RF source including slow wave tube with lateral outlet ports

Multiple radio frequency (RF) outlet ports are provided along the side of a slow wave tube to establish a distributed RF output in response to the transmission of an e.sup.- beam through the tube. The tube has a periodically rippled inner surface, and the outlet ports are spaced along the tube by substantially integral numbers of ripple periods. When implemented as a backward wave oscillator, RF power is extracted during a single pass through the tube; a travelling wave tube amplifier implementation is also possible. The separation of the RF extraction from the absorption of the e.sup.- beam at the end of the tube eliminates RF reflections and permits water cooling of the e.sup.- beam absorber. The RF extraction ports are also preferably configured as built-in mode converters from a TM.sub.01 cylindrical tube mode to a TE.sub.10 rectangular extraction mode, with four symmetrically arranged rectangular extraction waveguides at each extraction location combining their energies into a single TE.sub.10 output. Reductions in the cylindrical tube diameter after each extraction location reflect radiation back through the tube to cancel back-scattered radiation losses from the extraction ports.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates to radio frequency (RF) radiation sources, and more 
particularly to slow wave tubes that are coupled with electron beams to 
provide an RF source and to related energy extraction mechanisms. 
2. Description of the Related Art 
High power slow wave structures commonly consist of a cylindrical waveguide 
with a periodically varying inner wall radius in the form of a periodic 
series of ripples. These structures support electromagnetic waveguide 
modes, with some waves having phase velocities less than the speed of 
light. Slow wave tubes have been coupled with electron (e.sup.-) beams 
directed along the tube axis to generate RF power, specifically in the 
microwave regime (10.sup.9 -10.sup.11 Hz). 
Two devices of this type are generally categorized as backward wave 
oscillators (BWOs) and travelling wave tube amplifiers (TWTAs), and are 
described in J. Swegle et al., Phys. Fluids, 28(9), Sep. 1985, pages 
2882-2894, and W. W. Destler et al., "Microwave and Particle Beam Sources 
and Propagation" SPIE Vol 873, (1988), pages 84-91. With a BWO, a 
spontaneous generation of microwave power occurs at a frequency that is 
determined by a combination of the tube geometry and the e.sup.- beam 
current and voltage. In plasma-filled devices the frequency is also 
dependent on the plasma density. Instabilities occur within the tube when 
the e-beam's slow space charge wave has the same phase velocity as a 
structure mode. Under these conditions the beam's slow space charge wave 
can develop, resulting in the deceleration of beam electrons as beam 
bunching occurs. The decelerated electrons release energy which is 
systematically coupled into the electromagnetic wave field of the slow 
wave structure. These fields, which have an axial electric field 
component, enhance the bunching of the beam's space charge and thereby 
further decelerate the beam electrons, thus transferring more energy into 
the wave fields. As the positive reinforcement cycle continues, the 
structure's electromagnetic fields exponentially increase in amplitude at 
the frequency of the beam-structure resonance, resulting in a spontaneous 
generation of microwave power. 
In a BWO, the coupling of the slow space charge wave with the tube's modes 
occurs when the structure mode has a negative group velocity. This results 
in a transfer of e.sup.- beam energy to the electromagnetic wave field in 
a direction that is backward, or opposite, to the direction of the e.sup.- 
beam. The spontaneous generation of microwave power grows out of e.sup.- 
beam noise and the structure's internal feedback, with no input RF signal. 
The backward traveling RF wave is reflected off either the e.sup.- beam 
generator itself, or off a smaller diameter section of the tube near the 
e.sup.- beam generator which acts as a waveguide below cutoff for the 
operating frequency of the device as shown in FIG. 1. It then travels in a 
second pass through the tube for extraction at the opposite end of the 
tube from the e.sup.- beam generator. 
If the e.sup.- beam's slow space charge wave couples with a tube mode that 
has a positive group velocity, as opposed to the negative group velocity 
associated with a BWO, the slow wave structure is commonly known as a 
TWTA. In this case the transfer of e.sup.- beam energy to the wave field 
is forward, or co-directional, with the direction of the e.sup.- beam. RF 
excitation from an external source must be launched into the tube near the 
end that receives the e.sup.- beam for the signal to be grown 
exponentially as it propagates (in a single pass) along the length of the 
structure. 
