Scalings of energy confinement and density limit in stellarator/heliotron devices

Abstract

The paper presents a study of empirical scaling of energy confinement observed experimentally in stellarator/heliotron devices (Heliotron E, Wendelstein VII-A, L2, Heliotron DR) for plasmas heated by electron cyclotron heating and/or neutral beam injection. The proposed scaling of the gross energy confinement time is: , where P is the absorbed power (MW), n is the line average electron density (1020 m−3), B is the magnetic field strength on the plasma axis (T), a is the average minor radius (m) and R is the major radius (m). The empirical scaling of the density limit obtainable under the optimum condition is proposed to be: . These scalings for helical systems are compared with those in tokamaks. The energy confinement scaling has a similar power dependence as the L-mode scaling of tokamaks. The density limit scaling for helical systems seems to indicate an upper limit of the achievable density similar to that in many tokamaks. From the energy confinement time and the density limit , a beta limit can be derived: , which can be lower than the stability/equilibrium beta limit. Thus, from the viewpoint of designing a machine, the values of B, a and R should be selected with care because the dependence of the confinement time (or nτET) and of the above beta limit on these values is different.

Comparison of toroidal viscosity with neoclassical theory

“…This density dependence is a feature of anomalous transport, because strong density dependence is also observed in the energy transport, which is governed by anomalous transport. In fact, the global energy confinement shows strong density dependence in CHS, 11 as predicted by LHD scaling 12 ( E ϭ0.17P abs The differences between the parallel viscosity in the original paper and the toroidal viscosity in this paper are discussed. The approximations made in the original paper were a replacement of the Fourier series with (1/M ) ϫ(n -"B/B) and the replacement of toroidal viscosity with parallel viscosity (B ϷB) and (B -"B)/BϷn -"B).…”

Observation of Stable Superdense Core Plasmas in the Large Helical Device

“…The use of the LID increases pumping of edge-recycled particles and maintains low edge density and high edge electron temperature gradients. The low edge density also allows operation with higher core density than would be the case otherwise: the maximum core density in SDC plasmas is 3 that predicted by the Sudo empirical scaling for heliotron or stellarator devices [15].…”

Low-aspect-ratio stellarators with planar coils

“…As was discussed in [23], the neoclassical theory [24][25][26][27][28] predicts the following global energy-confinement time-scalings depending on the collisionality. For the so-called plateau regime of intermediate collisionality…”