Title of Thesis

Numerical Simulations Of Staged-Pinch Plasma For Thermonuclear Fusion Studies

Author(s)

Farah Deeba

Abstract
We have investigated the dynamics of staged pinch plasma using different types of stability criterion with a view to suppress Rayleigh-Taylor (R-T) instability. Fusion parameters in a staged pinch plasma device are estimated by considering double-gas puff as well as multicascade liner (N-multiple shells of finite thickness) system. First of all, the implosion dynamics of dense D-T fiber plasma driven by a double gas-puff z-pinch is examined in the presence of kinetic pressure. A modified snow-plow model has been used to describe the outer dynamics of imploding z-pinch plasma. We found that the inclusion of kinetic pressure introduces the usual plasma β-term. Our numerical results demonstrate that the fusion parameters can be achieved in a dense θ-pinch D-T fiber plasma for an optimum choice of density ratios of the test to driver gas at the interface position and the kinetic to magnetic pressure ratio. We expect that double gaspuff staged pinch device would be a more feasible approach to achieve fusion conditions with an enhanced stability. Since the shell thickness of the imploding plasma liner plays an important role in the stabilization of short-wavelength perturbations, causing R-T instability. First, we consider the implosion dynamics of a double-cascade configuration of two nested cylindrical shells with some initial radii and puff thicknesses that are imploded towards the axis under the action of J×B force. In order to achieve high density plasma at the final stage of collapse, D-T fiber plasma was seeded with high-Z Kr impurity so as to initiate radiative collapse. We choose different puff thickness so as to achieve stable implosion satisfying the criterion proposed by De Groot et al., [17]. Then we have also generalized the work by considering that the imploding z-pinch plasma is made up of discrete N-multiple shells of various thicknesses, radii and mass densities so as to reduce the total growth rate of R-T instability at the final stage of implosion. Our numerical results show that the plasma parameters of the D-T fiber sensitively depends upon the shell mass ratios and thicknesses. Large values of puff-thickness and mass-ratios provide stabilization against the R-T instability in the final stage of compression but adversely affects fusion conditions. For optimum values of puff-thicknesses and mass ratios, one can obtain fusion parameters of interest in a multicascade liner staged pinch device. In our zerodimensional code, we have used typical parameters of Sandia National Laboratories for which the amplitude of discharge current was 10 MA, with a pulse duration of 50 nsec. We have also used sinusoidal type current profile. To make our model calculations more realistic, we have used current stepping technique, which uses the circuit coupled equation. In this technique, a single current step is added to the primary pinching current. We found that with currentstepping method, one can obtain very high density and high temperature plasma with relatively small values of driving current (kA) which are delivered in μsec time scale. Thus for optimum choice of scaling parameters, staged pinch device with current-stepping technique seemed to be a more feasible approach to achieve fusion conditions.

1

1.1 Preamble
1.2 Layout of the Thesis

2.1 Introduction
2.2 Equilibrium Pinch
2.3 Dynamic Pinch
2.4 Instabilities in Pinch Devices
2.5 Types of Pinch Devices

3.1 Introduction
3.2 z-pinch Dynamics with Axial Magnetic Field
3.3 Dynamics of Fiber Plasma
3.4 Numerical Results
3.5 Double Gas-Pu¤ Staged Pinch Dynamics
3.6 Dynamical Model of Staged Pinch
3.7 Dynamics of the Inner -pinch Fiber Plasma

4.1 Introduction
4.2 Mathematical Modeling of Outer Multicascade z-Pinch
4.3 Dynamics of Seeded D-T Fiber Plasma
4.4 Numerical Results and Discussion

5.1 Theoretical Model for Multicascade z-Pinch
5.2 Dynamics of the Inner -Pinch
5.3 Numerical Results and Discussion

6.1 Introduction
6.2 Staged Pinch Dynamics with Current-Stepping
6.3 Dynamics of the Inner -pinch Fiber Plasma
6.4 Numerical Results and Discussion

7.1 Future Work