A simplified sectional view of a conventional structure that can function 
as a BWO is given in FIG. 1. An electron gun 100 transmits an e.sup.- beam 
through an internally rippled slow wave tube 102. Functioning as a BWO, a 
backward traveling RF wave is reflected off the end of the (smaller 
diameter) unrippled tube section 104 adjacent the e.sup.- gun, and emerges 
from the flared tube outlet 106. A structure that can function in a TWTA 
mode is shown in FIG. 2, in which the same reference numerals are used to 
indicate the same elements as in FIG. 1. An input RF signal is coupled 
into the side of the tube through a coupling port or ports 108 into a 
region which can propagate the RF signal downstream into the slow wave 
structure. To restrict the signal from propagating upstream and entering 
the e.sup.- gun, the smaller diameter tube section 104 which cannot 
propagate the RF signal is positioned upstream of the coupling region and 
downstream of the e.sup.- gun. In this mode the RF signal grows as it 
propagates forward through the tube, and is emitted without a reflection 
of its propagation direction. 
There are several undesirable limitations of both the BWO and TWTA. Since 
the RF signal is extracted from the same end of the slow wave tube where 
the e.sup.- beam is collected, special provisions must be made to extract 
the RF signal while terminating the e.sup.- beam. In magnetized devices 
the beam can be propagated out of the confining magnetic field region and 
allowed to expand, striking the waveguide wall. In alternative approaches 
various types of "beam dumps" in the form of plugs at the end of the 
waveguide tube have been employed, but they are difficult to design so 
that they do not interfere with the RF signal. In both elimination methods 
the e.sup.- beam impacting the waveguide or "dump" surface tends to result 
in the formation of plasma (which can adversely effect the radiation of RF 
power) at the end of the tube by partially reflecting, absorbing and/or 
scattering the RF signal. 
The permissible average e.sup.- beam power and energy, and thus the amount 
of average power that can be transferred to the RF signal, is also limited 
by the need to collect the e.sup.- beam at the same location at which the 
RF signal is extracted. The use of a simple water cooling system for the 
beam collector would permit operation at a higher e.sup.- beam duty cycle 
and average power. However, water cooling systems which require metal 
structures for effective heat transfer or re-circulating liquid coolant 
must be positioned in the throat of the RF radiating aperture and thus can 
interfere with the extraction of the RF signal. This limits the use of 
water cooling, with a consequent reduction in the duty cycle and average 
powers that might otherwise be achieved. 
In the case of a BWO, the backward direction of the RF signal as it is 
originally generated also leads to inefficiencies. The need to reflect the 
backward propagating RF wave at the input end of the tube, and then allow 
it to travel in a second pass to the outlet end of the tube, can result in 
a reduction in signal amplitude through wall losses, as well as adversely 
affecting the structure's conversion efficiency. 
The RF signal extracted from the slow wave tube is fundamentally in the 
TM.sub.01 (cylindrical waveguide) mode established by the dynamics of the 
RF generating interaction between the electron beam's space charge wave 
and the cylindrical waveguide's electromagnetic field components. However, 
a rectangular TE.sub.10 mode is generally preferred for radiating RF 
signals, since this mode can be easily managed and fed directly to antenna 
feeds for radiation. A separate mode converter is thus necessary to place 
the generated RF signal in the desired mode format for radiation. 
