[en] So-called zonal flows are known to play a significant role in tokamak plasma confinement by reducing the level of turbulent transport. It is shown that the presence of highly charged impurity ions strongly increases the collisional damping of these flows. A formula for the zonal-flow damping time is derived, which indicates that the damping is enhanced approximately by a factor Z_eff. In the case of large aspect ratio, the enhancement is considerably larger.

[en] The conditions under which rapid plasma rotation may occur in a three-dimensional magnetic field, such as that of a stellarator, are investigated. Rotation velocities comparable to the ion thermal speed are found to be attainable only in magnetic fields which are approximately isometric. In an isometric magnetic field the dependence of the magnetic field strength B on the arc length l along the field is the same for all field lines on each flux surface ψ. Only in fields where the departure from exact isometry, B=B(ψ,l), is of the order of the ion gyroradius divided by the macroscopic length scale are rotation speeds comparable to the ion thermal speed possible. Moreover, it is shown that the rotation must be in the direction of the vector ∇ψx∇B. (author)

[en] The theory of plasma confinement by non-axisymmetric magnetic fields is reviewed. Such fields are used to confine fusion plasmas in stellarators, where in contrast to tokamaks and reversed-field pinches the magnetic field generally does not possess any continuous symmetry. The discussion is focussed on magnetohydrodynamic equilibrium conditions, collisionless particle orbits, and the kinetic theory of equilbrium and transport. Each of these topics is fundamentally affected by the absence of symmetry in the magnetic field: the field lines need not trace out nested flux surfaces, the particle orbits may not be confined, and the cross-field transport can be very large. Nevertheless, by tailoring the magnetic field appropriately, well-behaved equilibria with good confinement can be constructed, potentially offering an attractive route to magnetic fusion. In this article, the mathematical apparatus to describe stellarator plasmas is developed from first principles and basic elements underlying confinement optimization are introduced. (review article)

[en] The collisionless time evolution of zonal flows in stellarator systems is investigated. An analytical solution of the kinetic and quasineutrality equations describing the residual zonal flow is derived for arbitrary three-dimensional systems without approximations in the magnetic geometry. The theory allows for an arbitrary number of particle species. It has been found that in stellarators the residual zonal flows are not in general steady but oscillate with a certain frequency. This frequency is determined by the speed of the bounce-averaged radial drifts of the particles trapped in the magnetic field and vanishes in tokamaks, where such net drifts are absent. A reduction of the bounce-averaged radial drifts in configurations optimized with respect to neoclassical transport results in a smaller zonal-flow frequency.

[en] The quasilinear particle flux arising from gyrokinetic instabilities is calculated in the electrostatic and collisionless approximation, keeping the geometry of the magnetic field arbitrary. In particular, the flux of electrons and heavy impurity ions is studied in the limit where the former move quickly, and the latter slowly, along the field compared with the mode frequency. Conclusions are drawn about how the particle fluxes of these species depend on the magnetic field geometry, mode structure and frequency of the instability. Under some conditions, such as everywhere favourable or unfavourable magnetic curvature and modest temperature gradients, it is possible to make general statements about the fluxes independently of the details of the instability. In quasi-isodynamic stellarators with favourable bounce-averaged curvature for most particles, the particle flux is always outward if the temperature gradient is not too large, suggesting that it might be difficult to fuel such devices with gas puffing from the wall. In devices with predominantly unfavourable magnetic curvature, the particle flux can be inward, resulting in spontaneous density peaking in the centre of the plasma. In the limit of highly charged impurities, ordinary diffusion (proportional to the density gradient) dominates over other transport channels and the diffusion coefficient becomes independent of mass and charge. An estimate for the level of transport caused by magnetic field fluctuations arising from ion-temperature-gradient instabilities is also given and is shown to be small compared with the electrostatic component. (paper)

[en] A study of the curvature pinch effect in various fusion devices (both tokamaks and stellarators) is presented. Canonical density profiles are calculated employing the theory developed by M. B. Isichenko, A. V. Gruzinov, P. H. Diamond, and P. N. Yushmanov [Phys. Plasmas 3, 1916 (1995)]. In tokamaks, it is found that the curvature pinch is relatively strong (especially in a spherical tokamak) and usually leads to a peaked density profile. In stellarators, the curvature pinch is weaker and can have either sign

[en] The equilibrium plasma rotation in a general toroidal magnetic field is nearly always subsonic and is determined by the requirement that the collisional particle transport should be ambipolar in lowest order in the small-ion-gyroradius expansion. Only in quasi-symmetric fields, where collisional particle transport is intrinsically ambipolar, can the plasma rotate freely and then only in the quasi-symmetry direction. Sonic rotation velocities are allowed in this case. In this paper the effect of rotation in a quasi-axisymmetric field is investigated, and it is found that the symmetry is broken when the rotation speed exceeds the diamagnetic speed appreciably, leading to reappearance of the non-intrinsically ambipolar 1/ν-transport regime. Fortunately, this transport scales with the fourth power of the rotation Mach number and is expected to be modest in most plasmas of interest.

[en] Short mean-free path two-fluid equations are employed to evaluate the lowest order nonambipolar radial current in plasma confined by a three-dimensional toroidal magnetic field. The result is used to obtain a necessary condition for intrinsic ambipolarity of plasma transport in such a field and to derive a criterion for the importance of the toroidal field ripple for collisional tokamak plasma rotation. The ripple effects on toroidal plasma rotation are found to be negligible if the characteristic perpendicular length scale is determined by the pedestal width of order the poloidal ion gyroradius (as may be the case in the H-mode regime), but may conceivably become important for more shallow plasma gradients.

[en] It is shown that one of the most important classes of orbit-optimized stellarators, so-called quasi-isodynamic ones, are immune to all the usual linear trapped-particle instabilities in the electrostatic and collisionless limit. This result, which is valid for frequencies below the electron-bounce frequency, follows from the requirement of positive entropy production and is thus independent of all other details of the magnetic geometry.

[en] >The condition of omnigenity is investigated, and applied to the near-axis expansion of Garren & Boozer (Phys. Fluids B, vol. 3 (10), 1991a, pp. 2805–2821). Due in part to the particular analyticity requirements of the near-axis expansion, we find that, excluding quasi-symmetric solutions, only one type of omnigenity, namely quasi-isodynamicity, can be satisfied at first order in the distance from the magnetic axis. Our construction provides a parameterization of the space of such solutions, and the cylindrical reformulation and numerical method of Landreman & Sengupta (J. Plasma Phys., vol. 84 (6), 2018, 905840616); Landreman et al. (J. Plasma Phys., vol. 85 (1), 2019, 905850103), enables their efficient numerical construction.