It is economical to devise ways and means to simplify a multi-species particle system. A partially ionized plasma consisting of electrons, ions and neutral particles can be described as a three-fluid, a two-fluid or a single-fluid system by appropriately combining the dynamics of each of the species. Here, one of the three possible two-fluid descriptions is discussed wherein the electron fluid and the neutral fluid are combined into one fluid, christened as ENe fluid, and treat the ions as the second fluid. It is found that the process of combining the electrons and the neutrals endows the neutrals with a negative electric charge. Hence, here is a plasma with heavy (with nearly the mass of the neutral particle) negatively charged particles along with the positively charged ions. After establishing the framework for the two-fluid, the ENe–ion, system, the characteristic electrostatic wave mode of this novel unmagnetized plasma is determined. A new mode of frequency $$\omega = \omega_{{{\text{EN}}}}$$ emerges in the limit $$(2\gamma_{{{\text{en}} }} + \gamma_{{{\text{ei}} }} )$$ $$\gg$$ ω, where $$\gamma_{{{\text{en}} }}$$ and $$\gamma_{{{\text{ei}} }}$$ are, respectively, the electron–neutral and the electron–ion collision frequencies. This is identified as a collective mode of the ENe fluid, a counterpart of the electron plasma mode in a fully ionized plasma.

In a recent paper (Krishan 2021), a two-fluid description of a partially ionized plasma was presented in which electron fluid and the neutral fluid were combined appropriately into one fluid, christened as ENe fluid, and treat the ions as the second fluid. Some of the electrostatic modes of this two-fluid system were studied. Here, I discuss another possibility in which the ion fluid and the neutral fluid are combined into one fluid, christened as INe fluid, and treat the electrons as the second fluid. There can be a huge variation between the relative masses of the neutrals and the ions. Thus both have to be treated as the inertia carrying species. After establishing the framework for the INe-electron fluids, some of the characteristic wave modes of this novel plasma are investigated.

A non-linear α − Ω dynamo in the partially ionized turbulent plasma in the presence of sub-surface velocity shear is studied with mean-field electrodynamics. Such a dynamo is probably operational in the near-surface region of the Sun, where the presence of both neutrals and the velocity shear (due to sub-surface shear layer in the rotation profile) is observationally well established. In particular, we show that the inclusion of ambipolar diffusion leads to a saturation of magnetic field amplitudes in the α − Ω dynamo. We also demonstrate that the temporal evolution of large-scale global magnetic fields follows the well-known pattern similar to the ‘butterfly’ diagram displayed by sunspots. As usual the velocity shear converts part of the poloidal into the toroidal magnetic field which in turn is regenerated largely by the combined kinetic plus Hall helicity, thus closing the dynamo loop. In addition, by allowing temporal variation in the helicity and ambipolar diffusion coefficient we are able to reproduce the grand-minimum type behaviour of the solar dynamo. Details of theoretical model along with numerical computations of dynamo equations in the partially ionized plasma are outlined. The solar surface dynamo model envisaged in this work could operate in conjunction with the global dynamo present in the bulk of the convection zone.

Plasma is one of the four fundamental states of matter; the other three being solid, liquid and gas. Several components, such as molecular clouds, diffuse interstellar gas, the solar atmosphere, the Earth's ionosphere and laboratory plasmas, including fusion plasmas, constitute the partially ionized plasmas. This book discusses different aspects of partially ionized plasmas including multi-fluid description, equilibrium and types of waves. The discussion goes on to cover the reionization phase of the universe, along with a brief description of high discharge plasmas, tokomak plasmas and laser plasmas. Various elastic and inelastic collisions amongst the three particle species are also presented. In addition, the author demonstrates the novelty of partially ionized plasmas using many examples; for instance, in partially ionized plasma the magnetic induction is subjected to the ambipolar diffusion and the Hall effect, as well as the usual resistive dissipation. Also included is an observation of kinematic dynamo in partially ionized plasmas.

The method of provocation is the easiest way of learning about a system. Provoke it and watch it reacting. The response holds a wealth of information on the nature of the system. One is quite familiar with the example of a pendulum, a simple pendulum, a string hanging vertically with its one end fixed to a beam and the other end carrying a small ball. In the steady state of the pendulum the ball is at rest. When the ball is displaced a little from its resting position and released, it sets into oscillations. It oscillates about its resting point with a period that depends on the restoring force that comes into play when the ball is displaced. The restoring force is the gravitational pull of the Earth. The period is a function of the length of the pendulum and the acceleration due to the gravity of the Earth.