A BWO with TE.sub.10 extraction waveguides at the opposite end of the tube 
from the e-beam source is illustrated in Phelps, "More Than 10 GW from a 
Relativistic BWO?" Third National Conference on High Power Microwaves 
Digest, December 1986, pages 240-244 (FIG. 6). However, the extraction 
waveguides require the radiation to undergo two full passes through the 
BWO before it can be extracted, additional unwanted modes could be 
excited, and only individual extractions are disclosed. An article in the 
same publication by Voss et al., "Characterization of a High Power 
Microwave Cross-Field Oscillator Operated at S-Band" pages 147-148, shows 
a slow wave tube with a single lateral extraction structure. With this 
device there would be an excitation of unwanted modes over appreciable 
bandwidths, there is no provision for multiple phase coherent outputs that 
can be used for a phased array antenna, the amount of power that can be 
extracted is quite limited, and the system is asymmetrical. In Wharton and 
Butler, "Relativistic O-Type Oscillator-Amplifier Systems" Intense 
Microwave and Particle Beams, Vol. 1226, Bellingham, Wash., 1990, page 23, 
two TWT amplifiers are driven by a single relativistic BWO master 
oscillator. Microwave samples are obtained from extraction ports near the 
input end of a BWO and coupled into respective TWTAs. There is no 
disclosure of any TM.sub.01 -to-TE.sub.10 mode conversion, the extraction 
will excite propagations other than (TM.sub.01 cylindrical waveguide 
modes) over appreciable bandwidths, the two output samples are used 
independent of each other, and again the outputs are not compatible as 
inputs to a phased array antenna. 
SUMMARY OF THE INVENTION 
The present invention seeks to provide a new coupling approach to high 
power RF extraction from a BWO or TWTA. Three significant differences from 
previous approaches are proposed. 1) A side extraction technique is used 
at the output to avoid interference from the mechanism used to collect the 
e.sup.- beam. 2) A specially designed 4-port coupler is utilized for this 
extraction to improve the RF coupling efficiency and maintain a pure mode 
condition within the cylindrical tube. 3) Multiple ports are used to 
provide a higher peak RF power through the use of multiple RF outputs that 
are phase coherent over the full RF pulse duration, and that can be 
combined to produce a steerable RF beam with a higher power than that 
which is attainable from a single RF output. The invention further seeks 
to provide for an inherent mode conversion from a TM.sub.01 cylindrical 
waveguide mode to a TE.sub.10 rectangular waveguide mode built into the RF 
extraction mechanism, thus eliminating the need for a separate mode 
converter. 
These goals are achieved with the use of an e.sup.- beam source, a slow 
wave tube that is positioned to receive an e.sup.- beam from the source, a 
mechanism for causing RF radiation to travel through the tube, and a novel 
outlet port arrangement distributed along the side of the tube for 
extracting RF radiation therefrom. The RF radiation can either be 
self-generated as in a BWO, or excited from an external RF source and 
amplified within the tube as in a TWTA. 
The slow wave tube has a periodically rippled inner surface, and the 
multiple outlet ports are positioned along the tube and have axial 
dimensions such that the phase coherence of the RF generation process is 
maintained. It is preferable to have the final RF power in a rectangular 
TE.sub.10 waveguide mode, but the generated energy is in a circular 
waveguide TM.sub.01 mode. A 4-port extraction technique solves this 
problem, with the extracted RF radiation from each of the ports combined 
into a single rectangular waveguide TE.sub.10 mode. 
Multiple outlet port regions are provided along the length of the tube to 
yield a plurality of phase coherent RF outputs that are useful as inputs 
to a phased array antenna. The multiple outlet ports also enable a 
distribution of the output RF signal along the length of the tube, and 
thus makes possible a higher total output power by reducing the risk of RF 
breakdown across a single port. In the TWTA application, in which the RF 
signal is progressively amplified during its propagation through the tube, 
the outlet ports are positioned at axial intervals such that the multiple 
RF outputs yield similar magnitudes and phase of RF power. The separation 
of the RF signal extraction from the end of the tube at which the e.sup.- 
beam is terminated also permits the use of a metallic water cooling system 
for the e.sup.- beam absorber, thus further increasing the system's 
average power capacity. 
These and other features and advantages of the invention will be apparent 
to those skilled in the art from the following detailed description, taken 
together with the accompanying drawings.

DETAILED DESCRIPTION OF THE INVENTION 
A BWO implementation of the invention is shown in FIG. 3. It includes a 
4-sectioned slow wave tube 2, forward and rear cylindrical extensions 4 
and 6 of the tube which do not propagate the RF energy, and an electron 
gun 8 that generates and directs an e.sup.- beam through the tube via rear 
extension 6. The e.sup.- beam exits the tube via the forward extension 4, 
and is absorbed by an electron-absorbent "beam dump" structure 10. The 
electron beam collector can be surrounded by a metallic water cooling 
system 12. The separation of the e.sup.- beam termination from the 
extraction of RF power from the slow wave tube 2, as described below, 
permits the use of a metallic water cooling system without interfering 
with the RF output. 
