L. J. Zheng

The super X divertor (SXD) and a compact fusion neutron source (CFNS)

A new magnetic geometry, the super X divertor (SXD), is invented to solve severe heat exhaust problems in high power density fusion plasmas. SXD divertor plates are moved to the largest major radii inside the TF coils, increasing the wetted area by 2–3 and the line length by 2–5. Two-dimensional fluid simulations with SOLPS (Schneider et al 2006 SOLPS 2-D edge calculation code Contrib. Plasma Phys. 46) show a several-fold decrease in divertor heat flux and plasma temperature at the plate. A small high power density tokamak using SXD is proposed, for either (1) useful fusion applications using conservative physics, such as a component test facility (CTF) or fission–fusion hybrid, or (2) to develop more advanced physics modes for a pure fusion reactor in an integrated fusion environment.

Kinetic analysis of the resistive wall modes in the ITER advanced tokamak scenario

It is found that n = 1 resistive wall modes in the ITER advanced scenario can be fully stabilized by modestly low rotation with a rotation frequency (normalized to the Alfven frequency at the magnetic axis) of about Ω = 0.0075. The existence of this stabilization scheme is proved with the AEGIS-K (Adaptive EiGenfunction Independent Solution-Kinetic) code, which provides a fully kinetic (non-hybrid) and self-consistent (non-perturbative) description of the system. Wave-particle resonances, shear Alfven continuum damping, trapped particle effect and the parallel electric effects are all taken into account. The rotation frequency for full stabilization is much larger than the diamagnetic drift frequency; therefore, finite Larmor radius effects are negligible. We also find that the rotation stabilization window opens first near the ideal wall limit.

AEGIS-K code for linear kinetic analysis of toroidally axisymmetric plasma stability

A linear kinetic stability code for tokamak plasmas: AEGIS-K (Adaptive EiGenfunction Independent Solutions-Kinetic), is described. The AEGIS-K code is based on the newly developed gyrokinetic theory [L.J. Zheng, M.T. Kotschenreuther, J.W. Van Dam, Phys. Plasmas 14 (2007) 072505]. The success in recovering the ideal magnetohydrodynamics (MHD) from this newly developed gyrokinetic theory in the proper limit leads the AEGIS-K code to be featured by being fully kinetic in essence but hybrid in appearance. The radial adaptive shooting scheme based on the method of the independent solution decomposition in the MHD AEGIS code [L.J. Zheng, M.T. Kotschenreuther, J. Comp. Phys. 211 (2006) 748] is extended to the kinetic calculation. A numerical method is developed to solve the gyrokinetic equation of lowest order for the response to the independent solutions of the electromagnetic perturbations, with the quasineutrality condition taken into account. A transform method is implemented to allow the pre-computed Z-function (i.e., the plasma dispersion function) to be used to reduce the integration dimension in the moment calculation and to assure the numerical accuracy in determining the wave-particle resonance effects. Periodic boundary condition along the whole banana orbit is introduced to treat the trapped particles, in contrast to the usual reflection symmetry conditions at the banana tips. Due to the adaptive feature, the AEGIS-K code is able to resolve the coupling between the kinetic resonances and the shear Alfven continuum damping. Application of the AEGIS-K code to compute the resistive wall modes in ITER is discussed.

Behavior of n = 1 magnetohydrodynamic modes of infernal type at high-mode pedestal with plasma rotation

Magnetohydrodynamic instabilities of high-mode (H-mode) pedestal are investigated in this paper with the inclusion of bootstrap current for equilibrium and rotation for stability. The jointed European torus-like equilibria of H-mode discharges are generated numerically using the VMEC code. It is found that, when the bootstrap current is taken into account, a safety-factor reversal or plateau can be generated near plasma edge. This confirms previous results of numerical equilibrium reconstructions using other types of codes. The n = 1 magnetohydrodynamic instabilities, where n is toroidal mode number, are investigated numerically in this type of equilibria using the AEGIS code. It is found that the infernal type harmonic can prevail at safety-factor reversal or plateau region. The toroidal plasma rotation effect with low Mach number is investigated. The numerical results show that the mode frequency is close to the rotation frequency at pedestal top, when the value of safety factor at plateau is slightly above a rational number. This mode frequency range seems to coincide with the experimentally observed frequencies of n = 1 edge harmonic oscillations (or outer modes) at the quiescent H-mode discharges.

