Modulational instability of ion-acoustic waves in electron–positron–ion plasmas

The stability of modulation of ion-acoustic waves in a collisionless electron–positron–ion plasma with warm adiabatic ions is studied. Using the Krylov–Bogoliubov–Mitropolosky (KBM) perturbation technique a nonlinear Schrödinger equation governing the slow modulation of the wave amplitude is derived for the system. It is found that for given set of parameters having finite ion temperature ratio (T _i /T _e ) the waves are unstable for the values of k lying in the range k _min<k<k _max. On increasing the ion temperature ratio (T _i /T _e ), it is found that k _min and k _max, both decreases and product PQ increases. The range of unstable region shifts towards the small wave number k, as temperature ratio (T _i /T _e ) increases. The positron concentration and temperature ratio of positron to electron, change the unstable region slightly. As positron concentration increases both k _min and k _max for modulational instability increases and maximum value of the product PQ shifts towards the larger value of k.     

Excitation of Langmuir waves by the lower energy cutoff behavior of power-law electrons

Langmuir waves (LWs), which are believed to play a crucial role in the plasma emission of solar radio bursts, can be excited by streaming instability of energetic electron beams. However, solar hard X-ray observations imply that the energetic flare electrons usually have a power-law energy distribution with a lower energy cutoff. In this paper, we investigate LWs driven by the power-law electrons. The results show that power-law electrons with the steepness cutoff behavior can excite LWs effectively because of the population inversion distribution below the cutoff energy (E _c ). The growth rate of LWs increases with the steepness index (δ) and decreases with the power-law index (α). The wave number of the fastest growing LWs (kλ _D ), decreases with the characteristic velocity of the power-law electrons ( \(v_{c}=\sqrt{2E_{c}/m_{e}}\) ) and increases with the thermal velocity of ambient electrons (v _T ). This can be helpful for us to understand better the physics of LWs and the dynamics of energetic electron beams in space and astrophysical plasmas.     

The brightness temperatures of solar type III bursts

There is a characteristic maximum brightness temperature T _B 10¹⁵K for type III solar radio bursts in the solar wind. The suggestion is explored that the maximum observed values of T _Bmay be attributed to saturation of the processes involved in the plasma emission. The processes leading to fundamental and second harmonic emission saturate when T _Bis approximately equal to the effective temperature T _Lof the Langmuir waves. The expected maximum value of T _Bis estimated for this saturation model in two ways: from the growth rate for the beam instability, and from the maximum amplitude of the observed Langmuir turbulence. The agreement with the observed values is satisfactory in view of the uncertainties in the estimates (a) of the intrinsic brightness temperature from the observed brightness temperature, (b) of the actual growth rate of the beam instability, which must be driven by local, transient features (that are unobservable using available instruments) in the electron distribution, and (c) in the k-space volume filled by the Langmuir waves, and this is consistent with the observational data on two well-studied events at the orbit of the Earth and with statistical data for events over a range of radial distances from the Sun.     

Two-dimensional distributions of physical parameters in the prominence of 1984 March 23

The spectral lines Hα Hβ and CaII K of a quiescent prominence are studied using the completely linearized model. The physical parameters (T_e, v_t, N_H) at several locations are obtained. Itis shown: (1) Near the axis of the prominence, kinetic temperature and hydrogen density decrease, while microturbulent velocity increases, with increasing height. (2) Near the edge, the kinetic temperature does not vary with height; but it increases from the center to the edge. (3) Hydrostatic equilibrium does not hold in prominences, and magnetic field plays an important role in supporting them.     

Empirical model of the E-region electron temperature around noon and at low magnetic activity

Electron temperature measurements made with Langmuir probes at E-region heights together with deviative absorption data show that the electrons are not in thermal equilibrium with the neutrals. Moreover, for very quiet days (A_p ? 7, K_p ? 1⁺ throughout the whole day) and hours close to noon the quotients between the electron and neutral gas temperature profiles have a similar behaviour. In this paper T_e profiles measured in situ with Langmuir probes and T_n, profiles given by neutral atmosphere models, both in the specified ionospheric conditions, are used to compute $\text{T}{}_{\mathrm{e}}\text{T}{}_{\mathrm{n}}$ profiles. Each of the profiles thus obtained is fitted by a Lorentzian curve and the variation with F_10.7 of its parameters is also fitted by simple mathematical expressions.     

