# Non-ideal plasmas

Non-ideal plasmas are characterized by the emergence of strong correlations, prevalence of quantum effects and onset of dissipative processes. Remarkable dense astrophysical objects such as white dwarfs and neutron star crusts, extreme ionized media such as those encountered in laser-solid interactions and hypervelocity impacts as well as novel engineered forms of soft matter such as complex plasmas are examples of non-ideal plasmas. The physics complexity, natural occurrence and technological significance of non-ideal plasmas is just beginning to be understood.

Plasmas are systems that consist of positively and negatively charged particles with approximately equal charge densities. Sometimes even the quasi-neutrality condition can be violated, see plasma sheaths and non-neutral plasmas. In all plasmas, the long-range nature of the Coulomb interaction leads to the prevalence of collective effects.

Plasmas can be divided into two broad categories: (a) "**Ideal plasmas"** (such as those in laboratory discharges and tokamaks as well as the solar wind and the interstellar medium), where the average interaction energy of any charged species is much smaller that its thermal energy. Such weakly coupled plasmas are characterized by an ideal equation of state and a rather trivial static structure. Nevertheless, the long-range nature of the Coulomb interaction potential as well as the presence of charge density and current density fluctuations still makes their dynamic response a complicated state-of-affairs, especially in the presence of external electro-magnetic fields. (b) "**Strongly coupled plasmas" **(such as those in dense astrophysical objects), where the average interaction energy of any charged species is comparable, larger or even much larger that its thermal energy. This can be realized for very high charge number numbers (the dust component in dusty or complex plasmas), for very low temperatures (the ion component in ultra-cold neutral plasmas) or for extremely high densities (high energy density matter). Strongly coupled plasmas are characterized by non-trivial thermodynamics and a static structure that features numerous co-ordination cells. The state of strongly coupled plasmas can be non-ideal gas, liquid, crystalline or even amorphous.

Plasmas can also be divided into two other broad categories: (a) "**Classical plasmas" **(typically gas-generated such as those in discharges or any inter-space medium), where the mean interparticle distance is much larger than the thermal de Broglie wavelength. These are characterized by a Maxwell-Boltzmann equilibrium distribution and the absence of diffraction as well as exchange effects. (b) "**Quantum plasmas" **(typically solid state generated such as the electron component of metals and the electron-hole plasmas of semi-conductors), where the mean interparticle distance is smaller or comparable to the thermal de Broglie wavelength. These are characterized by a Fermi-Dirac equilibrium distribution and the importance of the degeneracy pressure contribution.

Finally, plasmas can also be divided into another two broad categories: (a)** "Hamiltonian plasmas" **(such as those in tokamaks), where the charge over mass ratio is constant. These systems can be assumed to contain only free charges and the Hamiltonian phase-space principles apply. (b) "**Non-Hamiltonian plasmas" **(such as plasma-molecular systems, chemically active plasmas and dusty plasmas), where the charge over mass ratio varies. These systems contain both free charges and bound charges, are dissipative in nature and are open in terms of energy and particle exchange with their environment.

Standard plasmas taught in textbooks are ideal classical Hamiltonian plasmas. All other plasmas can be considered as "**non-ideal plasmas"**. It should be noted that two forms of non-ideality can be present simultaneously in a many-body system; for instance warm dense matter is always quantum and can also be strongly coupled, dusty plasmas are always non-Hamiltonian and can be strongly coupled, electrons in semi-conductors are always quantum and can also be strongly coupled, etc…

### Statistical mechanics of strongly coupled plasmas

A standard example is liquid, supercooled and crystal complex plasmas, where the dust species is dominant as far as energy and momentum transfer is concerned. Hence, in the relatively large spatial and slow temporal scales that are relevant for dust motion, the plasma can be essentially considered as one-component. The electrons and ions solely act as a neutralizing polarizable background that is also responsible for the dust charge and the dust interaction potential. This observation opens up the way for the theoretical description of complex plasmas and strongly coupled plasmas (in general) with the established statistical mechanics methods of the theory of simple liquids. The group specializes in the application and extension of statistical mechanics frameworks such as

- integral equation theory,
- classical density functional theory,
- perturbation theory,
- variational theory,
- generalized hydrodynamics,
- quasi-localized approximation,
- isomorph theory,
- memory function approach,
- mode coupling theory,
- replica theory

to the study of the thermodynamic, structural, dynamic and phase transformation properties of liquid plasmas. The group also performs molecular dynamics simulations of liquid plasmas that are employed to validate the theoretical models.

### Statistical mechanics of the uniform electron fluid in the warm dense matter and strongly coupled regimes

The uniform electron fluid consists of Coulomb interacting electrons that are treated as indiscernible fermions and are immersed in a rigid neutralizing background. It constitutes one of the most fundamental many-body systems in physics and chemistry that serves as the building block for the description of most realistic electronic systems. Despite its simplicity, it is incredibly rich in physics. Despite its importance, especially in the case of finite temperatures, there are many aspects that remain poorly investigated in extended portions of its phase diagram. This mainly originates from the strong interplay between Coulomb interactions, diffraction / exchange effects and thermal excitations that manifests itself in the absence of small parameters both with respect to the interaction strength and with respect to the degeneracy level. As a consequence, not only plasma kinetic theory but also condensed matter theory break down. The group specializes in the application and extension of statistical mechanics frameworks such as

- self-consistent dielectric formalism,
- linear density response theory,
- non-linear density response theory,
- quantum kinetic theory,
- classical mapping approach,
- method of moments approach,

to the study of the thermodynamic, structural, collective and dynamic properties of the uniform electron fluid in the warm dense matter and strongly coupled regimes.

### Statistical mechanics of non-Hamiltonian dusty plasmas

The group specializes in the extension of the fluctuation theory of ideal plasmas to include the dust component. In contrast to electrons / ions that are classically point particles whose microstate can be defined by position and momentum, dust has an internal structure. In its statistical description as a plasma species, its inner structure can be neglected only provided that additional variables are used to define its microstate. These mesoscopic variables, due to interaction with the plasma, vary with the local conditions and should be considered as new phase space variables. Examples include the dust charge, angular momentum, surface temperature and internal energy. Most important in all physical regimes is naturally the dust charge, since it dictates Coulomb interactions.

Even when considering only the dust charge, the effect in the microscopic phase-space densities is profound. Changes stem from the annihilation of plasma particles upon contact with the grain surface, the dust charge variability, the first-order discontinuities in dust trajectories due to plasma absorption and the dust impenetrability. In most physical scenarios, a continuous phase space approximation can be employed where **(a) **grains are treated as point particles in Coulomb interactions, **(b) **momentum transfer due to plasma absorption is assumed to be continuous, **(c) **the dust charge is assumed to vary continuously and not in elementary charge steps, **(d) **capture cross-sections are obtained from external models. In this case, the effect of dust in the Klimontovich system of equations can be summed up in: **(i) **the augmentation of the Liouville phase space to include the dust charge, **(ii)** the addition of the dust charging equation to Hamilton’s equations, **(iii) **dust grains acting as sinks of plasma particles.

Starting from the modified Klimontovich system, the unifying framework of plasma fluctuation theory enables investigations of the effect of dust in

- the spectral densities of fluctuations,
- the linear dielectric response of the medium,
- the stopping power of the medium,
- the Boltzmann equation and the collision integral,
- the Bremsstrahlung cross-sections,
- the wave scattering cross-sections,
- the wave transformation cross-sections,
- the radiation transport equation,
- the hydrodynamic equations and the transport coefficients.