Coulomb Interactions between Cosmic Rays and Charged Dust Grains

The head-on collision of dust acoustic solitary waves in a four-component unmagnetized dusty plasma with Boltzmann distributed electrons, nonthermal ions, and negatively charged dust grains as well as positively charged dust grains is investigated using the extended Poincaré-Lighthill-Kuo method. The effects of the ratio of electron temperature to ion temperature and the ratio of the positively charged dust grains mass to the negatively charged dust grains mass on the phase shift are studied. It is found that the presence of nonthermal ions plays a significant role on the collision of dust acoustic solitary waves. This study would be useful for investigations of plasma behavior in different regions of space, viz., cometary tails, upper and lower mesosphere, Jupiter’s magnetosphere, etc.

Supposing that the constituents of dusty plasmas are inertialess electrons, inertialess ions, and an admixture of negatively and positively charged inertial dust grains, and employing the nonlinear multi-fluid dusty plasma equations and Poisson's equation, we have derived dynamical equations for small amplitude nonlinear dust-acoustic waves, as well as the energy integral of a classical particle with a modified Sagdeev potential for large amplitude disturbances. The energy integral is analyzed both analytically and numerically to demonstrate the existence of rarefactive and compressive electrostatic potentials which travel faster than the effective dust-acoustic velocity. Compressive dust-acoustic potential exist only when there is a significant fraction of positively charged dust grains. Furthermore, the four-fluid dusty plasma system also admit double layers.

Collisions of ions with charged dust grains are important for the propagation of low frequency waves such as dust acoustic waves and dust ion-acoustic waves. The collision cross-sectional area of charged dust grains depends on the velocity of an ion beam. The collision cross-sectional area of charged dust grains with beam ions is measured. It is compared with the geometrical cross-sectional area of the grain. The experiment is performed in a dusty double-plasma device with glass beads of 8.9 μm in average diameter. The ion beam current and energy are measured with a directional retarding potential analyzer. It is observed that, when dust density inside the system is increased, the beam current ratio is reduced. From the reduction of the ion beam current, the effective cross-sectional area of the dust particle is estimated as a function of the beam energy.

The nonthermal source abundances of elements play a crucial role in the understanding of cosmic ray phenomena from a few GeV up to several tens of EeV. In this work a first systematic approach is shown that describes the change of the abundances from the thermal to the nonthermal state via non-linear diffusive shock acceleration by a temporally evolving shock. Hereby, not only time-dependent ionization states of elements contained in the ambient gas are considered, but also elements condensed on solid, charged dust grains which can be injected into the acceleration process as well. This generic parametrized model is then applied to the case of particle acceleration by supernova remnants in various ISM phases as well as Wolf-Rayet (WR) wind environments. We show that the overall low energy cosmic ray (LECR) distribution by WR explosions yield a significantly harder, which makes this contribution quite promising in order to explain the spectral hardening of the observed LECR flux of certain elements, such as helium, at rigidities of about 1 TV.

Electrostatic ion cyclotron waves are excited by axial ion beam in a dusty plasma via Cerenkov and slow cyclotron interaction. The dispersion relation of the instability is derived in the presence of positively/negatively charged dust grains. The minimum beam velocity needed for the excitation is estimated for different values of relative density of negatively charged dust grains. It is shown that the minimum beam velocity needed for excitation increases as the charge density carried by dust increases. Temperature of electrons and ions, charge and mass of dust grains, external static magnetic field and finite boundary of dusty plasma significantly modify the dispersion properties of these waves and play a crucial role in the growth of resonant ion cyclotron instability. The ion cyclotron modes with phase velocity comparable to the beam velocity possess a large growth rate. The maximum value of growth rate increases with the beam density and scales as the one-third power of the beam density in Cerenkov interaction and is proportional to the square root of beam density in slow cyclotron interaction.

The dust acoustic wave in a bounded dusty plasma with strong electrostatic interactions between dust grains

Main concerns of the present article are to investigate the effects of dust charging and trapped electrons on the solitary structures evolved in an inhomogeneous magnetized plasma. Such a plasma is found to support two types of waves, namely, fast wave and slow wave. Slow wave propagates in the plasma only when the wave propagation angle θ satisfies the condition θ≥tan-1{(1+2σ)-[(ndlh(γ1-1))/(1+ndlhγ1)]-v0u0}, where v0(u0) is the z- (x-) component of ion drift velocity, σ = Ti/Teff, ndlh = nd0/(nel0 + neh0), and γ1=-1Φi0[1-Φi01+σ(1-Φi0)] together with Ti as ion temperature, nel0(neh0) as the density of trapped (isothermal) electrons, Φi0 as the dust grain (density nd0) surface potential relative to zero plasma potential, and Teff=(nelo+neho)TelTeh/(neloTeh+nehoTel), where Tel(Teh) is the temperature of trapped (isothermal) electrons. Both the waves evolve in the form of density hill type structures in the plasma, confirming that these solitary structures are compressive in nature. These structures are found to attain higher amplitude when the charge on the dust grains is fluctuated (in comparison with the case of fixed charge) and also when the dust grains and trapped electrons are more in number; the same is the case with higher temperature of ions and electrons. Slow solitary structures show weak dependence on the dust concentration. Both types of structures are found to become narrower under the application of stronger magnetic field. With regard to the charging of dust grains, it is observed that the charge gets reduced for the higher trapped electron density and temperature of ions and electrons, and dust charging shows weak dependence on the ion temperature.

