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Theory and Simulation Laboratory

 

Summary

    Theory and Simulation Laboratory (TSL) of CPP-IPR conducts research in both basic plasma physics areas and applied concepts of plasma physics.
    The main areas of work of the laboratory includes

    MHD Simulation: The goal of the MHD analysis of Test Blanket Modules is to estimate the MHD pressure drop and velocity distribution over the Pb-17Li flow path when the TBM operates in a performance regime. The high performance regime depends on the required mass flow rate of Pb-Li for a maximum heat deposition in the ceramic breeders of the TBM and its efficient extraction flow parameters. We study the parameters affecting the heat transfer characteristics within the TBM under different flow conditions.

    Kinetic Simulation: Collisionless simulation of nonlinear plasma dynamics is one of the outstanding problems of plasma physics as well as a strong challenge in computational physics. The physics of collisionless plasma is well described by a self-consistent of a system of Vlasov and Maxwell equation. Due to its non-locality and non-linearity in many important situations no analytical solutions of the Vlasov equation can be found. Hence numerical solution and numerical simulation approaches are necessary. The present Vlasov code is based on time splitting and flux balance method. Using our code we study the direct evolution of distribution function such that we can have self-consistent electric field by solving Poisson’s equation and particle flux from first moment of distribution function at any time during evolution.

    PIC Simulation: Recently some endeavor has been put on to study various physical processes requiring PIC simulation in plasma. Research on extraction of negative ion source is one of them. The code under development will include Monte-Carlo-collisions to take into account various collision processes within the computational region.   
    Complex Plasma: Beside the presence of experimental facility available in CPP-IPR to do research on complex plasmas, the theory and simulation group also take deep effort to study theoretically and numerically various complex plasma processes.

    Fluid Simulation: Hall thrusters constitute an important electric propulsion technology for certain applications requiring low thrust levels, e.g. satellite station keeping and orbit transfer. The thrust in Hall thrusters is generated by ions being accelerated through annular plasma by the electric field set up between an anode and a cathode. This electric field is strongly coupled to an externally applied radial magnetic field which typically localizes the electric field near the channel exit. In our proposed work we are planning to develop a 2D steady state and transient fluid model of stationary Hall thrusters.

    Fusion Neutronics Modeling: The laboratory also conducts computer simulation in the area of fusion neutronics.

Ion Dynamics in a Magnetized Source-Collector Sheath

A bounded plasma is simulated with a spatially generated source in the presence of an oblique magnetic field. The kinetic Particle-In-Cell (PIC) technique has been used to track particles full kinetically. The plasma-facing surface is considered an absorbent for the charged particles. The plasma flow is assumed normal with respect to the surface and primarily controlled by the self-consistent internal electric field. The ions are observed to follow interesting dynamical behavior near the collector sheath. The low energetic ions reflect back to the ion source region at certain angles of inclination. The reflection seems to be prominent at a low angle of inclination.

Ion Dynamics

Figure 1. Variation of normalized sheath potential (normalized with electron temperature) for three different field angle with species temperature 5keV.


In this piece of work, the attempt is to visualize the source sheath formation in the presence of an external magnetic field and to analyze its influence on the ion dynamics. The kinetic PIC modeling of the problem has been adopted using the 2D-3V version of XOOPIC code, (Object-Oriented Particle-In-Cell on X-windows developed by the Plasma Theory and Simulation Group (PTSG) at the University of California, Berkley). XOOPIC is capable of handling two-dimensional space in Cartesian as well as cylindrical geometries. It has built-in electrostatic and electromagnetic solvers. The large volume data produced by XOOPIC has been post-processed using shell scripts. Few subroutines have also been developed in MATLAB to visualize the simulation data. The study is conducted to model the plasma flow behavior in environments like the tokamak limiter/divertor and is expected to yield a significant contribution to the field beside several other works performed with the same vision.

Ion Dynamics

Figure 2. Effect of the species temperature on the ion phase-space structure ($V_x-x$) for magnetic inclination angle ($\alpha = 5^°$). The structure starts to collapse with the decrease of species temperature.


The present work attempts to report the kinetic phenomenon of ion reflection from the collector sheath in the presence of an external magnetic field. Starting with source collector sheath, from Fig. 1 it is well understood that the particular events are not confined only to the electrostatic case as reported earlier. The potential drops at the source and the collector sheath varies with the temperature and magnetic field angle (α). For the particular ratio of mass ($m_i/m_e = 3670.4829652$) and temperature ($\tau = 1$), it agrees with findings in the work of Schwager et al.3 (see Fig. 3 reported in the paper). Although the effect of source electron temperature on the potentials was reported earlier, there was no report on the magnetic field dependence. The present study confirms that magnetic field angle has a strong impact on the potential structure even when the source electron temperature is same.

