Forward-wave Amplifiers Research Articles

Intelligent Forward-Wave Amplifier Design With Deep Learning and Genetic Algorithm

In this work, exploitation of artificial intelligence algorithms for the design of forward-wave amplifier is proposed and discussed. The multilayer perceptron (MLP), a quintessential example of deep learning, is employed to get the cost function, i.e., the relationship between the geometrical parameter set and dispersion characterization from only a small proportion of the parameter sets. Due to the structural complexity, there did not exist a closed-form solution and the neural network shows its superiority compared to the time-consuming numerical calculation. Subsequently, the genetic algorithm (GA) is used to find the parameter sets best matching the goals that broadband beam-wave interaction at specific voltages and even specific phases or frequencies, from the huge 4-D parameter-set space. The intuitive goals can be easily accessible, as long as the goals are within the ability of the parameter-set space and converting the goals into the goal functions for GA with some attempts and adjustments. As a practical example, the recently proposed defect photonic crystal waveguide is utilized to demonstrate the design pattern. Through almost full-automatic design with little judgment and analysis, a response of 14-GHz 3-dB bandwidth and 25-dB gain at the 168.5-GHz central frequency has been realized, indicating the effectiveness of the design pattern. This design pattern will ease researchers from numerous simulation work and help to get deeper insight of the structure.

Energy Plasmon Modes in Metamaterial-filled Double-layer Graphene-wrapped Cylindrical Waveguides

The characteristics of hybrid surface plasmon modes in a double-layer graphene cylindrical waveguide filled with metamaterials are theoretically investigated. The dispersion relation for different configurations of metamaterials (double positive (DPS)-graphene-double negative (DNG)-graphene-DPS and DNG-graphene-DPS-graphene-DNG) is derived by solving Maxwell’s equations for cylindrical symmetry and implementing impedance boundary conditions at the interface. The Kubo formalism is used for the modeling of the electromagnetic response of graphene. The influence of the interlayer distance of graphene, chemical potential of graphene, and permittivity of interlayer metamaterials on the dispersion curve, effective mode index, propagation length, and phase velocity are presented. It is observed that the existence of double layers of graphene along with metamaterials provides better control and tuning of the propagation of the surface waves. The coupled surface plasmon polariton (SPP) and surface phonon polariton (SPhP) in the optical regime are observed due to the coupling of electromagnetic waves between graphene layers. The forward- and backward-propagating surface waves for the fundamental mode are studied for different waveguide configurations. The active trapping of light and tunable fast and ultraslow plasmon modes for both forward and backward propagation modes for the proposed design may enable the realization of potential optoelectronic applications, such as modulators, fast forward-wave amplifiers, frequency selectors, back wave contra couplers, thermal sensors, circular polarizers, slow light devices, infrared (IR) and molecular spectroscopy, on-chip buffers, communication switches, and energy devices.

Excitation of parasitic waves in forward-wave amplifiers with weak guiding fields

To produce high-power coherent electromagnetic radiation at frequencies from microwaves up to terahertz, the radiation sources should have interaction circuits of large cross sections, i.e., the sources should operate in high-order modes. In such devices, the excitation of higher-order parasitic modes near cutoff where the group velocity is small and, hence, start currents are low can be a serious problem. The problem is especially severe in the sources of coherent, phase-controlled radiation, i.e., the amplifiers or phase-locked oscillators. This problem was studied earlier [Nusinovich, Sinitsyn, and Antonsen, Phys. Rev. E 82, 046404 (2010)] for the case of electron focusing by strong guiding magnetic fields. For many applications it is desirable to minimize these focusing fields. Therefore in this paper we analyze the problem of excitation of parasitic modes near cutoff in forward-wave amplifiers with weak focusing fields. First, we study the large-signal operation of such a device with a signal wave only. Then, we analyze the self-excitation conditions of parasitic waves near cutoff in the presence of the signal wave. It is shown that the main effect is the suppression of the parasitic wave in large-signal regimes. At the same time, there is a region of device parameters where the presence of signal waves can enhance excitation of parasitic modes. The role of focusing fields in such effects is studied.

