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Author(s):
V.L. Vdovin, T.Watari and A. Fukuyama
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Title:
3D Maxwell-Vlasov Boundary Value Problem Solution in Stellarator Geometry in Ion Cyclotron Frequency Range (final report)
Date of publication:
Dec. 1996
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Key words:
Helical Device, stellarator, ICRF heating, metric tensor, Jacobian, equilibrium, antenna, Maxwell-Vlasov, tensor, toroidal coupling
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Abstract:
In this report we develop the theory for the wave excitation, propagation and absorption in 3-dimensional (3D) stellarator equilibrium high beta plasma in ion cyclotron frequency range (ICRF). This theory forms a basis for a 3D code creation, urgently needed for the ICRF heating scenarios development for the constructed LHD [1] and projected W7-X [2] stellarators and for the stellarators being at operation (like CHS, W7-AS, etc.). The theory solves the 3D Maxwell-Vlasov antenna-plasma-conducting shell boundary value problem in the non - orthogonal flux coordinates (psi,theta,varphi), psi being magnetic flux function, theta and varphi being the poloidal and toroidal angles, respectively. All basic physics, like wave refraction, reflection and diffraction are firstly self consistently included, along with the fundamental ion and ion minority cyclotron resonances, two ion hybrid resonance, electron Landau and TTMP absorption. Antenna reactive impedance and loading resistance are also calculated and urgently needed for an antenna -generator matching. This is accomplished in a real confining magnetic frield being varying in a plasma major radius direction, in toroidal and poloidal directions, through making use of the hot dense plasma dielectric kinetic tensor. We expand the solution in Fourier series over toroidal (varphi ) and poloidal (theta) angles and solve resulting ordinary differential equations in a radial like psi - coordinate by finite difference method. The constructed discretization scheme is divergent - free one, thus retaining the basic properties of original equations. The Fourier expansion over angle coordinates has given to us the possibility to correctly construct the "parallel" wave number k_parallel and thereby to correctly describe the ICRF waves absorption by a plasma. The toroidal harmonics are tightly coupled with each other due to magnetic field inhomogenity of stellarators in toroidal direction. This is drastically different from axial symmetric plasma of the tokamaks. The inclusion in the problem major radius variation of magnetic field can strongly modify earlier results obtained for the straight helical, especially for high beta plasma, due to modification of locations of the two ion hybrid resonance layers. For W7-X Iike magnetic field topology the inclusion in our theory of a major radius inhomogenity of the magnetic field is a key element for correct description of RF power deposition profiles at all. The theory is developed in a manner that includes tokamaks and magnetic mirrors as the particular cases through general metric tensor (provided by an equilibrium solver) treatment of the wave equations. We describe the structure of newly developed stellarator ICRF 3D full wave code STELION, based on theory described in this report.
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