US3325677A

US3325677A - Depressed collector for crossed field travelling wave tubes

Info

Publication number: US3325677A
Application number: US322330A
Authority: US
Inventors: James E Orr
Original assignee: Litton Precision Products Inc
Current assignee: Northrop Grumman Guidance and Electronics Co Inc
Priority date: 1963-11-08
Filing date: 1963-11-08
Publication date: 1967-06-13
Anticipated expiration: 1984-06-13

Description

J. E. ORR

Luoooooooooo Original Filed April 5, 1962 DEPRESSED COLLECTOR FOR CROSSED FIELD TRAVELLING WAVE TUBES June 13, 1967 INVENTOR. J4me; i 6 Z/ ,2

/ z/wa United States Patent 3,325,677 DEPRESSED COLLECTOR FOR CROSSED FIELD TRAVELLING WAVE TUBES James E. Orr, Redwood City, Calif., assignor to Litton Precision Products, Inc., San Carlos, Califl, a corporation of Delaware Continuation of application Ser. No. 185,270, Apr. 5, 1962. This application Nov. 8, 1963, Ser. No. 322,330 3 Claims. (Cl. 3153.3)

This application is a continuation of my application Ser. No. 185,270, filed Apr. 5, 1962, now abandoned.

This invention relates to electron discharge devices and more particularly to an improved electron collection ar rangement in a crossed field travelling wave electron discharge device.

There is a class of electron discharge devices in which a travelling electromagnetic wave is propagated along a slow wave structure such that the phase velocity of the wave is in the range of speeds which can readily be obtained by electrons from relatively simple electron guns. In such devices an electron beam is projected along or through the slow wave structure and the individual electrons in the beam interact with the travelling wave to provide a net transfer of energy from the electron beam to the travelling electromagnetic wave.

Such devices fall into two classes, these being the linear beam, or O-type devices, and the crossed field, or M-type devices.

In the linear beam, or O-type device, a conventional electron gun accelerates electrons from the cathode and the resultant electron .beam is projected along a slow wave structure. The classical slow wave structure for use in such devices is a helix, and the electron beam is conventionally projected along the axis of the helix. The accelerator electrode of the electron gun is usually maintained at ground potential, as is the slow wave structure, and the cathode is maintained at a relatively high negative voltage with respect to ground. No magnetic field is involve-d in such devices except as may be used to maintain the electron beam in focus, and then the focusing magnetic field plays no part in the interaction between the electron beam and any wave travelling on the slow wave structure.

At this point it is noted that the unfortunate arbitrary selection of electricity polarity at a time when little was known about the nature of electricity, results in much confusion of terminology in reference to voltages, potential, and charges. For present purposes, any electrical current is, in fact, to be understood as the unidirectional motion of negatively charged electrons and that in electronic devices such motion of electrons occurs from negative toward more positive electrodes. As is well known to those skilled in the art, an electron has greater potential energy when it is at a location in an electrostatic field which is at a greater negative voltage and thus throughout the present specification the conventional designation of voltage polarity is utilized, but any references to electrons being at relatively higher or relatively lower potential refers to electrons being at field locations which are at relatively more negative or relatively more positive voltages, respectively.

Continuing now the description of an O-type travelling wave tube, the electrons are accelerated from a region of high potential, the cathode, past the accelerating anode and thus their entire energy is kinetic energy, since, as was previously stated, the anode and slow wave structure are being maintained at ground potential. The beam of electrons interacts with an electromagnetic wave propagating on the slow wave structure and there is a net overall decrease in the average velocity of the electrons 3,325,677 Patented June 13, 1967 and thus a net overall decrease in the kinetic energy of the electron beam. This energy is transferred to the electromagnetic wave and, by proper choice of design parameters, the device may function either as an amplifier to increase the strength of an applied electromagnetic wave or as an oscillator tube. i.e., it operates as a source of electromagnetic wave energy.

When the electron beam has traversed the entire slow wave structure and has left the region of interaction with the electromagnetic wave, it must then be collected and returned to the cathode of the electron gun. The conventional manner of collecting the electron beam in an O-type device is to position a collector electrode, which also is maintained at ground potential, directly across the path of the electron beam as it leaves the interaction region. The electrons impinging on the collector electrode are then returned through the power source to the cathode of the electron gun.

