Dusty plasmas are known to support a diverse range of instabilities, including both generalizations of standard plasma instabilities and ones caused by effects specific to dusty systems. It has been recently demonstrated that a novel broad class of streaming instabilities, termed resonant drag instabilities (RDIs), can be attributed to a particular resonance phenomenon, manifested by defective eigenvalues of the linearized dust/fluid system. In this work, it is demonstrated that this resonance phenomenon is not unique to RDIs and can be used as a framework to understand a wider range of instabilities, termed resonant instabilities. Particular attention is given to the filamentary ionization instability seen in laboratory dusty plasmas and to the two-stream instability. It is shown that, due to the commonalities in underlying physics between the dust-ion-acoustic two-stream instability and the acoustic RDI, these instabilities should be relevant in strongly overlapping regimes in astrophysical dusty plasmas. It is proposed that a similar overlap in the experimental accessibility of these modes (and of the filamentary instability) allows for the possibility of experimental investigation in the laboratory of complex and astrophysically relevant instability dynamics.
The formation of the gigantic dust-acoustic rouge waves (DARWs) in an electron depleted unmagnetized opposite polarity dusty plasma system is theoretically observed for the first time. The nonlinear Schrödinger equation (derived by utilizing the reductive perturbation method) has been analytically as well as numerically analyzed to identify the basic features (viz., height, thickness, and modulational instability, etc.) of DARWs. The results obtained form this investigation should be useful in understanding the basic properties of these rouge waves which can predict to be formed in electron de…
Motivated by observations of localized electrostatic wavepackets by the Voyager 1 and 2 and Cassini missions in Saturn's magnetosphere, we have investigated the evolution of modulated electrostatic wavepackets in a dusty plasma environment. The well-known dust-ion acoustic (DIA) mode was selected to explore the dynamics of multi-dimensional structures, by means of a Davey-Stewartson (DS) model, by taking into account the presence of a highly energetic (suprathermal, kappa-distributed) electron population in combination with heavy (immobile) dust in the background. The modulational (in)stabilit…
The propagation of electrostatic waves in an unmagnetized collisionless pair-ion plasma with immobile positively charged dusts is studied for both large- and small-amplitude perturbations. Using a two-fluid model for pair-ions, it is shown that there appear two linear ion modes, namely the "fast" and "slow" waves in dusty pair-ion plasmas. The properties of these wave modes are studied with different mass $(m)$ and temperature $(T)$ ratios of negative to positive ions, as well as the effects of immobile charged dusts $(δ)$. For large-amplitude waves, the pseudopotential approach is performed, …
New developments in the theory and numerical simulation of a recently proposed one-dimensional nonlinear time-dependent fluid model [K. Avinash, A. Bhattacharjee, and S. Hu, Phys. Rev. Lett. 90, 075001 (2003)] for void formation in dusty plasmas are presented. The model describes an initial instability caused by the ion drag, rapid nonlinear growth, and a nonlinear saturation mechanism that realizes a quasi-steady state containing a void. The earlier one-dimensional model has been extended to two and three dimensions (the latter, assuming spherical symmetry), using a more complete set of dynam…
The void, which is a dust-free region inside the dust cloud in the plasma, results from a balance of the electrostatic force and the ion drag force on a dust particulate. The ion drag force having numerous forms, some of which are based on models whereas others are driven from first principles. To explain the generation of voids, Avinash et al.[K. Avinash, A. Bhattacharjee, and S. Hu, AIP.CP649, III ICPDP, (2002)p121]proposed a time-dependent nonlinear model that describes the void as a result of an instability. We augment this model by incorporating the grain drift and by replacing the ion-dr…
The naturally persistent flow of hundreds of dust particles is experimentally achieved in a dusty plasma system with the asymmetric sawteeth of gears on the electrode. It is also demonstrated that the direction of the dust particle flowcan be controlled by changing the plasma conditions of the gas pressure or the plasma power. Numerical simulations of dust particles with the ion drag inside the asymmetric sawteeth verify the experimental observations of the flow rectification of dust particles. Both experiments and simulations suggest that the asymmetric potential and the collective effect are…
The properties of electrostatic transverse shear waves propagating in a strongly coupled dusty plasma with an equilibrium density gradient are examined using the generalized hydrodynamic equation. In the usual kinetic limit, the resulting equation has similarity to zero energy Schrodinger's equation. This has helped in obtaining some exact eigenmode solutions in both cartesian and cylindrical geometries for certain nontrivial density profiles. The corresponding velocity profiles and the discrete eigenfrequencies are obtained for several interesting situations and their physics discussed.
