桨叶实度及轴间距对摆线桨气动特性影响研究

悬停状态下,设计参数和摆线桨间距离对摆线桨的气动特性有较大影响。首先通过算例验证滑移网格计算方法应用于摆线桨悬停状态下气动力计算的准确性,然后研究摆线桨在不同半径、弦长和桨叶数时的气动参数特性,最后计算分析不同距离时,摆线桨间的气动干扰特性。结果表明:随着半径增大,桨叶气动力和单位面积上载荷均增大;弦长越大,气动力越大,桨叶单位面积上载荷反而越小;4叶片摆线桨产生的气动力比3叶片和6叶片大,而3叶片的桨叶载荷最大;合力偏转角分别随转速和实度的增大而减小;随着摆线桨间距离的增加,气动力损失系数和合力偏转角均减小。     

Interaction of non-perpendicular/parallel solar wind shock waves with the earth's magnetosphere

The interaction of travelling interplanetary shock waves with the bow shock-magnetosphere system is considered. We consider the general case when the interplanetary magnetic field is oblique to the Sun-planetary axis, thus, the interplanetary shock is neither parallel nor perpendicular. We find that an ensemble of shocks are produced after the interaction for a representative range of shock Mach numbers. First, we find that the system S ₊ R _– CS _– S ₊ appears after the collision of travelling fast shock waves S ₊ (Mach number M = 2 to 7) with the bow shock. Here, S _– and R _– represent the slow shock wave and slow rarefaction wave, and C represents the contact surface. It is shown that in the presence of an interplanetary field that is inclined by 45° to the radial solar wind velocity vector, the waves R _– and S _– are weak waves and, to the first degree of approximation, the situation is similar to the previously studied normal perpendicular case. The configuration, R ₊ C _m S _– S ₊ or R ₊ C _m R _– S ₊ where C _m is the magnetopause, appears as the result of the fast shock wave's collision with the magnetopause. In this case the waves S _– and R _– are weak. The fast rarefaction wave reflected from the magnetosphere is developed similar to the case for the collision of a perpendicular shock. The shock wave intensity is varied for Mach numbers from 2 to 10. Thus, in the limits of the first approximation, the validity of the one-dimensional consideration of the nonstationary interaction of travelling interplanetary shock waves with the bow shock-magnetosphere system is proved. The appearance of the fast rarefaction wave, R ₄, decreasing the pressure on the magnetosphere of the Earth after the abrupt shock-like contraction, is proved. A possible geomagnetic effect during the global perturbation of the SSC or SI⁺ type is discussed.An invited paper presented at STIP Workshop on Shock Waves in the Solar Corona and Interplanetary Space, 15–19 June, 1980, Smolenice, Czechoslovakia.     

Investigations of entrainment characteristics and shear-layer vortices evolution in an axisymmetric rear variable area bypass injector

In this study,firstly,for the axisymmetric RVABI,the change-rule of adverse pressure gradient caused by radial velocity during the transition of internal flow mode in variable geometry is summarized,and a Bypass Ratio(BR) iterative algorithm based on the empirical correlation of non-equilibrium pressure is proposed.The algorithm can estimate the nonlinear relationship between area ratio and BR,with an error range falling below 6.5%.Then,we discuss the favorable effect of uniform mixing on the th...     

Instability characteristics of a co-rotating wingtip vortex pair based on bi-global linear stability analysis

The Stereo Particle Image Velocimetry (SPIV) technology is applied to measure the wingtip vortices generated by the up-down symmetrical split winglet. Then, the temporal bi-global Linear Stability Analysis (bi-global LSA) is performed on this nearly equal-strength co-rotating vortex pair, which is composed of an upper vortex (vortex-u) and a down vortex (vortex-d). The results show that the instability eigenvalue spectrum illustrated by (ω_r, ω_i) contains two types of branches: discrete branch and continuous branch. The discrete branch contains the primary branches of vortex-u and vortex-d, the secondary branch of vortex-d and coupled branch, of which all of the eigenvalues are located in the unstable half-plane of ω_i > 0, indicating that the wingtip vortex pair is temporally unstable. By contrast, the eigenvalues of the continuous branch are concentrated on the half-plane of ω_i < 0 and the perturbation modes correspond to the freestream perturbation. In the primary branches of vortex-u and vortex-d, Mode P_u and Mode P_d are the primary perturbation modes, which exhibit the structures enclosed with azimuthal wavenumber m and radial wavenumber n, respectively. Besides, the results of stability curves for vortex-u and vortex-d demonstrate that the instability growth rates of vortex-u are larger than those of vortex-d, and the perturbation energy of Mode P_u is also larger than that of Mode P_d. Moreover, the perturbation energy of Mode P_u is up to 0.02650 and accounts for 33.56% percent in the corresponding branch, thereby indicating that the instability development of wingtip vortex is dominated by Mode P_u. By further investigating the topological structures of Mode P_u and Mode P_d with streamwise wavenumbers, the most unstable perturbation mode with a large azimuthal wavenumber of m = 5–6 is identified, which imposes on the entire core region of vortex-u. This large azimuthal wavenumber perturbation mode can suggest the potential physical-based flow control strategy by manipulating it.     

