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AbstractAxisymmetric equilibria with incompressible flows of arbitrary direction are studied in the framework of magnetohydrodynamics under a variety of physically relevant side conditions consisting, for example, in that the plasma temperature or the magnetic field modulus are uniform on magnetic surfaces. To this end a set of pertinent nonlinear ordinary differential equations (ODEs) are transformed to quasilinear ODEs and the respective initial value problem is solved numerically with appropriately determined initial values near the magnetic axis. Several equilibrium configurations are then constructed surface by surface. It turns out that in addition to the usual configurations with a magnetic axis, the non-field aligned flow results to novel toroidal shell equilibria in which the plasma is confined within a couple of magnetic surfaces. In addition, the flow affects the elongation and triangularity of the magnetic surfaces and opens up the possibility of changing the magnetic field topology by creating double toroidal shell-like configurations. [ABSTRACT FROM AUTHOR]

A previous proof of non-existence of tokamak equilibria with purely poloidal flow within macroscopic theory (Throumoulopoulos et al2006 Phys. Plasmas13122501) motivated this microscopic analysis near the magnetic axis for toroidal and 'straight' tokamak plasmas. Despite the new exact solutions of Vlasov's equation on the magnetic axis found here, the structure of macroscopic flows remains elusive. However, the treatment within a toroidal system of orthogonal coordinates and comparison with the straight case, which reveals the importance of toroidicity, is encouraging. [ABSTRACT FROM AUTHOR]

Abstract.The aim of the present work is to investigate tokamak equilibria with reversed magnetic shear and sheared flow, which may play a role in the formation of internal transport barriers (ITBs), within the framework of the two-fluid model in cylindrical geometry. The study is based on exact self-consistent solutions by means of which the impact of the magnetic shear, s, and the ?toroidal? (axial) and ?poloidal? (azimuthal) ion velocity components, vizand vi?, on the radial electric field, Er, its shear, |dEr/dr|, and the shear of the E?Bvelocity, ?E?B?|d/dr(E? B/B2)|, is examined. For a wide parametric regime of experimental concern it turns out that the contributions of the viz, vi? and pressure gradient (Pi) terms to Er, |Er?| and ?E?Bare of the same order of magnitude. The contribution of the Piterm is missing in the framework of magnetohydrodynamics (MHD) (G. Poulipoulis et al. 2004 Plasma Phys. Control. Fusion46, 639). The impact of son ?E?Bthrough the Piterm is stronger than that through the velocity terms; in particular for constant Bzthe ion pressure gradient contribution to ?E?Bat the point where dEr/dr=0 scales as (1?s)(2?s), whereas the ion flow contributions to ?E?Bscale as (1?s). The results indicate that, like MHD, the magnetic shear and the sheared toroidal and poloidal velocities act synergetically in producing electric fields and therefore ?E?Bprofiles compatible with the ones observed in discharges with ITBs; owing to the Piterm, however, the impact of son Er, |Er?| and ?E?Bis stronger than that in MHD. [ABSTRACT FROM AUTHOR]

Abstract.A necessary condition for the existence of general dissipative magneto-hydrodynamic equilibria is derived. The derivation comprises Ohm's law and the existence of magnetic surfaces, only in the sense of the Kolmogorov?Arnold?Moser (KAM) theorem. All other equations describing the system are only required for evaluating the condition for a specific case. [ABSTRACT FROM AUTHOR]

A generalised Grad–Shafranov equation that governs the equilibrium of an axisymmetric toroidal plasma with anisotropic pressure and incompressible flow of arbitrary direction is derived. This equation includes six free surface functions and recovers known Grad–Shafranov-like equations in the literature as well as the usual static, isotropic one. The form of the generalised equation indicates that pressure anisotropy and flow act additively on equilibrium. In addition, two sets of analytical solutions, an extended Solovev one with a plasma reaching the separatrix and an extended Hernegger–Maschke one for a plasma surrounded by a fixed boundary possessing an X-point, are constructed, particularly in relevance to the ITER and NSTX tokamaks. Furthermore, the impacts both of pressure anisotropy and plasma flow on these equilibria are examined. It turns out that depending on the maximum value and the shape of an anisotropy function, the anisotropy can act either paramagnetically or diamagnetically. Also, in most of the cases considered both the anisotropy and the flow have stronger effects on NSTX equilibria than on ITER ones. [ABSTRACT FROM AUTHOR]

The authors comments on the paper "An analytic functional form for characterization and generation of axisymmetric plasma boundaries." They mention that the proposed alternative form describe boundaries in the axisymmetric plasma between an X-point and D-shaped ones and can be used to study fusion plasmas.

We derive a generalized Grad–Shafranov equation governing helically symmetric equilibria with pressure anisotropy and incompressible flow of arbitrary direction. Through the most general linearizing ansatz for the various free surface functions involved therein, we construct equilibrium solutions and study their properties. It turns out that pressure anisotropy can act either paramegnetically or diamagnetically, the parallel flow has a paramagnetic effect, while the non-parallel component of the flow associated with the electric field has a diamagnetic one. Also, pressure anisotropy and flow affect noticeably the helical current density. [ABSTRACT FROM AUTHOR]

We extend previous work by two of the authors [Evangelias and Throumoulopoulos 2016 Plasma Phys. Control. Fusion58 045022] and find analytic solutions to a generalized Grad–Shafranov equation (GGSE) with pressure anisotropy, hollow toroidal current density and incompressible flow of arbitrary direction. By specifying the surface-function terms involved in the GGSE as quadratic functions of the poloidal magnetic flux function, we derive analytic tokamak pertinent equilibria. It turns out that, irrespective of the shape of the toroidal current density profile, which is noticeably affected by the pressure anisotropy, this anisotropy has a paramagnetic effect for and a diamagnetic one for . In addition, the parallel flow induces paramagnetism, while the residual toroidal flow associated with the electric field induces diamagnetism. The analytic results obtained here contribute to the physics understanding of axisymmetric equilibria with pressure anisotropy and flow, and can be employed for validating equilibrium codes. [ABSTRACT FROM AUTHOR]