A slab model is developed to study the excitation of lower hybrid instability triggered by the injection of a transverse neutral beam in a tokamak with magnetic shear. The lower hybrid mode is evanescent in the inner and outer region while propagating waves in the intermediate region. The neutral beam, on getting fully ionized in the plasma, resonantly couples with the lower hybrid wave in the intermediate region, driving the mode unstable. The theory of this process reveals that the growth rate...

A gyrokinetic formalism has been developed to study lower hybrid wave stabilization of ion temperature gradient driven modes, responsible for anomalous ion transport in the inner region of tokamak. The parametric coupling between lower hybrid and drift waves produce lower hybrid sideband waves. The pump and the sidebands exert a ponderomotive force on electrons, modifying the eigenfrequency of the drift wave and influencing the growth rate. The longer wavelength drift waves are destabilized by the lower hybrid wave while the shorter wavelengths are suppressed. The requiste lower hybrid power is in the range of ~900 kW at 4.6 GHz

A general analytical solution of the Grad–Shafranov equation is presented. Specific functional forms of pressure and plasma current are used; the solution allows arbitrary plasma size, aspect ratio, elongation, triangularity, current, and poloidal beta, without imposing undue constraints amongst those variables.

The standard Grad–Shafranov equation for axisymmetric toroidal plasma equilibrium is customary expressed in cylindrical coordinates with toroidal contours, and through which benchmark equilibria are solved. An alternative approach to cast the Grad–Shafranov equation in spherical coordinates is presented. This equation, in spherical coordinates, is examined for toroidal solutions to describe low ? Solovev and high ? plasma equilibria in terms of elementary functions.

The JET design, which started in 1973, introduced bold new concepts such as D-shaped plasmas in large tokamaks, a closed-loop tritium plant, and the use of beryllium as a first-wall material. It implied increasing by two orders of magnitudes the plasma volume and the heating power compared to the standard at the time. During the JET Joint Undertaking operation from 1978 to 1999, most of these design parameters were exceeded. After achieving all of its initial objectives, JET was upgraded and modified to establish H-mode scaling and to perform comprehensive studies of divertor and advanced tokamak concepts. JET holds all records in fusion power and energy and has allowed a unique experience in D-T operation to be gained. The JET results have made a decisive contribution to the scaling laws on which the basic layout and the dimensions of ITER are based. JET today under its new EFDA-JET organization is still the most powerful fusion device operating in the world, with potential to extend its performance even further. It has the essential mission to prepare for D-T burn in ITER and to train a new generation of scientists for developing fusion as an energy source.

A new approach to integration of magnetic field lines in divertor tokamaks is proposed. In this approach, an analytic equilibrium generating function (EGF) is constructed in natural canonical coordinates $(?,?)$ from experimental data from a Grad–Shafranov equilibrium solver for a tokamak. ? is the toroidal magnetic flux and ? is the poloidal angle. Natural canonical coordinates $(?,?,\varphi)$ can be transformed to physical position $(R,Z,\varphi)$ using a canonical transformation. $(R,Z,\varphi)$ are cylindrical coordinates. Another canonical transformation is used to construct a symplectic map for integration of magnetic field lines. Trajectories of field lines calculated from this symplectic map in natural canonical coordinates can be transformed to trajectories in real physical space. Unlike in magnetic coordinates [O. Kerwin, A. Punjabi, and H. Ali, Phys. Plasmas 15, 072504 (2008)], the symplectic map in natural canonical coordinates can integrate trajectories across the separatrix surface, and at the same time, give trajectories in physical space. Unlike symplectic maps in physical coordinates $(x,y)$ or $(R,Z)$, the continuous analog of a symplectic map in natural canonical coordinates does not distort trajectories in toroidal planes intervening the discrete map. This approach is applied to the DIII-D tokamak [J. L. Luxon and L. E. Davis, Fusion Technol. 8, 441 (1985)]. The EGF for the DIII-D gives quite an accurate representation of equilibrium magnetic surfaces close to the separatrix surface. This new approach is applied to demonstrate the sensitivity of stochastic broadening using a set of perturbations that generically approximate the size of the field errors and statistical topological noise expected in a poloidally diverted tokamak. Plans for future application of this approach are discussed.

The method of using internal magnetic surface information from soft x-ray (SXR) measurements to facilitate equilibrium reconstruction is explored. It is shown that useful information about the shape of the safety-factor q profile in DIII-D can be generally determined from the information inferred from surfaces of constant SXR emissivity. Comparisons of magnetic surfaces and the q profile reconstructed using external magnetic and SXR data against those using magnetic and motional Stark effect (MSE) data are presented. The reconstructed results using SXR and external magnetic data are found to reasonably agree with those derived from MSE and external magnetic data. The choice of an appropriate number of fitting parameters to reconstruct the q profile is also investigated.

A reduced set of equations for high-beta tokamak equilibria with flow comparable to the poloidal sound velocity is solved analytically. The solution includes higher-order terms of asymptotic expansions in terms of the inverse aspect ratio and indicates the modification of the magnetic structure and the departure of the pressure surfaces from the magnetic surfaces by sub- or super-poloidal-sonic flows. The analytical representation for the shift of the magnetic axis from the geometrical axis (the Shafranov shift) and that of the pressure maximum and the equilibrium beta limit are also obtained. The Shafranov shift is enhanced by a slightly super-poloidal-sonic flow and it produces a forbidden region of equilibrium by the poloidal-sonic flow. The physical mechanism of the shift of the pressure maximum from the magnetic axis due to the poloidal-sonic flow is discussed in analogy to those of the geodesic acoustic mode and the slow magnetosonic wave.

The characteristics of near-unity-? equilibria are investigated with two codes. CUBE is a multigrid Grad–Shafranov solver [Gourdain et al., J. Comput. Phys. 216, 275 (2006)], and Ophidian was written to compute solutions using analytic unity-? equilibria [Cowley et al., Phys. Fluids B 3, 2066 (1991)]. Results from each method are qualitatively and quantitatively compared across a spectrum of mutually relevant parameters. These comparisons corroborate the theoretical results and provide benchmarks for high-resolution numerical results available from CUBE. Both tools facilitate the exploration of the properties of high-? equilibria, such as a highly diamagnetic plasma and its ramifications for stability and transport.

42nd annual meeting of the division of plasma physics of the American Physical Society and the 10th international congress on plasma physics, Quebec City, Quebec (Canada), 2001.