The electron gun 8 is preferably implemented as described in U.S. Pat. No. 
4,912,367 to Schmuacher et al. and assigned to Hughes Aircraft Company, 
the assignee of the present invention. This type of device injects a high 
current density e.sup.- beam into the waveguide established by slow wave 
tube 2 and extensions 4 and 6. The e.sup.- beam current density is high 
enough to at least partially ionize the gas within the waveguide. The 
waveguide gas pressure is kept at a level, preferably within the 
approximate range of 1-to-5.times.10.sup.-5 Torr, that is sufficiently low 
to avoid voltage breakdown in the e.sup.- gun, but high enough to allow 
sufficient ionization to substantially neutralize space-charge blowup of 
the e.sup.- beam. By thus restricting the diameter of the e.sup.- beam, 
the use of externally applied magnetic fields that must ordinarily be 
maintained around the beam to limit it expansion is avoided. 
Other types of e.sup.- beam guns can also be used, but are not as 
preferable as the device described in U.S. Pat. No. 4,912,367. E.sup.- 
beam guns in general are described in J. Hansen, "US TWTS from 1 to 100 
GHz", Microwave Journal: 1989 State of the Art Ref. (1989), pages 179-193, 
and in R. B. Miller, Introduction to the Physics of Intense Charged 
Particle Beams, Plenum Press, New York, 1985, pages 31-76. 
A novel aspect of the structure shown in FIG. 3 is that RF radiation is 
extracted through a series of lateral tube extraction sections 14a, 14b, 
14c and 14d, rather than from the end of the waveguide in the vicinity of 
the beam dump 10. The extraction ports, illustrated as ports 14a, 14b and 
14c, are located in the side of slow wave tube 2; an additional extraction 
port 14d is located at the upstream waveguide end of the tube 2. 
The extraction ports 14a-14d couple into respective extraction waveguides 
16a, 16b, 16c, 16d which guide the RF signals away from the tube. In the 
BWO mode the backward directed RF radiation all along the length of the 
tube is phase coherent (in-phase) and at a substantially uniform power 
level. The RF outputs 18a, 18b, 18c and 18d from respective waveguides 
16a, 16b, 16c and 16d are accordingly all in phase with each other, and 
can therefore be directly applied to a phased array antenna. 
The amount of RF power extracted through each of the output ports 14a-14d 
can be varied according to the coupler design. Thus, by distributing the 
RF output among a plurality of ports as illustrated, a greater total RF 
power output can be achieved without breakdown than would be the case if 
only a single extraction port were used. 
The TWT and extraction ports are preferably configured to maintain phase 
coherency in the RF wave from one extraction port to the next. The RF 
wavelength is a function of the tube dimensions, the extraction port 
configuration and the periodicity of ripples 20, and is different at the 
extraction ports from its dimension in the tube sections between ports. 
The extraction ports are preferably distributed along the full length of 
the slow wave tube, and thus extract most or all of the generated RF power 
that is directed rearward. Since this power is extracted during the first 
pass through the tube, before reflection from the e.sup.- gun 8 or from a 
diameter reduction in the tube extension 6, an added degree of efficiency 
over the prior double-pass BWO is achieved. The reverse power level is 
fairly uniform along the length of the tube, with its absolute value 
dependent mainly upon the amount of time the system has been in operation. 
The ports can therefore be located at any desired locations along the 
tube, but the spacing between ports should be maintained as described 
above. Greatest efficiency is achieved when one of the ports (18) is 
located proximate to the end of the tube nearest the e.sup.- gun, and thus 
assures that substantially all of the RF energy is extracted before 
reflection. The fact that the average RF signal path length through the 
tube is shorter when a number of separate extraction ports are employed, 
resulting in a lower level of losses at the interior tube walls, provides 
a further enhancement to operational efficiency. 