Effects of Alloying Elements Ti, Cr, Al, and Hf on β-Nb5Si3 from First-principles Calculations

The energy, lattice parameters, electronic structures, and elastic constants of the intermetallic compound β-Nb₅Si₃ alloyed by Ti, Cr, Al, and Hf elements are investigated using first-principles methods based on plane-wave pseudopotential theory. From the impurity formation energy calculated, it is found that Ti, Cr, and Hf prefer to occupy the Nb_I, Nb_I, and Nb_II site, respectively, and that Al decreases the stability of β-Nb₅Si₃. Ti and Cr atoms reduce the c/a ratio of crystal lattices and Hf atom transforms the crystal lattice of β-Nb₅Si₃ from the tetragonal system to the orthorhombic system. The total state density of pure β-Nb₅Si₃ system and Ti, Cr, and Hf doped systems shows that Ti, Cr, and Hf improve the conductibility of β-Nb₅Si₃ system. The bulk modulus, shear modulus, and elastic modulus are obtained using Voight approximation equation. Ti and Cr increase the hardness and reduce the ductility of β-Nb₅Si₃. In contrast, Hf decreases the hardness and improves the ductility.     

Microstructure and Mechanical Properties of In-situ Synthesized Al2O3/TiAl Composites

Al2O3 particle-reinforced TiAl composites are successfully reaction-synthesized from the powder mixture of Ti, Al, TiO2, and Nb2O5, using the hot pressing reaction synthesis technique. The microstructure and mechanical properties of the as-sintered products are investigated. It is found that in the as-sintered products consisting of γ-TiAl, α2-Ti3Al, Al2O3, and NbAl3 phases, the fine Al2O3 particles tend to disperse on the grain boundaries. With the Nb2O5 content increasing, the grains are remarkably refined and the Al2O3 particles are dispersing more uniformly in the TiAl matrix, forming a partial lamellar structure containing α and lamellar phases. The hardness of the in-situ composites increases gradually, and the bending strength and the fracture toughness of the as-sintered products reach the maximum value of 398.5 MPa and 6.99 MPa·m^1/2, respectively, as the Nb2O5 content increases to 6 wt%.     

冷轧变形对Inconel 718合金δ相γ″相析出行为的影响

采用X射线衍射技术测定了冷轧Inconel718合金在860℃加热温度下的δ相和γ″相含量,研究了冷轧变形对δ相和γ″相析出行为的影响。结果表明,冷轧变形影响δ相的析出形貌,随冷轧变形量增加,δ相由针状向颗粒状转变。δ相析出的重量百分数与时间的关系符合Avrami方程,随冷轧变形量增加,n值减小,α值增加。在860℃加热温度下,等温15min时已有γ″相析出,随时间增加,γ″相含量增加,达到最大值后又降低。在试验中给定的时间条件下,随冷轧变形量增加,γ″相含量降低,而δ相含量增加。     

