Stability of Externally Driven Magnetic Islands in a Helical Plasma

Influence of external resonant magnetic perturbation (RMP) on a helical plasma is numerically investigated, using a set of reduced magnetohydrodynamic equations. Coexistence of the resistive interchange mode and RMP is simulated. In nonlinear simulations, saturated magnetic islands by the RMP typically show two states: oscillating small islands and locked large islands. In the former state, rotation of magnetic islands by neoclassical transport-driven poloidal flows disturbs growth of islands. On the other hand, in the latter state, locking of poloidal flows due to the RMP and growth of islands occur simultaneously. It is found that the curvature driven current enhances magnetic reconnection, and width of the large islands overcomes that of vacuum islands

Relationships between the Prediction of Linear MHD Stability Criteria and the Experiment in LHD

We analyze the relationship between the experimentally observed pressure gradients at resonant rational surfaces and the theoretically predicted ideal magnetohydrodynamics (MHD) unstable region of global modes in the large helical device (LHD). According to the stability analysis of the ideal MHD modes with a low toroidal mode number, we find that the ideal MHD mode gives a constraint on the operational regime of the pressure gradients in the core. In the edge, a clear saturation of the pressure gradients due to the ideal MHD instability has not been observed up to the high beta regime around 3% as the volume-averaged toridal beta value, where global ideal MHD modes are predictedto be unstable

Self-Sustained Divertor Oscillation Driven by Magnetic Island Dynamics in Torus Plasma

A new type of self-sustained divertor oscillation is discovered in the Large Helical Device stellarator, where the peripheral plasma is detached from material diverters by means of externally applied perturbation fields. The divertor oscillation is found to be a self-regulation of an isolated magnetic field structure (the magnetic island) width induced by a drastic change in a poloidal inhomogeneity of the plasma radiation across the detachment-attachment transitions. A predator-prey model between the magnetic island width and a self-generated local plasma current (the bootstrap current) is introduced to describe the divertor oscillation, which successfully reproduces the experimental observation

Onset of instability with collapse observed in relatively high density and medium beta regions of LHD

Edge MHD instabilities with pressure collapse are found in relatively high beta and low magnetic Reynolds number regions with a magnetic axis torus outward-shifted configuration of the large helical device (LHD), and characteristics and onset conditions of the instability are investigated. The instability has a radial structure with an odd parity around the resonant surface, which is different from that of the interchange instability typically observed in the LHD. The onset condition dependence on the magnetic axis location shows that the onset beta increases as the magnetic axis location moves more torus inwardly, and the instability appears only in limited configurations where the magnetic axis is located between 3.65 and 3.775 m. In such configurations, the resonant surface location is close to an index of the plasma boundary. This fact suggests that the distance between the resonant surface location and the plasma boundary plays an important role in the onset, and a possibility that the instability is driven by an external mode

Drift stabilization of ballooning modes in a high-⟨β⟩\langle \beta \rangle LHD configuration

Ideal MHD yields at best inconclusive predictions about the stability of the LHD heliotron for $\langle \beta \rangle \geq 3\%$. We investigate the impact of the drift stabilization of ballooning modes for the inward shifted LHD configuration (vacuum magnetic axis $R_0 \sim 3.5m$). The background equilibrium is considered anisotropic in which the neutral beam ions contribute about $1/4$ fraction of the total diamagnetic beta, $\langle \beta_{dia} \rangle$. A drift corrected ballooning mode equation obtained from the linearized gyrokinetic equation is expanded assuming that the hot particle drifts are much larger than the mode frequency. The fast particle pressure gradients contribute weakly to both the instability drive and the diamagnetic drift stabilization (which is dominated by the thermal ion diamagnetic drifts) for $\langle \beta_{dia} \in [0,4.8] \%$. In the single fluid limit (diamagnetic drifts ignored), the thermal pressure gradients drive ballooning modes in a broad region encompassing the outer $60-90 \%$ of the plasma volume at $\langle \beta_{dia} \rangle \approx 4.8 \%$. To stabilize these modes, we find that diamagnetic drift corrections must be invoked (mainly due to the thermal ions). The energetic ion diamagnetic drifts play a role only for low wave number values, $k_{\alpha}\leq 8$. It has been verified that the fast particle drift ordering imposed by the model is amply satisfied for on-axis hot particle to thermal density $N_{h0}/N_{i0} \approx 1\%$ even at high $\langle \beta_{dia} \rangle$

External RMP effect on locked-mode-like instability in helical plasmas

The slowing-down mechanism of the locked-mode-like instabilities with and without an island structure is investigated through the effects of an external RMP (resonant magnetic perturbation) on the instabilities. For both instabilities, the slowing-down duration decreases with the increase in the external RMP, and the RMP dependence is consistent with the braking model of the j × B force due to the interaction between the instabilities and the external RMP. Moreover, the relationship between the amplitude and the frequency of both locked-mode-like instabilities during the slowing down is consistent with the force balance model between the j × B force due to the external RMP and a viscous force. These results suggest that the slowing down of both locked-mode-like instabilities with finite external RMP occurs due to the j × B force driven by the external RMP