The extraction ports 14a-14d and extraction waveguides 16a-16d preferably 
have rectangular interior openings to couple the TM.sub.01 cylindrical 
waveguide mode to the TE.sub.10 rectangular waveguide mode for the 
extracted RF power. The extraction waveguides should be impedance matched 
with the slow wave tube to avoid RF reflections back into the tube. 
However, the provision of only a single lateral extraction port at each 
extraction location along the tube can lead to the excitation of other 
circular waveguide modes in the tube because of the asymmetries involved. 
An extraction structure that avoids this problem is illustrated in FIGS. 
4a and 4b. Rather than a single extraction guide such as 16b at a given 
location along the slow wave tube, four extraction ports and corresponding 
extraction waveguides 16b1, 16b2, 16b3 and 16b4 are provided at 90.degree. 
intervals around the circumference of the slow wave tube 2. The RF signals 
in guides 16b1 and 16b4 are combined into a single guide 22a via an 
H-plane T-connection 24, while the RF signals in waveguides 16b2 and 16b3 
are combined into a single RF signal in another waveguide 22b by a second 
H-plane T-connection 26. Finally, the RF signals in waveguides 22a and 22b 
are combined in a single final RF output waveguide 22c by a third H-plane 
T-connection 28. Numerous other designs for combining the extracted 
signals can be used, such as E-plane T-connections, hybrid couplers, or 
individual waveguide-to-coaxial adaptors that run from the extraction 
waveguides to a 4-way coaxial combiner. The waveguides would preferably be 
shaped to present a considerably smaller profile than the demonstration 
apparatus shown in FIG. 4a. 
Each of the waveguides employed in the extraction process at a given 
coupling location has a similar rectangular interior opening, such as 
interior opening 30 for the final waveguide 22c illustrated in FIG. 4b; 
the dimensions of the rectangular opening are selected to support the 
TE.sub.10 rectangular mode over a frequency range determined by the 
operation of the slow wave tube structure and optimized for the coupling 
from the TM.sub.01 cylindrical mode to the four rectangular TE.sub.10 
arms. An effective mode conversion from the TM.sub.01 mode within the slow 
wave tube to the TE.sub.10 in an external waveguide is thus achieved. 
The application of the invention to a TWTA is illustrated in FIG. 5, with 
elements common to FIG. 3 indicated by the same reference numerals. In 
this application, externally generated microwave radiation 32 is coupled 
into the end of the slow wave tube 2 in front of the extension tube 6, via 
a coupling waveguide 34, which preferably has the same 4-port 
circumferential arrangement as the RF extraction structure in FIG. 4a. 
This initiates a single pass transmission of RF radiation from the end of 
the slow wave tube adjacent the extension tube 6 to the opposite end of 
the slow wave tube adjacent the e.sup.- beam collector 10, with the RF 
radiation undergoing progressive amplification during its transit. A 
series of RF extraction ports 36a, 36b, 36c, 36d and associated extraction 
waveguides 38a, 38b, 38c, 38d are positioned along the length of the tube 
in a manner similar to extraction ports 14a-14d and waveguides 16a-16d of 
FIG. 3. 
The high power RF outputs from either the BWO of FIG. 3 or the TWTA of FIG. 
5 are phase coherent over the full RF pulse duration, and frequency 
tunable by adjustment of the e.sup.- beam voltage and current. The 
multiple outputs can be directly fed through electronically controlled 
phase shifters to radiating elements to produce a steerable RF beam, 
without the prior need for splitting a single RF source into multiple 
coherent sources. The prior distortion of the RF output beam obtained with 
the structure of FIG. 1, which was associated with its proximity to the 
e.sup.- beam collection, is avoided, and a water cooled beam collector can 
be used. Higher power levels are achievable through both the spatial 
distribution of the output RF signal, and the enhanced e.sup.- beam 
absorption capability. 
