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Notes: Abstract It is usually assumed that the ions of cosmic rays contribute nothing to the observable electromagnetic radiation. However, this is true only when these ions are moving in a vacuum or a quiet (nonturbulent) plasma. In the case of fast ions in a turbulent plasma, there is an effective nonlinear mechanism of radiation which is discussed in this paper. The fast ion (relativistic or nonrelativistic) moving in the plasma creates a polarization cloud around itself which also moves with the particles. The turbulent plasma waves may scatter on the moving electric field of this polarization cloud. In the process of this scattering an electromagnetic wave with frequency (2.7) is generated. Let ω1 and k1 be the frequency and wave vector of turbulent plasma waves,V is the velocity of the ion, and ϱ is the angle between the wave vector of electromagnetic radiation and the direction of the ion velocity. The method of calculating the probability of the conversion of plasma waves (k1) into electromagnetic waves (k) by scattering on an ion with velocityV is described in detal in Section 2 (Equation (2.14)). The spectral coefficients of spontaneous radiation in the case of scattering of plasma waves on polarization clouds created by fast nonrelativistic ions are given in (3.6) for an ion energy distribution function (3.4) and in (3.8) for more general evaluations. The Equations (3.9)–(3.13) describe the spectral coefficients of spontaneous emission for different modes of plasma turbulence (Langmuir (3.9), electron cyclotron in a weak (3.10) or strong (3.11) magnetic field and ion acoustic (3.12)–(3.13) waves). The coefficients of reabsorption or induced emission are given by Equations (3.14) and (3.16)–(3.19). There is a maser effect in the case of scattering of plasma waves on a stream of ions. The effective temperature of the spontaneous emission is given by Equation (3.15). The spectral coefficients of radiation due to scattering of plasma waves on relativistic ions are calculated in the same manner (Equations (4.14)–(4.15)). The total energy loss due to this radiation is given in Equations (4.23)–(4.25). The coefficients of induced emission are given in (4.26)–(4.28). The results are discussed in Section 5. It is shown that the loss of energy by nonlinear plasma radiation is much smaller than the ionization loss. However, the coefficients of synchrotron radiation of electrons and nonlinear radiation of ions under cosmic conditions may be comparable in the case of a weak magnetic field and fairly low frequencies (5.5)–(5.6). Usually the spectrum of nonlinear plasma radiation is steeper than in the case of synchroton radiation. Equation (5.10) gives the condition for nonlinear radiation to prevail over thermal radiation.

Notes: Abstract Recently, the question of the nonlinear relation between various plasma oscillations has been the subject of much attention as a result of a series of circumstances. The most important of these is the fact that in the majority of experiments on beam instabilities [1, 2] the intensity of the oscillations excited is very large, so that nonlinear effects in the interaction of oscillations must be significant. It should be noted that beam instability is not the only method of exciting highfrequency plasma oscillations. As was shown in [3], very intense oscillations may also be excited by beams of transverse waves of various frequency ranges, among which are powerful light beams [4]. Finally, excitation is possible by means of shock waves [5] and large-amplitude waves propagating through a plasma. Nonlinear coupling of plasma and low-frequency ion-sound oscillations leads, in particular, to the generation of the latter [6]. On the one hand, this is of interest as regards the problem of turbulent heating of a plasma, since the absorption of ion-sound oscillations in a plasma is usually stronger than the absorption of plasma oscillations. On the other hand, ion-sound oscillations may bring about the acceleration of low-energy ions due to the effects of induced Čerenkov absorption and radiation of waves by ions, as considered in the work of one of the authors [7], Although plasma oscillations accelerate particles more effectively [8], the injection conditions in the configuration for acceleration by plasma oscillations are very stringent v 〉 ve. The number of ions with such velocity for small ion temperatures Ti is small. Thus, the acceleration of ions will arise in this case as a result of the interaction of ion-sound oscillations until such time as their velocity reaches values of the order ve. This question is of interest not only for the acceleration of ions (heating) in the presence of high-frequency turbulence created by beams of charged particles or as a result of the action of powerful radiation on a plasma, but also for the problem of neutron radiation from powerful impulse discharges in a plasma and for a series of astrophysical problems. In what follows we consider a number of one-dimensional self-consistent problems regarding the interaction (decay and fusion) of plasma and ion-sound oscillations resulting from the induced Raman scattering of the former by the latter. It is shown that the development of instability in a turbulent plasma with a high level of excited plasma oscillations leads both to the excitation of ion-sound oscillations, and also to the appearance in the plasma oscillation spectrum of satellites differing from the basic frequency ω0e by a frequency of the order ω0i and with greater intensities for the lower frequencies. The qualitative change of the plasma oscillation spectrum may serve as an immediate indication of the excitation of ion-sound oscillations in the system. The results obtained allow one to trace the process of development of instabilities. It is shown that in a plasma with a high level of ion-sound oscillations “violet” satellites are excited in the plasma oscillation spectrum, while the intensities of the violet satellites have a tendency to level out and form a satellite plateau if the level of ion-sound waves is high enough.

Notes: Abstract A solution is obtained for the problem of the propagation of electromagnetic waves of arbitrary form through a plasma boundary on condition that the length of the wave train is much greater than the wave length. A solution is found both for the case of a wide spectrum of width Δω much greater than the plasma frequency ω0, as well as for a narrow spectrum. The results obtained enable us to draw conclusions about the time and space variation of the shape of electromagnetic pulses in a plasma. The passage of high frequency electromagnetic waves through a plasma is similar to that of a beam of charged particles [1, 2]. This is associated with the fact that decay processes are similar to Cerenkov radiation effects. The dynamics of the development of transverse wave instabilities in a uniform Isotropic plasma were studied in [2] assuming that the wave phase behaves stochastically. It was calculated here that instabilities develop quite differently in the case of a wide frequency spectrum than in the case of a narrow “monochromatic” spectrum. If we can speak of transverse quanta diffusion effects in the “field” of the generated longitudinal quanta in the first case, and if the resulting effects are closely similar to the nonlinear effects arising when beam instability develops [3, 4], then the development of instabilities in the case of a narrow spectrum leads to the appearance of red satellites in the transverse wave spectrum differing from the basic frequencyω by a quantity νω0 (ν=1, 2, 3,...). In this case the development of the instability corresponds to a tendency for a plateau over the satellites to appear. Attention should however be drawn to the fact that the dynamics of instability development in a semibounded plasma may be quite different. This is associated first with the different values of group velocities of transverse and longitudinal waves, and what is also important, with the effect of longitudinal wave accumulation in the boundary region if the length of the wave train is sufficiently large. The treatment of a similar problem for beam instabilities in paper [5] showed that a narrow transition layer may arise with a transverse wave energy density greatly in excess of the energy density of the injected beam. In what follows we examine the part played by boundary effects in the passage of pulses of electromagnetic waves through the boundary of the plasma. The cases of both narrow and wide spectra are considered. We note that in the case of narrow spectra the wave train must necessarily be greatly in excess of Δω−1, and the effects of the accumulation of oscillations will be appreciable. The phases of both transverse waves, and also generated longitudinal waves are assumed to be stochastic quantities. The boundary effects which have been treated may be applied both in the generation of longitudinal waves necessary for the effective acceleration of particles in a plasma as well as in the modulation and alteration of the initial transverse wave spectrum. It should also be stressed that these effects which have been considered could be applied for turbulent plasma diagnostics, as has already been pointed out in [2].