Excitation of parasitic waves near cutoff in forward-wave amplifiers

In this paper, excitation of parasitic waves near cutoff in forward-wave amplifiers is studied in a rather general form. This problem is important for developing high-power sources of coherent, phase controlled short-wavelength electromagnetic radiation because just the waves which can be excited near cutoff have low group velocities. Since the wave coupling to an electron beam is inversely proportional to the group velocity, these waves are the most dangerous parasitic waves preventing stable amplification of desired signal waves. Two effects are analyzed in the paper. The first one is the effect of signal wave parameters on the self-excitation conditions of such parasitic waves. The second effect is the role of the beam geometry on excitation of these parasitic waves in forward-wave amplifiers with spatially extended interaction space, such as sheet-beam devices. It is shown that a large-amplitude signal wave can greatly influence the self-excitation conditions of the parasitic waves which define stability of operation. Therefore the effect described is important for accurate designing of high-power amplifiers of electromagnetic waves.

Low-Voltage Operation of Ka-Band Folded Waveguide Traveling-Wave Tube

Low-voltage operation of millimeter-wave folded waveguide traveling-wave tube (TWT) was investigated using a 12 kV linear electron beam. Backward wave oscillation operated at second space harmonic was observed with output power of 20 W, linear tunability of 6% within 0.01 dB/MHz, and voltage-frequency stability of 0.56 MHz/V. The measured frequency and output power are in a good agreement with the predicted values using a particle-in-cell (PIC) code. In addition, backward-wave interaction at second-space harmonic as an amplifier was observed with a measured linear gain of 15 dB and a bandwidth of 0.3%. For forward wave interaction, a linear gain of 25 dB, bandwidth of 17%, and efficiency of 7% were predicted for fundamental space harmonic using a PIC code. Improvement in efficiency was predicted for the forward-wave amplifier where it was operated as an oscillator employing a delayed feedback. Output power was increased by 10 dB in the delayed feedback oscillator comparing with the backward-wave oscillator. The effect of period doubling due to potential fabrication inaccuracies on the stopband was studied experimentally. The folded waveguide TWT fabricated using the Lighographie, Galvanoformung, Abformung (LIGA) process operated at much higher frequencies is discussed.

Linear theory of multistage forward-wave amplifiers.

A small-signal theory describing multistage gyro-traveling-wave tubes (gyro-TWTs) is developed. Multistage configurations of gyro-TWTs as well as conventional TWTs seem to be attractive because of their principal ability to operate stably with a high gain, since the stability can be provided by a shortening of each stage while the gain increases with the number of stages. Two regimes of operation, far from cutoff and near cutoff, are considered. In the former case, the equations can be reduced to those describing conventional TWTs and free electron laser amplifiers. Thus a part of the results obtained is also valid for these devices. For two-stage configurations (two waveguides separated by a drift region) the effect of the difference in waveguide cutoff frequencies on the gain and bandwidth is studied. This effect has a common nature with stagger-tuning of cavities, which is widely used in conventional klystrons and gyroklystrons for bandwidth enlargement. The trade-off in gain and bandwidth of such "stagger-tuned," two-stage gyro-TWTs and TWTs is analyzed. Also, the theory of two-stage gyro-TWTs with tapered waveguides and external magnetic field is discussed.

Excitation of backward waves in forward wave amplifiers

The sources of coherent electromagnetic radiation based on amplification of traveling waves by electron beams have unique capabilities of wide band, high efficiency operation. The most critical issue in the development of such forward wave amplifiers is the self-excitation of parasitic backward waves in the interaction region. The developed theory allows one to analyze the nonlinear effect of suppression of parasitic backward waves by forward waves operating in the large-signal regime. The results of the analysis of traveling wave tubes (TWTs) and twystrons driven by linear electron beams and the results of the study of gyrodevices (gyro-TWTs and gyrotwystrons) driven by beams of gyrating electrons are presented. The gyrodevices are considered in the cases when the forward and backward waves are in resonance with electrons either at the first or second cyclotron harmonic. The results obtained allow one to estimate to what extent the coupling of an electron beam to the parasitic wave should be decreased in order to provide a stable, high efficiency amplification of the forward wave.

A dc-operated CFA chain for 1 MW, 5 kW at S-band

Development of a 60 dB gain, three-tube chain of forward-wave amplifiers is described. The chain is designed to fulfill state-of-the-art requirements for high efficiency, light weight, and minimum modulator power for use in advanced radar systems. Two 15-dE crossed-field amplifiers are driven by a traveling-wave tube with all stages dc-operated for 10 percent instantaneous bandwidth centered at 3.3 GHz. The TWT is gridded and the CFA's have beam cut-off electrodes.

