[en] Present day devices employ sufficiently high power auxiliary heating such that the pressure associated with the corresponding energetic particles is of the order of the thermal pressure. In particular, for NBI and ICRH, the fast ions are distributed anisotropically, and this has been shown to influence the equilibrium and MHD stability. In the present contribution, we aim to explore the influence of anisotropy on single particle orbits, and ultimately kinetic corrections to perturbations of MHD-like origin. New 3D single particle orbit equations have been derived and introduced into the guiding centre orbit code VENUS. These new equations of motion allow for a treatment of the pressure anisotropy and electromagnetic perturbations. VENUS uses the well established equilibrium and stability codes VMEC and TERPSICHORE as inputs, and follows a single particle on its orbit around 2D or 3D configurations. As a first application, the magnetic drift precession frequency is studied for both trapped and passing particles in a tokamak. The effects of parallel (P_parallel>P_perpendicular) and perpendicular (P? > Pk) anisotropy are shown, including poloidal dependence of the perpendicular pressure due to anisotropy. Also, an analytical expression of the toroidal drift frequency for trapped particles including magnetic shear, plasma elongation and radial pressure gradients is derived. Thus a comparison with already existing expressions is possible and all of them can be compared to independent orbit simulations. The VENUS code is also used for elucidating the effects of the different parameters on the toroidal drift frequency. Another application is the modification of fast particle orbits due to pressure anisotropy, especially for large orbit widths and small inverse aspect ratio ε. Finally, the inclusion of electromagnetic perturbations allows for an investigation of MHD-like perturbations and their impact on particle orbits as well as resonance phenomena. (Author)

[en] In magnetic confinement devices, the inhomogeneity of the confining magnetic field along a magnetic field line generates the trapping of particles within local magnetic wells. One of the consequences of the trapped particles is the generation of a current, known as the bootstrap current (BC), whose direction depends on the nature of the magnetic trapping. The BC provides an extra contribution to the poloidal component of the confining magnetic field. The variation of the poloidal component produces the alteration of the winding of the magnetic field lines around the flux surfaces quantified by the rotational transform. When reaches low rational values, it can trigger the generation of ideal MHD instabilities. Therefore, the BC may be responsible for the destabilisation of the configuration [1]. Having established the potentially dangerous implication of the BC, principally, in reactor prototypes, a method to compensate its harmful effects is proposed. It consists of the modelling of the current driven by externally launched ECWs within the plasma to compensate the effects of the BC. This method is flexible enough to allow the identification of the appropriate scenarios in which to generate the required CD depending on the nature of the confining magnetic field and the specific plasma parameters of the configuration. Both the BC and the CD calculations are included in a self-consistent scheme which leads to the computation of a stable BC+CD-consistent MHD equilibrium. This procedure is applied in this paper to simulate the required CD to stabilise a QAS and a QHS reactor prototypes. The estimation of the input power required and the effect of the driven current on the final equilibrium of the system is performed for several relevant scenarios and wave polarisations providing various options of stabilising driven currents. (Author)

[en] There are a large number of codes treating wave propagation in plasmas. All of these use very different approaches depending on what there are dedicated to study. The LEMan code [1], which was developed in CRPP, is designed to treat electromagnetic waves in the low-frequency range (i.e. Alfven and ion cyclotron domain) in a 3D geometry. With this constraint, the most obvious method was to use a full wave code. The reason for that is the variation of the plasma parameters during a period of the wave because the low frequency domain involves long wavelengths. Other methods like WKB are not fully adapted for this purpose. As a first step, developments were formulated with a cold model. The code solves the following relation derived from the Maxwell's equations. (Author)

[en] The study of wave propagation is an important topic in plasma physics as it can play a considerable role in heating or instability processes. The LEMan code is designed to treat low-frequency waves e.g. in the Alfven and ion-cyclotron domain. In this range of frequencies, the main points of interest are heating in the ion-cyclotron domain (ICRH) and the global Alfven modes that can be driven unstable by the fast ions resulting either from fusion reactions or from neutral beam injection (NBI). A warm model has been implemented in the LEMan code. To determine the corresponding dielectric tensor, the linearized Vlasov equation is solved by the same method used in, but retaining only the lowest order terms in the finite Larmor radius expansion. In order to compute the parallel gradient of the perturbed distribution function, the latter is decomposed in term of Fourier harmonics. A linear system is thus obtained and leads to a dielectric tensor whose form corresponds to a convolution connecting together the components of the Fourier series of the electric current density and field. Such a method permits to take into account the poloidal up shift of the parallel wave vector and to avoid using approximations that are quite delicate in stellarator geometries. In the Alfven range, the main kinetic effects that can be modelled with this formulation are the Kinetic Alfven Wave (KAW) and the electron Landau damping. Lack of symmetry in stellarator systems gives rise to a larger variety of global modes (TAE, HEA, MAE, etc...). These modes already exist in the cold model but can also be influenced by kinetic effects. Investigation will be done to see how the different methods act on the results. The computation of a straight helix has been done and points out the presence of a helicity-induced Alfven Eigenmode (HAE). Adding other effects like toroidicity to the previous geometry will influence the spectrum and may modify the characteristics of the HAE. (Author)