Charges on the dust grains immersed in a plasma vary in time. We follow the hydrodynamic approach to obtain dispersion relations for some low frequency electrostatic modes, taking into account charge fluctuation on the dust. We have used the description of the one dimensional fully electromagnetic particle code. There exists one spatial dimension and three velocity components. This is usually referred to as a model. Our analysis shows that the presence of the dust grains causes different effects in different frequency regimes.
An analytical model is presented for the description of nonlinear dust-ion-acoustic waves propagating in an unmagnetized, collisionless, three component plasma composed of electrons, ions and inertial dust grains. The formulation relies on a Lagrangean approach of the plasma fluid model. The modulational stability of the wave amplitude is investigated. Different types of localized envelope electrostatic excitations are shown to exist.
The nonlinear dynamics of coupled electrostatic upper-hybrid (UH) and Alfven waves (AWs) is revisited in a magnetized electron-ion plasma with charged dust impurities. A pair of nonlinear equations that describe the interaction of UH wave envelopes (including the relativistic electron mass increase) and the density as well as the compressional magnetic field perturbations associated with the AWs is solved numerically to show that many coherent solitary patterns can be excited and saturated due to modulational instability of unstable UH waves. The evolution of these solitary patterns is also sh…
A new model method for describing of the electrostatic screening in two-component systems (electron-ion plasmas, dusty plasmas, electrolytes, etc) is developed. The method is applicable to the systems of higher non-ideality degree. The expressions for all the screening parameters introduced in the previous paper (Part 1) of this work, as well as for an additional parameter characteristic for multi-component systems, are obtained. All these parameters are presented in a simple analytic form suitable for operative laboratory usage, especially for theoretical interpretation of experimental data.
By combining the results from a self-consistent 2D dusty plasma fluid model and a 3D N-body code, the equilibrium position and crystal structure were determined for dust particles levitated in the sheath in a modified Gaseous Electronics Conference (GEC) reference cell, in which the lower electrode was heated or cooled. The Debye length, charge and electric field were reconstructed on a sub-millimeter scale by applying a previously developed, independent method. However, this method seems to overestimate the charge, and hence underestimate the electric field. Even corrected for this fact, the …
A two-dimensional dust crystal levitated in the sheath of a modified Gaseous Electronics Conference (GEC) reference cell is manipulated by heating or cooling the lower electrode. The dust charge is obtained from top-view pictures of the crystal using a previously developed analytical model. By assuming a simple force balance, and measuring the radial confining force, the vertical electric field profile in the sheath is reconstructed. The dust crystal is shown to levitate on the plasma side of the Bohm point. Finally, it is shown that the ion drag plays an important role in the vertical force b…
In this paper a new model method for describing of the electrostatic screening in single-component systems which is free of Debye-Huckel's non-physical properties is presented. The method is appropriate for the determination of screening parameters in the case of the systems of higher non-ideality degree. The obtained screening characteristics are presented in a simple analytic form. The presented results make basic elements of a method for determination of screening characteristics in dense two-component plasmas, which are discussed in Part2 and Part 3 of this work.
A standard nonlinear Schrödinger equation has been established by using the reductive perturbation method to investigate the propagation of electrostatic dust-acoustic waves, and their modulational instability as well as the formation of localized electrostatic envelope solitons in an electron depleted unmagnetized dusty plasma system comprising opposite polarity dust grains and super-thermal positive ions. The relevant physical plasma parameters (viz., charge, mass, number density of positive and negative dust grains, and super-thermality of the positive ions, etc.) have rigorous impact to re…
A new electrostatic ramjet space engine is proposed and analyzed. The upper atmosphere (85 -1000 km) is extremely dense in ions (millions per cubic cm). The interplanetary medium contains positive protons from the solar wind. A charged ball collects the ions (protons) from the surrounding area and a special electric engine accelerates the ions to achieve thrust or decelerates the ions to achieve drag. The thrust may have a magnitude of several Newtons. If the ions are decelerated, the engine produces a drag and generates electrical energy. The theory of the new engine is developed. It is shown…
The Sagdeev pseudopotential method is used to investigate the occurrence and the dynamics of fully nonlinear electrostatic solitary structures in a plasma containing suprathermal hot electrons, in the presence of massive charged dust particles in the background. The soliton existence domain is delineated, and its parametric dependence on different physical parameters is clarified.
