Characteristics of traveling-wave tubes with periodic circuits

An analysis of an electron beam which interacts with a chain of coupled resonators is presented. Several important characteristics of traveling-wave tubes which employ periodic slow-wave circuits are described. It is found that, even for a lossless circuit, the gain does not become large near either pass band edge although the interaction impedance does become very large. Furthermore, useful amplification is found to occur outside the normal circuit pass band, particularly when the frequency is below the low-frequency cutoff where the circuit presents an inductive reactance to the beam. The problem of matching uniform transmission lines to the periodic circuit is discussed from the equivalent circuit point of view and it is shown that the terminating impedance which produces no reflection from the output end of the circuit when the beam is present may be appreciably different from that required when the beam is absent. The method of analysis applies to spatial harmonic operation, including backward spatial harmonics, as well as to synchronously tuned multicavity klystrons

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

Thermal Fluctuations: Modes versus the Continuum

The thermal fluctuation spectrum of the signal received on a patch electrode is examined and it is shown that the spectrum shows both the modes of the plasma and a continuous spectrum related to the independent-particle motions of plasma electrons. Modes whose axial phase velocity are more than 3–4 times the electron thermal speed are lightly Landau-damped and are clearly separated from the continuum. Long wavelength modes are "acoustic" in nature. If the axial phase velocity of a mode becomes less than 1–2 times the electron thermal speed, then the mode becomes strongly Landau-damped and it merges into the continuum. The mode velocities are of the order of wpa , where a is the plasma radius, so that the plasma radius must be at least several deBye lengths in order to have lightly damped modes. In general, the spectrum is a mixture of a continuous spectrum together with a finite number of modes which are Landau-damped by varying amounts, depending on their phase velocity relative to the electron thermal speed. Only in the extreme limit, wpa << vth does the continuous spectrum tend to a Gaussian of width k vth, characteristic of independent particles. The effect of the "load impedance" on the measurements is also discussed

Thermal excitation of modes in a non-neutral plasma

We examine theoretically the thermal fluctuations in a non-neutral plasma, as observed on a segmented electrode surrounding the plasma, using the Nyquist theorem. The fluctuation spectrum is peaked at frequencies which correspond to modes of the plasma. Measurement of these fluctuations and of the input admittance of the plasma in the vicinity of one of the mode resonances can be used to give a completely experimental, and non-destructive, measurement of the plasma temperature. Since some of the modes are negative energy modes and exhibit negative absorption due to the plasma rotation, a direct application of the Nyquist theorems will not give correct results for the non-axisymmetric modes. This problem is circumvented by first calculating the fluctuations in a frame rotating with the plasma and transforming to the laboratory frame. This results in a modification of Nyquist's theorem. Measurement issues are discussed

Dynamics of non-neutral plasmas

In this paper the focus is on the dynamics of two-dimensional cylindrical non-neutral plasmas. After reviewing some highlights of the non-neutral plasma dynamics, some recent two-dimensional results are described: vortex dynamics, diocotron instabilities of hollow profiles, collisionless damping of modes and fluid trapping by modes, fluid echoes, the cyclotron center of mass modes and warm plasma Bernstein modes, and temperature determination from fluctuation measurements. Attention is called to some unsolved problems

Numerical Study of Collisional Effects on Spatial Ion-Wave Echoes

Collisional effects on the second-order spatial ion-wave echo are studied numerically. General agreement is obtained with the experimental results of Ikezi, Takahashi, and Nishikawa. A critical argument is raised against the validity of the small collision approximation

Single Pulse Response of a Plasma

The conjecture by Hirschfield and Wachtel that a weak pulse of radiation can trigger the emission of a large delayed burst of coherent electron cyclotron radiation is examined critically. The effect is found to exist when the electrons have a single velocity perpendicular to the magnetic field, but disappears in a thermal equilibrium distribution

Echo Phenomena

Due to small nonlinearities, an ensemble of oscillators may exhibit echoes when subjected to multiple pulses of radiation near their resonant frequency. Cyclotron echoes from gyrating charged particles is discussed as an example

Space Charge Effects in Beam‐Type Magnetrons

A theoretical treatment of space charge effects in beam‐type magnetron amplifiers and oscillators is given. It is assumed that the beam is relatively thin and that the magnetic field is large. The "cyclotron waves" are not treated. A space charge parameter appears in this theory of magnetron‐type traveling‐wave interaction in a manner which is analogous to the manner in which QC appears in ordinary traveling‐wave interaction. A distinctive feature of the space charge waves in the magnetron case is that one increases along the beam and the other decreases along the beam. A simple physical explanation of this effect is given. This theory is then used to determine the starting conditions of an M‐type backward wave oscillator. It is found that when the tube is long in space charge wavelengths there is an appreciable reduction of starting current. When the space charge parameter approaches zero, the solutions found here reduce to the usual two‐wave solutions