Deep Impact: Working Properties for the Target Nucleus – Comet 9P/Tempel 1

In 1998, Comet 9P/Tempel 1 was chosen as the target of the Deep Impact mission (A’Hearn, M. F., Belton, M. J. S., and Delamere, A., Space Sci. Rev., 2005) even though very little was known about its physical properties. Efforts were immediately begun to improve this situation by the Deep Impact Science Team leading to the founding of a worldwide observing campaign (Meech et al., Space Sci. Rev., 2005a). This campaign has already produced a great deal of information on the global properties of the comet’s nucleus (summarized in Table I) that is vital to the planning and the assessment of the chances of success at the impact and encounter. Since the mission was begun the successful encounters of the Deep Space 1 spacecraft at Comet 19P/Borrelly and the Stardust spacecraft at Comet 81P/Wild 2 have occurred yielding new information on the state of the nuclei of these two comets. This information, together with earlier results on the nucleus of comet 1P/Halley from the European Space Agency’s Giotto, the Soviet Vega mission, and various ground-based observational and theoretical studies, is used as a basis for conjectures on the morphological, geological, mechanical, and compositional properties of the surface and subsurface that Deep Impact may find at 9P/Tempel 1. We adopt the following working values (circa December 2004) for the nucleus parameters of prime importance to Deep Impact as follows: mean effective radius = 3.25± 0.2 km, shape – irregular triaxial ellipsoid with a/b = 3.2± 0.4 and overall dimensions of ∼14.4 × 4.4 × 4.4 km, principal axis rotation with period = 41.85± 0.1 hr, pole directions (RA, Dec, J2000) = 46± 10, 73± 10 deg (Pole 1) or 287± 14, 16.5± 10 deg (Pole 2) (the two poles are photometrically, but not geometrically, equivalent), Kron-Cousins (V-R) color = 0.56± 0.02, V-band geometric albedo = 0.04± 0.01, R-band geometric albedo = 0.05± 0.01, R-band H(1,1,0) = 14.441± 0.067, and mass ∼7×10¹³ kg assuming a bulk density of 500 kg m⁻³. As these are working values, {i.e.}, based on preliminary analyses, it is expected that adjustments to their values may be made before encounter as improved estimates become available through further analysis of the large database being made available by the Deep Impact observing campaign. Given the parameters listed above the impact will occur in an environment where the local gravity is estimated at 0.027–0.04 cm s⁻² and the escape velocity between 1.4 and 2 m s⁻¹. For both of the rotation poles found here, the Deep Impact spacecraft on approach to encounter will find the rotation axis close to the plane of the sky (aspect angles 82.2 and 69.7 deg. for pole 1 and 2, respectively). However, until the rotation period estimate is substantially improved, it will remain uncertain whether the impactor will collide with the broadside or the ends of the nucleus.     

两种同类型胶片基础特性及检测应用比对

文摘针对如何在液体火箭发动机产品射线检测过程中,根据具体情况选择合适的射线胶片,达到既能保证射线检测图像质量又能提高检测效率减少检测成本的目的,本文通过对进口富士IX100型胶片和国产乐凯牌L7型胶片的特性和质量稳定性进行工艺对比试验。结果表明,L7型胶片本底灰雾度稍大于IX100型胶片,灵敏度逊于IX100型胶片,宽容度高于IX100型;但两者均属于GB/T19348.1—2003规定的T3范畴胶片,综合性能比较接近;L7型胶片适用于发动机上具有变截面的铝铸件、机加余量不大的钢铸件、钛铸件及大部分熔焊缝的射线检测。     

Microstructure evolution of a hypereutectic Nb–Ti–Si–Cr–Al–Hf alloy processed by directional solidification

In this work, the Nb–14Si–24Ti–10Cr–2Al–2Hf–0.1Y alloy(at.%) was processed by the liquid–metal-cooled directional solidification(DS) at 1750 C with withdrawal rates of 1.2, 6,18 mm/min and post heat treatment(HT) at 1450 C for 10 h. The microstructures of the directionally solidified and heat treated samples were investigated. The results show that the microstructure of directionally solidified alloy mainly consists of petaloid Nbss+ Nb5Si3eutectics and Ti-rich Nbss+ Nb5Si3+ Cr2Nb eutectics. With the increase of withdrawal rate, the primary Nb5Si3is eliminated, Nbss+ Nb5Si3eutectic cells turn round and connected with the microstructure refinement and Nbss+ Nb5Si3+ Cr2Nb eutectics turn to a river-like morphology. After heat treatment,Nbss+ Nb5Si3+ Cr2Nb eutectics disappeared and petaloid Nbss+ Nb5Si3eutectics turn to a specific fiber-mesh structure gradually, which is promoted by higher withdrawal rates. Furthermore,both the volume fraction of Cr2Nb and the content of Cr in Nbssof Nbss+ Nb5Si3eutectics change regularly with the increase of withdrawal rate and heat treatment at 1450 C for 10 h.     