Extracting environmental forces from noisy data is a common yet challenging task in complex physical systems. Machine learning represents a robust approach to this problem, yet is mostly tested on simulated data with known parameters. Here we use supervised machine learning to extract the electrostatic, hydrodynamic, and stochastic forces acting on micron-sized charged particles levitated in an argon plasma. Trained on simulated particle trajectories using more than 100 dynamical and statistical features, the model predicts system parameters with 50\% better accuracy than conventional methods,…
Ground state structures of finite, cylindrically confined two-dimensional Yukawa systems composed of charged superparamagnetic dust grains in an external magnetic field are investigated numerically, using molecular dynamic simulations and lattice summation methods. The ground state configuration of the system is identified using, as an approximation, the experimentally obtained shape of the horizontal confinement potential in a classical single layer dusty plasma experiment with non-magnetic grains. Results are presented for the dependence of the number density and lattice parameters of the du…
The ultra low frequency modes associated to the activated dust specie in a bounded cylinder orientation plasma has been investigated here. Here flow of all plasma particles is assumed along the axial coordinates where gradients in velocity are set to be along radial direction. This analysis has been carried out for both Maxwellian and non-Maxwellian (Kappa and Carins) dusty plasma where coupling of electrostatic dust acoustic and drift modes drives global vortex formations. The coefficients of the vortex solution has been affected strongly by the presence of superthermal particles. Significanc…
Over the past decade, dust particulate contamination has increasingly become an area of concern within the fusion research community. In a burning plasma machine design like the International Thermonuclear Experimental Reactor (ITER), dust contamination presents problems for diagnostic integration and may contribute to tritium safety issues. Additionally due to ITER design, such dust contamination problems are projected to become of even greater concern due to dust/wall interactions and possible instabilities created within the plasma by such particulates. Since the dynamics of such dust can i…
An analysis of databases of photographic images of ocean's surface, taken from various altitudes and for various types of rough ocean surface, revealed the presence of an ocean's skeletal structures (OSS). We make a stress on the phenomenon of OSS's blocks in the form of vertically oriented floating cylinders (VFC) because here we suggest the hypothesis that the VFC is a stimulator of initial phase of the "waterspout" phenomenon (WS). An analysis of the fine structure of VFC suggests the OSS to be a carrier/source of major electrodynamical properties of initial phase of every WS. This implies …
The weakly nonlinear regime of transverse paramagnetic dust grain oscillations in dusty (complex) plasma crystals is discussed. The nonlinearity, which is related to the sheath electric/magnetic field(s) and to the inter--grain (electrostatic/magnetic dipole) interactions, is shown to lead to the generation of phase harmonics and, in the case of propagating transverse dust-lattice modes, to the modulational instability of the carrier wave due to self--interaction. The stability profile depends explicitly on the form of the electric and magnetic fields in the plasma sheath. The long term evolut…
A versatile table-top dusty plasma experimental (DPEx) device to study flow induced excitations of linear and nonlinear waves/structures in a complex plasma is presented. In this {$Π$}-shaped apparatus a DC glow discharge plasma is produced between a disc shaped anode and a grounded long cathode {tray} by applying a high voltage DC in the background of a neutral gas {(Argon)} and subsequently a dusty plasma is created by introducing micron sized dust particles that get charged and levitated in the sheath region. A flow of the dust particles is induced in a controlled manner by adjusting the pu…
A variety of experimental techniques for the generation of subsonic/supersonic dust fluid flows and means of measuring such flow velocities are presented. The experiments have been carried out in a $Π-$shaped Dusty Plasma Experimental (DPEx) device with micron size kaolin/Melamine Formaldehyde (MF) particles embedded in a background of Argon plasma created by a direct current (DC) glow discharge. A stationary dust cloud is formed over the cathode region by precisely balancing the pumping speed and gas flow rate. A flow of dust particles/fluid is generated by additional gas injection from a sin…
It is well known that the form of grain size distribution strongly influences the linear dielectric response of a dusty plasma. In previous results [IEEE Trans. Plasma Sci. 29, 182 (2001)], it was shown that for a class of size distributions, there is an equivalence to a Lorentzian distribution of mono-sized particles. The electrostatic response to a slowly moving test charge, using a second order approximation can then be found [Phys. Lett. A 305, 79 (2002)]. It is also well known [Phys. Plasmas 10, 3484 (2003)] that the dynamical charging of grains in a dusty plasma enhances the shielding of…
In order to give a basis for the structure and correlation analysis of fine particle (dusty) plasma and colloidal suspensions, thermodynamic treatment of mixtures of macroscopic and microscopic charged particles within the adiabatic response of the latter is extended to include the case where the system is finite and weakly inhomogeneous. It is shown that the effective potential for macroscopic particles is composed of two elements: mutual Yukawa repulsion and a confining (attractive) Yukawa potential from their `shadow' (the average charge density of macroscopic particles multiplied by the mi…
