Identification of a non-thermal X-ray burst with the Galactic magnetar SGR J1935+2154 and a fast radio burst using

Neoclassical toroidal plasma viscosity (NTV) torque induced by non-axisymmetric magnetic perturbation in the collisionless regimes in tokamaks is modelled by solving the bounce-averaged drift kinetic equation numerically. The detailed comparison between the numerical and the analytic solutions of NTV is discussed in this paper. In different asymptotic limits of the collisionless regimes, the numerical solutions are in good agreement with the analytic results. The numerical results are different from the analytic results calculated from the smoothly connected formula in the transit regimes. The pitch angle scattering is especially important in the regime. The final difference between the numerical and the analytic results can be up to a factor of 2 near the transition between the non-resonant and resonant regimes. This reveals the importance of the boundary condition of the pitch angle space. The sign of the electric field is found to be important in the calculation of the NTV torque. It shows that the effect of the resonant particles makes the NTV torque more important for the lower collisionality and lower rotation cases, which are the International Thermonuclear Experimental Reactor relevant conditions. It also shows that the electron NTV torque is important in the low collisionality case. This numerical method can be applied for modelling the NTV torque in different collisionality regimes and their transitions in tokamaks without additional approximations.

Bumpiness in a magnetic field enhances the magnitude of the plasma viscosity and increases the rate of the plasma flow damping. A general solution of the neoclassical toroidal plasma viscosity (NTV) torque induced by nonaxisymmetric magnetic perturbation (NAMP) in the collisionless regimes in tokamaks is obtained in this Letter. The plasma angular momentum can be strongly changed, when there is a small deviation of the toroidal symmetry caused by a NAMP of the order of 0.1% of the toroidal field strength. It is known that the magnetic fields used in confining plasmas are usually spatially nonuniform or bumpy. The bumpiness of the fields increases the plasma viscosity and consequently the rate of the plasma flow damping. When the collision frequency is smaller than the bounce or transit frequency of the particles that traverse through the bumpiness of the fields, particles experience the resistance of the field when they either reflect back or slow down by the fields. This resistance enhances the plasma viscosity. The underlying physics can occur in any magnetized plasmas confined by the spatially nonuniform fields.The magnetic field of a tokamak is designed to be toroidally symmetric. Realistically, there is always a slight nonaxisymmetric magnetic perturbation (NAMP) due to an intrinsic error field, magnetohydrodynamics (MHD) perturbations in the plasma and external magnetic perturbation applied to control edge localized modes (ELMs) [1,2] and resistive wall modes (RWMs) [3]. In stellarators, the plasma diffusion in collisionless regimes induced by the helical magnetic field has been developed since the 1960s [4]. The neoclassical viscosity can also be obtained by solving the drift kinetic equation numerically [5]. However, the ordering of the NAMP in tokamaks is different from that in stellarators. In the last few years, the neoclassical toroidal plasma viscosity (NTV) theory in different asymptotic limits of the collisionless regimes [6][7][8][9][10][11] has been developed to describe the plasma momentum dissipation induced by the NAMP field in tokamaks.The importance of the NTV torque in momentum confinement has been highlighted by the most recent experimental observations. Strong magnetic braking effect without mode locking during the application of NAMP has been observed in the experiments in tokamaks [12][13][14][15]. The NTV torque is a good candidate to explain the observed braking effect.The experimental regime in present tokamaks as well as the International Thermonuclear Experimental Reactor (ITER) [16] covers both the 1= and À ffiffiffi p regimes and their transitions. Here, is the collisionality. The typical collisionality regime on DIII-D [13] and JET [15] are close to the transition of 1= and À ffiffiffi p regimes. Furthermore, particles with different energy are in different collisionality regimes. In order to model the toroidal plasma rotation with NAMP and compare it with the observation, we need to know the exact NTV solution in the transition regimes, as well as in the asymptotic limits of t...

The structure and catalytic applications of hexaaluminates.

The non-resonant magnetic braking effect induced by an Non-Axisymmetric Magnetic Perturbation (NAMP) is investigated on JET and TEX-TOR. The collionality dependence of the torque induced by the = 1 NAMP field is obtained on JET. The observed torque is located mainly in the plasma core (normalized < 0.4). It increases with decreasing collisionality. The calculation shows that it is close to the transition between the − √ and the superbanana plateau regimes in the plasma core. The NTV torque is modeled by using the smoothly connnected formula in the collisionless regimes. The calculated collisionality dependence shows the same tendency as the experimental observation due to the resonant particle effect. The strongest NTV torque is also located in the plasma core because of the resonant particle effect. However, the magnitudes of the NTV torque is still about 1-2 orders smaller than the observed ones on JET. There is no obvious braking effect with / = 6/2 NAMP generated by the Dynamic Ergodic Divertor (DED) on TEXTOR. The calculated NTV torque on TEXTOR is also very small.