[en] The potential performance and flexibility of a compact, quasi-axisymmetric (QAS) stellarator design, has been addressed by studying the effects of varied pressure and rotational transform profiles on the global, ideal magnetohydrodynamic (MHD) stability and the energetic particle transport. The CAS3D and TERPSICHORE code packages were used in the MHD studies while the ORBITMN/ORBIT3D code package was used for the transport simulations of the three field period QAS. To assess robust performance in a medium-size experiment, the VMEC code was used to obtain magnetic flux surfaces for 30 equilibria near the design point, while keeping the boundary shape and the average beta fixed at 3.8%. The plasma equilibria obtained were designated P0X/I0Y as follows: P00/I00 was the baseline configuration. P01, P02 and P03 were defined so that P01 was similar to P00, P02 was more peaked than P01, while P03 was broader than P01. P04 was a very broad, parabolic pressure profile and P05 was the pressure profile used in helias reactor studies based on the W7-X design. The iota profiles were chosen as follows: I01 was linear, maintaining i(0) and i(a) the same as in I00. I02 and I03 were based on I01 and also kept i(0) and i(a) as in the baseline case, but with edge shear increased by a factor of 1.5 and 2. I04 was a linear iota profile with i(0) as for the other profiles, but i(a) higher than 0.5, similar to I01. The pressure and iota profiles are shown in Ref. [2]

[en] A fully kinetic assessment of the stability properties of toroidal drift modes has been obtained for a case for the Large Helical Device [A. Iiyoshi , Nucl. Fusion 39, 1245 (1999)]. This calculation retains the important effects in the linearized gyrokinetic equation, using the lowest-order ''ballooning representation'' for high toroidal mode number instabilities in the electrostatic limit. Results for toroidal drift waves destabilized by trapped particle dynamics and ion temperature gradients are presented, using three-dimensional magnetohydrodynamic equilibria reconstructed from experimental measurements. The effects of helically trapped particles and helical curvature are investigated

[en] The LHD Heliotron has achieved β≥3% with 10 MW tangential neutral beam injection based on negative ion beam technology that produces energetic ions at 180 keV. Furthermore, there are indications that these β levels obtained in the experimental discharges exceed the predictions of the ideal magnetohydrodynamic (MHD) model with respect to local and global stability. (Author)

[en] A kinetic ballooning mode theory is developed from the gyrokinetic equation in the frequency range for which the ions are fluid, the thermal electron response is adiabatic and the hot electrons are non-interacting due to their large drift velocity. Trapped particle effects are ignored, The application of the quasineutrality condition together with the parallel and binomial components of Ampere's Law reduces the gyrokinetic equation to a second order ordinary differential equation along the equilibrium magnetic field lines. The instability dynamics are dominated by the pressure gradients of the thermal species in the fluid magnetohydrodynamic limit. The resulting equation combines features of both the Kruskal-Oberman energy principle and the rigid hot particle energy principle proposed by Johnson et al. to model the Astron device

[en] The bootstrap current j_b connected with collisional movements of the charged particles trapped in the local mirror fields. Many theoretical, numerical and experimental investigations for different tokamaks and heliotron-stellarators are devoted to the boot-strap current calculation. For nonaxisymmetric toroidal systems there are several models and approaches. The problems are connected with the complicated 3D structure of the stellarator magnetic fields. The quasi-analytical fluid moment or sol-called Shaing-Callen approach has a compact semi-analytical form derived in. This form (without the collisional dependence, for the low-collisional regime) constitutes the basis for several numerical tools with the self-consistent iterative equilibria- the SPBSC code and the TERPSICHORE-BOOTSP code. (Author)

[en] Simulations of wave propagation in the low-frequency range are made using the three- dimensional code LEMan. This permits to study wave heating and fast ion destabilisation. This code solves a wave equation derived from the linearised Maxwell equations. Until now, all the calculations have been performed within a cold formulation. A warm model is now under development. The methodology is unchanged but the dielectric tensor has now finite temperature effects. It is calculated from the Vlasov equation but it does not take into account finite Larmor Radius terms. Nevertheless, effects in the direction parallel to the equilibrium magnetic field are retained and the parallel vector is computed exactly. This last component has a particularly simple form thanks to the Fourier decomposition in toroidal and poloidal angles. From the previous version of LEMan, a numerical effort has been made to parallelise the code with MPI. This permits to improve the efficiency of computing and run cases needing more memory. It is particularly interesting for 3D warm model cases which require increased cpu and memory limit for the calculation of the dielectric tensor. But it is useful in the cold model, too. For instance, in the ICRF domain, you have to take a great number of Fourier modes into account when the wavelengths become small compared with the plasma dimensions. (author)