Study of toroidal flow generation by ion cyclotron range of frequency minority heating in the Alcator C-Mod plasma

The averaged toroidal flow of energetic minority ions during ICRF (ion cyclotron range of frequencies) heating is investigated in the Alcator C-Mod plasma by applying the GNET code, which can solve the drift kinetic equation with complicated orbits of accelerated energetic particles. It is found that a co-directional toroidal flow of the minority ions is generated in the region outside of the resonance location, and that the toroidal velocity reaches more than 40% of the central ion thermal velocity (Vtor ∼ 300 km/s with PICRF ∼ 2 MW). When we shift the resonance location to the outside of |r/a|∼0.5, the toroidal flow immediately inside of the resonance location is reduced to 0 or changes to the opposite direction, and the toroidal velocity shear is enhanced at r/a ∼ 0.5. A radial diffusion equation for toroidal flow is solved by assuming a torque profile for the minority ion mean flow, and good agreements with experimental radial toroidal flow profiles are obtained. This suggests that the ICRF driven min...

Diamagnetic drift effects on the low-n magnetohydrodynamic modes at the high mode pedestal with plasma rotation

The diamagnetic drift effects on the low-n magnetohydrodynamic instabilities at the high-mode (H-mode) pedestal are investigated in this paper with the inclusion of bootstrap current for equilibrium and rotation effects for stability, where n is the toroidal mode number. The AEGIS (Adaptive EiGenfunction Independent Solutions) code [L. J. Zheng and M. T. Kotschenreuther, J. Comp. Phys. 211 (2006)] is extended to include the diamagnetic drift effects. This can be viewed as the lowest order approximation of the finite Larmor radius effects in consideration of the pressure gradient steepness at the pedestal. The H-mode discharges at Jointed European Torus is reconstructed numerically using the VMEC code [P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)], with bootstrap current taken into account. Generally speaking, the diamagnetic drift effects are stabilizing. Our results show that the effectiveness of diamagnetic stabilization depends sensitively on the safe factor value (qs) at the safety-fact...

Shielding of the error field by a liquid metal wall in tokamaks

It is shown that the error field in a tokamak can be shielded by a flowing liquid metal wall. In particular, a flowing liquid metal wall can prevent resonance amplification of the error field by the plasma near its no-wall stability limit.

The sensitivity of tokamak magnetohydrodynamics stability on the edge equilibrium

Due to the X-point singularity, the safety factor tends to infinity as approaching to the last closed flux surface. The numerical treatments of the near X-point behavior become challenging both for equilibrium and stability. The usual solution is to cut off a small fraction of edge region for system stability evaluation or simply use an up-down symmetric equilibrium without X-point as an approximation. In this work, we assess the sensitivity of this type of equilibrium treatments on the stability calculation. It is found that the system stability can depend strongly on the safety factor value (qa) at the edge after the cutting-off. When the edge safety factor value falls in the vicinity of a rational mode number (referred to as the resonant gap), the system becomes quite unstable due to the excitation of the peeling type modes. Instead, when the edge safety factor is outside the resonant gaps, the system is much more stable and the predominant modes become the usual external kink (or ballooning and infern...

Axisymmetric global Alfvén eigenmodes within the ellipticity-induced frequency gap in the Joint European Torus

Alfven eigenmodes (AEs) with toroidal mode number n = 0 (i.e., axisymmetric) have been observed in the ellipticity-induced frequency range in the Joint European Torus. The axisymmetric modes are of interest because they can be used to diagnose fast particle energy distributions at the mode location. The modes were identified as global Alfven eigenmodes (GAEs), with the ellipticity of the plasma cross-section preventing strong continuum damping of the modes. The MHD codes CSCAS, MISHKA, and AEGIS were used to compute the n = 0 Alfven continuum, eigenmode structure, and continuum damping. For zero ellipticity, a single mode exists at a frequency below the Alfven continuum branch. This mode has two dominant poloidal harmonics with poloidal mode numbers m = ±1 that have the same polarity; therefore, it is an even mode. For finite ellipticity, the continuum branch splits into two branches and the single GAE splits into two modes. An even mode exists below the minimum of the top continuum branch, and the freque...

Ideal magnetohydrodynamic theory for localized interchange modes in toroidal anisotropic plasmas

Ideal magnetohydrodynamic theory for localized interchange modes is developed for toroidal plasmas with anisotropic pressure. The work extends the existing theories of Johnson and Hastie [Phys. Fluids 31, 1609 (1988)], etc., to the low n mode case, where n is the toroidal mode number. Also, the plasma compressibility is included, so that the coupling of the parallel motion to perpendicular one, i.e., the so-called apparent mass effect, is investigated in the anisotropic pressure case. The singular layer equation is obtained, and the generalized Merciers criterion is derived.