H. J. de Blank

Identification of plasma-edge-related operational regime boundaries and the effect of edge instability on confinement in ASDEX Upgrade

Local edge parameters on the ASDEX Upgrade tokamak are investigated at the L-mode to H-mode transition, during phases with various types of edge-localized modes (ELMs), and at the density limit. A scaling law for the boundary electron temperature, , is found which describes the H-mode threshold for deuterium-puffed discharges with favourable ion -drift direction. The region of stable operation is bounded by type I ELMs near the ideal ballooning limit and by a minimum temperature necessary to avoid thermal instability of the plasma edge. Stationary operation with type III ELMs imposes an upper limit on the edge temperature. Within the entire range of boundary densities investigated , both L-mode and H-mode are found to be accessible. During type I ELMy H-mode, a relation of global confinement with the edge pressure gradient is found which is connected with a loss of the favourable density dependence predicted by the ITER-92P and ITER-93H ELMy H-mode scalings. At high density, better confinement is achieved in H-modes with an edge pressure gradient below the ideal ballooning limit, e.g. during type III ELMy H-mode with impurity-seeded radiation.

MHD stability and disruption physics in ASDEX Upgrade

The MHD activity giving rise to the beta - and the density limit in ASDEX Upgrade is analyzed. A detailed description of the MHD phenomena occuring prior to and during disruptions is given. The MHD characteristics of the different ELM types occurring in ASDEX Upgrade are described.

Theory of the m =1 kink mode in toroidal plasma

The energy principle of ideal magnetohydrodynamics (MHD) is used to study the ideal MHD stability of the m=1 internal kink mode in a toroidal plasma. The equilibrium configurations that are considered allow for a broad region where the safety factor q is close to unity. This region may extend to the magnetic axis, or may be a singular layer. The minimization of the energy functional yields an implicit equation for the growth rate that can be solved by simple numerical means. The examples that are treated numerically retain the essential features of experimentally expected q profiles. The growth rate depends very sensitively on the q profile close to unity and increases with the width of the q≊1 layer. The highest values are of the order of the inverse aspect ratio e divided by the poloidal Alfven time. Nonmonotonic profiles with q>1 on axis are more unstable than monotonic q profiles with q<1. In the latter case, the mode tends to be localized in the q≊1 region instead of in the center.

Bifurcation theory for the L-H transition in magnetically confined fusion plasmas

The mathematical field of bifurcation theory is extended to be applicable to 1-dimensionally resolved systems of nonlinear partial differential equations, aimed at the determination of a certain specific bifurcation. This extension is needed to be able to properly analyze the bifurcations of the radial transport in magnetically confined fusion plasmas. This is of special interest when describing the transition from the low-energy-confinement state to the high-energy-confinement state of the radial transport in fusion plasmas (i.e., the L-H transition), because the nonlinear dynamical behavior during the transition corresponds to the dynamical behavior of a system containing such a specific bifurcation. This bifurcation determines how the three types (sharp, smooth, and oscillating) of observed L-H transitions are organized as function of all the parameters contained in the model.

Two-dimensional electric current effects on a magnetized plasma in contact with a surface

Significant electric fields both parallel and perpendicular to a magnetic field have been observed and modeled self-consistently in an ITER divertor relevant plasma–wall experiment. Due to magnetization, electric current is found to penetrate the plasma beam outside of the cascaded arc plasma source with a length scale proportional to , where He and Hi are the electron and ion Hall parameters, respectively. Plasma rotation measurements and chemical erosion profiles at a carbon target demonstrate that for a sufficiently well-magnetized plasma, a current through the target causes plasma–wall sheath potentials to significantly increase in a region of net ion collection while for the conditions studied, regions of net electron collection remain unaffected. The plasma–wall sheath profile at the target has been characterized experimentally as a function of negative target potential.

Guiding Center Motion

Abstract The motion of charged particles in slowly varying electromagnetic fields is analyzed. The strength of the magnetic field is such that the gyro-period and the gyro-radius of the particle motion around field lines are the shortest time and length scales of the system. The particle motion is described as the sum of a fast gyro-motion and a slow drift velocity.

Collisionless reconnection in instabilities and due to external forcing

Collisionless magnetic reconnection due to electron inertia is numerically investigated in two-dimensional, externally forced systems and unstable configurations. A common characteristic of reconnection in the two cases, associated with the effects of electron inertia and temperature, is a faster than exponential scale collapse. This collapse creates structures that are much narrower than the inertial reconnection layer, such as a very localized, X-shaped current distribution. The nonlinear evolution at this small scale is largely independent of large scale features such as the initial and boundary conditions which constitute the differences between driven and unstable cases. However, only in forced reconnection cases ion viscosity is found to stop the scale collapse of the current. High numerical resolution made the detailed investigation of small scale structure formation and continued scale collapse possible.

MHD activity as seen in soft x-ray radiation

Tokamak plasmas are in a state of permanent reorganization due to strong MHD activity. Central MHD phenomena can be observed with pinhole cameras in which silicon wafers with additional foils record soft x-ray emission from the plasma along many chords with high temporal resolution. To separate the repetition time and the characteristic radius of various MHD phenomena such as sawteeth and, in H-mode, ELMs from these chord-integrated measurements, the method of singular-value decomposition is of great value. Moreover, the helical (1,1) MHD mode is analysed in great detail. In a zeroth approximation, the minimum and maximum values of the spatial eigenvectors are used to determine the radius of the q = 1 surface. In a next step, a model of the (1,1) mode is developed which evaluates the line-integrated signals in elliptical geometry. This serves for interpolation and thereby improves spatial resolution. Finally, the information is added into a fast equilibrium reconstruction code which leads to improved current profile identification.

Stability of localized modes in rotating tokamak plasmas

The ideal magnetohydrodynamic stability is investigated of localized interchange modes in a large-aspect ratio tokamak plasma. The resulting stability criterion includes the effects of toroidal rotation and rotation shear and contains various well-known limiting cases. The analysis allows for a general adiabatic index, resulting in a stabilizing contribution from the convective effect. A further stabilizing effect from rotation exists when the angular frequency squared decreases radially more rapidly than the density. Flow shear, however, also decreases the stabilizing effect of magnetic shear through the Kelvin–Helmholtz mechanism. Numerical simulations reveal the merits and limitations of the performed local analysis.

Steady state off-axis sawtoothing in the Rijnhuizen Tokamak project

A family of off-axis, or annular, instabilities has been studied using Thomson scattering, soft X-ray emission, and two electron cyclotron emission diagnostic systems. In the Rijnhuizen tokamak (RTP) [N. J. Lopes Cardozo et al., Plasma Physics and Controlled Nuclear Fusion Research 1992 (International Atomic Energy Agency, Vienna, 1993), Vol. 1, p. 271] these phenomena are invoked in a controlled way in discharges with specific (off-axis) deposition of electron cyclotron heating (ECH) and persist during most of the heating period, or during many current diffusion times. Based on coherent mode analysis at the crash time, the instabilities are associated with resonant surfaces near simple rational values of q (32, 2, and 3). A parameter study shows an increase of reheat rate and a decrease of sawtooth period with increasing ECH power and — in contrast to observations in other experiments — with increASING density as well.