PLASMA POSITION CONTROL AND CURRENT PROFILE RECONSTRUCTION FOR TOKAMAKS
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PLASMA POSITION CONTROL AND CURRENT PROFILE RECONSTRUCTION FOR TOKAMAKS * F. Saint-Laurent_, B. Faugeras, C. Boulbe, S. Bremond, P. Moreau, J. Blum, Association Euratom CEA, CEA/DSM/IRFM Cadarache, 13108 Saint-Paul-lez-Durance, France. Laboratoire J. A. Dieudonné, Université de Nice-Sophia-Antipolis, F-06100 Nice, France Abstract In large size tokamaks, plasma performances in term of internal temperature, radiated power, stored kinetic en- ergy are growing year after year. A precise control of the plasma position is a key issue in order to avoid damages on the first wall of the device. Such a control is essential when high-power long-duration plasmas have to be per- formed as on the Tore Supra tokamak. The current carried by the plasma can be localized using magnetic measure- ments (pick-up coils) outside the plasma. The plasma boundary can thus be identified and controlled on real time in less than a few milliseconds. In order to get information on the current distribution inside the plasma, more sophisticated calculation must be performed. The 2D Grad-Shafranov equation describing the force balance between kinetic pressure and Lorentz force in an axisymmetric toroidal geometry must be solved. Such a solver has been successfully implemented in C++ and installed on Tore Supra device.
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- viding flux
- plasma
- machine protection
- european fusion
- time step
- supra real
- sensors
- magnetic measurements
- flux de surface
PLASMA POSITION CONTROL AND CURRENT PROFILE RECONSTRUCTION FOR TOKAMAKS * # §§ § F. Saint-Laurent, B. Faugeras, C. Boulbe, S. Bremond, P. Moreau, J. Blum, Association Euratom CEA, CEA/DSM/IRFM Cadarache, 13108 Saint-Paul-lez-Durance, France.§ Laboratoire J. A. Dieudonné, Université de Nice-Sophia-Antipolis, F-06100 Nice, Francecoils and toroidal flux loops. From these measurements Abstract the plasma boundary can be reconstructed, assuming an In large size tokamaks, plasma performances in term of axisymmetric geometry and no current flowing between internal temperature, radiated power, stored kinetic en-the plasma boundary and the sensors. In present days to-ergy are growing year after year. A precise control of the kamaks the shape of the plasma boundary is routinely plasma position is a key issue in order to avoid damages identifiable in real-time in less than a few milliseconds. on the first wall of the device. Such a control is essential Such a procedure provides precise information for when high-power long-duration plasmas have to be per-plasma boundary but only poor information inside the formed as on the Tore Supra tokamak. The current carried plasma itself. It can be improved by solving the 2D Grad-by the plasma can be localized using magnetic measure-Shafranov equation (GS) which describes the axisymmet-ments (pick-up coils) outside the plasma. The plasma ric plasma equilibrium and thus identifies the non-linear boundary can thus be identified and controlled on real distribution of plasma current. The GS equation describes time in less than a few milliseconds. the balance between Lorentz force j × B and the force∇pIn order to get information on the current distribution inside the plasma, more sophisticated calculation must bedue to kinetic pressure, together with the quasi static form performed. The 2D Grad-Shafranov equation describingof the Maxwell equation (Ampere’s theorem and conser-the force balance between kinetic pressure and Lorentzvation of magnetic induction). The GS equation reads: force in an axisymmetric toroidal geometry must be (1) solved. Such a solver has been successfully implemented in C++ and installed on Tore Supra device. It is fast Where, enough to enable a real time equilibrium reconstruction. Because magnetic measurements are no longer suffi-(2) cient to constrain the solution when detailed information ψ(r, z) is the poloidal magnetic flux function, randzare on current distribution inside the plasma are mandatory, the two remaining cylindrical coordinates, andµ0 isthe other measurements must be introduced as external con-magnetic permeability of the vacuum. The right hand side straints in the solver. A few examples of such an imple-of (1) represents the toroidal componentjφthe plasma of mentation will be discussed. current density which is governed byp′,fandf′functions. Solving (1) with given boundary conditions from mag-INTRODUCTION netic measurements is a free boundary problem in which In the field of fusion plasma studies, the Tore Supra to-the plasma boundary is free to evolve. This is an ill-posed kamak explores the way of high-power long-duration problem which needs a dedicated algorithm to be solved. plasma discharges. When operating such discharges, the first wall, located inside the vacuum vessel in front of the ITERATIVE ALGORITHM plasma, must sustain the huge heat flux (10 MW/m2) re-The goal of a real-time equilibrium code is to identify leased by the high temperature plasma following both the plasma boundary together with the flux surface ge-convection and radiation processes. Dedicated high heat ometry outside and inside the plasma, and finally the cur-flux components have been manufactured and are cur-rent density profile. rently used. Nevertheless some of these components are LetWbe the domain representing the vacuum vessel of not designed to sustain a direct contact with the plasma. the Tokamak, and∂Wboundary. In Tore Supra the its Real-time identification and control of the plasma plasma boundary is determined by the contact with a lim-boundary and position are thus mandatory to safely oper-iter D. Thus the boundary is associated to the last closed ate the device. The control takes advantage of the current magnetic flux surface. The regionWpthe containing carried by the plasma. The magnetic field induced by this plasma is defined as current can be measured outside the plasma by pick-up ___________________________________________ *Work supported by the European Communities under the contract of whereψb= maxDψ. Association between EURATOM and CEA, was carried out within the framework of the European Fusion Development Agreement. TheMagnetic measurements provide both Dirichlet condi-views and opinions expressed herein do not necessarily reflect those of tionψ= h,using toroidal flux loops, and Neumann condi-the European Commission. # francois.saint-laurent@cea.fr