A model is presented to explain the normal mode features of dust particles in a planar zigzag crystal chain for the first and second neighbors. The degrees of freedom of particles are the longitudinal and transverse displacements in plane coupled by the first and second neighbor harmonic forces in two-dimensions (2D). The constant electric force duded to the electrodes to keep the zigzag structure is calculated. The coupling between transverse and longitudinal dust-lattice (DL) modes is derived. The latter is considered due to the energy of the electrostatic (Yukawa) potential. Moreover couple…
A 2D hydrodynamical model is developed and analyzed for the steady state of a driven-dissipative dust clouds confined in an azimuthally symmetric toroidal system which is in dynamic equilibrium with background unbounded streaming plasma. Its numerical solution not only confirms the analytical structure of the driven dust vortex flow in linear limit as reported in previous analysis, but also shows how the dust vortices are strongly affected by the nonlinear convection of the flow itself. Effects of various system parameters including external driving field and Reynolds number (Re) are investiga…
The spontaneous rotation of small dust clusters confined inside a cubical glass box in the sheath of a complex plasma was observed in experiment. Due to strong coupling between the dust particles, these clusters behave like a rigid-body where cluster rotation is contingent upon their configuration and symmetry. By evaluating the effects of distinct contributing forces, it is postulated that the rotation observed is driven by the net torque exerted on the cluster by the ion wake force. The configuration and symmetry of a cluster determines whether the net torque induced by the ion wake force is…
We study the secondary electron emissions induced by the impact of electrons on dust grains and the resulting dust charging processes in the nonequilibrium dusty plasma with power-law distributions. We derive new expressions of the secondary emitted electron flux and the dust charging currents that are generalized by the power-law q-distributions, where the nonlinear core functions are numerically studied for the nonextensive parameter q. Our numerical analyses show that the power-law q-distribution of the primary electrons has a significant effect on the secondary emitted electron flux as wel…
In the last experiment with the PK-3 Plus laboratory onboard the International Space Station, interactions of millimeter-size metallic spheres with a complex plasma were studied~[M. Schwabe {\it et al.}, New J. Phys. {\bf 19}, 103019 (2017)]. Among the phenomena observed was the formation of cavities (regions free of microparticles forming a complex plasma) surrounding the spheres. The size of the cavity is governed by the balance of forces experienced by the microparticles at the cavity edge. In this article we develop a detailed theoretical model describing the cavity size and demonstrate th…
The creation of a spatially extended stable DC complex plasma crystal is a big experimental challenge and a topical area of research in the field of dusty plasmas. In this paper we describe a newly built and commissioned dusty plasma experimental device, DPEx-II, at the Institute for Plasma Research. The device can support the formation of large sized Coulomb crystals in a DC glow discharge plasma. The plasma in this L-shaped table-top glass chamber is produced between a circular anode and a long tray shaped cathode. It is characterized with the help of various electrostatic probes over a rang…
Ion-acoustic modes propagating in unmagnetized dusty plasmas are studied by applying a generic collisionless fluid model. An Eulerian-to-Lagrangean variable transformation leads to a new system of evolution equations, which may be combined into a single (rather complex) equation for the mean ion density. The linear and weakly nonlinear oscillations regimes are studied and their modulational stability is investigated. This study extends known previous results on the Lagrangian description of electron- or ion-acoustic electrostatic plasma modes. The relevance with the description of dust-ion aco…
Collections of micrometer sized solid particles immersed in plamsa are used to mimic many systems from solid state and fluid physics, due to their strong electrostatic interaction, their large inertia, and the fact that they are large enough to be visualized with ordinary optics. On Earth, gravity restricts the so called dusty plasma systems to thin, two-dimensional layers, unless special experimental geometries are used, involving heated or cooled electrons, and/or the use of dielectric materials.In micro-gravity experiments, the formation of a dust-free void breaks the isotropy of three-dime…
A comprehensive exploration of regional dust evacuation in complex plasma crystals is presented. Voids created in 3D crystals on the International Space Station have provided a rich foundation for experiments, but cavities in dust crystals formed in ground-based experiments have not received as much attention. Inside a modified GEC RF cell, a powered vertical probe was used to clear the central area of a dust crystal, producing a cavity with high cylindrical symmetry. Cavities generated by three mechanisms are examined. First, repulsion of micrometer-sized particles by a negatively charged pro…
The current-driven electrostatic ion-cyclotron (EIC) instability is studied in presence of a transverse dc electric fields in a collisional magnetized dusty plasma. We derive the appropriate charging equation self consistently by using the Vlasov equation.