The presence of a Langmuir wave in an unmagnetized plasma is shown to allow parametric decay of an electromagnetic wave into two electromagnetic waves, which is otherwise not allowed due to wave number mismatch. The decay occurs at plasma densities below one ninth the critical density and the decay waves propagate at finite angles to the pump laser. Above the threshold, the growth rate scales linearly with the amplitude of the Langmuir wave and the amplitude of the pump electromagnetic wave. The frequency ω of the lower frequency decay wave increases with the angle its propagation vector makes with that of the pump. The growth rate, however, decreases with ω.

The lower solar atmosphere is a partially ionized plasma consisting of electrons, ions, and neutral atoms. In this, which is essentially a three-fluid system, the Hall effect arises from the treatment of the electrons and ions as two separate fluids and the ambipolar diffusion arises from the inclusion of neutrals as the third fluid. The Hall effect and ambipolar diffusion have been shown to be operational in a region beginning from near the photosphere up to the chromosphere. In a partially ionized plasma, the magnetic induction is subjected to ambipolar diffusion and the Hall drift in addition to the usual resistive dissipation. These nonlinear effects create sharp magnetic structures which then submit themselves to various relaxation mechanisms. A first-principles derivation of these effects in a three-fluid system and an analytic solution to the magnetic induction equation in a stationary state are presented, which in the general case includes the Hall effect, ambipolar diffusion, and ohmic dissipation. The temporal evolution of the magnetic field is then investigated under the combined as well as the individual effects of the Hall drift and ambipolar diffusion to demonstrate the formation of steep magnetic structures and the resultant current sheet formation. These structures have just the right features for the release of magnetic energy into the solar atmosphere.

We study Compton scattering in plasma medium via an effective field theory, by incorporating the contributions of longitudinal as well as transverse permittivities with their temperature dependent dispersive terms. We show that the introduction of the longitudinal mode not only increases the cross-section many-fold than in the case of vacuum, but also leads as a consequence to a well collimated and mono-energetic spectrum of scattered electrons, with the divergence ∼6 mrad, suggesting that this approach has potential application to laser plasma accelerators.

We study the effect of the density and temperature on Compton scattering in a plasma, with particular emphasis on the quality of the scattered electron beam. We find that the longitudinal mode in the plasma plays a dominant role in producing collimated and mono-energetic electron spectrum. The beam profile is, however, sensitive to the plasma parameters such as its density and temperature. We make a careful study of this sensitivity and distinguish regions in the parameter space in which the quality of the beam profile is good from the regions in which it is poor. These findings are potentially useful in understanding the physics of laser plasma accelerators.

We study the complexity of supergranular cells using the intensity patterns obtained from the Kodaikanal Solar Observatory during the 23rd solar cycle. Our data consists of visually identified supergranular cells, from which a fractal dimension D for supergranulation is obtained according to the relation P ∝ A D/2, where A is the area and P is the perimeter of the supergranular cells. We find a difference in the fractal dimension between active and quiet region cells in the ascending phase, during the peak and in the descending phase which is conjectured to be due to the magnetic activity level.

The partially ionized part of the solar atmosphere is investigated within the framework of a single-fluid magnetohydrodynamic (MHD) description including the non-ideal effects such as the Hall effect and the ambipolar diffusion in the generalized Ohm’s Law. In this paper, we study the propagation and damping of an Alfvén-like mode in the partially ionized solar atmosphere. It is found that the Hall effect, in addition to introducing strong dispersion, breaks the symmetry between the co- and the counter-propagating wave modes at the length scale approaching the Hall length-scale. The Hall effect creates short wavelength mode with circular polarization. The damping of Alfvén- like mode, in a partially ionized solar atmosphere, is found to be caused mainly by the Coulomb and the Cowling diffusivity. A comparison of the Hall (ηH), the Cowling (ηA) and the Coulomb (η) diffusivities shows that the ambipolar effect is dominant beyond the height of 175km above the solar surface, for the solar model given by Cox (2000) [Cox, A.N., 2000. Allen’s Astrophysical Quantities, fourth ed. Springer, New York] and chosen magnetic field.

We study the energetics of the accretion-induced outflow and then plausible jet around black holes/compact objects using a newly developed disc-outflow coupled model. Inter-connecting dynamics of outflow and accretion essentially upholds the conservation laws. The energetics depend strongly on the viscosity parameter α and the cooling factor f which exhibit several interesting features. The bolometric luminosities of ultra-luminous X-ray binaries (e.g. SS433) and family of highly luminous AGNs and quasars can be reproduced by the model under the super-Eddington accretion flows. Under appropriate conditions, low-luminous AGNs (e.g. Sagittarius A∗) also fit reasonably well with the luminosity corresponding to a sub-Eddington accretion flow with f→1.