求解具有多层试验数据成败型单元混联系统可靠性近似限的信息论方法

研究了求解具有多层成败型试验数据时,系统可靠性置信下限近似解的信息论方法,给出了各层试验数据综合的方法和步骤,推导了各层数据信息论方法折合及综合的计算公式。根据单元试验信息提供的信息量与系统折合试验应提供的信息量相等的原则,将多层试验数据逐级折合为系统的等效成败型数据,导出了等效成败型数据信息论方法折合的基本公式;结合可靠性工程的基本原理,根据单个成败型单元可靠性评定的经典精确置信限方法,给出了系统可靠性置信下限的近似解。并以实例形式说明了该方法的具体应用。     

Evolution into contact of the low-mass close binary systems

We investigated the effect of mass accretion on the secondary components in close binomy systems (M _total ≤ 2.5 M _⊙ M _2,0 ≤ 0.75 M _⊙) exchanging mass in the case A. The evolution of the low-mass close binary systems (M _total ≤ 2.5 M _⊙) exchanging the mass in the case A depends on the three main factors:

-the initial mass ratio (q ₀ = M _2,0/M _1,0), which determines the rate of mass transfer between components;

-the inital mass of the secondary component (M _2,0) and

-the effectiveness of the heating of the photosphere of the secondary component, by infalling matter.

The second factor allows to divide all systems into two essentially different groups:

1. systems in which the secondary component is a star with a radiative envelope, or with a thin convection zone in the uppermost layers;
2. and systems in which secondary component has a thick convective envelope or is fully convective.

The systems from the first group evolve into contact in a characteristic time scale 10⁵ – 10⁷ years, and reach contact after transfering of 0.03 – 0.3 M _⊙. The mass exchange proceeds only in a thermal time scale. For the systems from the group b the effectiveness of the heating of the stellar surface is the most important. In the case when the entropy of the newly accreted matter is the same as the surface entropy of the secondary, a convective star should shrink upon accretion. Then contact binaries are not formed. In the case when the entropy of the infalling matter is greater then that on the surface, the reaction of the secondary is different. The radius of the secondary component grows rapidly in response to accretion, and the systems reaches contact after the 10³ – 3 10⁶ years, and after transfer of 0.002 – 0.2. M _⊙. The reaction of the secondary is determined by the formation of the temperature inversion layer below the stellar surface. Full references in: Sarna, M.J. and Fedorova, A.V. (1988) “Evolutionary status of W UMa-type Binaries — Evolution into contact”, Astron. Astrophys., in press.     

Magnetospheric Science Objectives of the <Emphasis Type="Italic">Juno</Emphasis> Mission

In July 2016, NASA’s Juno mission becomes the first spacecraft to enter polar orbit of Jupiter and venture deep into unexplored polar territories of the magnetosphere. Focusing on these polar regions, we review current understanding of the structure and dynamics of the magnetosphere and summarize the outstanding issues. The Juno mission profile involves (a) a several-week approach from the dawn side of Jupiter’s magnetosphere, with an orbit-insertion maneuver on July 6, 2016; (b) a 107-day capture orbit, also on the dawn flank; and (c) a series of thirty 11-day science orbits with the spacecraft flying over Jupiter’s poles and ducking under the radiation belts. We show how Juno’s view of the magnetosphere evolves over the year of science orbits. The Juno spacecraft carries a range of instruments that take particles and fields measurements, remote sensing observations of auroral emissions at UV, visible, IR and radio wavelengths, and detect microwave emission from Jupiter’s radiation belts. We summarize how these Juno measurements address issues of auroral processes, microphysical plasma physics, ionosphere-magnetosphere and satellite-magnetosphere coupling, sources and sinks of plasma, the radiation belts, and the dynamics of the outer magnetosphere. To reach Jupiter, the Juno spacecraft passed close to the Earth on October 9, 2013, gaining the necessary energy to get to Jupiter. The Earth flyby provided an opportunity to test Juno’s instrumentation as well as take scientific data in the terrestrial magnetosphere, in conjunction with ground-based and Earth-orbiting assets.     

Influences of milling and grinding on machined surface roughness and fatigue behavior of GH4169 superalloy workpieces

