Page 9 - Drift-wave stability in the field-reversed configuration

092518-9 Onofri et al.
Phys. Plasmas 24, 092518 (2017)
FIG. 13. Electrostatic potential developed in the divertor of an FRC at the axis r 1⁄4 0, as a function of the magnetic field expansion K 1⁄4 BM =B, for two simulations with Te 1⁄4 250 eV and Ti 1⁄4 1000 eV (black line) and Ti 1⁄4 100 eV (red line). The dashed lines represent the theoretical curves from Eq. (16) for Ti 1⁄4 1000 eV (black) and Ti 1⁄4 100 eV (red), showing good agreement. The case V z 1⁄4 const (green) is also shown as reference.
A similar effect is observed when neutral gas is injected near the mirror throat to maintain the plasma concentration in the confinement vessel. Figure 14 compares two simula- tions with gas puff at the mirror throats and without gas puff. In both cases, Te 1⁄4 250 eV and Ti 1⁄4 1000 eV. The plasma is slowed down due to collisions with neutrals, and the flow accelerates in the expander. The simulations show that with gas puff, the plasma acceleration in the divertors is higher and the potential profile is steeper. The effect of the gas on the plasma flow depends on the location where the gas is injected. When gas puff is used for fuelling, it is useful to know which injection location gives the best results on the formation of the electrostatic potential. Our simulations show that if the location of the gas puff is chosen correctly, the plasma acceleration overcomes the negative effect of the slowdown and has a positive effect on the creation of an electrostatic potential. To study how the potential depends on the location of the gas puff, we did three simulations with different gas puff locations, and the results are shown in Fig. 15. The steepest potential profile is observed when the gas is injected at the mirrors. This is the case where the plasma has the lowest velocity at the mirrors because it is slowed down by the gas injected at this location. On the other hand, in the case where the gas is slowed down before it reaches the mir- ror, its velocity at the mirror is higher and the potential develops more slowly. In the case where the gas is injected outside the mirrors, the plasma speed at the mirror is sonic,
FIG. 14. Effect of the gas puff at the mirror throats. Electrostatic potential developed in the divertor of an FRC at the axis r 1⁄4 0 for two simulations with Te 1⁄4 250 eV and Ti 1⁄4 1000 eV, with gas puff (red line) and without gas puff (black line), is shown. The dashed lines represent the theoretical curves from Eq. (16) for the case with no gas puff (black) and with gas puff (red). The case V z 1⁄4 const (green) is also shown as reference.
FIG. 15. Effect of the position of the gas puff near the mirror throat on the potential development. Electrostatic potential at the axis r 1⁄4 0 for three sim- ulations with Te 1⁄4 250 eV and Ti 1⁄4 1000 eV and different gas puff locations is shown. The solid lines show the cases of gas injected at the mirror (z 1⁄4 63:5 m, black line), before the mirror (z 1⁄4 63 m, blue line), and after the mirror (z 1⁄4 64 m, red line). The dashed lines show the theoretical curves obtained from Eq. (14). The case V z 1⁄4 const from Eq. (16) (dashed green line) is also shown as reference.
and it is slowed down by the injected gas after it exits the mirror. When the plasma flow is slowed down, the density increases and the potential becomes positive. In this case, the particle flux is not conserved between the mirror and the end of the divertor because there is a source of the plasma due to the ionization of the gas. In this case, the formation of a neg- ative potential is even slower than predicted by Eq. (16) for Vz 1⁄4 const. In Fig. 15, the simulation results are compared with the potential obtained from Eq. (14) for the density pro- files produced by the simulations. The agreement between the simulations and the theoretical curves is very good. These results indicate that the best location for the gas puff is at the mirrors or in the confinement vessel close to the mir- rors, while injecting the gas outside the mirrors has a nega- tive effect on the formation of the electrostatic potential.
VI. MIRROR EFFECTS
In Sec. IV, we showed that the particle flux through the mirrors calculated by the code is larger than observed in experiments. The code does not include the kinetic mirror confinement, which allows only particles that are in the loss cone to be lost axially. In the MHD code, there is no distinc- tion between trapped and passing particles, and all the plasma that reaches the mirrors is lost. In the MHD model, the flux is limited by decreasing the cross section of the flux tube at the mirrors. We used a higher plug field to reduce the particle flux by decreasing the plasma cross section at the plugs. This was done to emulate the kinetic mirror confine- ment, which is not included in the Q2D code.
In the case of low collisionality, si sk, the ion con- finement is kinetic, with two different populations of trapped and passing particles. The kinetic transport in the FRC SOL is different than in mirror machines because there is a source of particles that diffuse through the separatrix and enter the SOL, forming two populations of trapped and passing par- ticles. Here, we present a simple model to show how the par- allel plasma flux is modified when the kinetic effects of mirror confinement are taken into account.
We consider two ion populations: particles trapped by the mirrors in the SOL and passing particles. In a steady