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Perpendicular transport of magnetic fields in stationary MHD: ideal MHD flows and resistive MHD annihilation solutions
Název práce v češtině:
Název v anglickém jazyce: Perpendicular transport of magnetic fields in stationary MHD: ideal MHD flows and resistive MHD annihilation solutions
Klíčová slova: space plasmas, ideal and resistive Magnetohydrodynamics (MHD), magnetic annihilation, ordinary differential equations
Klíčová slova anglicky: space plasmas, ideal and resistive Magnetohydrodynamics (MHD), magnetic annihilation, ordinary differential equations
Akademický rok vypsání: 2015/2016
Typ práce: projekt
Jazyk práce: angličtina
Ústav: Astronomický ústav UK (32-AUUK)
Vedoucí / školitel: doc. Mgr. Michal Švanda, Ph.D.
Řešitel:
Konzultanti: Dieter Nickeler
Zásady pro vypracování
The aim of the project is to analyse how magnetic fields are transported by perpendicular flows in ideal and resistive MHD. This is done to get insight into nonlinear MHD flows and the nature of magnetic annihilation by solving ordinary differential equations.

1. The student will get insight into the field of nonlinear fluid dynamics of highly conducting plasma (ideal and resistve MHD).
2. Formulating the problem of ideal/resistive MHD for 1D configurations.
3. Solving compressible ideal MHD equations for 1D
4. Solving resistive MHD equations for different resistivity models for 1D
5. Comparison of ideal/resistive results, conclusions for magnetic annihilation solutions
Seznam odborné literatury
Magnetic annihilation, published as Chapter3 in "Magnetic reconnection: Theory and application", E. Priest and T. Forbes, Cambridge University Press, 2000 (and references therein)
Resistive stagnation point flows at a current sheet, B. Sonnerup and E. Priest, J. Plasma Physics 14(2), pp.283-294
Some comments on magnetic field reconnection, E. Priest and S. Cowley, J. Plasma Physics 14(2), pp.271-282
Exact solutions for steady state incompressible magnetic reconnection, I.J.D. Craig and S.M. Henton, Astrophys. Journal, 450, pp.280-288, 1995
Předběžná náplň práce
Calculating or at least estimating the correct rate of magnetic flux being destroyed in space plasmas to produce energy outburst (e.g. solar flares) heating (e.g. of the corona) or acceleration of plasma (e.g. magnetospheric substorms or CMEs) is very difficult, as different physical processes and parameters are involved. Magnetic annihilation or to say magnetic flux transport is a process, being necessary to produce global instabilities or global dynamical plasma processes as, e.g. magnetic reconnection or reconnective annihilation.
The student will investigate the effects of a variable resistivity on the occurence of magnetic annihilation. For this, he/she will develop an analytical or/and numerical model for one-dimensional flows (and fields), implement various approaches for the resistivity, and discuss the implications on the results. The restriction in dimension is necessary to exclude the classical stagnation point related problems, and also to keep the necessary mathematics on a reasonable and tractable level. i.e. ordinary differential equations (analytical methods should be used and maybe mathematica). Such a study has not been performed yet but is of great importance for our general understanding of magnetic reconnection processes.
Předběžná náplň práce v anglickém jazyce
Calculating or at least estimating the correct rate of magnetic flux being destroyed in space plasmas to produce energy outburst (e.g. solar flares) heating (e.g. of the corona) or acceleration of plasma (e.g. magnetospheric substorms or CMEs) is very difficult, as different physical processes and parameters are involved. Magnetic annihilation or to say magnetic flux transport is a process, being necessary to produce global instabilities or global dynamical plasma processes as, e.g. magnetic reconnection or reconnective annihilation.
The student will investigate the effects of a variable resistivity on the occurence of magnetic annihilation. For this, he/she will develop an analytical or/and numerical model for one-dimensional flows (and fields), implement various approaches for the resistivity, and discuss the implications on the results. The restriction in dimension is necessary to exclude the classical stagnation point related problems, and also to keep the necessary mathematics on a reasonable and tractable level. i.e. ordinary differential equations (analytical methods should be used and maybe Mathematica). Such a study has not been performed yet but is of great importance for our general understanding of magnetic reconnection processes.
 
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