As described thus far, energy can be lost from the system by scattering 
from the outlet ports. The invention effectively cancels the effects of 
back-scattering through the tube, while at the same time reinforcing the 
extraction of radiation in a TE.sub.10 mode, using a principle of 
operation illustrated in the diagram of FIG. 6. The RF radiation of a wave 
propagating from left-to-right through the slow wave tube 2 immediately 
prior to an outlet port 36 is represented by arrow 40, with the arrow's 
head indicating the phase of the radiation. At the port, some of the RF 
energy is coupled out in a TE.sub.10 mode through the rectangular 
waveguide 38 (arrow 42), some of the energy is scattered from the outlet 
port including a back scattered component (arrow 44), and the remainder is 
transmitted along the tube past the outlet port (arrow 46). In each case, 
the direction of propagation is indicated by the dashed line arrow that 
extends orthogonally from the radiation arrow. The back-scattered 
component 44 corresponds to an energy loss that would be desirable to 
eliminate. 
A more energy efficient operation is achieved by reducing the diameter of 
the RF guiding structure downstream from the outlet ports 36a-36d to 
reflect back a portion of the transmitted radiation, with the reflection 
characteristics controlled so that the back-scattered radiation 44 is 
cancelled. The diameter reduction 48 is spaced from the outlet port by 
approximately an integral number of radiation half-wavelengths for this 
purpose. The proportion of the radiation that is reflected will depend 
upon the relative diameters of the tube prior to and after the diameter 
reduction 48. Assuming the diameter reduction is located an odd number of 
half-wavelengths from the outlet port, the radiation will undergo a 
180.degree. phase shift during transit from the outlet port to the 
diameter reduction, and another 180.degree. phase shift during the reverse 
transit. However, an additional 180.degree. phase shift is also imposed 
upon the reflected radiation at the point of reflection, so that the 
reflected wave 50 will be 180.degree. out-of-phase with the transmitted 
wave. 
A portion of the reflected radiation 50 is coupled out through the 
rectangular waveguide 38 (arrow 52), in-phase with the forward-directed 
extracted radiation 42, while the remainder (arrow 54) continues past the 
outlet port 180.degree. out-of-phase with the back-scattered radiation 44. 
The reflected radiation 52 that is coupled out through the outlet 
waveguide 38 will thus constructively add to the extracted radiation 42 
already present, while the reflected radiation 54 that continues back past 
the outlet port will destructively add to the back scattered radiation 44. 
With an appropriate selection for the dimension of extraction waveguide 38 
and the relative amount of tube diameter reduction 48, the reflected 
radiation 54 that continues back through the tube can effectively cancel 
the back scattered radiation 44, while the sum of the extracted radiation 
components 42 and 52 can be fixed at a desired extraction percentage of 
the total radiation initially propagating along the tube. A lower limit to 
the tube diameter after reduction is set by the need to provide enough 
open area for the e.sup.- beam to continue past the diameter reduction. 
FIGS. 7 and 8 show a demonstration of this type of operation in which 
essentially 100% of the continuous waveguide energy through a cylindrical 
tube 2 was coupled out through a set of four rectangular extraction 
waveguides 38-1, 38-2, 38-3, 38-4, spaced at 90.degree. intervals around a 
circumference of the tube 2. To accomplish this, the diameter reduction 48 
(see FIG. 8) was sufficient to totally cut off propagation of the 
TM.sub.01 mode, causing the energy that was transmitted past the 
extraction waveguides to be totally reflected back through the tube. The 
dimensions of the extraction ports 36-1, 36-2, 36-3, 36-4 as generally 
shown in FIG. 7 for the rectangular waveguides were selected so that the 
back-scattered radiation was effectively cancelled by the reflected 
radiation that continued back past the extraction ports. For any 
particular system, the sizes of the extraction ports can be determined 
empirically or by computer modelling; in the specific demonstration 
illustrated in the drawings the tube diameter was 3.5 cm, the extraction 
ports were 0.8 cm long in the direction of the tube axis, and the tube's 
diameter after the reduction 48 was 2.0 cm. Since the desired dimension 
for the extraction waveguide 38 was not a standard size, the extraction 
waveguides were stepped up to standard dimensions via a series of steps 56 
that were spaced one-quarter wavelength apart from each other to avoid 
reflections. 
