In the Large Helical Device (LHD), the highest operational averaged beta value has been expanded from 3.2% to 4% in the last 2 years by increasing the heating capability and exploring a new magnetic configuration with a high aspect ratio. Although the magneto-hydrodynamic (MHD) stability properties are considered to be unfavourable in the new high aspect configuration, the heating efficiency due to neutral beams and the transport properties are expected to be favourable in a high-beta range. In order to clarify the effect of the global ideal MHD unstable mode on the operational regimes in helical systems, especially the beta gradients in the peripheral region and the beta value, the MHD analysis and the transport analysis are performed in a high-beta range of up to 4% in LHD. In a high-beta range of more than 3%, the maxima of the observed thermal pressure gradients at a low order rational magnetic surface in the peripheral region are marginally unstable to the low-mode-number ideal MHD instability. Though a gradual degradation of the local transport in the region has been observed as beta increases, a disruptive degradation of the local transport does not appear in the beta range up to 4%.

A formulation of the anisotropic pressure magnetohydrodynamic equilibrium problem for three-dimensional plasmas with imposed nested magnetic surfaces is developed based on a bi-Maxwellian model of the distribution function for the energetic particle species. The hot particle distribution function satisfies the constraint . Large parallel and perpendicular anisotropy factors can be explored within the model through the choice of the hot particle perpendicular to parallel temperature ratio T⊥/T‖. A fixed boundary version of the VMEC code has been adapted to numerically compute three-dimensional anisotropic pressure equilibria. Applications to a 10-field period Heliotron device and a 2-field quasiaxisymmetric stellarator demonstrate that the pressures do not vary significantly around the magnetic surfaces when the total parallel pressure p‖ is larger than its perpendicular counterpart p⊥. For off-axis hot particle deposition with p⊥ > p‖, p⊥ concentrates in the region where the energetic particles are generated. On the other hand, p‖ is distributed roughly uniformly around the flux surfaces in the Heliotron but is localized on the low field side in the quasiaxisymmetric machine. The hot particle density structure correlates more closely with the corresponding perpendicular rather than with parallel pressure. The specific form for the definition of β that best correlates with the Shafranov shift is identified.

In low density discharges of a Large Helical Device (LHD), anisotropic pressure is expected because the LHD has powerful tangential neutral beam injection systems. We study the behaviour of the ratio of the observed saddle loop flux to the diamagnetic flux, and the results are compared with the predicted beam pressure anisotropy by a Monte Carlo technique and the steady state Fokker–Planck solution. We show the possibility of the degree of pressure anisotropy being estimated by magnetic measurements in the LHD.

We analyse the change of plasma boundaries due to changes in beta in large helical device plasmas based on electron temperature and density profile measurements, and compare the change with the prediction by a MHD equilibrium code without a priori assumptions of the nested magnetic surfaces, the HINT code. In the open magnetic field line region, which is predicted to exist at high beta, a small but non-zero electron pressure and its gradient are observed. The shift of the geometric centre of the peripheral magnetic surface due to the beta value is systematically consistent with the prediction, which suggests that the HINT code is quite a useful method for identifying the shape and location of the plasma boundary in heliotron plasmas with a divertor configuration. However, in the open field line region, a discrepancy arises because the electron mean free path is much shorter than the connection length of the magnetic field line to a wall, which suggests that the additional effects such as the inertial effect and/or the viscosity in the equilibrium force equation should be taken into account.

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