Vol. 18, No. 12 (1962)
1962, 18 (12): 621-628. doi: 10.7498/aps.18.621
Starting from the dispersion relation we have discussed low energies π-N scattering amplitude with isospin positive part. It is shown that for P1/2+ -wave, the results evaluating from CGLN formula are essentially in agreement with experiments. But for S-wave, when comparing with experiments, even the sign of CGLN results is wrong. Further they are increasing as energy very rapidly that exceeds the limit allowed by the unitary condition. From analysis it is shown that one cannot solve this problem and at the same time keep the agreeing of the calculated P1/2+-wave results with the experiments by introducting a π-π S-wave interaction. But alternatively if we attacked from the π-N S-partial wave dispersion relation with one subtraction, then the results agree with the experiments fairly well. So it is likely that the π-π S-wave interaction plays an unimportant role in it.
1962, 18 (12): 629-635. doi: 10.7498/aps.18.629
In this paper we studied the Maxwell's equations in imhomogeneous and anisotropic media as an operator. It is defined in a bounded region, which can be comprehended as a resonant cavity in micro-wave technique. But these cavities are filled with ferrite, plasma or other gyrotropic medium, all these new media become more and more important in practice. We proved that under some concrete conditions imposed on μ, ε and restrictions on the boundary value, the operator of Maxwell's equations becomes a symmetric one. The symmetry and self-adjoint property give much convenience in eigenfunction expansion problems. Besides, we derived the orthogonality of characteristic oscillation and reciprocity theorem in general.If it does not satisfy the conditions of symmetry, we introduced the concept of adjoint-cavity. The so-called adjoint cavity coincides with the primary cavity in geometrical shape, but both μ, ε and boundry conditions do not coincide. It has some properties similiar with self-adjoint cavity in orthogonality and reciprocity theorem.
ABOUT ONE METHOD OF FINDING THE GREEN TENSOR FUNCTIONS OF ELECTROMAGNETIC FIELD IN ANISOTROPIC MEDIA
1962, 18 (12): 636-645. doi: 10.7498/aps.18.636
In this paper, we suggest one method of finding the Green tensor functions in whole space, which are defined in formula (3). Some times it is also called the elementary solution of the corresponding differential equation. All this method is based on Fourier transform. Owing to complexity, we are obliged to make some simplifications. Magneto-gyrotropic media and electric-gyrotropic media are considered separately. For magneto-gyrotropic medium, such as ferrite, μ, is a tensor while ε remains scalar. Conversely, for electric-gyrotropic medium, such as plasma, ε is tensor and μ remains scalar. Taking advantage of the smallness of matrix μp (defined in (15)) we make an expansion in power series of μp, and carry out the calculations in first order approximation. The concrete results are expressed in formulae (23)、(25)、(28)、(32) and (33). The physical meaning of Γ and the effective region of the asymptotic expansions are discussed.
1962, 18 (12): 646-656. doi: 10.7498/aps.18.646
In a ferroresonant circuit containing incandescent lamps of suitable capacity, flickering phenomenon was observed. In the present paper, the explanation about this flickering phenomenon is given, the condition under which this flicker takes place is pointed out, and the method of computing the flicker period is given. The experiment data agree with he theoretical results approximately.
1962, 18 (12): 657-669. doi: 10.7498/aps.18.657
In this paper the principle of simulating an axial and plane symmetrical magnetic field by a resistance network analogue is analysed. The method of current injection has also been discussed and the formula for the second order approximation was given. Based on the above principle, a resistance network analogue with associated apparatus was constructed. The central part of the network contains 10×14 units. It is extended by end strips to 28 and 32 units in z and r directions respectively. Experiments have been done with this network for several types of field, which have precise solutions analytically. Errors of the network under various conditions were noted and its origin traced. Experience shows that the analogue is reliable. It shortens considerably the time required for the design of many complex magnetic configurations.