The atmospheric winds at ionospheric altitudes exhibit irregular short‐period wavelike components that have been observed through their distortion of meteor ionization trails and rocket vapor trails. An explanation for these components was proposed by Hines in his theory for internal atmospheric gravity waves in an isothermal medium. The isothermal theory is refined here to unify the treatment of acoustic, gravity, and evanescent waves in a gravitational atmosphere and to explain the physical processes behind these atmospheric motions. A technique is developed for the solution of the complete hydrodynamic equations that avoids the fatal difficulties normally caused by ‘Viscous waves’ and their thermal counterpart. This technique is used to solve the general problem of gravity wave propagation in a realistic atmosphere for a wide range of wave parameters. The height of maximum wind amplitude and the fraction of reflected energy have been plotted from the results of these calculations. These maxima are also compared with simpler analytic approximations and experimental observations.

Electromagnetic signals that propagate through the magnetosphere exchange energy with nonthermal charged particles by the cyclotron‐resonance mechanism. The interaction is due to a Doppler shift of the propagation frequency ω to the cyclotron frequency ωc of the charged particle that allows the particle to resonate with the electromagnetic fields. The dominant exchange is between electrons around 1 kev and VLF whistlers that propagate in the right‐hand mode and between protons around 1 kev and ULF whistlers (Pc 1 geomagnetic micropulsations) that propagate in the left‐hand mode. The complex wave number k(ω) = kr + iki for propagation in a hot uniform plasma parallel to a static magnetic field is assumed to describe whistler properties locally in the magnetosphere. The power transfer function A(ω), which relates the input and output power spectrums, is determined by the path integral of ki along a geomagnetic flux tube. Spectrums of A for both VLF and ULF whistlers have been evaluated for a variety of energy and pitch‐angle distributions of the form E−n sinm α. In general, A has an amplification maximum just below a sharp absorption cutoff, which is consistent with observations. The detailed input‐output spectrums of whistlers that are necessary to test the theory are not available yet. When these spectrums are measured, this interaction may provide a possible method for mapping the phase space distribution of nonthermal particles in the magnetosphere.

The lifetime of protons in the Van Allen radiation belts is limited by several loss mechanisms. During geomagnetically quiet periods the principal ones are probably Coulomb scattering and charge exchange with the components of the partly ionized exosphere. The Coulomb scattering lifetime has been calculated as a function of proton energy and equatorial scattering density by Wentworth, MacDonald, and Singer [1959]. The charge exchange lifetime is calculated here using experimentally measured cross sections.

The radiation from an electron in a homogeneous magnetoplasma has some unu sual properti es as a consequence of the dispersive anisotropic nature of the medium. Attention is confine d to emi ssion in the ordinary (whistler) mode frequen cy band below the cyclotron resonance and the extraordinary mode frequency band around the plas ma freque ncy where the indices of refraction are ap preciably greater than one and vary signifi cantly. Due to the large indi ces, electrons can emit Cere nkov radiation over a limited band of nonrelativisti c e ne rgies . The cyclotron radiation which is generated by the gyration s of elec tron s is complicated also by thi s property of th e medium which permits both normal emi ssion due to "slower than li ght " moti on a nd a nom alous e mi ssion due to " fa ster than light" motion . In the ordinary mode, for example, th e anomalous cyclotron radi ation is emitted into the forward he misphere with res pect to the guiding ce nter motion of the electron wh ereas th e normal radiation is emitted into the backw ard he mi sph ere. In thi s paper th e freque ncy spectra and angular patterns of the average radia ted powe r are calcul ated by th e Ha milto nian method whi c h avoid s a direc t calc ulation of th e co mplicated electromagneti c fi eld vectors . The theory of e mi ssion in di s persive ani sotro pi c medi a with a hermiti an di electric te nso r by Kolomenskii and E idm an is th oroughl y re vie wed a nd exte nded to include relativi sti c e nergies; the co mpl icated anal yti c formulas for the power are evaluated for several spec ial cases; and th e res ults are appli ed to rece nt inte rpretations of ve ry low-freq ue ncy (V LF) and low-frequ e ncy (LF) emi ssions from elec trons in th e magnetos ph ere. The main co nclu sions of the work are as foll ows: (1 ) In th e ordin ary (whi stle r) mode mos t of the ene rgy is radi ated alon g wave normals at la rge angles to th e mag neti c fi eld at freque ncies othe r th an the rectilin early Dopp ler-s hifted fund a mental cyclotron harmonic whi ch is co ntrary to ass umptions of ce rtain VLF e mi ss ion theori es.(2) The reso nan ce s ingul ariti es in th e indi ces fo r a cold , colli sionless plas ma mu st be e liminated to ac hi e ve finit e power leve ls, but unfortunately the di electri c tenso r for th ermal motion is extre mely co mplex and for colli sions is non-hermiti a n; co nsequ e ntly, a n arbitrary upp er limit is imposed on th e indi ces in order to make a qu a ntitative es tim ate of th e powe r. (3) Based on th is approximation th e total power in the ordin ary mode is a slowl y varying fun ction of fr equ ency a nd electron energy with an average level of 10-30 W /(c/s) per electron. (4) This le vel is inadequate to exp lain observed VLF signals on th e bas is of in cohere nt emi ssion, but co herent e mi ssion from bunches of electrons can give th e obse rved power level of 10-14 W /c m 2 (c/s) above the ionos phere; he nce, the onu s of explaining the co mplex di spersion pattern s of VLF e mi ssions is l...

Fifty-seven nose whistlers recorded at five stations between April 1958 and June 1962 have been used to test the validity of model magnetospheric electron distributions and two theories for the upper cutoff frequency of the whistler signal. Five electron density distributions [constant, exp (3R./R), (RJR) +8, (Re/R) +• exp (3RJR), and (RJR(Oø)) +' exp (--3RJR(O ø) q-3R./R)] were tested, but only the ones with an (R./R) +• factor produce self-consistent results. In these cases, the ratios of •, the upper cutoff frequency, to ]o(0ø), the equatorial gyrofrequency, are scattered, most whistlers having •/•(0 ø) •> 0.5. This indicates that the cutoff is probably not caused by escape of high-frequency components from fieldaligned ducts. On the other hand, the assumption that the cutoff above • is caused by a thermal Doppler shift in the cyclotron resonance is strongly supported. For these whistlers the resonant particle energies at • range between 0.2 and 2.0 key, and in this interval the differential energy spectrum of the normalized density, No-•dN(E)/dE, is a remarkably smooth function which varies ss E -• with no significant height (3 < R(Oø)/R, • 5) or time variation.Since this spectrum is non-Maxwellian, the damping is attributed to nonthermal electrons in the tail of the energy distribution and a 'temperature' for the distribution cannot be extracted from the data.