Surface topography of superalloy GH4169 workpieces machined by milling and grinding is different significantly. Meanwhile, surface roughness, as one of the main indicators of machined surface integrity, has a great influence on the fatigue behavior of workpieces. Based on analyzing the formation mechanism and characteristics of surface roughness utilizing different machining processes and parameters, the machined surface roughness curve can be decoupled into two parts utilizing frequency spectrum analysis, which are kinematic surface roughness curve and stochastic surface roughness curve. The kinematic surface roughness curve is influenced by machining process,parameters, geometry of the cutting tool or wheel, the maximum height of which is expressed as R'_z.By subtracting the kinematic part from the measurement curve, the stochastic surface roughness curve and its maximum height R'_zcan be obtained, which is influenced by the defects of cutting tool edge or abrasive grains, built-up edges(BUE), cracks, high frequency vibration and so on. On the other hand, the results of decoupling analysis of surface roughness curves indicate that Raand Rz values of milling GH4169 are 2–5 times and 1–3 times as high as those of grinding, while R'_zvalue of milling is 13.85%–37.7% as high as that of grinding. According to the results of fatigue life tests of specimens machined by milling and grinding, it can be concluded that fatigue behavior of GH4169 decreases with the increase of R'_zmonotonically, even utilizing different machining processes.     

The Cool Interstellar Medium

Infrared spectroscopy and photometry with ISO covering most of the emission range of the interstellar medium has led to important progress in the understanding of the physics and chemistry of the gas, the nature and evolution of the dust grains and also the coupling between the gas and the grains. We review here the ISO results on the cool and low-excitation regions of the interstellar medium, where T _gas≲ 500 K, n _H∼ 100–10⁵ cm⁻³ and the electron density is a few 10⁻⁴. JEL codes: D24, L60, 047 Based on observations with ISO, an ESA project with instruments funded by ESA Member States (especially the PI countries: France, Germany, The Netherlands, and the United Kingdom), and with the participation of ISAS and NASA.     

Quantification of parametric uncertainty in γ-Reθ model for typical flat plate and airfoil transitional flows

Owing to the lack of physical knowledge of boundary layer transition, the γ-Re_θ transition model introduces closure parameters, which increase the uncertainty of transition prediction. The objective of this work is to quantify the uncertainties of closure parameters in the quantities of interests and identify the key parameters. The six closure parameters in the uncertainty intervals are used as input variables, and the uncertainties of the output results are propagated by a stochastic expansion based on the point-collocation nonintrusive polynomial chaos method. The relative contribution of each parameter to uncertainty is evaluated by the Sobol index. The computational cases include natural and bypass transitional flows on zero-pressure-gradient flat plates, and subsonic and transonic flows around airfoils. For most cases, c_e2, c_a2, and c_a1 dominate the uncertainty, and the influence of σ_θt is also significant when the history effects of flow are evident. The contribution of parameters in airfoils is more complex than that in flat plates. The transonic airfoil case shows that flow separation dramatically changes the distribution of Sobol indices, which poses a challenge to the accurate prediction of transition. Generally, c_e2 and c_a2 are the key parameters of the γ-Re_θ model.     

