Keywords : Tokamak, dynamical system, transport barrier, symplectic mappings, Hamiltonian systems, toroidal magnetic field, subdiffusion, Cantori, noble numbers, plasma confinement, scaling laws Internal transport barriers (ITB's) observed in tokamaks are described by a purely magnetic approach. Magnetic line motion in toroidal geometry with broken magnetic surfaces is studied from a previously derived Hamiltonian map in situation of incomplete chaos. This appears to reproduce in a realistic way the main features of a tokamak, for a given safety factor profile and in terms of a single parameter L representing the amplitude of the magnetic perturbation. New results are given concerning the Shafranov shift as function of L. The phase space (ψ, θ) of the "tokamap" describes the poloidal section of the line trajectories, where ψ is the toroidal flux labelling the surfaces. For small values of L, closed magnetic surfaces exist (KAM tori) and island chains begin to appear on rational surfaces for higher values of L, with chaotic zones around hyperbolic points, as expected. Island remnants persist in the chaotic domain for all relevant values of L at the main rational q-values.Single trajectories of magnetic line motion indicate the persistence of a central protected plasma core, surrounded by a chaotic shell enclosed in a double-sided transport barrier : the latter is identified as being composed of two Cantori located on two successive "most-noble" numbers values of the perturbed safety factor, and forming an internal transport barrier (ITB). Magnetic lines which succeed to escape across this barrier begin to wander in a wide chaotic sea extending up to a very robust barrier (as long as L 1) which is identified mathematically as a robust KAM surface at the plasma edge. In this case the motion is shown to be intermittent, with long stages of pseudo-trapping in the chaotic shell, or of sticking around island remnants, as expected for a continuous time random walk.For values of L 1, above the escape threshold, most magnetic lines succeed to escape out of the external barrier which has become a permeable Cantorus. Statistical analysis of a large number of trajectories, representing the evolution of a bunch of magnetic lines, indicate that the flux variable ψ asymptotically grows in a diffusive * E-mail : j.misguich@cea.fr 1 manner as (L 2 t) with a L 2 scaling as expected, but that the average radial position rm(t) asymptotically grows as (L 2 t) 1/4 while the mean square displacement around this average radius asymptotically grows in a subdiffusive manner as (L 2 t) 1/2 . This result shows the slower dispersion in the present incomplete chaotic regime, which is different from the usual quasilinear diffusion in completely chaotic situations. For physical times tϕ of the order of the escape time defined by xm(tϕ) ∼ 1, the motion appears to be superdiffusive, however, but less dangerous than the generally admitted quasi-linear diffusion. The orders of magnitude of the relevant times in Tore Supra are finally discus...

The classical problem of the motion of a charged particle in a slowly varying electromagnetic field is reconsidered in the framework of ‘pseudo-canonical transformations’ in a Hamiltonian formalism. As compared with Littlejohn's important recent work, we develop a method which we believe to be more transparent. It consists, in essence, of exploiting directly the requirement that the Lie brackets of the guiding centre variables be independent of the (new) gyrophase. By using this method, we construct explicitly the complete set of functional relationships between the guiding centre variables and the particle variables, up to second order in the drift parameter є These expressions are valid for magnetic and electric fields of arbitrary geometry (within the drift approximation), which may be slowly varying in time.

The design value for ITER is based on operation at n/n GW = 0.85, β n = 1.8 and H98(y, 2) = 1. These values have been routinely achieved in JET in argon seeded ELMy H-mode discharges in different divertor configurations and with different triangularities. Two main scenarios are emerging from the experiments. 13 Affiliations 1, 4 and 5 are partners in the Trilateral Euregio Cluster (TEC).

This paper reports on ITER-relevant ICRF physics investigated on JET in 2003 and early 2004.Minority heating of helium three in hydrogen plasmas -( 3 He)H -was systematically explored by varying the 3 He concentration and the toroidal phasing of the antenna arrays. The best heating performance (a maximum electron temperature of 6.2keV with 5MW of ICRF power) was obtained with a preferential wave launch in the direction of the plasma current. A clear experimental demonstration was made of the sharp and reproducible transition to the mode conversion heating regime when the 3 He concentration increases above ~2%. In the latter regime the best heating performance (a maximum electron temperature of 8keV with 5MW of ICRF power) was achieved with dipole array phasing, i.e. a symmetric antenna power spectrum. Minority heating of deuterium in hydrogen plasmas -(D)H -was also investigated but was found inaccessible, because this scenario is too sensitive to impurity ions with Z/A=1/2 such as C 6+ , small amounts of which directly lead into the mode conversion regime. Minority heating of up to 3% of tritium in deuterium plasmas was systematically investigated during the JET Trace Tritium experimental campaign (TTE). This required operating JET at its highest possible magnetic field (3.9 to 4T) and the ICRF system at its lowest frequency (23MHz). The interest of this scenario for ICRF heating at these low concentrations and its efficiency at boosting the suprathermal neutron yield were confirmed, and the measured neutron and gammay ray spectra permit interesting comparisons with advanced ICRF code simulations.Investigations of finite Larmor radius effects on the RF-induced high-energy tails during second harmonic (ω=2 ω c ) heating of a hydrogen minority in D plasmas clearly demonstrated a strong decrease of the RF diffusion coefficient at proton energies ~1MeV, in agreement with theoretical 4 expectations. Fast wave heating and current drive experiments in deuterium plasmas showed effective direct electron heating with dipole phasing of the antennas, but only small changes of the central plasma current density were observed with the directive phasings, in particular at low single pass damping. New investigations of the heating efficiency of ICRF antennas confirmed its strong dependence on the parallel wavenumber spectrum. Advances i n topics of a more technological nature are also summarized: ELM studies using fast RF measurements, the successful experimental demonstration of a new ELM-tolerant antenna matching scheme, and technical enhancements planned on the JET ICRF system for 2006, themselves equally strongly driven by the preparation for ITER.5

ELMy H-mode experiments at JET in 2000/mid-2002 have focused on discharges with normalized parameters for plasma density, energy confinement and beta similar to those of the ITER Q DT = 10 reference regime (n/n GW ∼ 0.85, H 98(y,2) ∼ 1, β N ∼ 1.8). ELMy H-mode plasmas have been realized reaching or even exceeding those parameters in steady-state conditions (up to ∼5 s or 12τ E) in a reproducible way and only limited by the duration of the additional heating phase. These results have been obtained (a) in highly triangular plasmas, by increasing the average a Researcher at NFSR Belgium. b Partners in the Trilateral Euregio Cluster (TEC). c See annex in IAEA 2002 J. Pamela IAEA-CN94/OV-1/1.4.