**1. Plasma diagnostic methods**

To understand a plasma state and its characteristics, numerous experimental techniques, mechanisms, devices, theoretical models, and computational packages have been developed as diagnostic tools for measuring the plasma parameters such as the plasma electron density and temperature [1, 2] as well as their spatial profiles and dynamics. These diagnostic techniques are used to adequately describe both low-temperature and high energy density plasmas. In some situations, the measurements by these techniques cause perturbations in plasmas and are termed as active diagnostic techniques, while passive ones do not perturb plasmas. Based on the degree of ionization, the plasmas can broadly be classified into cold and hot plasma states, which accordingly demand for various types of diagnostics to

precisely estimate the plasma parameters for optimal understanding of the physics of plasmas. This includes both theoretical and experimental findings. The most common techniques for cold and hot plasmas (*Te* ≥ few keV) are the Langmuir probes in the form of planar, cylindrical, or spherical electrodes in plasmas with a goal to monitor the plasma parameters. The probes can be of several types, namely, single and/or double probes, which are used for density, temperature, and floating potential measurements. Emissive and magnetic probes work more efficiently for plasma potential measurement and wave field amplitude and phase diagnostics, respectively, while the Rogowski for antenna current measurements. There are many complications, for example, the plasma potential and density can fluctuate or drift during the time of probe measurements. In some complications, since the probe draws a large amount of currents from a plasma and perturbs the initial state of the plasma, it may lead to the erroneous measurements; even then, the Langmuir probe diagnostics are widely used and this is because of the fact that they are relatively simple to use, cheap, and give reliable values of important plasma parameters.

**2. Dusty plasma and test charge technique**

*DOI: http://dx.doi.org/10.5772/intechopen.92460*

equilibrium, Landau damping rate, etc.

**91**

The most common ingredient of astrospace plasmas is the dust component in addition to electrons and ions, found everywhere in earth atmospheres, in comets, in planetary rings, in interstellar clouds, in interplanetary space, in interstellar medium, etc. Dust grains may exist in the form of ice particles, metallic and dielectric materials, and are highly charged species due to different charging processes. For instance, the absorption of ambient electrons and ions on dust grain surface may lead to the negatively charged dust grains, while thermionic and secondary electron emissions as well as ultraviolet photoionization give rise to positively charged dust grains. Thus, a multispecies dusty plasma can be assumed as more complex plasma than conventional electron-ion plasma, for dust size, mass, and charge variations. Being an abundant component of the space and industrial plasmas [4, 5], dusty plasma has always attracted lots of interests for studying new distinct features of plasma modes [6, 7] with a static and dynamic background of dust grains both analytically and experimentally [8–10]. Numerous linear and nonlinear [viz., solitons, shocks, vortices, etc.] dusty modes and associated instabilities are investigated

*Plasma Diagnostic Methods: Test Charge Response in Lorentzian Dusty Plasmas*

using the frameworks of perturbative and nonperturbative schemes.

The behavior of charged particles in plasmas can be described by the wellknown fluid and kinetic theories [4, 11], essentially helpful for studying the basic properties of plasma waves and instabilities, depending strongly on the observed phenomena. Laboratory plasmas have effectively been modeled by fluid description, where charged fluids of plasma species are assumed in temporal and spatial configurations. But, it has been observed that fluid theory does not account for velocity space coordinate and is insufficient to study the wave phenomena in nonequilibrium plasmas, where particle distributions show significant deviations from the equilibrium states. Hence, fluid theory is unable to explain the wave-particle interactions that could lead to collisionless Landau damping phenomenon and many other interesting features of collective modes and instabilities. Conversely, kinetic theory adequately describes the physical phenomena in real time and phase space configurations, providing all information about plasma waves, instabilities, plasma

Test charge techniques [12, 13] can be utilized to study the shielding of test charges in collisional [14] and turbulent [15] plasmas, the electric field [16], and farfield potential of a test charge in a nonuniform magnetoplasma [17], the wake-field excitations in charge fluctuating dusty plasmas [18], the two-body correlations [19], the energy loss of test charges [20], etc. If a test particle is projected into the plasma with a constant speed, its charge density is coupled with the plasma charge density by the space charge effects. Consequently, the test charge is screened by a cloud of opposite sign charges leading to the short-range Debye-Hückel (DH) potential. Of course, the speed of test charge significantly matters in plasmas when it is considered with respect to thermal speeds of plasma species. The interaction potentials and energy loss of charged particles have been recognized in many research areas, for example, in ion-cluster interaction with condensed matter [21, 22], in inertial confinement fusion [23–25], in particle acceleration [26], in low-temperature laboratory plasmas [27, 28], and in dense plasmas for heavy-ion energy deposition [29].

Montgomery et al. [13] employed the test charge technique to obtain far-field potential distribution around a test charge, which decays as the inverse cube of the distance from test charge in electron-ion Maxwellian plasmas. Subsequent investigations of shielded potentials have been phenomenally influenced by the ionic motion [30], electron-electron collisions [14, 31], and plasma turbulence [15]. The electrostatic potential [32] due to small and large test charge velocities has been

On the other hand, in certain plasma sources like tokamak plasmas, strong currents are generated, which give rise to various kinds of magnetohydrodynamic (MHD) instabilities. For this, a magnetic probe is used, which is beneficial especially for measuring either local magnetic fields or its fluctuations not only in tokamaks but also in laser-produced plasmas (LPP). Furthermore, the amplitude of current flowing into the plasma can be estimated by integrating the induced magnetic field around the plasma column by utilizing the so-called Rogowski coil. However, in some plasmas (especially high temperature), it is not feasible to utilize material probes for determining the plasma parameter like plasma electron density. Therefore, a nonperturbing approach is needed to diagnose the plasma. In such a scenario, the electromagnetic spectrum is utilized. But the electromagnetic wave intensity must be low enough to the level that it will not result in plasma perturbation. For probing the high-density plasmas, a lower wavelength is required as a probe. This justifies the utilization of infrared radiation in tokamak and ultraviolet radiation for measuring the plasma electron density in LPP. The variation of the polarizing angle involving the beam probe in the presence of magnetic field can also be used for diagnostics of tokamak plasmas.

Interestingly, the evaluation of appropriate plasma parameters may be carried out by spectroscopy of emitted radiations as used generally from the beginning of plasma physics. This technique for emission measurements has been particularly making significant contributions over the past five decades for the fact that plasmas produced for nuclear fusion research exhibit intense emission in the X-ray region. Astrophysical applications further justify the wide interest in X-ray emission from plasmas. The phase soft X-ray (so defined due to their low penetrating power) indicates electromagnetic radiations with a wavelength in range 1Å ≤ *λ*≤300Å (or, in terms of photon energy *hv*, 300 eV ≤*hν*≤10 keV). Hard X-rays below 1 Å are occasionally produced in plasmas for highly accelerated electrons, like runaway electrons in tokamak plasmas and suprathermal electrons in LPP [3]. The characteristics of soft X-ray spectra like line intensities, line profiles, and continuum intensities can be investigated to determine the electron densities by Stark broadening, while the ion densities from the absolute radiation intensities and ion temperatures using the Doppler broadening of spectral lines [2].

The particle measurement method is another scheme for investigating the characteristics of plasmas by using the beam of fast particles. It has received much attention in the studies of inertial confinement fusion and energy deposition in a medium driven by cluster-ion and fast heavy-ion beams, as well as in plasma accelerators and low-temperature laboratory plasmas.
