Recently analysis of ion-neutral momentum exchange explained electric field formations not only for the tokamak boundary but also for the arc discharge and earth ionosphere 1. The radial electric field (Er) formation is induced by the ion gyro-center shift of ion-neutral charge exchange reactions in which only perpendicular momentum transfer is counted. In parallel momentum exchange between the plasma and neutral, the electron-neutral momentum exchange can play an important role especially when the plasma is accelerated in an electric field such as ohmic discharge of tokamaks. Therefore the unbalanced momentum exchange between plasma and neutral can generated the intrinsic rotation. It is found that the strong electric fields of ionosphere such as black aurora and tokamak edge are induced by the ion-neutral momentum exchange. Another similarity between black aurora and tokamak edge is that there are circular structure which are occurring periodically with ExB drift. The left side of Fig.1 is the TV image of black aurora showing circular structure. The formation of black aurora vortex can be regarded as a distortion by the ExB 2. The right side of Fig.1 is the calculated image of ELMs from ECEI diagnostics on KSTAR .
The electric field formation by ion-neutral collision on black aurora includes a retarded ExB drift due to the nature of weakly ionized plasma, which is approximately 3 km/sec. The calculated value of black aurora ExB drift is agreed with the observation . This article suggests that the formation mechanism of ELMs on tokamak can be related with the origin of black aurora vortex. Understanding of ELM formation is an important breakthrough for the controlled nuclear fusion.
The intrinsic rotation of plasma in tokamak is one of the subjects which are not explained thoroughly so far in spite of great importance for the future fusion devices such as ITER. Here we report a new analysis of plasma-neutral momentum exchange, which generates the intrinsic plasma rotation in tokamaks. At early current ramp-up stage, ions are under acceleration in co-current direction and electrons are under acceleration in countercurrent direction. These accelerations continue until the momentum loss by the collisions with neutrals. The average distance that charged particle moves before the collision with neutrals is the mean free path λ. The plasma is under acceleration of electric force of qE, here q is a charge and E is the electric field induced by the loop voltage. The energy gain by this force is qEλ and it is equal to the kinetic energy. Here the magnitude of ion momentum is different from the electron momentum because the ratio of mass to cross-section is different. However, when the collision frequency is considered for the case where the accelerated velocity is higher than the thermal velocity, the magnitude of momentum change per unit time becomes the same for the ion and electron. This means exactly the same amount of momentum transfer from ions to neutrals in co-current direction occurs from electrons to neutrals in counter-current direction so that they are cancelled out. This momentum change balance is natural since the driving mechanism of momentum change in both directions are the same electric force. However, the momentum change balance can be broken when other mechanisms are involved. There are at least two extra mechanisms that break the balance. The first mechanism is that the thermal velocity is actually higher than electrically accelerated velocity. The second mechanism is the influence from impurity ions. For the case of carbon enriched tokamak, there is a high possibility of C6+ or C3+ impurity contributions. The main ion (D+) contribution to the momentum transfer to the fueling neutrals (D0) is 100% momentum transfer by charge exchange reaction. But collision of C6+ ion with D0 makes charge exchange resulting C5+ and D+. And C5+ goes back to C6+ by the electron impact ionization. Then these two processes eventually makes an ionization of the main ion, which is not a momentum transfer to the neutral. Other carbon ions such as C3+ can make charge exchange with deuteron neutrals and the result is the same as C6+. If the main ion density is same as C3+ ion with no other impurities, so that the effective ion charge (Zeff) is 2.5, then the electron density is 4 times larger than the main ion density. And the magnitude of momentum transfer from electron to neutral in the counter-current direction is also 4 times of ion to neutral in co-current direction. So the momentum change balance is broken and neutrals are accelerated in the countercurrent direction. This momentum transfer acts as a force and it becomes acceleration when divided by the mass of plasma. Finally the toroidal rotation can be calculated by the integration of acceleration during the time constant τ which is related with the plasma confinement time.
This is because the momentum transferred to the neutrals goes back to plasma by the interaction between plasma and neutrals such as a charge exchange, and the plasma experiences this acceleration while the particles stay in the tokamak. Fig.2 shows the calculated toroidal rotation based on the above mechanism for a typical ohmic discharge of tokamak. It is found that the impurity ratio is governing parameter for the intrinsic rotation. In this article, the summary of plasma-neutral momentum exchange analysis will be presented including similarity study of black aurora and ELMs, as well as the application of the toroidal rotation in ohmic discharge.
1 Kwan Chul Lee, Phys. Plasma 24, 112505 (2017)
2 T.J. Hallinan, and T. N. Davis, Planet. Space Sci., 18, 1735-1744 (1970)
3 Jaehyun Lee, Gunsu Yun, et al, Phys. Rev. Lett., 117, 075001 (2016)
4 Y. Obuchi. T. Sakanoi, et al, J. Geophys. Res., 116, A00K07 (2011)
|Country or International Organization||Korea, Republic of|
|Affiliation||National Fusion Research Institute|