Page 4 - Gyrokinetic particle simulation of a field reversed configuration

052307-4 Gupta et al.
Phys. Plasmas 23, 052307 (2016)
transport. The classical model has an inverse dependence on electron temperature in contrast to the Bohm model, which has a direct dependence on electron temperature
g1⁄4fclgcl þfBgB; gg
v 1⁄4fclvclþfBvB; (10) e ve e ve e
v 1⁄4fclvclþfBvB: i vi i vi i
Classical coefficients are standard coefficients given in NRL plasma formulary.33 Bohm coefficients are such that the resulting diffusion is in the kTe=16eB form. The electron-ion equilibration coefficient is classical, and ion viscosity has both classical as well as Bohm components. As the resistivity is anomalous, the Ohmic heating term is equally distributed between electrons and ions. These coefficients have local de- pendence on plasma parameters, and singularity at O point (B 1⁄4 0) is avoided by using a limiting (minimum) magnetic field.
All Equations (1)–(6) are solved numerically using finite differences in the spatial direction and a semi-implicit solver in time. At every time step (dt), MC code is called to get var- ious source terms due to NB fast particles. In the MC code, neutral particles are injected at a constant rate into the back- ground FRC plasma and get ionized due to ionization proc- esses such as charge exchange, electron impact, or ion impact. For typical C-2 parameters, charge exchange is the dominant mechanism of ionization for neutral beam par- ticles. The warm neutrals are generated inside the FRC by this process, and their effects on fast particles and back- ground plasma are self consistently included. The trajectories of the resulting fast ions are solved using Lorentz’s equation in the presence of Coulomb collisions. From the slowing down distribution, the spatial distribution of fast particle den- sity, current, momentum, and energy transfer terms are
calculated. These source terms due to fast particles are included in the transport equation to update the plasma parameters.
III. EXPERIMENTAL OBSERVATIONS
Recent experimental shots of C-2 plasma have shown an initial increase of wall magnetic field (measured by wall mag- netic probes), which decreases later in time. Experimentally, these shots are obtained with neutral beams under the condi- tions of better wall conditioning (lithium coated walls) and higher magnetic field on the open field lines far from the FRC. The experimental results showing increasing excluded flux radius (calculated from the measured wall magnetic field) are shown in Fig. 3(a) and have an error of 65%. Experimentally, it has also been observed that after 1 ms or so, the shine-through (untrapped beam fraction estimated using secondary electron emission detectors) increases in time and is shown in Fig. 3(b). This result clearly indicates that there is a continuous reduction of beam coupling with the FRC plasma after 1ms. Shine-through measurement has an error of 68%.
It has also been observed that controlling the open field plasma parameters has a strong effect on the FRC perform- ance. Figure 4 shows that the plasma life time increases with strong end mirror plugs in the presence of high magnetic field in the formation region, which connects the magnetic plugs and confinement vessel. However, in the presence of
FIG. 3. Experimental characteristics relevant to the transport studies: (a) Time evolution of measured excluded flux radius ðRD/Þ of various shots, showing increase in radius before 1 ms. (b) Time evolution of neutral beam shine-through showing the decoupling of NBI from FRC.
FIG. 4. Experimental characteristics relevant to the transport studies contin- ues. Top figure shows the time evolution of excluded flux radius (RD/) with changing mirror magnetic field. Higher mirror plug voltage indicates the higher mirror plug magnetic field. FRC lifetime is extended in the presence of strong mirror plugs. Bottom figure shows that the lifetime of FRC increases with mirror plugs voltage in the presence of higher formation mag- netic field (BFS).