It was observed quite early in the development of such devices that the collector electrode became heated to high temperature by the impinging electron beam and it was frequently found necessary to provide some means for cooling the collector to prevent it from being melted by the impinging electron beam. Of course, any such heating of the collector electrode, whether cooled or not, results in a decrease in the overall efiiciency of the device, since the thermal energy represented by this heating, as supplied from the power source of the device, constitutes an energy loss.

As the design of such devices became more sophisticated, it was recognized that this collector electrode heating could be reduced, and thus the overall efficiency of the devices increased, by maintaining the collector electrode at some voltage intermediate the cathode voltage and the slow wave structure voltage. The potential of this collector electrode, frequently termed a depressed collector, is then higher than that of the slow wave structure and the accelerating electrode of the electron gun, but less than that of the cathode of the electron gun. The electrons in the beam, upon leaving the interaction region, then approach the collector electrode by motion against a potential gradient and the electrons must give up kinetic energy by slowing down in order to approach or reach the collector, since the law of conservation of energy requires that the sum of the potential and kinetic energy of each electron remains constant. The electrons are thus collected at lower velocities and there is less heating of the collector electrode.

Ideally, the collector electrode would be maintained at such a potential that the electrons can just reach it and thus impinge upon it at zero velocity. However, since the electrons have delivered different amounts of energy to the electromagnetic wave on the slow wave structure and thus leave the inter-action region with dilfering velocities, the collector electrode must be maintained at a potential no higher than that which sets up a field gradient such that the work to be done by the electron when moving against the gradient can be delivered by the kinetic energy of the slowest electron leaving the interaction region so that even this slowest electron can be collected, and is not repelled. Any electrons faster than the slowest electron impinge upon the collector with a finite velocity and thus finite kinetic energy, and this kinetic energy is then lost as heat in the collector electrode.

A crossed field, or M-type, travelling wave electron discharge device ditfers in several important respects from the linear beam, or O-ty-pe device, which was just described. In the crossed field device, there is spaced from the slow wave structure, which may conventionally take the form of an interdigital delay line, a sole electrode, which is usually everywhere at an equal distance from the slow wave structure. Thus, the sole electrode may be parallel to the slow wave structure in a physically linear tube, or may be concentric with the slow wave structure in a physically circular tube. An electrostatic field is established between the sole electrode and the slow wave structure. Conventionally, the slow wave structure is maintained at ground potential and a relatively high negative voltage is applied to the sole electrode, thereby impressing on it a relatively high potential in the meaning of the term as defined above. A magnetic field is provided which is transverse to the electrostatic field throughout the interaction region between the slow wave structure and the sole electrode.

An electron gun is positioned at one end of the interaction region to inject electrons into the interaction region in a direction substantially parallel to the slow wave structure and the sole electrode. Conventionally, the cathode of the electron gun is maintained at a potential intermediate that of the slow wave structure and that of the sole electrode. 7

As is well known to those skilled in the art, such a crossed electrostatic-magnetic field arrangement provides for velocity sorting of any electrons traversing the region, in which electrons having an initial velocity of E/ B, where E represents the intensity of the electrostatic field and B rep-resents the intensity of the magnetic field, continue down the interaction region parallel to the sole electrode and the slow wave structure, and in which the electrons having a velocity slower than E/B are drawn by the electrostatic field towards the slow wave structure and the electrons having a velocity faster than E/B are deflected by the magnetic field towards the sole electrode. In practice, the electron guns used in such devices are designed to supply electrons having as near this velocity as possible so that a maximum number of electrons traverses the length of the interaction region when there is no interaction between the electrons and any electromagnetic wave being propagated on the slow wave structure.

When the electron beam enters the interaction region, the individual electrons of the beam have a substantially uniform kinetic energy, which is a function of the accelerating field in the electron gun, and a potential energy which is a function of the electrostatic potential of the location in which the beam is injected into the interaction region. When an electromagnetic wave having a phase velocity which is substantially equal to the velocity of the electron beam is being propagated on the slow wave structure, an injected electron may enter the interaction region at a time at which the electrical field component of the wave tends either to draw the electron towards the slow wave structure or to force the electron nearer the sole electrode.