Magnetosphere Imaging Instrument (MIMI) on the Cassini Mission to Saturn/Titan

The magnetospheric imaging instrument (MIMI) is a neutral and charged particle detection system on the Cassini orbiter spacecraft designed to perform both global imaging and in-situ measurements to study the overall configuration and dynamics of Saturn’s magnetosphere and its interactions with the solar wind, Saturn’s atmosphere, Titan, and the icy satellites. The processes responsible for Saturn’s aurora will be investigated; a search will be performed for substorms at Saturn; and the origins of magnetospheric hot plasmas will be determined. Further, the Jovian magnetosphere and Io torus will be imaged during Jupiter flyby. The investigative approach is twofold. (1) Perform remote sensing of the magnetospheric energetic (E > 7 keV) ion plasmas by detecting and imaging charge-exchange neutrals, created when magnetospheric ions capture electrons from ambient neutral gas. Such escaping neutrals were detected by the Voyager l spacecraft outside Saturn’s magnetosphere and can be used like photons to form images of the emitting regions, as has been demonstrated at Earth. (2) Determine through in-situ measurements the 3-D particle distribution functions including ion composition and charge states (E > 3 keV/e). The combination of in-situ measurements with global images, together with analysis and interpretation techniques that include direct “forward modeling’’ and deconvolution by tomography, is expected to yield a global assessment of magnetospheric structure and dynamics, including (a) magnetospheric ring currents and hot plasma populations, (b) magnetic field distortions, (c) electric field configuration, (d) particle injection boundaries associated with magnetic storms and substorms, and (e) the connection of the magnetosphere to ionospheric altitudes. Titan and its torus will stand out in energetic neutral images throughout the Cassini orbit, and thus serve as a continuous remote probe of ion flux variations near 20R _S (e.g., magnetopause crossings and substorm plasma injections). The Titan exosphere and its cometary interaction with magnetospheric plasmas will be imaged in detail on each flyby. The three principal sensors of MIMI consists of an ion and neutral camera (INCA), a charge–energy–mass-spectrometer (CHEMS) essentially identical to our instrument flown on the ISTP/Geotail spacecraft, and the low energy magnetospheric measurements system (LEMMS), an advanced design of one of our sensors flown on the Galileo spacecraft. The INCA head is a large geometry factor (G ∼ 2.4 cm² sr) foil time-of-flight (TOF) camera that separately registers the incident direction of either energetic neutral atoms (ENA) or ion species (≥5^∘ full width half maximum) over the range 7 keV/nuc < E < 3 MeV/nuc. CHEMS uses electrostatic deflection, TOF, and energy measurement to determine ion energy, charge state, mass, and 3-D anisotropy in the range 3 ≤ E ≤ 220 keV/e with good (∼0.05 cm² sr) sensitivity. LEMMS is a two-ended telescope that measures ions in the range 0.03 ≤ E ≤ 18 MeV and electrons 0.015 ≤ E≤ 0.884 MeV in the forward direction (G ∼ 0.02 cm² sr), while high energy electrons (0.1–5 MeV) and ions (1.6–160 MeV) are measured from the back direction (G ∼ 0.4 cm² sr). The latter are relevant to inner magnetosphere studies of diffusion processes and satellite microsignatures as well as cosmic ray albedo neutron decay (CRAND). Our analyses of Voyager energetic neutral particle and Lyman-α measurements show that INCA will provide statistically significant global magnetospheric images from a distance of ∼60 R _S every 2–3 h (every ∼10 min from ∼20 R _S). Moreover, during Titan flybys, INCA will provide images of the interaction of the Titan exosphere with the Saturn magnetosphere every 1.5 min. Time resolution for charged particle measurements can be < 0.1 s, which is more than adequate for microsignature studies. Data obtained during Venus-2 flyby and Earth swingby in June and August 1999, respectively, and Jupiter flyby in December 2000 to January 2001 show that the instrument is performing well, has made important and heretofore unobtainable measurements in interplanetary space at Jupiter, and will likely obtain high-quality data throughout each orbit of the Cassini mission at Saturn. Sample data from each of the three sensors during the August 18 Earth swingby are shown, including the first ENA image of part of the ring current obtained by an instrument specifically designed for this purpose. Similarily, measurements in cis-Jovian space include the first detailed charge state determination of Iogenic ions and several ENA images of that planet’s magnetosphere.This revised version was published online in July 2005 with a corrected cover date.     

Al含量对空心阴极等离子烧结Ti/Ni等原子比TiNiAl合金组织和力学性能的影响

 采用空心阴极等离子烧结工艺制备了Ti/Ni等原子比的Ti_50-x/2Ni_50-x/2Al_x(x=0,3,6,9)合金,研究了Al含量对合金微观组织以及力学性能的影响。结果表明:未添加铝的合金微观组织主要由NiTi基体、强化相Ti₂Ni、Ni₃Ti及孔隙组成;随着Al含量的提高,合金中Ti₂Ni(Al)数量不断增多,孔隙数量和孔径不断增加,Ni₃Ti(Al)数量不断减少,在Ti_45.5Ni_45.5Al₉中还生成了少量Ni₂TiAl相;合金的抗弯强度随Al含量的提高而增加,并在Al含量为6%时达到最大值296.3 MPa;合金的硬度随铝含量的提高而增加,Ti_45.5Ni_45.5Al₉的硬度值为295.6 HV。     

Non-linear resonant excitation of whistler mode waves in the Earth's ionosphere

We examine the resonant non-linear interaction in the Earth's ionosphere of two powerful high frequency radio beams with frequencies f ₁ and f ₂ (both larger than the plasma frequency at F2_max) and wave numbers k ₁ and k ₂ such that a whistler mode wave can be excited with a frequency f ₃ = f ₁ — f ₂ and a wave number k ₃ = k ₁ – k ₂. The feasibility of an effective ground based installation, sited at low latitudes, is discussed and the field strength of the wave emerging from a 10 km wide ionospheric region illuminated by the beams is evaluated for a range of transmitted frequencies, beam orientations and plasma frequencies in the interaction region. It is suggested that the longitude dependence of the enhancement of VLF noise bands detected by the Ariel 3 satellite may be due to a non-linear interaction of this type between any two or more medium wavelength signals from areas where there is a high concentration of commercial broadcasting stations, such as the NE region of the U.S.A.