We study the complexity of supergranular cells using the intensity patterns obtained at the Kodaikanal solar observatory during the solar maximum. Our data consists of visually identified supergranular cells, from which a fractal dimension D is obtained according to the relation P proportional to A(D/2) where A is the area and P is the perimeter of the cells. We find a difference in the fractal dimension between the active and the quiet region cells which is conjectured to be clue to the magnetic activity level.

The lower solar atmosphere consists of partially ionized turbulent plasmas harbouring velocity field, magnetic field and current density fluctuations. The correlations amongst these small scale fluctuations give rise to large scale flows and magnetic fields which decisively affect all transport processes. The three fluid system consisting of electrons, ions and neutral particles supports nonideal effects such as the Hall effect and the ambipolar diffusion. Here, we study magnetic transport by ambipolar diffusion and compare the characteristic timescales of the laminar and the turbulent ambipolar diffusion processes. As expected from a turbulent transport process, the time scale of the turbulent ambipolar diffusion is found to be smaller by orders of magnitude as compared with the laminar ambipolar diffusion.The nonlinearity of the laminar ambipolar diffusion creates magnetic structures with sharp gradients which are amenable to processes such as magnetic reconnection and energy release therefrom for heating and flaring of the solar plasma.

A nonlinear stability analysis of a uniformly rotating gas in a gravitational field has been performed. One dimensional non-linear equations have been solved by the double-Lagrangian transformation method. An explosive instability is shown to exist in contrast to the linear Jeans instability wherein a uniform rotation of the gas quenches the instability.

We study the complexity of supergranular cells using the intensity patterns obtained at the Kodaikanal Solar Observatory during the solar maximum. Our data consist of visually identified supergranular cells, from which a fractal dimension D for supergranulation is obtained according to the relation P ∝ A D/2 , where A is the area and P the perimeter of the supergranular cells. We find a fractal dimension of about 1.12 for active region cells and about 1.25 for quiet region cells, a difference that could be attributed to the inhibiting effect of the magnetic field.

The power spectra of the velocity, the magnetic field and the density fluctuations and their inter-relationships are investigated in the turbulent, Solar wind using the dimensional approach of the Kohnogorovic type. While the velocity and the magnetic field fluctuations are dynamically related within the framework of the magnetohydrodynamic (MHD) turbulence, the density fluctuations could behave as a passive scalar and be simply convected by the velocity or the magnetic field fluctuations or they could dynamically participate in the joint production mechanism of all the fluctuations. The spectrum of the density fluctuations can distinguish between these two possibilities. Further the inclusion of the Hall effect, arising from the two fluid treatment, near the ion- inertial scale generates different spectra for the velocity and the magnetic fluctuations adding steeper branches to the ideal MHD spectra. Which spectrum would the density fluctutions, behaving as a passive scalar, follow in such a case? The answer leads to the interesting consequence that the electron density fluctuations and the ion density fluctuations have different spectra at. spatial scales equal to and smaller than the ion-inertial scale. This result clearly demonstrates the two fluid picture brought in by the Hall effect.

The solar surface dynamo has become an active area of research in an attempt to understand the origin of a variety of magnetic field structures on the sun. The major modification that needs to be incorporated in the standard dynamo process is the inclusion of the partial ionization of the gas in the layers underlying and overlaying the photosphere along with the effects associated with the multifluid nature of the system. This not only changes the inertia carrying species but also substantially modifies the temporal and spatial evolution of the magnetic induction. The energy equation also carries the import of these non-ideal effects. The effects such as the Hall effect and the ambipolar diffusion take the dynamo study beyond the realm of the ideal magnetohydrodynamics. In this paper, a first principle formulation of the solar surface dynamo problem has been attempted.

The formation of the Sweet-Parker current sheet, in fact a slab, is studied for a partially ionized plasma. The effects arising from the ion-neutral drag, the ambipolar diffusion, the resistivity resulting from electron-neutral and electron-ion collisions, and the Hall electric field are important for determining the dimensions of the current slab as well as the magnetic reconnection rate. It is the Hall effect that transforms the sheet into a slab. Along with the slab configuration, the out-of-plane plasma flow generated jointly by the Hall and the ambipolar effects is an important signature result. Although the ambipolar effect enhances and the Hall effect depletes the reconnection rate, its quantitative estimate may, at best, be considered only a pointer, owing to the lack of information on the precise physical conditions near the reconnection region in astrophysical settings.

It is shown that, in addition to the Thomson scattering, the absorption due to the electron-electron, electron-ion and the electron -atom collisions in a partially ionized cosmic plasma would also contribute to the optical depth of the cosmic microwave background (CMB). The absorption depth depends on the plasma temperature and frequency of the CMB radiation. The absorption effects are prominent at the low frequency part of the CMB spectrum. These effects when included in the interpretation of the CMB spectrum may necessitate a revised view of the ioniziation of the universe.