Since the slow wave structure is being maintained at ground potential, as was previously described, those electrons which are attracted closer to the slow wave structure find themselves in a region of lower potential, and give up a portion of their potential energy to the electromagnetic wave. Some electrons actually strike the slow wave structure, thus being collected, and give all their potential energy to the wave. This energy transfer may be viewed in either of two ways. In the first of these, the crossed fields may be thought to maintain the electrons at a uni form velocity and as the electron is drawn by the wave into a region of lower potential, that portion of the poten- 'tial energy of the electron greater than that of the region of lower potential into which it enters is delivered to the electromagnetic wave. In the second of these, the electron may be considered to interact with the travelling wave and deliver a portion of its kinetic energy to the wave. This results in a decrease of velocity of the electron and the slowed electron is drawn by the electrostatic field closer to the slow wave structure. In so doing the electron fans to a region of lower potential; thus it is immediately accelerated by the electrostatic field back to its initial velocity, but is now in a region of lower potential.

In either event it is seen that the net result is that the electron delivers potential energy to the electromagnetic wave and that in a crossed field device energy is delivered to the travelling wave in a fundamentally different man ner than in the linear beam, or *O-type device.

Conversely, those electrons which enter the interaction region in a region of an electric field which tends to force the electrons away from the slow wave structure and towards the sole electrode are driven into an area of higher potential. These electrons must extract energy from the travelling wave in order that they may take on a greater potential energy themselves. Those electrons which are attracted towards the slow wave structure, thereby delivering energy to the travelling Wave, are termed favorably focused electrons; while those which are attracted towards the sole electrode, thereby extracting energy from the travelling wave, are termed unfavorably focused electrons. The favorably focused electrons tend to be drawn more and more into the electromagnetic wave and thus continue to deliver their potential energy to the wave, While the unfavorably focused electrons are driven away from the electromagnetic wave and tend to take less and less energy from the wave as they approach the sole electrode. There is thus a net transfer of energy from the electron beam to the electromagnetic wave. By proper choice of design parameters, crossed field devices also can be designed either as amplifiers or oscillators.

When the electrons have traversed the entire interaction region they must be collected and returned to the cathode of the electron gun. Again, the conventional method of electron collection in the prior art is to provide a collector electrode at the end of the interaction region, which collector electrode is maintained at ground potential. Those skilled in the art are aware that a collector electrode at such a potential is heated by the impinging electron beam in a similar manner as was described in connection with the O-type devices previously, and that such heating, and the resultant thermal losses, decreases the overall efficiency of the device.

From a superficial examination it would appear that the collector electrode could again be operated at a depressed voltage, i.e., at a higher potential, than the slow wave structure and that a higher efiiciency in electron collection could then be obtained as is the case in O-type devices. However, because of the previously described fundamental difference in the nature of operation of the M-type and the O-type devices, such a collector electrode arrangement cannot be satisfactorily utilized. This is because electrons may leave the interaction region of an M-type device with a constant velocity but with any potential between that of the sole electrode and that of the slow wave structure, depending upon the position in the interaction region which the electron occupies at the time it leaves the interaction region. Thus, the collector electrode must be operated at a potential sufiiciently low to collect even those electrons which are at ground potential, because, if the collector is operated at any higher potential, some of the electrons will not have sufiicient energy to reach the collector electrode. 7

It is accordignly an object of the present invention to provide an improved crossed field travelling device.

It is another object of the present invention to provide an improved electron collection arrangement for a crossed field travelling wave device in which the electrons are more efiiciently collected.

It is yet another object of the present invention to provide an improved crossed field travelling wave device in which a collector electrode is efficiently operated at a higher potential than the slow wave structure upon which all electrons in the collection region which have suflicient energy to reach this higher potential are collected.

Briefly stated, and in accordance with one embodiment of the present invention, a crossed field travelling wave device such as was described is provided with two collector electrodes in the collector region. One of these colleector electrodes, which may be termed the conventional collector electrode, is positioned on the same side of the electron beam as is the slow wave structure and is maintained at slow wave structure potential. The other collector electrode, which may be termed the depressed collector electrode, is maintained on the same side of the electron beam as is the sole electrode and is held at some higher potential, conveniently cathode potential. Most electrons entering the collector region are the previously discussed unfavorably phase focused electrons, since most of the favorably focused electrons are collected on the slow wave structure in the interaction region. These electrons entering the collector region thus have sufiicient energy to return to cathode potential and are efficiently collected at greatly reduced velocity on the surface of the depressed collector. The remaining electrons which do not have such suificient energy are collected on the surface of the conventional collector.

