveguide section 11 . the coaxial waveguide section 11 has an inner conductor 20 and an outer conductor 22 . the electron beam 12 passes through a beam bunching channel 24 passing through the inner conductor 20 . the beam then passes through a cascade of electromagnetically coupled doubly re - entrant energy extraction cavities . the cascade of doubly re - entrant extraction cavities is comprised of a second cavity 26 having a second gap 28 , a third cavity 30 having a third gap 32 , a fourth cavity 34 having a fourth gap 36 and a fifth cavity 38 having a fifth gap 40 . the electron beam 12 leaves the interaction structure 10 after passing across the fifth gap 40 . the cavities 16 , 26 , 30 , 34 , 38 resonate , creating gap voltages 42 , 44 , 46 , 48 , 50 across the gaps 14 , 28 , 32 , 36 , 40 , respectively . fig1 shows the shape of one of the cavities of the interaction structure 10 along with a computer simulation showing electric field lines 52 . a gap voltage across the gap 54 generates the electric field lines 52 flowing from the cavity into the electron beam channel 13 . returning to fig1 the electric fields of the buncher cavity 16 cause velocity modulation of the electron beam 12 . the velocity modulation of the electric beam 12 causes bunching of the electron beam 12 as it drifts through the substantially field - free beam bunching channel 24 . the bunched electron beam 12 then transfers energy to the electric fields of the cascade of energy extraction cavities 26 , 30 , 34 , 38 . the electromagnetic energy 61 is extracted from the interaction structure through an output window 60 of electromagnetically coupled to the cascade of energy extraction cavities 26 , 30 , 34 , 38 . each of the energy extraction cavities 26 , 30 , 34 , 38 , is coupled to the following cavity through coupling slots in the walls of the cavities . the cascade of energy extraction cavities 26 , 30 , 34 , 38 is coupled to and provides feedback to the buncher cavity 16 through a wave channel 56 passing between the inner 20 and outer 22 conductors of the coaxial waveguide section 11 . a tuner 58 can be installed in the coaxial waveguide section 11 . the tuner 58 has a portion adjustably extending into the wave channel 56 and serves to tune the resonant frequency of the interaction structure 10 , creating a feedback condition so that the cavities will oscillate . the interaction structure of the present invention has characteristics similar to those of a periodically loaded waveguide . the axial profile of the wave function in a periodically loaded waveguide is periodically distorted by the wall loading , resulting in an infinite number of spatial fourier components . all components have the same group velocity , but different phase velocities . a stack of coupled cavities terminated by conducting plates at both ends results in a field that is the superposition of two propagating waves of equal amplitude and oppositely directed group velocity . the two propagating waves form a standing wave corresponding to an integer multiple of a half guide wavelength along the structure . a resonator with “ n ” cavities has a total of “ n ” cavity resonances and “ n - 1 ” coupling slot resonances . cold test models ( no electron beam ) were built in the c - band to compare the properties of the complex extended interaction structure of the present invention to that of an interaction structure without the integral coupling and bunching section . each of the models has five cavities and four slots coupling the cavities to each other . the models do not include the tuner 58 or the output window 60 . fig1 a shows a graph of the cavity and slot resonance frequencies of the model without the integral coupling and bunching section . the resonances of the cavities are shown at 62 , 64 , 66 , 68 , 70 and the resonances of the slots are shown at 72 , 74 , 76 , 78 : fig1 b shows a graph of the cavity and slot resonance frequencies of the model having the integral coupling and bunching section separating the first and second cavities . the resonances of the cavities are shown at 80 , 82 , 84 , 86 , 88 and the resonances of the slots are shown at 90 , 92 , 94 , 96 . thus “ n ” cavity resonances and “ n - 1 ” coupling slot resonances are shown in the graphs . the length of the wave channel separating the first and second cavities is approximately a half wavelength of the “ 2π ” or “ 0π ” cavity mode ( indicated at 62 , 80 in fig1 a and 13b , respectively ). consequently , the resonant frequency of the 2π cavity remains substantially unchanged , as shown by 62 , 80 in fig1 a and 13b , respectively , while those of the other cavity resonances are modified by the addition of the integral coupling and bunching section . fig1 a is a graph showing the relative field strengths for the 2π cavity resonance at the five doubly re - entrant cavity gap positions of the c - band cold test models both with the integral coupling and bunching section ( illustrated by “ o ” in the figure “) and without the integral coupling and bunching section ( illustrated by “ x ” in the figure “). each of the models exhibit very similar gap voltage profiles for this mode . fig1 b is a graph showing the relative field strengths for the π / 5 cavity resonance at the five doubly re - entrant cavity gap positions of c - band cold test models both with the integral coupling and bunching section ( again illustrated by “ o ” in the figure “) and without the integral coupling and bunching section ( again illustrated by “ x ” in the figure “). the π / 5 cavity mode is indicated at 64 , 82 in fig1 a and 13b , respectively . the gap voltage profiles of the π5 mode illustrated in fig1 b , as expected , are significantly different from those of the 2π mode illustrated in fig1 a . although the field null of the π / 5 has been shifted from the third gap to the second gap due to the insertion of the integral coupling and bunching section , the gap field profiles for the two configurations are not significantly different . these tests indicate that insertion of the integral coupling and bunching section produces a relatively small effect on the basic properties of the resonant modes , especially those of the 2π cavity if the wave channel of the integral coupling and bunching section is chosen to be a half wavelength of the mode . fig1 illustrates a ku - band oscillator 128 based on the interaction structure 10 . by scaling the various parameters , the present invention can be used to design and construct oscillators having other frequency bands as well . the main body includes the complex extended interaction structure 10 , a double - anode pierce electron gun 118 , and a two - stage depressed collector 120 . other types of electron guns can be used with the invention to produce other types of electron beams . the interaction structure 10 , electron gun 118 , collector 120 , tuner 58 , and output window 60 are connected with high to ultra - high vacuum connections . the magnetic field is provided by a permanent magnet assembly which employs high performance ndfeb material . fig1 shows the focusing magnet system 154 with calculated magnetic field contours 156 . calculated ( indicated by squares ) and measured ( indicated by triangles ) magnetic field profiles are shown in fig1 . the vertical axis illustrates the axial magnetic field , measured in gauss , and the horizontal axis illustrates the axial distance , measured in centimeters , along the oscillator with the cathode serving as the “ 0 cm ” reference point . fig1 plots the radial profile of the electron gun 118 along its center or “ z - axis ”. the axis begins at the cathode 166 , designated as “ 0 cm ”, and extends to the right towards the interaction structure 10 . the figure shows a focus electrode 167 , a first anode 168 and a second anode 170 of the electron gun 118 . superimposed on the electron gun radial profile are equipotential lines 172 , the electron beam profile 12 as well as the axial magnetic field profile 174 of fig1 . the left vertical axis thus measures the radius , in centimeters , of the electron gun 118 , equipotential lines 172 and electron beam 12 along the electron gun &# 39 ; s center axis . the right vertical axis measures the magnetic field , in gauss , along the electron gun &# 39 ; s center axis . the perveance of the electron gun ( calculated and measured ) is 0 . 24 × 10 − 6 . the interaction structure 10 , at ground potential , forms a part of the second anode . fig2 plots the ω - β or dispersion diagram of the ku - band uniformly stacked coupled - cavity structure as constructed from the measured resonant frequencies of the cavity modes . electron beam and rf field interaction structure of fig1 can be divided by its principal effect into the electron bunching section 98 and the energy extraction section 100 . phase synchronism for extended interaction in the energy extraction section requires : where ν b is the beam velocity and ν ph (= ω / β ) is the phase velocity of the interacting rf component . the ω - β diagram of fig2 thus fixes the electron velocity by equation 1 and hence the operating voltage of the electron gun used to produce the electron beam 12 . the β = 0 mode ( referred to as he 2π mode ) normally has the largest coupling impedance , because the electron beam can be synchronized to experience the maximum field at all of the cavity gaps as illustrated in fig1 a . the interaction structure was designed for beam - wave interactions in the second spatial harmonic of the 2π mode ( the 4π component ). the bunching channel 24 allows for bunching of the electron beam 12 . by changing the length of the bunching channel 24 , the oscillator 128 can operate in different modes . the ku - band oscillator 128 was thus operated in the π / 5 mode . for the oscillation to take place in the interaction structure configuration of fig1 the phase shift around a complete loop between the first and second cavities 16 , 26 must be an integer multiple 2π . this condition is written as : in equation [ 2 ], ω is the resonant frequency , δφ is the phase lag of the second gap 28 with respect to the first 14 , where τ is the transit time of the electrons through the coaxial section 11 and the length l of the beam bunching channel 24 is expressed in terms of the wavelength λ by a multiplication factor α . the π / 2 term in equation [ 2 ] accounts for the 90 ° difference between the maximum ac velocity and maximum ac density . this is because electron bunches form around those electrons which are not velocity modulated in the first gap . substituting equation [ 3 ] into equation [ 2 ], the wavelength cancels out , resulting in : in addition to meeting the requirements of equation [ 4 ], a threshold beam current is also required to start the