Plasma turbulence is a phenomenon that occurs when small-scale fluctuations in the plasma density, temperature, and electric and magnetic fields grow and interact nonlinearly, leading to energy transfer across different scales and regions. Plasma turbulence is ubiquitous in nature and affects many processes such as fusion energy, space weather, and astrophysical phenomena.

One of the main challenges in studying plasma turbulence is to capture the wide range of spatial and temporal scales involved, from microscopic to macroscopic. Continuum simulations are a powerful tool to address this challenge, as they can resolve the plasma dynamics in both real and velocity space, using a grid-based numerical method. Continuum simulations can also incorporate realistic physics models, such as kinetic effects, collisions, and electromagnetic interactions.

Some of the recent advances in continuum simulations of plasma turbulence, focusing on three topics: 

(1) the development of efficient and accurate algorithms for solving the plasma equations on high-performance computing platforms; 

(2) the application of continuum simulations to study turbulent transport and heating in fusion plasmas; and 

(3) the extension of continuum simulations to include multi-scale and multi-physics effects, such as coupling between different plasma species and regimes. We will also discuss some of the future directions and challenges in this field of research.

In 1942, Hannes Alfvén introduced the existence of Alfven waves in a plasma which are transverse magnetic tension wave travelling along magnetic field lines. Today, Alfven waves are treated to an important mechanism in many geophysical astrophysical hydromagnetic systems for transporting energy and momentum. Due to its non-linearity nature, it has got a wide applications in various physical processes as such it has been topic of research for long time. The nonlinear Alfven waves has a crucial role in plasma heating, re-connection, turbulence, interplanetary shocks, etc. The dynamics of the nonlinear Alfven wave has been studied in a broad manner both analytically and numerically and its basic phenomena is being understood in a space plasma or a laboratory plasma. The results obtained from numerical method is compared with in situ data taken from Space Physics Data Facility (SPDF).

Although the solar wind is characterized by spatial and temporal variability across a wide range of scales, long-term averages of in-situ measurements reveal clear radial trends: changes in average values of basic plasma parameters (e.g., density, temperature, speed, and magnetic field) with distance from the Sun. Parker Solar Probe (PSP) has reached closer to the Sun than any previous spacecraft. To establish our current understanding of radial trends, data from PSP will be compiled into a dataset spanning several solar radii from the Sun. The radial trend in each parameter will be checked against expected fits. These radial trends will benefit research groups in the validation of global heliospheric simulations and in the development of new deep-space missions. 

Why should we care about factorization, at all? Because we want to find a set of numbers that are co-prime to each other. Why is that important? All the One-Time-Passwords (OTP) we receive in our mobiles or, all the automatically generated ‘strong’ passwords we get as password suggestions, are generated via cryptographic algorithms that require such large co-prime numbers. As of now, there is no single mathematical expression to find prime numbers. Thus we need to rely on smart factorization algorithms. Quantum algorithms that run on quantum computers, have been shown to be much faster than our traditional classical algorithms. In this project we are trying to learn and use few such quantum algorithms and test their speed on real quantum computers. 

Euler equation is one of the most crucial equations to study in the field of atmospheric or oceanographic or plasma turbulence. To make accurate prediction of weather or oceanic flows or plasma stability, one needs to develop very accurate numerical solvers. The solutions of such partial differential equations are very sensitive to initial conditions as well as numerical errors. Feeling the importance of computational modeling of fluid equations, aviation and fusion industries have started investing aggressively in developing better algorithms to simulate hydro-dynamic and hydro-magnetic turbulence. In this project, we are trying to learn a few such algorithms to solve Euler equation and compare their accuracy with each other