Magnetic field perturbations due to finite-beta operation in stellarators have been simulated by using the three-dimensional free-boundary equilibrium code VMEC to overcome the limitations imposed by averaged equilibrium and fixed-boundary methods. Results of these computations have been compared with analytic predictions for cylindrical stellarator models and confirm a linear relationship between the average beta and the plasma dipole moment. Only a weak sensitivity of the computations to details of the pressure profile is found. The distortion of the magnetic surfaces can be significant even at moderate beta, so that careful modelling is required when analysing the data.

In order to understand the relationships between confinement and space potential (electric field) and between confinement and density fluctuations, plasma parameters in the ELMO Bumpy Torus Scale (EBT-S)[in Plasma Physics and Controlled Nuclear Fusion Research (IAEA, Tokyo, 1974), Vol. 2, p. 141; Plasma Phys. 25, 597 (1983)] have been measured systematically for a wide range of operating conditions. Present EBT plasma parameters do not show a strong dependence on the potential profile, but rather exhibit a correlation with the fluctuations. The plasma pressure profile is found to be consistent with the profile anticipated on the basis of the flute stability criterion for a marginally stable plasma. For a heating power of 100 kW, the stored energy density is found to be restricted to the range between 4.5×1013 eV-cm−3 and 7×1013 eV-cm−3. The lower limit remains constant regardless of heating power and pertains to plasmas lacking an equilibrium and/or stability. The upper limit increases with heating power and is found to result from the onset of instabilities. In between the two limits is a plasma that is in an equilibrium state and is marginally stable. Operational trajectories exist that take the EBT plasma from one limit to the other.

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The toroidal current observed during electron cyclotron heating in the Advanced Toroidal Facility torsatron is identified as bootstrap current. The observed currents, ranging between +4 and -2 kA, agree well with predictions of neoclassical theory in magnitude and parametric dependence, as determined by systematic scans of quadrupole (shaping) and dipole (magnetic axis shift) moments of the poloidal magnetic field. It has been shown that the bootstrap current in a stellarator can be externally controlled, and zero-current operation can be achieved.PACS numbers: 52.25.Fi, 52.55.Dy, 52.55.Hc, The existence of bootstrap current-a toroidal plasma current produced by density and temperature gradients-is predicted by theory. 1,2 It is caused by viscosity of the trapped and untrapped particles that tends to relax the diamagnetic flow velocity, and, as a consequence, produces a current. This current is important for steady-state operation of toroidal confinement devices, because it would reduce current-drive needs in tokamaks and jeopardize current-free operation in stellarators. Therefore, in both devices it is necessary to understand the physics of the bootstrap current and to find ways to control it. The existence of bootstrap currents has been confirmed in several toroidal devices. 3-9 Recent experiments in the Advanced Toroidal Facility (ATF) have gone one step farther and shown that the measured bootstrap current agrees with predictions of neoclassical theory 10 " 12 by changing the neoclassical viscosity through variations of the magnetic-field structure. This demonstration is feasible because of the flexibility in controlling the magnetic configuration in ATF and the absence of other current sources.Neoclassical theory predicts that, in the low-collisionality limit, the bootstrap current density is given bywhere/, (f c ) is the fraction of trapped (circulating) particles, V/? is the gradient of plasma pressure, Bp is the poloidal field, and Gb is the magnetic geometry factor, which is normalized to that in the axisymmetric tokamak (Gb = 1).' 1 The geometry factor depends on the magnetic-field structure-in particular, on the harmonic content of |B| along a magnetic-field line. In a stellarator, the magnetic field contains axisymmetric, helical, and mixed components, whose modenumber spectrum can be externally controlled. Therefore, by varying the |B| harmonics, the bootstrap current can be externally controlled. In a plasma of finite collisionality, the bootstrap current decreases with increasing collision frequency. The collisionless regime for the helically trapped particles is more easily accessible than that for toroidally trapped particles because of the shorter helical connection length. The direction of the bootstrap current associated with helically trapped particles is opposite to that of the usual bootstrap current, because the viscous force caused by these trapped particles damps primarily the toroidal (rather than the poloidal) flow and admits a residual approximately poloidal (rather than toroidal) fl...

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