Page 2 - Gyrokinetic particle simulation of a field reversed configuration

052307-2 Gupta et al.
Phys. Plasmas 23, 052307 (2016)
simultaneously for the first time for an FRC transport study: first, to what extent are transport coefficients enhanced over their classical values, and second, what are the functional forms for each transport coefficients. In this paper, the ques- tion that which transport model fits better to the experimental observables is addressed.
We have seen ample hints that the experimental ion transport is nearly classical (including the beam compo- nents28–30), while the electron heat transport and particle transport are enhanced over those of the classical rates. Furthermore, even though anomalies exist in these, the trans- port in these channels seems to reduce as the electron tem- perature rises.1 Because of these clues, we have decided to take the following approach: We introduce the enhancement factors multiplying to the various classical transport coeffi- cients, e.g., resistivity, particle, and heat conductivities. These factors are constant throughout a simulation and are adjusted iteratively in order to match experimental values initially and their overall time evolution. Importantly, we find that despite fitting being done only at one point of time (initial value), the qualitative overall temporal evolution of various transport behaviors matches with the experimental observations globally, indicating consistent processes are present throughout a discharge. We have also tried other models, for example, taking electron thermal transport and resistivity as the local Bohm transport while the ion transport as classical. Such an attempt has produced the plasma decay- ing in few micro-seconds, some two orders of magnitude faster compared to the observed experimental lifetimes.
To get a better understanding of the role of neutral beams on FRC performance in C-2 plasma, a plasma trans- port code (Q1D) was developed at TAE. The formulation of Q1D code is similar to the CFRX code; however, it also includes the source and sink terms due to fast beam particles. The source and sink terms are calculated using a Monte- Carlo (MC) code and are updated at every time step. Coupling of fluid transport code Q1D with MC code incorpo- rates the effects of fast beam particles on the background FRC plasma and vice versa.31
The numerical transport analysis of C-2 experimental shots indicates that multiple times classical transport coeffi- cients, with local dependence on plasma parameters, can simulate the experimentally observed profiles. The FRC resistive diffusion is nearly 5 times classical, electron ther- mal conductivity is nearly 20 times classical, and ion ther- mal conductivity is nearly classical. With these transport coefficients and classical behavior of fast particles, Q1D transport calculation can simulate the time evolution of the
FIG. 1. Improvement of normalized excluded flux radius (RD/) of C-2 plas- mas with beams, guns, and better wall conditioning.
experimentally measured excluded flux radius calculated from wall magnetic probes,13 all six cords of line-integrated density measured by CO2 interferometry,9 electron tempera- tures measured using Thomson scattering,10 and ion temper- atures measured using spectroscopy.11,12
This paper is organized as follows: Section II describes the details of the Q1D transport model along with the trans- port equations. Some of the features of the experimental results are presented in Section III. Simulation results along with their comparison with the experimental results will be presented in Section IV. Finally, conclusions will be pre- sented in Section V.
II. Q1D TRANSPORT MODEL
The basic assumption in the Q1D model is that the FRC plasma is highly elongated in the axial direction, which allows a straight field line approximation for the magnetic field20,21 and an assumed geometry is shown in Fig. 2. In this simplified geometry, magnetic field lines at r 1⁄4 0 are directed in one direction with a magnitude that decreases as we move radially outwards. The field becomes zero at the null point (O-point) and then changes direction and increases in magni- tude as we move further away from the axis. Inside the sepa- ratrix, field lines on either side of the null point are connected axially. The transport equations become one- dimensional (radial) representing the mid-plane of the experiment, but are complemented in three ways to capture two-dimensional effects, hence the name Q1D for Quasi-1D.
FIG. 2. Geometry of the FRC in Q1D model depicting density profile and inside/outside magnetic field line connection.