oscillation in the interaction structure . in equation [ 4 ], ν b can be varied by electron beam voltage adjustment and δφ can be varied by tuning of resonant frequency . the beam voltage is restricted by equation [ 1 ] for synchronous interaction of the beam 12 and wave in subsequent cavities , so the tuner 58 is installed in the coaxial waveguide section 11 to tune the relative phase angle δφ . the optimum drift length for the beam bunching channel 24 must also be determined . when the space force is taken into consideration , the ac beam current reaches its maximum value at a quarter of a plasma oscillation length following the velocity modulation . hence , the optimum distance between the first 14 and second 28 gaps is written : in equation [ 5 ], ω q is the reduced plasma frequency defined as ω = f ( n b e 2 / ε o m e ) ½ [ 6 ] where n b is the electron density , m e is the electron mass , e is the charge of an electron and f is the reduction factor which depends on the beam 12 and beam bunching channel 24 radii . parameters for the calculation of the optimum drift length based on the maximum operating beam current and comparison with the actual drift length 148 used in the ku - band oscillator 128 . the shape and dimensions for each one of the cavities of the ku - band structure is shown in fig1 . the cavity radius 122 should be approximately 0 . 313 cm and the cavity length 124 should be approximately 0 . 56 cm . as illustrated in fig4 coupling slots of the first two cavities are aligned at the same azimuthal position and connected by the wave channel 56 of the coaxial section 11 . the length of the coaxial wave channel is a half wavelength ( 0 . 89 cm ) of the 2π mode . tuning of the relative phase angle between the first two gaps [ δφ in equation 4 ] is achieved by a ceramic plunger radially inserted into the wave channel 56 of the coaxial section 11 by using the tuner 58 . alternatively , other suitable materials can be inserted into the wave channel 56 using other methods in order to tune the relative phase angle . coupling slots of the energy extraction cavities are alternately aligned at opposite ends of a diameter . the axial period 126 as illustrated in fig1 is set to 0 . 74 cm . the oscillator was operated in the π / 5 mode , but as a result of the electron bunching the oscillator can be made to operate in any other mode by providing coaxial electron drift sections with different lengths . this property distinguishes the present invention from conventional eio &# 39 ; s which can only obtain optimal efficiency and output in the 2π mode . table 2 lists the operating parameters for the first oscillator . for the purpose of comparison , a second five - cavity oscillator was also built with identical components but without the coaxial section . table 2 also lists the operating parameters for the second oscillator . fig2 a and 21b illustrate test results for oscillator # 2 and oscillator # 1 respectively . the vertical axes indicate power , measured in watts , and efficiency , while the horizontal axes indicate beam current measured in milliamps . the figures illustrate output power , electronic efficiency and overall efficiency as a function of the beam current . comparison of fig2 b with fig2 a clearly indicates a significant efficiency enhancement due to the insertion of the coaxial section 11 . ballistic bunching in the coaxial section 11 improves continuously with increasing beam current , as is evidenced by the continued rise of the electronic efficiency in fig2 b . on the other hand , as illustrated in fig2 a , the electronic efficiency of oscillator # 2 , without the coaxial section , tends to saturate early during the rise of the beam current . this is a further indication of the greater power capability of the interaction structure of the present invention . fig2 - 12 illustrate the pieces used in constructing the ku - band interaction structure 10 of one embodiment of the present invention . first , referring to fig2 and 4 , the interaction structure 10 is constructed from a first cavity piece 102 , a left coaxial section piece 104 , a right coaxial section piece 106 , a second cavity piece 108 , a third cavity piece 110 , a fourth cavity piece 112 and a fifth cavity piece 114 . the pieces can be machined from stainless steel , aluminum , copper , or combinations of materials selected to provide the proper strength and conductivity for the cavity walls . the electron beam channel 13 passes through the interaction structure 10 . water cooling channels 116 can be passed through the interaction structure 10 . cooled water can be circulated through the water cooling channels 116 in order to remove heat from the interaction structure 10 caused by electromagnetic ohmic heating and interception of the electron beam 12 by the walls of the structure . as illustrated in fig3 the pieces are attached together using conventional vacuum connection techniques to form a common vacuum between the cavities , wave channel 56 and the electron beam channel 13 . the vacuum can be such that the oscillator operates at a pressure in the range of 10 − 7 to 10 − 9 torr . for example grooves can be machined in the faces of the pieces and o - rings inserted in the grooves . the pieces can then be forced together to form a vacuum connection utilizing screws passing through holes also passing through the faces . alternatively , circular knife edges can be machined into the faces and copper gaskets positioned so that the knife edges dig into the copper upon tightening of the screws . fig5 a and 5b show the first cavity piece 102 of the interaction structure of fig2 , 4 . the first cavity piece 102 includes a portion of the first cavity 16 as well as portions of the water cooling channels 116 . passing through the center of the first cavity piece 102 is the electron beam channel 13 . fig6 a and 6b show the left coaxial section piece 104 of the interaction structure of fig2 . the left coaxial section piece 104 includes a portion of the first cavity 16 , a portion of the wave channel 56 as well as portions of the water cooling channels 116 . passing through the center of the left coaxial section piece 104 is a portion of the beam bunching channel 24 section of the electron beam channel 13 . a first coupling slot 130 is formed in an end wall of the first cavity 16 for coupling to the wave channel 56 . as shown in fig2 and 4 , the left coaxial section piece 104 has a portion of a tuner port 140 machined to accommodate a portion of the tuner 58 . fig7 a and 7b show the right coaxial section piece 106 of the interaction structure of fig2 , 4 . the right coaxial section piece includes a portion of the second cavity 26 , a portion of the wave channel 56 as well as portions of the water cooling channels 116 . passing through the center of the right coaxial section piece 106 is a portion of the beam bunching channel 24 section of the electron beam channel 13 . a second coupling slot 132 is formed in an end wall of the second cavity 26 for coupling between the wave channel 56 and the second cavity 26 . as shown in fig2 and 4 , the right coaxial section piece 106 also has a portion of the tuner port 140 machined to accommodate a portion of the tuner 58 . fig8 a and 8b show the second cavity piece 108 of the interaction structure of fig2 , 4 . the second cavity piece 108 includes a portion of the second cavity 26 , a portion of the third cavity 30 , as well as portions of the water cooling channels 116 . passing through the center of the second cavity piece 108 is a portion of the electron beam channel 13 . a third coupling slot 134 is formed in the end wall connecting the second cavity 26 and the third cavity 30 . as shown in fig2 and 4 , the second cavity piece 108 also has a portion of an output window port 142 machined to accommodate a portion of the output window 60 . fig9 a and 9b show the third cavity piece 110 of the interaction structure of fig2 , 4 . the third cavity piece 110 includes a portion of the third cavity 30 , a portion of the fourth cavity 34 , as well as portions of the water cooling channels 116 . passing through the center of the third cavity piece 110 is a portion of the electron beam channel 13 . a fourth coupling slot 136 is formed in the end wall connecting the third cavity 30 and the fourth cavity 34 . the third cavity piece 110 also has a portion of the output window port 142 machined to accommodate a portion of the output window 60 . fig1 a and 10b show the fourth cavity piece 112 of the interaction structure of fig2 , 4 . the fourth cavity piece 112 includes a portion of the fourth cavity 34 , a portion of the fifth cavity 38 , as well as portions of the water cooling channels 116 . passing through the center of the fourth cavity piece 112 is a portion of the electron beam channel 13 . a fifth coupling slot 138 is formed in the end wall connecting the fourth cavity 34 and the fifth cavity 38 . the fourth cavity piece 112 also has a portion of the output window port 142 machined to accommodate a portion of the output window 60 . fig1 a and 11b show the fifth cavity piece 114 of the interaction structure of fig2 . the fifth cavity piece 114 includes a portion of the fifth cavity 38 as well as portions of the water cooling channels 116 . passing through the center of the fifth cavity piece 114 is a portion of the electron beam channel 13 . fig1 shows an enlarged view a cavity inner end wall of the cavities illustrated in fig6 a , 6 b , 7 a , 7 b , 8 a , 8 b , 9 a , 9 b , 10 a , 10 b . the electron beam channel 13 extends through the center and a coupling slot 146 represents one of the coupling slots 130 , 132 , 134 , 136 , 138 for coupling between the cavities . the interaction structure of the present invention is not limited to utilizing a single integral coupling and bunching section . additional integral coupling and bunching sections can be utilized in an interaction structure 160 . further , the interaction structure of the present invention is not limited to five cavities . a greater or lesser number of cavities can be used . for example , fig2 shows a six cavity embodiment of the present invention utilizing two coaxial sections 150 , 152 . each of the coaxial sections 150 , 152 has a tuner port 162 , 164 extending into its respective wave channel . the power leaves the interaction structure 160 through an output port 176 . while the above description contains many specific features of the invention , these should not be construed as limitations on the scope of the invention , but rather as exemplary embodiments thereof . many other variations are possible . accordingly , the scope of the invention should be determined not by the embodiments illustrated , but by the appended claims and their legal equivalents .