A two-dimensional complex plasma containing active Janus particles was studied experimentally. A single layer of micron-size plastic microspheres was suspended in the plasma sheath of a radio-frequency discharge in argon at low pressure. The particle sample used was a mixture of regular particles and Janus particles, which were coated on one side with a thin layer of platinum. Unlike a suspension consisting of regular particles only, the suspension with inclusion of Janus particles did not form an ordered lattice in the experimental conditions used. Instead, the particles moved around with hig…
The collective dynamics of annulus dusty plasma formed between a co-centric conducting (non-conducting) disk and ring configuration is studied in a strongly magnetized radio-frequency (rf) discharge. A superconducting electromagnet is used to introduce a homogeneous magnetic field to the dusty plasma medium. In absence of the magnetic field, dust grains exhibit thermal motion around their equilibrium position. The dust grains start to rotate in anticlockwise direction with increasing magnetic field (B $>$ 0.02 T), and the constant value of the angular frequency at various strengths of magnetic…
A model for the condensation of a dusty plasma is constructed by considering the spherical shielding layers surrounding a dust grain test particle. The collisionless region less than a collision mean free path from the test particle is shown to separate into three concentric layers, each having distinct physics. The method of matched asymptotic expansions is invoked at the interfaces between these layers and provides equations which determine the radii of the interfaces. Despite being much smaller than the Wigner-Seitz radius, the dust Debye length is found to be physically significant because…
Dust-acoustic (DA) waves (DAWs) and their modulational instability (MI) have been investigated theoretically in a plasma system consisting of inertial opposite polarity (positively and negatively) warm adiabatic charged dust particles as well as inertialess non-extensive $q$-distributed electrons and non-thermal ions. A nonlinear Schrödinger (NLS) equation is derived by using the reductive perturbation method. It has been observed from the analysis of NLS equaion that the modulationally stable solitary DAWs give rise to the existence of dark envelope solitons, and that the modulationally unsta…
The neutrals in the Earth environment are in fact free and subjected to drag forces (by ions). In this study we show that drag or friction forces in the ionosphere-thermosphere system initiate changes in the plasma flow, neutral wind, and the conductivity, as well. Ions and electrons embedded in neutral wind field of velocity u acquire drifts perpendicular both to the initial neutral wind velocity and to the ambient magnetic field producing a perpendicular electric current. This perpendicular electric current is defined by a conductivity derived previously and the polarization electric field u…
Within the problem of the finding of the mean potential energy of the charged particle in the plasma in this work a classification of physical systems (electrolytes, dusty plasmas, plasmas) is made based on consideration, or lack thereof, of a few special additional conditions. The system considered here, as well as other systems which are described with those additional conditions imposed are treated as the systems of the "closed" type, while the systems where those conditions are fully neglected - as being of the "open" type. In the our previous investigation one- and two component systems w…
We report an experimental observation of multiple co--rotating vortices in a extended dust column in the background of non--uniform diffused plasma. Inductively coupled RF discharge is initiated in the background of argon gas in the source region which later found to diffuse in the main experimental chamber. A secondary DC glow discharge plasma is produced to introduce the dust particles into the plasma. These micron sized poly-disperse dust particles get charged in the plasma environment and transported by the ambipolar electric field of the diffused plasma and found to confine in the potenti…
