Space Charge Mode Research Articles

Effect of Various Boundary Conditions on the Instabilities in Transferred Electron Bulk Oscillators

Transferred-electron bulk-negative-differential-conductivity devices with nonuniform geometry, field, and doping distributions are analyzed. Numerical solutions of the conduction equations was possible due to the novel scheme introduced to account for the area variation in the direction transverse to the electron flow. The simulation results show that the space-charge travel can be controlled with the applied bias voltage for concentric and some other nonuniform geometries. This results in the possibility of tuning the frequency over two octaves. The nature of the frequency control characteristic is shown to be dependent on the device geometry. Dipole space-charge nucleates due to nonuniform geometry without any necessity of initialization or doping fluctuations. Multiple space-charge formation is observed to occur in an oscillation cycle as a result of sequential decay processes. Space-charge modes in nonuniform geometries display polarity dependence. Divergent and convergent geometries are shown to favor dipole and accumulation-type space charges, respectively. Analysis of devices with doping gradients demonstrate the equivalence of these gradients to the geometry nonuniformities. The analytical solutions of the conduction equations indicate the simple dependence of the space-charge behavior on the geometry. The space-charge nucleation, growth, propagation, and decay are related to the time variation of the cathode field and the domain voltage.

Nonlinear amplification of sound in a piezoelectric semiconductor

The results of the nonlinear analysis of acoustoelectric effects previously derived in connection with the acoustoelectric domain are applied here to the time independent amplification of ultrasonic waves of finite amplitude, and the correction to the linear theory which arises out of the acoustoelectric current is derived. The coupled space charge mode plays a critical part in maintaining electrical neutrality and in determining the correction to the growth constant is enhanced for omega > omega om, unaffected for omega = omega om and decreased for omega < omega om, and a downward frequency shift occurs for all frequencies ( omega om=frequency for maximum gain). The frequency shift is an order of magnitude weaker than change in growth constant.

Modes of Avalanche Diodes and Their Associated Circuits

This paper attempts to put in perspective the modes of operation of avalanche diodes. Although theoretical treatments exist that encompass all known aspects of avalanche diode behavior, the compartmentalization of behavior into well-understood special cases is of enormous help to the device and circuit designer in understanding the peculiarities encountered in experimental work. The degree of compartmentalization is, of course, an arbitrary choice but the distinction of five modes seems appropriate. These are, respectively, the IMPATT, TRAPATT, and parametric modes, which are potentially useful, and the space-charge feedback and thermal modes, which probably are not. The latter two are important, however, in that they constitute a means of diode self-destruction. The presentation is tutorial and will hopefully remove some of the confusion introduced by the varied names employed by workers in the field to describe basically simular results. The approach is one of reason rather than legalism, and should this particular compartmentalization stand the test of time, appropriate nomenclature will no doubt be decided by an international committee.

A theory of acoustoelectric domains in piezoelectric semiconductors II. Non-linear interactions

A non-linear theory using the Krylov-Bogoliubov method is developed of the growth and propagation of an acoustoelectric wave and its interaction with a space charge mode, in which the non-linearity derives solely from the drift current. First order differential equations are derived which describe the space and time development of non-linearities and it is shown that these propagate with a well-defined velocity which we have called the non-linear interaction velocity. In the case considered this velocity is near to the piezoelectrically stiffened velocity of sound νs(1 + K2)½. A general expression for the acoustoelectric current is obtained and the importance of a non-electronic loss mechanism for providing an excess field under conditions of zero linear gain is pointed out. Coupled first-order differential equations are derived which describe the time-independent travelling space profiles of the amplitude and wavelength shift of the acoustic mode, and the amplitude of the space charge mode. The waveform of the acoustic wave contains principally only the first (fundamental) and second harmonics and has a saw-tooth appearance. Comparison with a numerical computation shows that this harmonic content is surprisingly successful even in the case of substantial carrier bunching. The theory is generalized to include an arbitrary number of random-phase acoustic modes with essentially the same frequency and acoustoelectric properties. This has the effect of enhancing the acoustoelectric field, increasing the interaction with the space charge mode and making the wavelenth increase more rapidly with amplitude.

A theory of acoustoelectric domains in piezoelectric semiconductors III. Domain solution

A model for an acoustoelectric domain is obtained by solving the non-linear growth equations derived previously via the Krylov-Bogoliubov method. It is shown that the shape of the acoustic flux profile is determined by a combination of coherent and incoherent effects, the former arising from a non-linear self-interaction of a single acoustic mode, the latter arising from the interaction of all the random-phase waves in the domain with a space-charge mode. Although a flat-topped region is a possibility, the domain fields and flux intensity required for such a saturation are so high that in most practical cases it is unlikely to occur. The common situation is therefore one in which the flux profile in both edges is hyperbolic and symmetrical, the two hyperbolic wings meeting in the centre to give a cusp of high flux intensity (greater, similar100 w cm-2) and high electric field (greater, similar104v/cm-1). The domain travels at the velocity νs(1+K2)½ and the field outside the domain is at the threshold (zero net gain). Domain widths are typically 100-1000 μm. Since the field profile is hyperbolic the domain voltage does not converge, which implies some time dependence of profile though this will be weak in many cases. The downward frequency shift of the maximum-gain acoustic modes can be 30% or more. The whole basis of the model is that there is a non-electronic loss mechanism.

