Compact optimized stellarators offer novel solutions for confining high-β plasmas and developing magnetic confinement fusion. The three-dimensional plasma shape can be designed to enhance the magnetohydrodynamic (MHD) stability without feedback or nearby conducting structures and provide driftorbit confinement similar to tokamaks. These configurations offer the possibility of combining the steady-state low-recirculating power, external control, and disruption resilience of previous stellarators with the low aspect ratio, high β limit, and good confinement of advanced tokamaks. Quasiaxisymmetric equilibria have been developed for the proposed National Compact Stellarator Experiment (NCSX) with average aspect ratio 4-4.4 and average elongation ∼1.8. Even with bootstrap-current consistent profiles, they are passively stable to the ballooning, kink, vertical, Mercier, and neoclassicaltearing modes for β > 4%, without the need for external feedback or conducting walls. The bootstrap current generates only 1/4 of the magnetic rotational transform at β = 4% (the rest is from the coils); thus the equilibrium is much less non-linear and is more controllable than similar advanced tokamaks. The enhanced stability is a result of 'reversed' global shear, the spatial distribution of local shear, and the large fraction of externally generated transform. Transport simulations show adequate fast-ion confinement and thermal neoclassical transport similar to equivalent tokamaks. Modular coils have been designed which reproduce the physics properties, provide good flux surfaces, and allow flexible variation of the plasma shape to control the predicted MHD stability and transport properties.
Physics issues are discussed for compact stellarator configurations which achieve good confinement by the fact that the magnetic field modulus |B| in magnetic co-ordinates is dominated by poloidally symmetric components. Two distinct configuration types are considered: (1) those which achieve their drift optimization and rotational transform at low β and low bootstrap current by appropriate plasma shaping; and (2) those which have a greater reliance on plasma β and bootstrap currents for supplying the transform and obtaining quasi-poloidal symmetry. Stability analysis of the latter group of devices against ballooning, kink and vertical displacement modes has indicated that stable β values on the order of 15% are possible. The first class of devices is being considered for a low β near term experiment that could explore some of the confinement features of the high β configurations.
Neutral-beam injection of up to 2.5 MW into plasmas in the ISX-B tokamak (R0 = 0.93 m, a = 0.27 m, BT = 0.9–1.5 T, Ip = 70–210 kA, n̄e = 2.5–10×1013 cm−3) has created plasmas with volume-averaged beta of up to ∼ 2.5%, peak beta values of up to ∼ 9%, and root-mean-square beta values of up to ∼ 3.5%. Energy confinement time is observed to decrease by about a factor of two as beam power goes from 0 to 2.5 MW; the decrease is caused predominantly by the electron confinement time falling below the predictions of ‘Alcator scaling’ by a factor of 3–4 at high beam power. An empirical relationship of the form fits our measurements over a wide range of plasma parameters. The function f(Pb), where Pb is the beam power, is linear for Pb ≤ 1.2 MW but tends to saturate for 1.2 MW ≤ Pb ≤ 2.5 MW. Although the equilibria attained in ISX-B are predicted to be above the threshold for the ideal magnetohydrodynamic (MHD) ballooning instability, no evidence of these modes is observed.
In the first four years of the LHD experiment, several encouraging results have emerged, the most significant of which is that MHD stability and good transport are compatible in the inward shifted axis configuration. The observed energy confinement at this optimal configuration is consistent with ISS95 scaling with an enhancement factor of 1.5. The confinement enhancement over the smaller heliotron devices is attributed to the high edge temperature. We find that the plasma with an average beta of 3% is stable in this configuration, even though the theoretical stability conditions of Mercier modes and pressure driven low-n modes are violated. In the low density discharges heated by NBI and ECR, internal transport barrier (ITB) and an associated high central temperature (>10 keV) are seen. The radial electric field measured in these discharges is positive (electron root) and expected to play a key role in the formation of the ITB. The positive electric field is also found to suppress the ion thermal diffusivity as predicted by neoclassical transport theory. The width of the externally imposed island is found to decrease when the plasma is collisionless with finite beta and increase when the plasma is collisional. The ICRF heating in LHD is successful and a high energy tail (up to 500 keV) has been detected for minority ion heating, demonstrating good confinement of the high energy particles. The magnetic field line structure unique to the heliotron edge configuration is confirmed by measuring the plasma density and temperature profiles on the divertor plate. A long pulse (2 min) discharge with an ICRF power of 0.4 MW has been demonstrated and the energy confinement characteristics are almost the same as those in short pulse discharges.
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