By Stephen Jardin
Assuming no past wisdom of plasma physics or numerical equipment, Computational tools in Plasma Physics covers the computational arithmetic and methods had to simulate magnetically limited plasmas in sleek magnetic fusion experiments and destiny magnetic fusion reactors. principally self-contained, the textual content provides the elemental ideas priceless for the numerical answer of partial differential equations. in addition to discussing numerical balance and accuracy, the writer explores a few of the algorithms used this present day in adequate intensity in order that readers can examine their balance, potency, and scaling homes. He specializes in mathematical versions the place the plasma is taken care of as a undertaking fluid, given that this can be the main mature plasma version and so much appropriate to experiments. The ebook additionally emphasizes toroidal confinement geometries, rather the tokamak—a very profitable configuration for confining a high-temperature plasma. a number of the uncomplicated numerical options provided also are applicable for equations encountered in a higher-dimensional part area. probably the most demanding examine components in smooth technological know-how is to strengthen compatible algorithms that bring about good and exact ideas which can span proper time and house scales. This publication presents a good operating wisdom of the algorithms utilized by the plasma physics group, supporting readers on their strategy to extra complex learn.
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Additional info for Computational Methods in Plasma Physics (Chapman & Hall CRC Computational Science)
Three standard closures for two-fluid MHD, resistive MHD, and ideal MHD have been presented. The MHD equations can be written in conservation form reflecting global conservation of mass, magnetic flux, momentum, and energy. The conservation form of the equations is Introduction to Magnetohydrodynamic Equations 25 not always the best starting point for numerical solution, but they do provide an invaluable check on the global accuracy of the solutions. The ideal MHD equations are a subset of the more complete system of MHD equations.
0 . .. exp(2πikj/N ) · · · . · .. φN −1 . 34 Computational Methods in Plasma Physics The matrices corresponding to Eqs. 7) are exact inverses of one another. 8) where, we recall, S1 = uδt/δx and S2 = αδt/δx2 . Assuming that the coefficients S1 and S2 are constants, we transform each φnj in Eq. 7) and select out only a single Fourier component k. 9) where we have used the identity exp(iα) = cos α + i sin α and have introduced the k dependent angle θk = −2πk/N. 11) where is the amplification factor.
24). 2: Consider a circular cross section periodic cylinder with minor radius a and periodicity length 2πR. ) The normal component of the magnetic field vanishes at the boundary r = a. Show that it is possible to have an arbitrarily large magnetic field B and self consistent current density J that satisfy the force-free condition J × B = 0. 2) but where there exists a small pressure µ0 p B 2 . If the relative error in computing B is δB and if the conservative form of the energy equation is used, Eq.