Theoretical analysis of log-periodic circuits in microwave amplifiers

The feasibility of applying the log-periodic concept to microwave amplifiers has been investigated. This approach, successfully utilized in antenna design, offers the potential of greater bandwidth at a given power level than attainable from existing uniform devices. Log-periodic devices analogous to klystron, traveling-wave, and hybrid amplifiers have been studied. The dimensions of each section, including the beam diameter, in a log-periodic amplifier are a constant factor times those of the preceding section. Thus the general outline of such devices is conical. These devices have been simulated on a digital computer using a model in which the coupling between periodic sections is provided by one space-charge mode and one circuit mode. The accuracy of this model has been verified by simulation of existing traveling-wave tubes. Computer results on a 100kW log-periodic "klystorn," using a backward-wave circuit with a total taper ratio of 4.6 to 1, indicate that a useful bandwidth of approximately 3 to 1 can be obtained. Increasing the mechanical taper increases the bandwidth in direct proportion. Computer results on log-periodic versions of helix traveling-wave tubes are also given.

Conservation of Small-signal Power on an Electron Beam with Rectangular Velocity Distribution

ABSTRACT For the simple case of an electron beam with rectangular velocity distribution an exact calculation is made of the small-signal power in the space charge and gas modes before and after a d.c.-velocity jump. The precise means by which power conservation is achieved in the velocity jump is determined and the results of Siegman and Shaw, which first demonstrated the lack of conservation of power in the space-charge waves of multi-velocity electron beams, are explained and put on a rigorous basis.

Orthogonal waves on electron beams

The propagation of slow electrokinetic waves on finite electron beams which fill a conducting tunnel is discussed for modes of axial symmetry. In addition to the familiar space-charge modes, a pair of modes exists which are related to the vortex frequency ( \omega_{\upsilon} = \omega_{c} - 2\theta_{0} ). The finite magnetic field introduces a coupling between these modes. A set of four orthogonal modes can be derived by the use of matrix transformations, thus eliminating the necessity of solving a complicated characteristic equation. For infinitely high magnetic fields, the two additional modes disappear and the four modes reduce to the fast and slow space-charge waves.

Coupling of Modes between a Slow-Wave Plasma Mode and a Helix

Propagation of waves in a transmission system consisting of a plasma column and a coaxial helix is investigated. The propagating characteristics of the structure are analyzed by a straightforward field analysis. It is demonstrated that the field solution can be reduced to a simple circuit equation describing two coupled tuned circuits. This analytical result shows that the propagation of waves in the plasma-helix structure can be described by a purely capacitive coupling of modes between the space-charge modes of plasma column and the helix mode. The result of this study is compared with the earlier Russian work by Bulgakov et al. The limitation of the perturbation techniques is discussed and the condition for the validity of the small perturbation assumption is given. The experimental method of separating and measuring the two coupled modes of propagation by means of mode-selecting techniques is described.

Space-charge Wave Parametric Amplifiers†

ABSTRACT An electron beam which is velocity modulated in the form of a fast space-charge mode at frequency w1 called the pump frequency, will parametrieally amplify a signal at frequency at which is applied to the beam in the form of a fast space-charge wave at w1However, due to the non-linear nature of the beam, idler frequencies lw+ mw1 (where l and m are zero or positive or negative integers) will be generated on the beam. Although in principle fast mode noise can be removed from the beam, it would be extremely awkward to attempt removal at very many of these idler frequencies. Experimental and theoretical studies indicate that noise from these higher idlers will prove serious. Accordingly, we propose to couple the signal and pump to the beam by moans of a slow wave structure with certain peculiar characteristics. The pump mode is taken as the travelling wave tube normal mode which is now growing, y3 in Pierce's notation. By varying uothe d.c. beam velocity, the phase velocity of the pump mode on the b...

Traveling-Wave Couplers for Longitudinal Beam-Type Amplifiers

The equations governing traveling-wave interaction between an electron beam and a slow-wave circuit are formulated in terms of amplitudes of circuit mode and slow and fast space charge modes. The resulting equations are solved to find expressions for the matrix which relates the mode amplitudes at the output of the traveling-wave coupler to the mode amplitudes at the input. The properties of this matrix are discussed and numerical values given for Kompfner Dip. Matrices for velocity jumps and drift regions are also given, and the characteristics of couplers which are preceded by or followed by a drift region and velocity jump are discussed. It is shown that necessary and sufficient conditions for the removal of beam noise from the fast space-charge wave by any lossless coupler are that, for a circuit input, there be no circuit output (M11 = 0) and no slow space-charge wave output (M21 = 0). These results are then applied to the design of fast space-charge wave couplers for longitudinal beam type parametric amplifiers.

Space-charge waves on annular beams in drift tubes

The general theory of the excitation of space-charge modes on an annular electron beam in a cylindrical drift tube is established for the case of infinite magnetic-focusing field. Computations for various tunnel diameters have been made, showing that, if thin annular beams are utilized, the normalized tunnel diameter which is around unity for a solid beam may be increased by a considerable factor. This factor is about 4 for a particular case. Variations of the spacing between beam and tunnel consequent upon aberrations of the focusing system should not introduce serious loss of gain or variation in performance. Since annular beams can be designed for higher perveances than can solid beams, important gains in performance can be expected.

Factors influencing the design of multi-cavity klystrons

Some of the factors which must be considered in the design of a multi-cavity klystron are examined. The electron beam and cavities should be designed so as to maximize a figure of merit—the product of the voltage gain and the bandwidth of one stage of the amplifier. The limitations on the low-level bandwidth obtainable imposed by the effects of the couplings between non-adjacent cavities can be minimized by the appropriate choice of the number and separation of the cavities. In terms of the simple space-charge-wave theory the cavities should be separated by a quarter of a plasma wavelength, but consideration of the higher-order space-charge modes shows that the optimum spacing depends on the exact beam configuration. The high-level bandwidth can be maximized by the correct design of the output cavity and external circuit, but the results which can be obtained depend on the behaviour of the electron beam at high signal levels. The theory of this, and of the debunching behaviour of the beam at long drift lengths, is not well established, and an experimental approach is required.