Dependence of the resonant magnetic perturbation penetration threshold on plasma parameters and ions in helical plasmas

We investigate the penetration threshold of resonant magnetic perturbation (RMP) by the external coils in the Large Helical Device (LHD) for various plasma aspect ratio configurations. The qualitative dependence on the collisionality is opposite to that in a high plasma aspect configuration; this is a quite unique property first found in the LHD. We also investigate the threshold dependence on the ion species, and find that the threshold in deuterium discharges is much smaller than that in hydrogen discharges. In all cases the thresholds are higher as the poloidal rotation becomes faster, which shows that poloidal rotation is the dominant driver to the RMP shielding. This is qualitatively consistent with the torque balance model between the electromagnetic and poloidal viscous torques. In a configuration of the LHD, the dependence of the threshold on the density is qualitatively similar to that in Ohmic tokamak plasmas, but the beta dependence is opposite to that of tokamaks. The difference arises from the cause of the viscous torque

Three-dimensional anisotropic pressure free boundary equilibria

Free boundary three-dimensional anisotropic pressure magnetohydrodynamic equilibria with nested magnetic flux surfaces are computed through the minimisation of the plasma energy functional $W={\int}_{V}{d^3}x\left[{B^2}/(2\mu_0)+p_{||}/(\Gamma-1)\right]$. The plasma–vacuum interface is varied to guarantee the continuity of the total pressure $\left[{p}_{\perp}+{B^2}/(2\mu_0)\right]$ across it and the vacuum magnetic field must satisfy the Neumann boundary condition that its component normal to this interface surface vanishes. The vacuum magnetic field corresponds to that driven by the plasma current and external coils plus the gradient of a potential function whose solution is obtained using a Green's function method. The energetic particle contributions to the pressure are evaluated analytically from the moments of the variant of a bi-Maxwellian distribution function that satisfies the constraint ${\bf B\cdot\nabla}{\cal F}_h=0$. Applications to demonstrate the versatility and reliability of the numerical method employed have concentrated on high-β off-axis energetic particle deposition with large parallel and perpendicular pressure anisotropies in a 2-field period quasiaxisymmetric stellarator reactor system. For large perpendicular pressure anisotropy, the hot particle component of the pperpendicular distribution localises in the regions where the energetic particles are deposited. For large parallel pressure anisotropy, the pressures are more uniform around the flux surfaces

Vertical profiles and two-dimensional distributions of carbon line emissions from C2+−C5+ ions in attached and RMP-assisted detached plasmas of large helical device

In Large Helical Device (LHD), the detached plasma is obtained without external impurity gas feed by supplying an m/n = 1/1 resonant magnetic perturbation (RMP) field to a plasma with an outwardly shifted plasma axis position of Rax = 3.90 m where the magnetic resonance exists in the stochastic magnetic field layer outside the last closed flux surface. The plasma detachment is triggered by the appearance of an m/n = 1/1 island when the density, increased using hydrogen gas feed, exceeds a threshold density. The behavior of intrinsically existing impurities, in particular, carbon originating in the graphite divertor plates, is one of the important key issues to clarify the characteristic features of the RMP-assisted plasma detachment although the particle flux still remains on some divertor plates even in the detachment phase of the discharge. For this purpose, vertical profiles and two-dimensional (2-D) distributions of edge carbon emissions of CIII to CVI have been measured at extreme ultraviolet wavelength range, and the results are compared between attached and RMP-assisted detached plasmas. It is found that the CIII and CIV emissions located in the stochastic magnetic field layer are drastically increased near the m/n = 1/1 island O-point and in the vicinity of both inboard and outboard edge separatrix X-points during the RMP-assisted detachment, while those emissions are only enhanced in the vicinity of the outboard edge X-point in attached plasmas without RMP. The result clearly indicates a change in the magnetic field lines connecting to the divertor plates, which is caused by the growth of the m/n = 1/1 edge magnetic island. In contrast, the intensity of CVI emitted radially inside the magnetic island significantly decreases during the detachment, suggesting an enhancement of the edge impurity screening. The measured carbon distribution is analyzed with a three-dimensional edge plasma transport simulation code, EMC3-EIRENE, for the attached plasmas without RMP. It is found that the narrow strip-shaped impurity trace emitted along the edge X-point and its width are sensitive to the cross-field impurity diffusion coefficient, DZ⊥. As a result, the value of DZ⊥ of C3+ ions is evaluated to be 20 times larger than that of the bulk ions in the Rax = 3.90 m configuration, while the reason is unclear at present. The measured 2-D carbon distribution is also discussed and compared to the structure of the m/n = 1/1 magnetic island, which quickly expanded during the appearance of the plasma detachment