Start-oscillation conditions in nonuniform backward-wave oscillators

The effects of nonuniformities in the circuit phase velocity and the beam potential on the start-oscillation conditions of an O-type backward-wave oscillator (BWO) are investigated. The nonuniformities include linear, quadratic, and exponential circuit phase velocity tapers and beam potential gradients. It is shown that for weak circuit phase velocity tapers or voltage gradients the start-oscillation current may be lower than that of a uniform tube; however, when the taper or gradient is made stronger than a particular value which depends on the operating parameters, a no-oscillation region results. The latter result indicates that such nonuniformities may be utilized to suppress backward-wave oscillations in forward-wave amplifiers.

Noise-figure calculations for crossed-field forward-wave amplifiers

The problem of finding an adequate model for derivation of noise-figure expressions for crossed-field forward-wave amplifiers is investigated. The modified Llewellyn-Peterson equations are used for the portion of the beam near the cathode. Four waves, two cyclotron waves and two space-charge waves, are used for the space connecting the gun and interaction region. Noise-figures are found by considering five waves in the interaction region. The results are very close to those found when only the space-charge waves are considered in the development of the equations for both drift and interaction regions. A matrix, like the space-charge-wave matrix for O-type beams, giving the transformation of beam fluctuations along a drifting, crossed-field stream including the effects of four waves is presented. Expressions for fluctuations of transverse velocity and beam center of gravity are derived to account for all the excitation quantities which are believed to be important in crossed-field amplifiers. The transformation of fluctuations of beam position, or center of gravity, along an accelerating stream is derived. Calculated values of noise figures are far in excess of experimental values. The reasons for the discrepancies are discussed.

General velocity tapers for phase-focused forward-wave amplifiers

General velocity tapers for phase-focused forward-wave amplifiers

The dematron—A new crossed-field amplifier

A nonreentrant beam, distributed-emission, crossed-field, forward-wave amplifier, the DEMATRON, is described. The difficulties encountered by early experimenters in achieving gain in excess of 6 db in nonreentrant, crossed-field amplifiers are overcome in the DEMATRON by use of either an electron velocity taper or circuit velocity taper. A crossed-field amplifier design theory is given which is based on the use of equivalent magnetrons, and which takes into account the need for velocity compensation. In practice, electron velocity compensation is accomplished by either changing the sole-anode spacing, or by varying the dc magnetic field or a combination of both. Experiments with the DEMATRON have yielded gains in excess of 10 db over a 15 per cent bandwidth. Power levels between 300 and 500 kw have been achieved at an operating voltage of 25 kv. The design theory has been experimentally shown to be quite satisfactory in the large-signal, saturated gain region of operation, However, the lack of adequate small-signal theory has thus far prevented full optimization of the velocity compensation.

Multiple-stream Crossed-field Interaction†

ABSTRACT The dispersion equations are developed using admittance matching techniques for both the crossed-field double-beam forward-wave amplifier and the double-beam drift-space amplifier. The input boundary value problem is solved by matching the a.c. displacement and the a.c. charge density at the input boundary. The gain is found to be considerably greater for the double-beam device than for each of the beams acting separately. The relative ease of obtaining Brillouin flow with thin beams in practical devices makes this an attractive way of increasing the gain. A non-linear analysis is made and the results for the two-beam case are compared with those for a thick Brillouin stream and those for a non-slipping laminar stream. Graphs are presented showing the reduction in gain due to d.c. slip in crossed-field interaction.

Low-noise backward-wave amplifiers

The characteristics of backward-wave amplifiers are briefly reviewed and related to general receiver problems which exist in broad-band high-power systems. It is emphasized that a backward-wave amplifier of sufficiently low noise figure offers potential solution to several of these problems and would be more useful in some cases than a conventional low-noise traveling-wave tube. The problems encountered in noise reduction in backward-wave amplifiers are discussed and compared with those for forward-wave amplifiers. Gain, bandwidth, and noise-figure characteristics of experimental S-band tubes are presented. Very low noise figures have been achieved for tuning ranges up to half an octave with minimum programming of the gun potentials. A noise figure of 3.7 db at the center of the tuning range has been attained and was reproducible after several hundred hours of operation. This node figure is well below the usual theoretical minimum and is made possible by the unique geometry of the annular cathode and gun. The results to date indicate that the backward-wave type of amplifier is feasible for receiver applications and may satisfy the increasingly apparent need for rapidly tunable selective preamplification.