For a complete understanding of the invention, together with other objects and advantages thereof, reference may be 'had to the attached drawings, in which:

FIGURE 1 is a schematic representation of a crossed field backward wave oscillator and power supply circuit therefor in accordance with the present invention;

FIGURE 2 is a graphic illustration of the electron density of the electron beam as it leaves the interaction region as a function of the position between the sole electrode and slow wave structure in a typical crossed field travelling wave device; and

FIGURE 3 is an enlarged view of the collector region of the device of FIGURE 1 and illustrates how electrons are efiiciently collected at low velocities on the surface of the depressed collector.

Referring now to FIGURE 1, therein is shown a schematic representation of a crossed field backward wave oscillator which embodies the present invention. It is to -be expressly understood, however, that the invention is not limited to utilization in backward wave oscillators, but is equally applicable to any form of crossed field travelling wave device such as a forward wave amplifier. Also, the device may be circular in form, instead of the shown linear device. The device includes a suitable vacuum envelope, represented schematically by the dash line 12, and magnetic pole pieces 14 for establishing a magnetic field of intensity B within the device. The magnetic field is represented by the encircled X in the device. An electron gun consisting of a cathode 16, a grid 18, and an accelerator electrode is positioned at one end of device 10. A sole electrode 24 and a slow Wave structure 26 define an interaction region 28 in which the electron beam from the electron gun interacts with a backward wave on slow wave structure 26. Slow Wave structure 26 is shown to be a conventional interdigital delay line but the invention is not limited to use with such a delay line, but may be used with any desired form of slow wave structure. Slow wave structure 26 is terminated in a suitable attenuator 34 which attenuates any forward waves on slow wave structure 26. The electron collector region includes a conventional collector 36 positioned adjacent the slow wave structure 26 and a depressed collector 32 having a curved surface 46 adjacent the sole electrode 24. The operation of this improved electron arrangement will be later described in detail.

As shown in FIGURE 1, slow wave structure 26, attenuator 34, and conventional collector 36 are maintained at ground potential. Variable voltage source V applies a relatively large negative voltage to cathode 16; voltage source V applies a negative voltage relative to cathode 16 to sole electrode 24, voltage source V applies a negative voltage relative to cathode 16 to grid 18 and voltage source V applies a positive voltage relative to cathode 16 to accelerate cathode 20.

The operation of the electron gun is well known to those skilled in the art. Electrons emitted from cathode 16 are accelerated by the electric field established between cathode 16 and accelerator electrode 20. The magnetic field B deflects the electrons into the interaction region 28, in which region the electron beam is subjected to the crossed electric field of intensity E established between sole electrode 24 and slow wave structure 26 by voltage sources V and V and the magnetic field of intensity B established by magnetic pole pieces 14. As is well known to those skilled in the art and as was previously described, the electrons seek to maintain velocity E/B and to traverse down the interaction region 28 in the direction normal to both the electric field E and the magnetic field B. In so travelling, the electrons interact with an electromagnetic wave travelling on slow wave structure 26 and there is a net transfer of energy from the beam to the travelling wave. In the shown backward Wave oscillator, electromagnetic wave energy is removed from slow wave structure 26 by any suitable output means 30.

As was previously described, the favorably focused electrons are drawn closer and closer to the slow wave structure 26, delivering their potential energy to the travelling wave while maintaining a constant velocity, until in a suitably designed device essentially all such electrons are collected on the slow wave structure 26. The unfavorably focused electrons extract energy from the travelling wave and move closer to the sole electrode, thereby entering a region of higher potential and having a net energy greater than they had at the time they left the cathode.

FIGURE 2 shows a graphic representation of the electron intensity in the region between the slow wave structure 26 and sole electrode 24 at the end of the interaction region just prior to the electrons entering the collector region. As shown therein, most of the remaining uncollected electrons are located in a region relatively close to the sole potential just beneath the point of cathode potential between the slow wave structure and the sole electrode. In the prior art devices, all electrons in the collector region were collected by a collector electrode at ground potential and thus these electrons were accelerated as they approached this ground potential electron and their entire energy was dissipated as heat on the surface of the collector electrode. This resulted in two major problems in the prior art devices, the first being the obvious decrease in efficiency caused by this loss of energy and the second being the excess heating of the collector electrode which must dissipate all the energy of the electrons leaving the interaction region.

