Numerical Simulation and Optimal Control in Plasma Physics: by Jacques Blum

By Jacques Blum

This monograph on modelling, numerical simulation, and optimum regulate of equilibrium of the plasma in Tokamak fusion reactors covers new iteration designs that have simply entered provider (JET, TFTR, and JT60), are less than development (TORE Supra), or are projected (INTOR and NET). the 1st 5 chapters take care of the desk bound challenge of axisymmetric equilibrium of the plasma--modelling and numerical simulation, mathematical lifestyles of an answer for a simplified version, and identity and static regulate of the boundary of the plasma. ultimate chapters deal with the evolution of equilibrium at the time-scale of thermal diffusion within the plasma, and the steadiness and dynamic regulate of displacements of the plasma.

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If 1 is not an eigenvalue of ¢(",) and if a is taken sufficiently small. This is possible M. 86) is convergent. :, u ~ u -+ u 0+1 n '""' (l-o:)u +20'u n+l/3 -au n+2/3 37 Numerical Methods The main inconvenience with this algorithm is the slowness of its convergence. 87) (:: and for '. 3. In order to apply Newton's algorithm it is necessary that the linearization of (P 1) should exist and be invertible for each of the successive iterates 1fn. 1. :;Q. moreover D Q either consists of a ~~ number of vertices of the triangulation We use the fact that 1f is finite or is the union of a finite number of The discrete versions of hypotheses HI, H2, H3 thus take the form: Hi) sUP1f- is attained at a unique vertex of 7" ..

30). 1. 31) >I ~ 0 on az - 0 IIp h(r)g(>lN)dS " IIp On ro fl 1M , Ilv I HM) > sup D {I Axisymmetric Equilibrium where the support for jB is k U Bi u ncv and lOp is the characteristic function i=l This formulation will be used in Chapter III in order to study the existence of Op. of 15 o a solution of this problem for a simplified model. 11). 3: In Choice of the function g( Tokamaks whose magnetic m) : surfaces have circular section, experimental observations allow the toroidal current density to be expressed as a function of pIa where a is the minor radius of the plasma and p is the minor radius of the magnetic surface under consideration : In a neighbourhood of the magnetic axis.

11 - - ,~ -- ~ Limiter Return arm of the magnetic circuit Triangulation of a meridian section of TFR.

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