An ion beam propagating through a magnetized potassium plasma cylinder having negatively charged dust grains drives electrostatic ion-acoustic waves to instability via Cerenkov interaction. The phase velocity of sound wave increases with the relative density of negatively charged dust grains. The unstable wave frequencies and the growth rate increase, with the relative density of negatively charged dust grains. The growth rate of the unstable mode scales as one-third power of the beam density. The real part of frequency of the unstable mode increases with the beam energy and scales as almost the one-half power of the beam energy.

The dynamics of small electrically charged dust grains within the rigidly corotating regions of planetary magnetospheres such as those of Jupiter and Saturn is considered. Depending on whether one is inside or outside the synchronous orbit, it is possible to have different populations of both positively and negatively charged particles moving in equilibrium circular orbits either in the prograde or retrograde sense. Not all these are stable, however, to small perturbations, such as would be produced by the gravitational tug of a neighboring satellite. The stable perturbed grains will perform a motion that can be described as an elliptical gyration about a guiding center which is in uniform circular motion. For different values of the specific charge, the ratio of the semiaxes of this ‘epicyclic’ ellipse lies between 1/2 and 1, while the gyration frequency ω of the grain about the guiding center lies between the Kepler frequency ΩK and ω0 (which is the grain gyrofrequency in a nonrotating frame). In the environments of Jupiter and Saturn, where the grains are expected to be negatively charged both in the sunlit side and in the shadow and which move in the prograde sense, their guiding centers must have speeds intermediate to the Kepler speed and the corotation speed. Such particles with a unique specific charge (and therefore a specific size) could have a 1:1 magneto‐gravitational resonance with a neighboring satellite. A dispersion relation between ω and the wavelength λ of the perturbed orbits in the frame of the perturbed satellite has been derived. This result has been used to discuss the appearance and disappearance of the waves in the F ring of Saturn elsewhere. We merely point out here that, while the existence of a single well‐defined wavelength implies a dust size distribution sharply peaked at a diameter of about 1 µ, the present theory also anticipates this situation. The only collisionless (and therefore nonevolving) state of small electrically charged dust grains moving in the same orbit is when they have precisely the same specific charge and therefore the same size (assuming the same density), since the electrical potential is the same for all sizes.

In a magnetized inhomogeneous plasmas, usual version of the KdV equation is found to modify by presence of charged dust grains. The density gradient in the plasma shows its dependence on the recombination rate, ion to electron temperature ratio, obliqueness of the magnetic field and the drift velocity of the ions. In the said plasma, only the compressive solitary structures are found to propagate corresponding to two different types of modes. A significant effect of magnetic field and charged dust grains is found on these structures, though these structures show weak dependence on the ionization rate of neutral atoms. Interestingly the solitons with prominent tailing structures are evolved in the plasma under the effect of stronger density gradient and higher recombination.

A rigorous theoretical investigation has been made on the nonlinear structures, mainly, dust-acoustic (DA) solitary and shock waves propagating in a strongly coupled dusty plasma consisting of strongly coupled correlated positively and negatively charged inertial cold dust fluid, weakly correlated inertialess Maxwellian electron and ion fluids. The presence of arbitrary (negative and positive) charged dust grains in such a plasma system causes the presence opposite potentials (positive and negative) DA solitary and shock structures and significantly modify it’s basic features. The results obtained from this analysis can be employed in understanding the nature of plasma waves both in laboratory and space plasma system.

We investigate the instability features excited in complex plasmas in the Saturn’s middle magnetosphere (SMM) in the region between the orbits of Dione and Rhea. It comprises of bipolar dust grains (fluids), Maxwellian cold electrons and ions (primarily protons, H+, and water-group ions, W+), and suprathermal electrons. The term “bipolar” signifies the dust population containing both positive and negatively charged dust grains. The charged dust dynamics incorporates the effects of the pressure gradient force, Lorentz force, and ion-neutral drag forces. Given the variability of the SMM, fluctuations in the dust grain potential are properly anticipated and incorporated in our model formalism. A standard cylindrical wave mode analysis leads to a generalized monic linear sextic dispersion relation. It is shown mainly that the explored instability propagates as a dust-acoustic wave (DAW) mode with a frequency of 10−2 s−1 and phase velocity of 1 − 2 cm s−1 in realistic Saturnian plasma conditions. The multi-parametric influences on the DAW growth rate and its non-trivial variation are extensively explored in light of the previously reported experimental (microgravity) and observational (Cassini) data.

A numerical simulation model is presented to study an important effect of dust charging on waves and instabilities in unmagnetized dusty plasmas. In this study, the background plasma is treated as a two-component fluid whose density self-consistently varies due to dust charging. The dust is treated with a particle-in-cell model in which the dust charge varies with time according to the standard dust-charging model. An ion acoustic streaming instability due to dust charging when the ion fluid drifts with respect to stationary charged dust grains and electrons is investigated. The numerical simulation results show good agreement with theoretical predictions and provide further insight into dust-charging effects on wave modes and instabilities in dusty plasmas.

Field emission characteristics of gold dust grains

A rigorous theoretical investigation has been made on the nonlinear propagation of dust-ion-acoustic shock waves in a multi-component magnetized pair-ion plasma (PIP) having inertial warm positive and negative ions, inertialess non-thermal electrons and positrons, and static negatively charged massive dust grains. The Burgers’ equation is derived by employing the reductive perturbation method. The plasma model supports both positive and negative shock structures in the presence of static negatively charged massive dust grains. It is found that the steepness of both positive and negative shock profiles declines with the increase of ion kinematic viscosity without affecting the height, and the increment of negative (positive) ion mass in the PIP system declines (enhances) the amplitude of the shock profile. It is also observed that the increase in oblique angle raises the height of the positive shock profile, and the height of the positive shock wave increases with the number density of positron. The applications of the findings from the present investigation are briefly discussed.