Traveling-wave amplifiers and backward-wave oscillators for VHF

An important aspect of the design of traveling-wave amplifiers and backward-wave oscillators for frequencies below 500 mc is the problem of obtaining a tube of reasonably small physical dimensions. Hollow beams of greater perveance than is obtainable with solid beams offer one method of reducing the size of such tubes by permitting operation at a lower voltage and greater gain per wavelength, for a specified beam power, than is possible in a solid beam tube. Some aspects of the design of minimum size hollow-beam forward-wave amplifiers using single helix circuits and backward-wave oscillators using bifilar helix circuits are presented. Several tubes of these types for operation below 500 mc have been built. Amplifier bandwidths and oscillator tuning ranges in excess of four to one in frequency have been obtained experimentally. Amplifier efficiencies in excess of 20 per cent and oscillator efficiencies in excess of 10 per cent have been achieved.

The Large-Signal Behavior of Crossed-Field Traveling-Wave Devices

A large-signal theory for the interaction between a slow wave and a beam of electrons traveling in crossed dc electric and magnetic fields is formulated. The adiabatic equations of motion are used, space-charge forces are neglected, but phase focusing by the rf field and loss of the beam at the anode and sole plate are taken into account. The limits of validity of the conventional small-signal theory are obtained, and an analog computer is employed to follow the interaction to power saturation. Results are presented for a forward-wave amplifier, backward-wave amplifier, and backward-wave oscillator. It is shown that for very short lengths the backward-wave amplifier may give superior results to the equivalent forward-wave amplifier but that otherwise greater gain and efficiency can be obtained with a forward-wave amplifier. However, it is shown that there is a mode of operation for a backward-wave tube equivalent to an oscillator started by and then locked to the input signal, a condition unlike anything obtained in the equivalent longitudinal twt. Also, it is shown that in a forward-wave or backward-wave tube, the gain is dependent on the input signal and may increase as the input signal level is increased. However, it is apparent that this type of device has inherently a low gain, especially when designed for high efficiency. Consequently, some suggestions which have been made for improving this deficiency are examined.

An Experimental Transverse-Current Traveling-Wave Tube

A transverse current traveling-wave tube employing a flat helix and a skew beam has been built and tested both as a forward wave amplifier and as a backward wave oscillator. The tube operates as an amplifier over the frequency range from 1 to 2 kmc with a power output of the order of 30 milliwatts. Tests on the tube indicated a gain vs voltage characteristic markedly different from that obtained with a conventional traveling-wave tube, particularly with respect to the wide range of current and voltage over which a large amount of attenuation in excess of the cold insertion loss of the circuit was observed. The general shapes of the curves of gain vs current and the gain and saturation power level vs frequency are as predicted from theory and display significant differences from calculated curves for an equivalent conventional tube. The nonlinear behavior of the tube, as a function of input signal level, follows the general pattern predicted from qualitative arguments. The output power is constant to within 0.05 db over an input power range of 20 to 30 db. With two signals of different frequencies supplied to the input of the tube, a region of operation was observed in which, with the input amplitude of one signal fixed, the output amplitudes of both signals were independent of the amplitude of the other (variable) input signal.

Theory of the Transverse-Current Traveling-Wave Tube

An analysis is presented of a traveling-wave tube in which unmodulated dc current is continuously introduced along the length of the tube and is removed after traveling a fixed distance in the presence of the circuit field. This change in the dc current distribution as compared with that of a conventional traveling-wave tube results in three forward growing waves instead of one, one growing exponentially as in the conventional tube, one growing linearly, and one growing as the square of distance. Expressions for the over-all gain of a forward-wave amplifier of this type are derived as a function of the usual parameters plus an additional parameter related to the distance traveled by electrons in the interaction space. The power output of this device is found to depend on saturation of individual current elements rather than of the beam as a whole, with the result that, after saturation is once reached, the power output is independent of input power. An estimate of the value of the saturation power level is obtained from the linear analysis.

Concerning the Noise Figure of a Backward-Wave Amplifier

The noise figure of a traveling-wave amplifier has been derived as a function of circuit loss and space charge. The minimum-obtainable noise figure of the backward-wave amplifier is shown to be the same as the minimum-obtainable noise figure of the forward-wave amplifier, i.e., about 6 db. The noise figure of an ordinary backward-wave amplifier has been measured as a function of gain. The calculated noise figure checks well with the measured values.