Resonant Ones Research Articles

Wideband circulator adjustment using the n = ±1 and n = 0 electromagnetic-field patterns

In its matched condition the scattering-matrix eigenvalues of the 3-port junction circulator lie equally spaced on a unit circle. As the frequency is varied, these eigenvalues rotate in the complex plane at different speeds, and the phase relation between them no longer corresponds to an ideal circulator. This is primarily due to the fact that the reference eigenvalue is normally associated with a nonresonant field pattern and the other two eigenvalues are associated with resonant ones. The purpose of the letter is to describe a new adjustment procedure in which the reference eigenvalue is associated with a resonant field pattern also. If the Q factors of all three field patterns are made the same, the three eigenvalues will all rotate at the same speed, around the unit circle. The bandwidth of the circulator will then be very wide.

The nonlinear theory of electromagnetic wave attenuation in plasmas

The absorption of a circularly polarized electromagnetic wave which propagates in a plasma along a magnetic field is analyzed. The exact equations of particle motion in the resonance region are solved with aid of elliptic functions. It is shown that the nonlinear damping constant has an oscillatory form. For t→0, it coincides with the constant obtained on the basis of linear theory, while for t→∞, in the absence of collisions, it tends to zero. The influence of collisions on wave absorption is studied. It is shown that with allowance for collistions, the damping constant depends on the amplitude of both the H1 and H1 −3/2 waves. The analysis of slowly decaying waves may be based on a model proposed by Dawson [1] and later modified in [2,3]. According to this model, all plasma particles are grouped into resonant and nonresonant ones. The velocity distribution function of the nonresonant particles is assumed to be the same as in the case of undamped waves. The distribution function of resonant particles at the initial instant is assumed to be Maxwellian. The nonlinear equations of motion of the resonant particles are integrated exactly. The damping constant is defined as the ratio of the energy expended by the wave at the resonant particles to the total energy of the wave. In nonlinear formulation, resonant absorption appears to be nonstationary. After a time lapse on the order of several vibrational period of a particle captured by the wave, nonstationary absorption ceases, and stationary absorption, created by infrequent collisions, becomes essential. It is noteworthy that absorption of this type has been studied by V. E. Zakharov and V. I. Karpman [4] for the case of plasma waves.