Hollow current profile scenarios for advanced tokamak reactor operations

Abstract

Advanced tokamak scenarios are a possible approach to boosting reactor performances. Such schemes usually trigger current holes, a particular magnetohydrodynamics equilibrium where no current or pressure gradients exist in the core of the plasma. While such equilibria have large bootstrap fractions, flat pressure profiles in the plasma core may not be optimal for a reactor. However, moderate modifications of the equilibrium current profile can lead to diamagnetism where most of the pressure gradient is now balanced by poloidal currents and the toroidal magnetic field. In this paper, we consider the properties of diamagnetic current holes, also called "dual equilibria," and demonstrate that fusion throughput can be significantly increased in such scenarios. Their stability is investigated using the DCON code. Plasmas with a beta peak of 30% and an average beta of 6% are found stable to both fixed and free-boundary modes with toroidal mode numbers n =1-4, as well as Mercier and high-n ballooning modes. This is not surprising as these scenarios have a normal beta close to 3.

Tokamak equilibria with nearly zero central current: the current hole

“…The safety factor q is a monotonically increasing function of radius of flux surface; q(0) < 2 while q ∼ 10 at the edge of the inner high beta equilibrium. The stability analysis showed that this kind of equilibrium with an average beta of 6% and a peak value of 30% is stable to both fixed and free-boundary modes with toroidal mode numbers n = 1-4 as well as Mercier and high-n ballooning modes [93]. Although the toroidal current density is zero in the high beta current hole described above, its flux surface average is definitely positive on each flux surface.…”

“…As already noted in section 2, though the value of B Z is not zero but finite, the slope of B Z in the high beta current hole is flat as well as in the 'conventional' current hole. The value of B Z is typically small in the high beta current hole as shown in [93]. In fact there is no lower limit in B Z in the high beta current hole if the pressure gradient is accordingly reduced so as to avoid the diamagnetic hole.…”

“…Such equilibria were shown to be stable to low n internal kink modes but unstable to n = 1 external kink [91]. The equilibrium with a zero toroidal current region stable to the external kink mode is obtained by inserting the high beta equilibrium solution inside a 'conventional' current hole equilibrium [92,93]. This 'dual equilibrium' has a central zero toroidal current region surrounded by a finite current region.…”

Efficiency of wave-driven rigid body rotation toroidal confinement

“…Stellarators and tokamak are the two main configurations designed according to this principle 1,2 . We note in passing that, in particular tokamak equilibria referred to as current hole configurations, the magnetic rotational transform can be achieved with zero toroidal current and poloidal magnetic field on axis [3][4][5] .…”

Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad–Shafranov equation by extension from polygonal subdomains

“…Another challenging configuration of physical relevance is the family of equilibria with a so-called "current hole". This name refers to equilibria for which there is an extended region in the plasma core where the toroidal current J φ is nearly zero [44,45,46,47,48]. The "near absence" of the current (thus the name "hole") corresponds to a core region with almost constant pressure.…”