FIGURE 3 shows an enlarged view of the collector region of the device 10 of FIGURE 1 and illustrates how, in accordance with the present invention, most of the electrons on the collector region are efficiently collected at cathode potential, thereby recovering most of their potential energy, and at relatively low velocities, thereby causing less heating of the collector electrode surfaces, to overcome the above discussed disadvantages of the prior art devices. The dashed lines 38 and 40 represent the trajectories of electrons leaving the interaction region 28 and entering the collector region of the device. It will be appreciated by those skilled in the art that since depressed collector electrode 32 is maintained at a lower potential than is sole electrode 24, that the electrons leaving the interaction region 28 abruptly enter a region in which the E/B ratio is substantially decreased. Since the velocity of the electrons leaving the interaction region 28 is defined by the E/B ratio in the interaction region, these electrons appear in the collector region to be injected electrons having an initial velocity substantially 'higher than the new synchronous velocity E/B established in the collector region and, as is well known to those skilled in the art, such electrons having a higher velocity tend to follow a cycloidal pattern such as is represented 'by the dashed line 40, making a complete loop and continuing in their initial direction. The position of depressed collector electrode 32 is chosen such that the electrons occupying the position represented by point 42 of the graph of FIGURE 2 follow the trajectory 38 of FIGURE 3 and these electrons are collected at the bottom point of their loop on the surface 46 of the depressed collector 32. The velocity of the electrons at this point in their cycloidal loop is substantially zero and the electrons are thus collected with substantially no kinetic energy. Those electrons which are positioned between the point 42 and sole electrode 24 as they leave interaction region 28 are collected with a finite velocity on depressed collector electrode 32 at some point prior to that shown by trajectory 38 while those electrons which are positioned between point 42 and slow wave structure 26 as they leave the interaction region 28 follow trajectories such as trajectory 40 and are collected on conventional electrode 36. These latter mentioned electrons do not have suflicient total potential and kinetic potential energy to again reach cathode potential.

The collection of these latter mentioned electrons on conventional collector electrode 36 is facilitated by having the surface 46 of depressed collector 32 curve upward toward conventional collector 36 so as to increase the electric field intensity in this region to attract the electrons closer to conventional collector 36.

It will be appreciated by those skilled in the art that the number of electrons collected on depressed collector 32 can be changed by varying the vertical position of depressed collector 32, with a greater proportion of the electrons being collected as depressed collector 32 is moved upward in the drawing. However, in accordance with the presently preferred embodiment of the present invention, depressed collector 32 is positioned so that the largest number of electrons, those represented at point 42 on the graph, are collected at zero velocity on surface 46 of depressed collector 32.

.It will be further appreciated by those skilled in the art that depressed collector 32 need not be operated at cathode potential but may be operated at any potential between that of slow wave structure 26 and sole electrode 34. However, several advantages accrue from utilizing cathode potential. These are that it is not necessary to provide an additional power supply and that depressed collector 32 may be internally connected to cathode 16, and a device incorporating the present invention may be placed directly in the socket of a prior art device which did not use such a depressed collector arrangement, whereby the advantages of the present invention may be utilized in existing equipment. Thus in the presently preferred embodiment of the invention, depressed collector 32 is maintained at cathode potential.

While the invention is thus disclosed and several embodiments described, the invention is not limited to these shown embodiments. Instead, many modifications will occur to those skilled in the art which lie within the spirit and scope of the invention. Accordingly it is intended that the invention be limited in scope only by the appended claims.

What is claimed is:

1. A crossed field travelling wave electron discharge device comprising, aslow wave structure, a sole electrode spaced from said slow wave structure and defining therewith an interaction region, means for establishing crossed electric and magnetic fields in said interaction region, means including a cathode positioned at one end of said interaction region for injecting an electron beam into said interaction region, and electron collecting means positioned at the other end of said interaction region, said collecting means including a first collector electrode maintained at the same potential as said cathode for collecting those electrons in the electron beam leaving said interaction region and having sufiicient kinetic and .potential energy to return to cathode potential 'and a second collector electrode maintained at the same potential as said slow wave structure for collecting the other electrons in said electron beam leaving said interaction region which have delivered energy to an electromagnetic wave on said slow wave structure in said interaction region and which no longer have sufiicient kinetic and potential energy to return to cathode potential.

