Theory of hydromagnetic propagation in the ionospheric waveguide
Theory of hydromagnetic propagation in the ionospheric waveguide
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电离层波导中的水磁传播理论
DOI：
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发表时间：
1968
期刊：
影响因子：
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通讯作者：
P. Greifinger
中科院分区：
文献类型：
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作者：
C. Greifinger;P. Greifinger
在本文中，我们考虑低频（Pc 1）水磁波在电离层管道中的传播，这是由 F2 电离峰值附近的阿尔文速度最小值引起的。我们考虑存在均匀静磁场的不均匀（垂直方向）波导，并处理磁子午线平面中水平传播的情况。波导中的传播由电场水平分量的两个耦合方程控制。对于夜间条件，感兴趣的电离区域从足够高的高度开始，离子与中性粒子的碰撞频率与离子回旋加速器频率相比很小，这两个分量变得不耦合，并且只需要考虑各向同性或快波。然而，在白天条件下，必须考虑快波和慢波之间的耦合；为了简化分析，在这种情况下假设静态场是均匀的。为了获得波导方程的解析解，需要对相关电离层参数的高度依赖性进行解析近似；构建这种近似值是为了适合一天中不同时间和太阳黑子活动的各种条件下的一些代表性表格电离层剖面。在适当的边界条件下求解波导方程会导致复（水平）波数和角频率之间相当复杂的色散关系。色散关系的解规定了波导中允许的传播频带。结果表明，每个频段（包括最低频段）都有一个低频截止，并且低频截止的存在是边界条件的结果，而不是某些理论中假设的衰减的结果。针对所考虑的每个条件，获得两个最低频带的色散方程的数值解。根据波数实部对频率的依赖性，可以确定截止频率以及相速度和群速度，而虚部则提供衰减长度。对于夜间条件，衰减并不大，传播距离可以达到数千公里，而白天传播则受到衰减的限制，只能达到数百公里的距离。对于夜间最低条件，计算出的波导截止约为 0.4 cps，最低频段的群速度约为 720 km/sec，两者与实验相符。最后，指出对于地面信号而言，由于传输系数随高频频率呈指数下降，因此存在有效的高频“截止”（在任何频段）。
In this paper, we consider the propagation of low-frequency (Pc 1) hydromagnetic waves in the ionospheric duct, which results from the minimum in the Alfven speed near the F2 ionization peak. We consider an inhomogeneous (in the vertical direction) waveguide in the presence of a uniform static magnetic field and treat the case of horizontal propagation in the plane of the magnetic meridian. Propagation in the waveguide is governed by two coupled equations for the horizontal components of the electric field. For nighttime conditions, where the ionized region of interest starts at sufficiently high altitude that the collision frequency of ions with neutrals is small compared with the ion cyclotron frequency, the two components become uncoupled, and only the isotropic, or fast wave, need be considered. For daytime conditions, however, coupling between the fast and slow waves must be taken into account; to simplify the analysis, the static field is assumed uniform in this case. To obtain analytic solution of the waveguide equations, it is necessary to have analytic approximations to the height dependence of the relevant ionospheric parameters; such approximations are constructed to fit some representative tabulated ionospheric profiles for a variety of conditions of time of day and sunspot activity. Solution of the waveguide equations subject to the appropriate boundary conditions results in a rather complicated dispersion relation between complex (horizontal) wave number and angular frequency. The solutions of the dispersion relation prescribe the allowed bands of propagation in the guide. It is shown that each band, including the lowest, has a low-frequency cutoff, and that the existence of a low-frequency cutoff is a consequence of the boundary conditions and not of attenuation, as assumed in some theories. Numerical solutions of the dispersion equation are obtained for the two lowest bands for each of the conditions considered. From the dependence of the real part of the wave number on frequency, the cutoff frequencies and the phase and group velocities are determined, while the imaginary part provides the attenuation length. For nighttime conditions, attenuation is not large, and propagation can take place over distances of thousands of km, whereas daytime propagation is restricted by attenuation to distances of the order of hundreds of km. For nighttime minimum conditions, the calculated waveguide cutoff is about 0.4 cps, and the group velocity for the lowest band is about 720 km/sec, both in reasonable agreement with experiment. Finally, it is pointed out that there is an effective high-frequency ‘cutoff’ (in any band) as far as ground-level signals are concerned due to an exponential decrease of transmission coefficient with frequency at high frequencies.