Dust acoustic shock waves in a suprathermal dusty plasma with dust charge fluctuation

The properties of small but finite amplitude dust acoustic (DA) shock waves are studied in a charge varying dusty plasma with ions and electrons having kappa velocity distribution. We obtain the global Debye length including the influence of suprathermality effects and dust charge fluctuations. It is shown that the effects of suprathermality of ions/electrons and dust charge fluctuation significantly modify the basic properties of DA shock wave. We observe that only negative DA shock waves will be excited in this model. The amplitude of DA shock wave increases with deviation of electrons or ions from Maxwellian distribution via decrease of spectral index, κ _j (j=i,e denotes, ions and electrons, respectively). Also, it is indicated that the amplitude and steepness of the shock front decreases with an increase in the ion temperature.     

Influence of suprathermality on the obliquely propagating dust-acoustic solitary waves in a magnetized dusty plasma

Dust-acoustic (DA) solitary waves are investigated in a magnetized dusty plasma comprising cold dust fluid and kappa-distributed ions and/or electrons. The influence of suprathermal particles, obliqueness, and ion temperature on the DA solitary waves is investigated. We find that only negative DA solitary waves will be excited in this model. Also it is shown that the amplitude of the DA solitary wave decreases with deviation of electrons or ions from Maxwellian distribution via decrease of κ _e or κ _i . The effect of the temperature of the ion decreases with the amplitude and steepness of the solitary wave front.     

Fundamental emission for type III bursts in the interplanetary medium: The role of ion-sound turbulence

It is argued (a) that the onset times of type III radio emission and of the streaming electrons implies that type III bursts in the interplanetary medium are generated predominantly at the fundamental, (b) that in view of recent observations of ion-sound waves in the interplanetary medium the theory of the generation of the bursts should be revised to take account of these waves, and (c) the revised theory favours fundamental emission. A detailed discussion of the effect of ion-sound waves on type III bursts is given. The most important results are: (1) Ion-sound waves cause enhanced (over scattering off thermal ions) fundamental emission. (2) Second harmonic emission is also enhanced for T _e> 5 × 10⁵ K, e.g., low in the corona, but is suppressed for T _e< 5 × 10⁵ K, e.g., in the interplanetary medium. (3) The bump-in-the-tail instability for Langmuir waves can be suppressed by the presence of ion-sound waves; it may be replaced by an analogous instability in which fundamental transverse waves are generated directly, with no associated second harmonic, but there are unresolved problems with theory for this process. (4) Very low frequency ion-sound waves can scatter type III radiation. (5) Although the ion-sound waves which have been observed are at too high a frequency to be relevant for these processes, it seems likely that ion-sound waves of the required frequencies are present and do play important roles in the generation of type III bursts.     

Recombination of electrons with H3+ and H5+ ions

The dissociative recombination coefficients α for capture of electrons by H₃⁺ and H₅⁺ ions have been determined as a function of electron temperature T_e using a microwave afterglow-mass spectrometer apparatus. At ion and neutral temperatures T_u+ = T_n = 240 K, the coefficient α (H₃⁺) is found to vary slowly with T_e at first, decreasing from 1.6 × 10^?7 cm³/s at T_e = 240 K to 1.2 × 10^?7 cm³/s at T_e = 500 K, thereafter falling as T_e^?1 over the range 500 K ? T_e, ? 3000 K. These results, which have a ± 20% uncertainty, agree satisfactorily over the common energy range (0.03–0.36 eV) with the recombination cross sections determined in merged beam measurements by Auerbach et al. At T₊ = T_n = 128 K, the coefficient α(H₅⁺) is found to be (1.8 ± 0.3) × 10^?6 [T_e(K)/300]^?0.69 cm³/s over the range 128 K ? T_e ? 3000 K, with a more rapid decrease, as T_e^?1, between 3000 K and 5500 K. The implications of these results for modelling planetary atmospheres and interstellar clouds are briefly touched on.     

