Partially ionized plasmas have only recently started getting attention as a research topic especially in the context of cosmic objects and environs. More often than not, the neutral particles have been treated as collision partners for the dominant charged components of a plasma. Alternately, there are cases where the neutrals are the dominant component, and therefore they become the main source of inertia in a partially ionized plasma. There is a lot to investigate in the intermediate circumstances. A glimpse of the three-fluid, the two-fluid, the single-fluid pictures, along with the special case of a weakly ionized plasma has been attempted in the previous chapters. The study is far from complete!

In this chapter, a few research problems, in continuation of the subject matter presented in this book are listed chapterwise. These are the research problems I myself would have liked to pursue had I enough resources at my disposal.

The Three-fluid Description The three-fluid description of a partially ionized plasma has been given in Section 2:3 where it was assumed that the plasma consisted of electrons, ions with fixed electric charge Ze and neutrals. It is however, possible, in such a system, that some of the neutrals pick up electric charges due to electron attachment, charge exchange, ionization or acquire an electric dipole moment due to polarization depending upon the temperature of the plasma. The charging of the neutrals is akin to the charging of the dust grains in a dusty plasma and should be included in the set of Eqs (2.119)–(2.134) along with the assurance of the electric charge conservation. Some efforts in this direction have been made, for example, in the context of the stability of cold solar prominence material high up in the atmosphere against the solar gravity.

The Two-fluid Description

The electron fluid and the ion fluids were combined to construct the magnetohydrodynamic (MHD) fluid in Subsection 2.4.1. The MHD fluid and the neutral fluid then form the two-fluid description of a partially ionized plasma.

In this chapter, we shall attempt to introduce the reader to some specific issues arising in partially ionized plasmas as they exist in varied astrophysical sites. We have taken the solar atmosphere as a prime example, as it spans a wide range of plasma parameters which present circumstances for suitable application of the four different descriptions of a partially ionized plasma. A variety of issues such as the equilibrium, the waves and the instabilities giving rise to turbulence, summon our attention. A few examples of the equilibrium states of a partially ionized plasma in its different descriptions have been presented in Chapter 3.

Here, we shall explore in some detail the existence of equilibrium structures, including gravitational, rotational, magnetic and multifluid effects. The Hall equilibrium of the partially ionized plasma, in particular, brings out a new spatial scale which is larger than the ion inertial scale. The double curl nature of the solutions maps the velocity and the magnetic field on short spatial scales. The equilibrium of the partially ionized plasma under the dominance of the ambipolar effect reveals the existence of extremely sharp magnetic structures embedding large current densities. Such structures enable the heating of the plasma through the excitation and saturation of plasma instabilities.

Equilibrium of Partially Ionized Structures in the Solar Atmosphere

The solar atmosphere consists of layers which widely differ in their density, temperature and magnetization properties. While the distribution of the atmospheric matter consisting of neutral hydrogen, hydrogen plasma and ions of various elements is essentially a result of the gravitational stratification, the temperature and the magnetic field variations are extremely large being governed by the local energetics. The outermost layer called the solar corona becomes visible only during solar eclipses. It is at a temperature of more than a million degree Kelvin and consists of a fully ionized hydrogen plasma and trace ions, such as iron and calcium, in various states of ionization. The next identifiable layers are respectively the transition region and the chromosphere. The chromosphere has a temperature of tens of thousands of degree Kelvin and rises to a million degree Kelvin in the very narrow transition region. The next lower layer is the photosphere. It is the layer from which we receive the visible radiation. The colour of the visible radiation (a near yellow) tells us that the photosphere is approximately at a temperature of 6000 degree Kelvin.

Retirement is a time to indulge oneself, determine your own deadlines and to meet them at your own pace. The cooking breaks are no brakes! This is how I came to write this book, my second, after my superannuation; the first one is called Plasmas; The First State of Matter.

I was introduced to the topic of partially ionized plasmas by Professor Kumar Chitre who handed me the A. Brandenburg and E. G. Zweibel paper (1995, Ap. J., 448, 734) during my visit to the Tata Institute of Fundamental Research sometime in the year 2000. This resulted in our paper ‘Ambipolar diffusion in the solar atmosphere’.

Partially ionized plasmas again came into my line of sight in the year 2005 when I visited the University of Tokyo campus near Edogawadai to work with Professor Yoshida-sansei. Since then, I have been studying plasma-typical problems in partially ionized plasmas. Around the same time I was also collaborating with Professor Swadesh Mahajan on the role of the Hall effect in diverse circumstances. It turned out that in the weakly ionized plasma model of a partially ionized plasma, the ion inertial scale, a hallmark of the Hall effect, gets multiplied by the inverse of the ionization fraction. As a result, the effective ion inertial scale acquires a much larger value than its counterpart in a fully ionized plasma. This was reported in “Equilibrium structures in partially ionized rotating plasmas within Hall magnetohydrodynamics”. During my visit to Professor S. Masuda's group in Nagoya University, Professor K. Shibata and I discussed the possibility of observing this new inertial scale phenomena on the solar atmosphere with a future solar mission. Additionally, during my visits to the Kyoto University and the National Astronomical Observatory of Japan, Mitaka, Tokyo, I had discussions on the mean field dynamo in partially ionized plasmas with Professor S. Tsuneta's group. The highly positive response from my peers galvanized me into pursuing the area further, and my own desire to present partially ionized plasmas as a subject in its own right resulted in this book.

We have developed the basic mathematical framework to study the dynamics of a partially ionized plasma as the three-fluid, the two-fluid, the single-fluid and the weakly ionized plasma systems in Chapter 2. The various equilibria of these systems have been explored in Chapter 3. We are now set to study the excitation of waves in these systems. The three-fluids in the presence of a magnetic field support a host of waves, depending upon the nature of the restoring forces. These forces come into play when a system is disturbed from its equilibrium state by a very tiny amount. The restoring forces tend to restore the system back to the equilibrium and the oscillations are set in, in the process. For example, a bend in the otherwise uniform magnetic field generates a restoring force which tries to straighten the field lines. Similarly, the compressions and the rarefactions in the system execute oscillations in an attempt to maintain a uniform mass density. The tiny disturbance to the equilibrium state ensures that the resulting oscillations have tiny but finite amplitudes which do not depend on the magnitude of the disturbance. The system is linearized about its equilibrium state. These circumstances generate a linear response of the system and the ensuing waves are said to be the linear waves. The linear response of the system gives the dispersion relation, the phase and the group speeds, the polarization and the relative estimates of the mechanical and the electromagnetic energy densities of the waves. The waves can be studied in each of the four descriptions of a partially ionized plasma given in Chapter 2. We shall begin with the fourth description, namely, the weakly ionized plasma, and then go on to consider the single-fluid (SPIF), the two-fluid and the three-fluid models.

Waves in a Weakly Ionized Plasma

A weakly ionized plasma is well described by the set of Eqs (2.220)–(2.226) along with the final form of the induction Eq. (3.245) including the time dependence. Let us write here the equations required to study the waves.