By Stephen Jardin

ISBN-10: 1439810214

ISBN-13: 9781439810217

Assuming no past wisdom of plasma physics or numerical equipment, Computational equipment in Plasma Physics covers the computational arithmetic and methods had to simulate magnetically restricted plasmas in glossy magnetic fusion experiments and destiny magnetic fusion reactors. principally self-contained, the textual content provides the fundamental strategies priceless for the numerical answer of partial differential equations. besides discussing numerical balance and accuracy, the writer explores a number of the algorithms used at the present time in sufficient intensity in order that readers can research their balance, potency, and scaling houses. He specializes in mathematical types the place the plasma is taken care of as a undertaking fluid, due to the fact that this is often the main mature plasma version and so much appropriate to experiments. The publication additionally emphasizes toroidal confinement geometries, relatively the tokamak—a very profitable configuration for confining a high-temperature plasma. the various simple numerical options offered also are acceptable for equations encountered in a higher-dimensional section house. essentially the most difficult study components in sleek technology is to boost appropriate algorithms that result in reliable and actual suggestions that may span proper time and area scales. This booklet offers an exceptional operating wisdom of the algorithms utilized by the plasma physics group, aiding readers on their solution to extra complex research.

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Extra info for Computational Methods in Plasma Physics (Chapman & Hall CRC Computational Science)

Example text

64) Eq. 64) can be used to replace Eq. 63). 4 Other Equation Sets for MHD The equation sets corresponding to the closures listed in the previous sections are by no means exhaustive. Higher-order closures exist which involve integrating the stress tensor and higher-order tensors in time [15]. These become very complex, and generally require a subsidiary kinetic calculation to complete the closure of the highest-order tensor quantities. Additional closures of a more intermediate level of complexity exist in which the pressure stress tensor remains diagonal but is allowed to have a different form parallel and perpendicular to the magnetic field [16].

Thus, making the substitution φnj,l → φ˜k,m rn exp(−2πikj/N − 2πiml/N ) in Eq. 24) and dividing through by the common exponential factor, we have r− 1 + 2iSx sin θk + 2iSy sin θm = 0, r where Sx = uδt/δx, Sy = vδt/δy, θk = −2πk/N , θm = −2πm/N . This is a quadratic equation in r that can be written r2 + 2ibr − 1 = 0, where b = Sx sin θk + Sy sin θm is purely real. 6 1 . 25) Accuracy and Conservative Differencing Stability is not the only property that makes one finite difference approximation to a partial differential equation superior to another.

2). In an implicit method, some spatial derivatives are evaluated at new time points as, for example, in this equation φn+1 = φnj − j uδt n+1 αδt n+1 φj+1 − φn+1 φ − 2φn+1 + φn+1 j−1 + j j−1 . 3) The unknowns at the advanced time, φn+1 ; j = 0, · · · , N , are seen to be couj pled together by the spatial derivative operators in Eq. 3), so that solving for these unknowns requires inversion of a matrix. This is true of implicit methods in general, while it is not the case for explicit methods. We will see that generally implicit methods are more stable and allow larger time steps δt, but explicit methods require less computational effort for each time step.

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Computational Methods in Plasma Physics (Chapman & Hall CRC Computational Science) by Stephen Jardin


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