2. A crossed field travelling wave electron discharge device comprising, a slow wave structure, a sole electrode spaced from said slow wave structure and defining therewith an interaction region, means for establishing crossed electric and magnetic fields in said interaction region, means including a cathode positioned at one end of said interaction region for injecting an electron beam into said interaction region, and electron collecting means positioned at the other end of said interaction region, said collecting means including a first collector electrode positioned adjacent said sole electrode and a second collector electrode positioned adjacent said slow wave structure, means for maintaining said first collector electrode at the same potential as said cathode for collecting those electrons in the electron beam leaving said interaction region and having sufiicient kinetic and potential energy to return to cathode potential and means for maintaining said second collector electrode at the same potential as said slow wave structure for collecting the other elec trons in said electron beam leaving said interaction region which have delivered energy to an electromagnetic wave on said slow wave structure in said interaction region and which no longer have sufiicient kinetic and potential energy to return to cathode potential.

3. A crossed field travelling wave electron discharge device comprising, a slow wave structure, a sole electrode spaced from said slow wave structure and defining therewith an interaction region, means for establishing crossed electric and magnetic fields in said interaction region, means including a cathode positioned at one end of said interaction region for injecting an electron beam into said interaction region, and electron collecting means positioned at the other end of said interaction region, said collecting means including a first collector electrode positioned adjacent said sole electrode and a second collector electrode positioned adjacent said slow wave structure, means for maintaining said first collector electrode at the same potential as said cathode for collecting those electrons in the electron beam leaving said interaction region and having suflicient kinetic and potential energy to return to cathode potential and means for maintaining said second collector electrode at the same potential as said slow wave structure, for collecting the other electrons in said electron beam leaving said interaction region which have delivered energy to an electromagnetic wave on said slow wave structure in said interaction region and which no longer have suflicient kinetic and potential energy to return to cathode potential, said first collector electrode having a curved electron collecting surface which converges toward the electron collecting surface of said second collecting electrode in the direction away from said interaction region;

References Cited UNITED STATES PATENTS 2,774,913 12/1956 Charles 31539.3 2,853,641 9/1958 Webber 3155.38 2,925,521 2/1960 Dench 31539.3 X 3,003,119 10/1961 Favre '315---39.3 X 3,073,991 1/1963 Osepchuk 315-35 X 3,084,278 4/1963 White 315--39.3 3,172,004 3/ 1965 Von Gutfeld et al. 315--3.5 3,188,515 6/1965 Kompfner 315--5.38

JOHN W. HUCKERT, Primary Examiner. DAVID J. GALVIN, Examiner.

A. J. JAMES, Assistant Examiner.

Claims

1. A CROSSED FIELD TRAVELLING WAVE ELECTRON DISCHARGE DEVICE COMPRISING, A SLOW WAVE STRUCTURE, A SOLE ELECTRODE SPACED FROM SAID SLOW WAVE STRUCTURE AND DEFINING THEREWITH AN INTERACTION REGION, MEANS FOR ESTABLISHING CROSSED ELECTRIC AND MAGNETIC FIELDS IN SAID INTERACTION REGION, MEANS INCLUDING A CATHODE POSITIONED AT ONE END OF SAID INTERACTION REGION FOR INJECTING AN ELECTRON BEAM INTO SAID INTERACTION REGION, AND ELECTRON COLLECTING MEANS POSITIONED AT THE OTHER END OF SAID INTERACTION REGION, SAID COLLECTING MEANS INCLUDING A FIRST COLLECTOR ELECTRODE MAINTAINED AT THE SAME POTENTIAL AS SAID CATHODE FOR COLLECTING THOSE ELECTRONS IN THE ELECTRON BEAM LEAVING SAID INTERACTION REGION AND HAVING SUFFICIENT KINETIC AND POTENTIAL ENERGY TO RETURN TO CATHODE POTENTIAL AND A SECOND COLLECTOR ELECTRODE MAINTAINED AT THE SAME POTENTIAL AS SAID SLOW WAVE STRUCTURE FOR COLLECTING THE OTHER ELECTRONS IN SAID ELECTRON BEAM LEAVING SAID INTERACTION REGION WHICH HAVE DELIVERED ENERGY TO AN ELECTROMAGNETIC WAVE ON SAID SLOW WAVE STRUCTURE IN SAID INTERACTION REGION AND WHICH NO LONGER HAVE SUFFICIENT KINETIC AND POTENTIAL ENERGY TO RETURN TO CATHODE POTENTIAL.