Flowing afterglow studies of temperature dependencies for electron dissociative recombination of HCNH, CH3CNH and CH3CH2CNH and their symmetrical proton-bound dimers

A study has been made using a variable temperature flowing afterglow Langmuir probe technique (VT-FALP) to determine the equilibrium temperature dependencies of the dissociative electron-ion recombination of the protonated cyanide ions (RCNH⁺, where R=H, CH₃ and C₂H₅) and their symmetrical proton-bound dimers (RCNH⁺NCR). The power law temperature dependencies of the recombination coefficients, α_e, over the temperature range 180 to 600 K for the protonated ions are α_e(T)(cm³ s⁻¹)=3.5±0.5×10⁻⁷ (300/T)^1.38 for HCNH⁺, α_e(T)=3.4±0.5×10⁻⁷ (300/T)^1.03 for CH₃CNH⁺, and α_e(T)=4.6±0.7×10⁻⁷ (300/T)^0.81 for CH₃CH₂CNH⁺. The equivalent values for the proton-bound dimers are α_e(T)(cm³ s⁻¹)=2.4±0.4×10⁻⁶(300/T)^0.5 for (HCN)₂H⁺ to α_e(T)=2.8±0.4×10⁻⁶(300/T)^0.5 for (CH₃CN)₂H⁺, and α_e(T)=2.3±0.3×10⁻⁶(300/T)^0.5 for (CH₃CH₂CN)₂H⁺. The relevance of these data to molecular synthesis in the interstellar medium and the Titan ionosphere are discussed.     

Beam propagation and Langmuir wave generation in a plasma with κ distribution function

Using a kappa velocity distribution function for the electrons of the background plasma, the dynamics of a beam of hot electrons streaming through the plasma and the generation of Langmuir waves are investigated in the frame work of quasilinear theory. It is shown that the Langmuir waves are strongly damped by high energy tail of the Kappa distribution function. The spatial expansion of the beam is reduced and the spectral density of Langmuir waves becomes narrower. The height of the plateau in the beam distribution function increases at small velocities and the average velocity of beam is larger than that of a Maxwellian distribution. The influence of Kappa velocity distribution function on the gasdynamical parameters is investigated. It is found that, the height of plateau in the beam distribution function, and its lower velocity boundary are enhanced while, the local beam width in velocity space decreases.     

Frequency splitting in stria bursts: Possible roles of low-frequency waves

The kinematics of the process L ± F→ L′ are explored where L represents a parallel Langmuir wave, F represents a low frequency fluctuation and L′ represents a secondary Langmuir wave, and the results are used to discuss (a) a possible interpretation of the frequency splitting in stria bursts in terms of the processes L ± F → L′, L′ ± F′ → t, where t represents a transverse wave, and (b) second harmonic emission due to the processes L ± s→ L′, L + L′ → t, where s represents an ion sound wave. The following results are obtained:

1. The processes L ± s → L′ are allowed only for k _s < 2k _L ± k ₀, respectively, with k ₀ = ω _p /65 V _e .
2. The inclusion of a magnetic field does not alter the result (1) and adds further kinematic restrictions related to angles of propagation; the kinematic restriction T _e > 5 × 10⁵ K for second harmonic emission through process (b) above is also unchanged by inclusion of the magnetic field. The effect of a spread in the wavevectors of the Langmuir waves on this restriction is discussed in the Appendix.
3. For parallel Langmuir waves the process L - F → L′ is forbidden for lower hybrid waves and for nearly perpendicular resonant whistlers, and the process L + F → L′ is allowed only for resonant whistlers at ω _F ? 1/2ω _p (Ω _e /ω _p )².
4. The sequential three wave processes L ± s → L′, L′ ± s → t and L + F → L′, L′ ± F′ → t encounter difficulties when applied to the interpretation of the splitting in split pair and triple bursts.
5. The four-wave process L ± F ± F′ → t is kinematically allowed and provides a favourable qualitative interpretation of the splitting when F denotes a resonant whistler near the frequency mentioned in (3) above. The four wave processes should saturate under conditions which are not extreme and produce fundamental plasma emission with brightness temperature T _t equal to the effective temperature T _L of the Langmuir waves.

     

Numerical simulation of electromagnetic emissions in the solar wind plasma with non-thermal electron distribution

Dynamics of fundamental and second harmonic electromagnetic emissions are simulated in the solar wind plasma in the presence of non-thermal electron distribution function in which primary Langmuir waves are driven by an electron beam. The electron velocity distribution function is separated into two distributions representing the distribution of the ambient electrons (Maxwellian) and the suprathermal electrons (non-thermal electrons). The effects of the non-thermal electrons on the generation of primary Langmuir waves, emission rates of the fundamental (F) and harmonic waves (H) and their distributions are investigated. The both of the F and H emissions are sensitive to the characterizes of the non-thermal electrons. It is found that in the presence of non-thermal electrons the production of the Langmuir waves decreases and consequently the levels of fundamental and second harmonic waves are reduced. The emission rate of the fundamental transverse waves decreases and its peak moves slightly toward smaller wave-numbers.     