This manuscript, presents a theoretical study of the linear and nonlinear characteristics of acoustic and drift waves in a bounded inhomogenious dusty plasma which has potential applications in space and lab environments. In this analysis, flow of all plasma particles is assumed to be along the axial direction whereas gradients in velocity are considered to be along the radial direction. First we study coupling of dust modified ion acoustic (DMA) and drift (DMD) waves (linear analysis) at fast time when dynamics of dust remain inactive, later formation of nonlinear vortex like structures are e…
The nonlinear propagation of electrostatic dust-acoustic (DA) waves in a magnetized dusty plasma consisting of negatively charged mobile dusts, nonthermal fast electrons and trapped ions with vortex-like distribution is studied. Using the reductive perturbation technique, a Korteweg-de Vries (KdV)-like equation is derived which governs the dynamics of the small-amplitude solitary waves in a magnetized dusty nonthermal plasma. It is found that due to the dust thermal pressure, there exists a critical value $(β_c)$ of the nothermal parameter $β~(>1)$, denoting the percentage of energetic electro…
We investigate the possibility of cosmic ray (CR) confinement by charged dust grains through resonant drag instabilities (RDIs). We perform magnetohydrodynamic particle-in-cell simulations of magnetized gas mixed with charged dust and cosmic rays, with the gyro-radii of dust and GeV CRs on $\sim\mathrm{AU}$ scales fully resolved. As a first study, we focus on one type of RDI wherein charged grains drift super-Alfv{é}nically, with Lorentz forces strongly dominating over drag forces. Dust grains are unstable to the RDIs and form concentrated columns and sheets, whose scale grows until saturating…
In this paper, the collective dynamics of the large aspect ratio dusty plasma is studied over a wide range of discharge parameters. An inductively coupled diffused plasma, which creates an electrostatic trap to confine the negatively charged grains, is used to form a large volume (or large aspect ratio) dusty plasma at low pressure. For introducing the dust grains into the potential well, a unique technique using a secondary DC glow discharge plasma is employed. The dust dynamics is recorded in a 2-dimension (2D) plane at a given axial location. The dust fluid exhibits wave like behavior at lo…
Structural changes of self-organized vortices in Jupiter atmospheres such as Great Red Spot (GRS) and White Ovals are demonstrated using an electrostatically bounded charged dust cloud in an unbounded streaming plasma as the prototype for various driven-dissipative complex flow systems in nature. Using a 2D hydrodynamic model, the steady state flow solutions are obtained for the volumetrically driven dust cloud in a bounded domain of aspect-ratio of 1.5 relevant to the current size of GRS and a driving sheared ion flow similar to the part of zonal jets streaming through the GRS. These nonlinea…
The paper reports on the dynamics of a 3-dimensional dusty plasma in a strong magnetic field. An electrostatic potential well created by a conducting or non-conducting ring in the rf discharge confines the charged dust particles. In the absence of the magnetic field, dust grains exhibit a thermal motion about their equilibrium position. As the magnetic field crosses a threshold value (B $>$ 0.02 T), the edge particles start to rotate and form a vortex in the vertical plane. At the same time, the central region particles either exhibit thermal motion or $\vec{E} \times \vec{B}$ motion in the ho…
We investigate the propagation characteristics of electrostatic waves in a magnetized pair-ion plasma with immobile charged dusts. It is shown that obliquely propagating (OP) low-frequency (in comparison with the negative-ion cyclotron frequency) long-wavelength "slow" and "fast" modes can propagate, respectively, as dust ion-acoustic (DIA) and dust ion-cyclotron (DIC)-like waves. The properties of these modes are studied with the effects of obliqueness of propagation $(θ)$, the static magnetic field, the ratios of the negative to positive ion masses $(m)$ and temperatures $(T)$ as well as the…
The localized deposition of the energy of a laser pulse, as it ablates a solid target, introduces high thermal pressure gradients in the plasma. The thermal expansion of this laser-heated plasma into the ambient medium (ionized residual gas) triggers the formation of non-linear structures in the collision-less plasma. Here an electron-proton plasma is modelled with a particle-in-cell (PIC) simulation to reproduce aspects of this plasma expansion. A jump is introduced in the thermal pressure of the plasma, across which the otherwise spatially uniform temperature and density change by the factor…