FIG. 9 is a graph showing the theoretical computer modelled and actual 
results achieved with the 100% extraction demonstration. The horizontal 
axis represents the signal frequency, normalized to a TM.sub.01 cutoff 
frequency of 1.0, while the vertical axis indicates the non-extracted 
energy at each frequency that was returned back through the tube; the 
"return loss" vertical axis scale is a measure of the returned radiation 
at each frequency compared to the energy of the radiation initially 
transmitted at that frequency. The tube and extraction waveguides were 
tuned to a normalized frequency of 1.54, but other frequencies over a wide 
bandwidth could have been selected. Curve 58 shows the projected results 
from computer modelling, while curve 60 shows the actual results. With a 
return loss of about 30 dB at the tuned normalized frequency of 1.54, a 
very high level of efficiency was demonstrated. 
A balance in the energy extracted through the four rectangular waveguides 
at each extraction site is provided by their circular symmetry. Ideally, 
each extraction port would couple one-quarter of the desired output level. 
FIG. 10 shows the coupling that was measured for one of the extraction 
waveguides; the theoretical best would be a flat 6 dB line, corresponding 
to 25% of the input energy. In FIG. 10 the extracted energy begins to 
decline rapidly at a normalized frequency just below 1.3. This corresponds 
to the results shown in FIG. 9, in which a return loss of about 3 dB 
(corresponding to 50 % transmission and 50 % reflection) was observed at a 
normalized frequency just below 1.3. 
Measurements were also made of the insertion loss for the total mode 
converter illustrated in FIG. 4a, comparing the TE.sub.10 rectangular 
waveguide output to the TM.sub.01 cylindrical waveguide input. The results 
are shown in FIG. 11. An insertion loss of essentially 0 dB was observed 
at the normalized 1.54 tuned frequency, while a bandwidth of approximately 
25% was obtained between the 1 dB insertion loss points above and below 
the tuned frequency. This represents a very wide and satisfactory 
bandwidth over which effective operation can take place. 
It is important to avoid the excitation of any modes other than the 
TE.sub.10 mode, since additional mode excitations add to the system's 
energy losses and degrade its bandwidth. The manner in which the present 
invention achieves a wide bandwidth without exciting unwanted modes is 
illustrated in FIG. 12. The cutoff frequencies for various possible 
propagation modes below which the mode will not propagate (for an infinite 
length waveguide) are indicated, with the TM.sub.01 mode having a 
normalized frequency of 1.0; the cutoff frequencies vary inversely with 
the tube diameter. A desired bandwidth is indicated by the hatched area 
62. While numerous different propagation modes could theoretically be 
excited within this bandwidth, none of them are excited by the 4-port 
extraction system of the present invention, in which four extraction ports 
are spaced at 90.degree. intervals around the circumference of the slow 
wave tube at each extraction site. For example, the TE.sub.11 mode would 
be excited by 1-port extraction system, and the TE.sub.21 mode would be 
excited by a 2-port extraction system. The next mode above the desired 
TM.sub.01 that would be excited by the invention's 4-port extraction 
system is the TE.sub.41 mode. However, the normalized cutoff frequency for 
this mode is about 2.25, which is considerably above the upper end of the 
desired band. 
While theoretically the bandwidth could extend all the way from the 1.0 
TM.sub.01 cutoff point up to the edge of the TE.sub.41 cutoff frequency, 
for practical systems in which the circular waveguide is of limited length 
a safety margin should be left above the TM.sub.01 and below the TE.sub.41 
cutoff frequencies. This is because, in approaching the TM.sub.01 cutoff 
from a higher frequency level, a dispersion effect accompanied by very 
large variations in the waveguide impedance are encountered. Also, in 
approaching the TE.sub.41 cutoff from a lower frequency level, TE.sub.41 
propagations are encountered that decay with waveguide length but can 
still be significant at frequencies below the nominal cutoff frequency for 
limited length waveguides. Accordingly, band edge margins on the order of 
20-25% both above the TM.sub.01 and below the TE.sub.41 cutoff frequencies 
would normally be expected and acceptable. 
While several illustrative embodiments of the invention have been shown and 
described, numerous variations and alternate embodiments will occur to 
those skilled in the art. Such variations and alternate embodiments are 
contemplated, and can be made without departing from the spirit and scope 
of the invention as defined in the appended claims.