Stochastic wave growth, power balance, and beam evolution in type III solar radio sources

Energy-balance arguments are combined with the stochastic-growth theory of type III radio sources to determine the properties of the source in average dynamical equilibrium with the beam, and the beam's long-term evolution. Purely linear stochastic-growth theory has previously emphasized that the beam evolves to a state close to marginal stability. Small mean residual deviations from marginal stability are present at dynamical equilibrium and these lead to residual energy flows that feed the waves observed in situ and by remote receivers; consequently the beam energy is depleted. Here, dynamical equilibrium beam and wave levels are estimated for the first time and it is found that the main sink of beam-driven Langmuir waves is either via electrostatic decay into product Langmuir and ion-sound waves or via scattering by short-wavelength density fluctuations, depending on the conditions. Improved estimates of energy branching ratios imply that, at 1 AU from the Sun, typically 20% of the beam energy is converted to Langmuir waves that are scattered off low-frequency density fluctuations and then dissipated, with almost all the remaining waves undergoing electrostatic decay, although as little as one-third of the Langmuir waves may decay in atypical circumstances. Of order 10^–3 of the beam energy is converted into sound waves, which are mostly dissipated, and of order 10^–5 is converted into potentially observable electromagnetic waves. The mean lifetime of the Langmuir waves at 1 AU is 1–40 s, while that of the beam is of order 1000 s. The beam density decreases relative to that of the background as the beam propagates. For most parameters, analysis of energy losses from the beam to the waves shows that the beam velocity decreases at roughly the same rate as the thermal velocity of the background plasma. It is argued from these considerations, and from in situ observations at 1 AU, that these trends imply that only the densest and fastest type III beams will be able to penetrate much past 1 AU from the Sun. This implies a low-frequency cutoff to type III emission at roughly 10 kHz, in good agreement with recent Ulysses remote observations, showing their consistency with in situ measurements.     

Temperature variation of the plasma sheet during substorms

The temperature and density of the plasma in the Earth's distant plasma sheet at the downstream distances of about 20–25 R_e are examined during a high geomagnetic disturbance period. It is shown that the plasma sheet cools when magnetospheric substorm expansion is indicated by the AE index. During cooling, the plasma sheet temperature, T, and the number density, N, are related by $\text{T ∝ N}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$ (adiabatic process) in some instances, while by T ∝ N^?1 (isobaric process) in other cases. The total plasma and magnetic pressure decreases when $\text{T ∝ N}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$ and increases when T ∝ N^?1. Observation also indicates that the dawn-dusk component of plasma flow is frequently large and comparable to the sunward-tailward flow component near the central plasma sheet during substorms.     

Generation of intermediate drift bursts in solar type IV radio continua through coupling of whistlers and Langmuir waves

The possible generation of intermediate drift bursts in type IV dm continua through coupling between whistler waves, traveling along the magnetic field, and Langmuir waves, excited by a loss-cone instability in the source region, is elaborated. We investigate the generation, propagation and coupling of whistlers. It is shown that the superposition of an isotropic background plasma of 10⁶K and a loss-cone distribution of fast electrons is unstable for whistler waves if the loss-cone aperture 2α is sufficiently large (sec α?4); a typical value of the excited frequencies is 0.1 ω _ce (ω _ce is the angular electron cyclotron frequency). The whistlers can travel upwards through the source region of the continuum along the magnetic field direction with velocities of 21.5–28 v _A (v _A is the Alfvén velocity). Coupling of the whistlers with Langmuir waves into escaping electromagnetic waves can lead to the observed intermediate drift bursts, if the Langmuir waves have phase velocities around the velocity of light. In our model the instantaneous bandwith of the fibers corresponds to a frequency of 0.1–0.5 ω _ce and leads to estimates of the magnetic field strength in the source region. These estimates are in good agreement with those derived from the observed drift rate, corresponding to 21.5–28 v _A, if we use a simple hydrostatic density model.     