Propagation of Electrostatic Surface Wave

We have tried to develop an analytical model using fluid theory to show that the decay of two seemingly independent nonlinear structures namely the dust void and dust soliton strongly depends on plasma ionisation parameter in an unmagnetized complex plasma system. Numerical solution of model equations using MATLAB has shown that the evolution of dust voids and their subsequent decay in a time frame is intimately related with ionization parameter. Similar result also holds good in case of dust solitons where stability of soliton is found to depend critically upon ionization parameter. Most importantly, it is observed that time of collapse of a dust soliton precedes the onset time of a dust void decay and therefore soliton decay acts as a precursor for void decay to occur in the given system. It has been found that the increasing value of ionization parameter ($\mu$) increases the duration of stable structure in both the cases. On further increase of ionization parameter, the sign of the soliton changes and the rarefactive solitions are seen to propagate.

IECF cylindrical
IECF spherical

Figure 3: (a) Evolution of dust density ($N_d$) with time ($T$) for the ionization value, $\mu = 0.2$. Inset figure represents the dust density profile at the breaking point ($T_b^v = 0.0852$) of dust void. (b) Solitary wave structure in the same dusty plasma system for the same ionization value ($\mu$). Inset figure represent the time ($T_b^s = 0.06$) and breaking pattern of solitary wave structure.

Evolution of dust ion acoustic soliton in the presence of superthermal electrons

Propagation of solitary wave in dusty plasmas started to draw the attention of the physicists since the early 90s. The presence of superthermal particles seems to have a great impact on such waves, as they indicate the existence of non-thermal systems. It has been observed that the superthermal population is capable of altering the nature of the plasmas waves. In the present paper, the effect of the superthermal electron population on the dust ion acoustic solitary wave has been explored. The plasma is considered un-magnetized and composed of two components of superthermal electrons (of two distinct temperature) along with positive ions, and negative dust particles. A major part of the work has been concentrated on the stability of the solitary structures considering the effect of the superthermal parameter. In addition, the dust charge has been considered as a variable and a detailed analysis has been provided on the same. The proposed plasma model is most suitable for analyzing Saturn magnetosphere and can be extended to any space plasmas with superthermal population.

Dust Soliton
Dust Soliton

Figure 3: Propagation of the dust density for $\kappa_c=7.0$, $\kappa_h=10.0$, $T_{ec}=10~eV$, $T_{eh}=100~eV$, $\mu_c=0.5$, $\mu_h=0.493$, $\mu=0.007$, and $\delta=0.001$.

Figure 4: Propagation of the dust density for $\kappa_c=100.0$, $\kappa_h=100.0$, $T_{ec}=10~eV$, $T_{eh}=100~eV$, $\mu_c=0.5$, $\mu_h=0.493$, $\mu=0.007$, and $\delta=0.001$.

The influence of superthermal electrons on the propagation of Dust Ion Acoustic solitons is studied by numerically solving the KdV equation. The steady state solution of the KdV equation is used as an initial perturbation in the time dependent study. It has been observed that both the potential and ion number density can sustain the shape and size of the initial perturbation, while the dust density behaves differently.

The propagation of the solitary wave of the dust density is examined for different values of the superthermal parameters. It has been observed that the presence of superthermal electrons accelerates the damping of the wave. The dust density is also sensitive to the cold electron concentration in the plasma. More the number of cold electron component, more is the disturbance in the initial perturbation. Other than that, it also responds strongly to the temperature ratio of the electrons. Superthermal electrons with equal temperature results in a quite relaxed density profile. In summary, the presence of superthermal particles significantly alter the nature of the waves in the dusty plasmas.

Dust Soliton
Dust Soliton

Figure 5: The dispersion curve of the DIA wave with $\mu_c=0.5$, $T_{ec}=10~eV$, $T_{eh}=100~eV$, $\delta=0.001$, $\mu=0.007$, and $(a)$ $\kappa_c=7.0$, $\kappa_h=10.0$ (blue line), $(b)$ $\kappa_c=100.0$, $\kappa_h=100.0$ (red line).

Figure 6: The wave number dispersion of the damping of the DIA wave with $\mu_c=0.5$, $T_{ec}=10~eV$, $T_{eh}=100~eV$, $\delta=0.001$, $\mu=0.007$, and $(a)$ $\kappa_c=7.0$, $\kappa_h=10.0$ (blue line), $(b)$ $\kappa_c=100.0$, $\kappa_h=100.0$ (red line).

The dispersion of the wave frequency and damping rate with the wave number seems to bring another perspective to the present theory. The presence of superthermal electrons appears to have larger role in the wave damping process. The results obtained from the present investigation would be helpful in understanding the nonlinear structures in space dusty plasma like Saturn magnetosphere.

Fusion Neutronics Modeling

Recent Research Outcomes

   
Computational Region for the PIC simulation
Electro and Ion density distribution respectively
Variation of electric potential with the sheath width in dusty plasma
         
   
Hall thruster initial grid generation
Plot of electron distribution function in the (x-v) plane
Modelling of 20 degree toroidal section of IN-DEMO using Solidworks

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