Page 7 - Gyrokinetic particle simulation of a field reversed configuration

052307-7 Gupta et al.
TABLE II. Simulated power balance analysis is in agreement with the ex-
Phys. Plasmas 23, 052307 (2016)
explain the discrepancy in the experimental and numerical
values. Similarly, the Ohmic power discrepancy can also be
explained as follows. In the presence of neutral beams as
substantial fast particle population builds-up, the background
plasma is pushed radially outwards resulting in relaxation of
plasma profiles. As the FRC current is mostly diamagnetic,
the plasma current decreases mostly inside the FRC and is
mainly concentrated around the separatrix. As the Ohmic
power is gJ2dV, the Ohmic heating source inside the FRC decreases. However, experimentally, rigid rotor current pro- file with no modification due to fast particle and uniform re- sistivity is used to calculate the Ohmic heating power. These differences lead to an over-estimation of Ohmic heating power in experiment.
Simulation can also provide information about the trapped poloidal flux evolution in FRC, which is difficult to measure experimentally. Figure 9 shows the simulated flux evolution profile in the presence of neutral beams. To show the effects of neutral beams on flux evolution, another simula- tion with same initial parameters is carried out in the absence of neutral beams. The results are shown by the green line in Fig. 9. In C-2 experiments, an FRC without neutral beams has smaller lifetime than predicted by green curve, as it requires higher transport coefficients to simulate. This means that the neutral beams play a role in reducing the plasma transport in C-2. The presence of neutral beam fast particles has multifold effects on FRC plasma: (1) direct electron heating by fast par- ticles, (2) relaxation of plasma profiles in response to the buildup of fast particle current, and (3) current drive due to the anomalous plasma resistivity in comparison to classical behavior of fast particles, i.e., effective Ohkawa current. From Fig. 9, we can estimate the flux input rate from the neutral beams. Near t1⁄40, both with and without neutral beams, trapped poloidal flux decay rate is same and is given as Dw=Dt 3:9 Wb/s. This flux decay rate is consistent with the resistivity given in Table I. In the presence of neutral beams, Dw=Dt 0 from 1 ms to 2 ms. Thus, the net flux input rate due to NBI is Dw=Dt 3:9 Wb/s.
V. CONCLUSIONS
Recently, record FRC lifetime and particle and energy confinement times have been observed in C-2 experiments using neutral beams, better edge plasma conditions in the presence of axial plasma guns, and strong end magnetic plugs. Experimental results indicate that the excluded flux radius increases in time and begins to decrease around 1 ms, coinciding with rise in measured shine-through. It also shows that controlling the open field line parameters also affects the overall performance of the FRC.
For this purpose, the Quasi-1D transport code coupled with the Monte Carlo code for neutral beam fast particles was developed at TAE to simulate the C-2 discharges. Our analysis indicates that the plasma resistive transport is much less than the local Bohm diffusion coefficient; as with Bohm transport coefficients, FRC decays in less than 100ls in con- trast to experimental lifetime of few ms. Multiple times clas- sical transport is a good paradigm for simulating the time evolution of experimental FRC parameters. The resistive
perimental analysis.
Metric Heating (MW)
Losses (MW)
Thermal energy (kJ)
Energy confinement time sE (ms)
Experimental Simulation
Compression 0.7 0.6 Neutral beams 0.9 0.3 Ohmic 0.6 0.2 Convective 2.1 1.7 Conductive 1.3 1.1 Radiative 0.2 0.2 2.1 1.8 0.6 0.6
Ð
analysis for FRC is updated to include the effect of fast par- ticles due to neutral beams. In the presence of neutral beams, the FRC global energy confinement time is given as
1 sE1⁄4W1⁄4Phþ1 :
(11)
Pl Wsw
Here, W 1⁄4 ð3=2ÞNkT is the thermal energy with total inven- tory (N) inside excluded flux radius, T 1⁄4 Ti þ Te, and sw is the e-folding decay time of thermal energy. The total FRC heating power is Ph 1⁄4Pc þPo þPnb, with Pc is the com- pressional power, Po is the Ohmic heating power, and Pnb is the fast ion heating power due to neutral beams. The total FRC power losses are: Pl 1⁄4 Pn þ Pr þ Pcon, where Pn is the convective power losses due to particle loss, Pr is the radia- tion losses, and Pcon is the conductive losses. The compari- son of experimental and numerical calculation of power balance is shown in Table II.
The comparison of experimental and numerical power balance analysis indicates that the numerically observed energy gain and loss terms are close to the experimentally observed values, except for the Ohmic and neutral beam heating terms. In experiments, estimates from the measured global parameters have some uncertainty; however, transport simulations allow direct calculation of each term. For exam- ple, experimentally, neutral beam power deposited inside FRC is calculated in the excluded flux radius using fixed plasma parameters and slowing down distribution. However, numerically, plasma parameters are evolving, and beam dep- osition profile is self consistently calculated inside FRC using a Monte Carlo code. These factors, along with the dif- ference in separatrix radius and excluded flux radius, can
FIG. 9. Simulated trapped poloidal flux (W) evolution with and without neu- tral beams. Sustainment from 1 to 2 ms is shown in the presence of neutral beams.