The range of validity of the two-body approximation in models of terrestrial planet accumulation: II. Gravitational cross sections and runaway accretion

The validity of the two-body approximation in calculating encounters between planetesimals has been evaluated as a function of the ratio of unperturbed planetesimal velocity (with respect to a circular orbit) to mutual escape velocity when their surfaces are in contact (V/V_e). Impact rates as a function of V/V_e are calculated to within ～20% by numerical integration of the equations of motion. It is found that when V/V_e > 0.4, the two-body approximation is a good one. At low velocities (V/V_e < 0.1) two-body “collision-course” trajectories fail to lead to impacts. On the other hand, at these low velocities many impacts result from encounter trajectories with unperturbed separation distances far beyond the two-body gravitational radius. These two effects tend to cancel, and the resulting impact rates remain within a factor of ～3 of the two-body value in spite of these major differences in the nature of the impact trajectories. Therefore, on the average, the two-body approximation is useful well below the value of V/V_e for which it fails to describe individual encounters, and the required corrections are not large. As a consequence of this “anomalous gravitational focusing” planetesimals will continue to interact even when their orbits are noncrossing. This reduces the difficulty with premature isolation of planetesimal embryos during accumulation. Quantitatively, when 0.06 ? V/V_e ? 0.2, the impact rate varies approximately with the fifth power of the radius of the larger body, and is about a factor of 3 above that predicted using the conventional two-body gravitational cross-section formula. At lower values of V/V_e , the impact rate increases less rapidly. Finally, at the lowest values of V/V_e (<.02), the impact rate increases only in proportion to the geometric cross section, as a consequence of the swarm being essentially two dimensional for large unperturbed encounter distances. The gravitational enhancement in effective cross section is thereby limited to a value of about 3000. This leads to an optimal size for growth of planetesimals from a swarm of given eccentricity, and places a limit on the extent of runaway accretion.     

Heat balance for the high-temperature component of a solar flare

Shortly after the occurrence of the impulsive spikes of the two-ribbon flare of May 21, 1980, a temperature analysis of the X-ray emitting flare plasma showed the presence of a low-temperature component [n = 15 × 10¹⁰ cm^#X2212;3; T = 20 × 10⁶ K] and a high-temperature component [n = 2 × 10¹⁰ cm^#X2212;3; T = 40 × 10⁶ K]. The mean free path of an electron in the hot component is comparable to the size of the source (≈ 10⁴ km). Heat losses from the hot source can therefore not be described with classical formulae. Theoretical arguments show that most likely the electron to ion temperature ratio T _e/T_i in the hot plasma is close to unity. This implies the presence of a hot ion component (T _i ≈ 40 × 10⁶ K) as well. Under these conditions (T _e ≈ T _i) heat flux limitation by electrostatic turbulence is ineffective. However, reduction of the heat flux is still possible due to the breakdown of classical theory. It is demonstrated that only non-classical current dissipation processes can sustain a hot source against cooling by a saturated heat flux. Investigation of the collisionality as a function of position along a magnetic loop shows that the breakdown of classical theory should be expected to occur first near the base of the loop. We conclude that the newly discovered hot source is important for the energy budget of the flare, even if the heat losses are considerably reduced. It is estimated that for the May 21, 1980 flare a total of about 10³¹ ergs were necessary to maintain the hot source against heat losses over the time period that it was observed (≈ 10 min).     

A study of the Bremsstrahlung of plasma at about 1 A.U. in times of quiet sun and flare activity

In space plasma, especially in the interior of plasma with weak magnetic field, Bremsstrahlung is the main mechanism of loss of the plasma energy. As shown by our calculations of the Bremsstrahlung of plasma at 1 A.U. in times of quiet sun and flare activity, the variation of intensity of plasma radiation I_f is directly related to the frequency of the electromagnetic wave. When the frequency f is close to that of plasma f_pe, the intensity of radiation is greatly enhanced. With increasing frequency, the enhancement of the radiation intensity with frequency exhibits a slow logarithmic decrease. The brightness temperature T_b is directly proportional to the electron temperature of plasma T_e and to the optical depth of medium. The overall tendencies of variations of T_b and I_f with frequency are identical. For the same frequency, the values of I_f and T_b are lower in time of quiet sun than in time of flare activity.