Statistics – Applications
Scientific paper
Jan 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt.........3y&link_type=abstract
Thesis (PH.D.)--COLUMBIA UNIVERSITY, 1995.Source: Dissertation Abstracts International, Volume: 56-06, Section: B, page: 3257.
Statistics
Applications
Magnetic Field
Scientific paper
In this thesis, we study the evolution of magnetic field (the so-called dynamo problem) in astrophysical plasmas and laboratory plasmas. Firstly, we consider dynamos relevant to astrophysical plasmas. We study the effect of the back -reaction of finite large-scale magnetic field on the flow (so-called self-consistent problem). We find that even for the case in which energy in the small-scales is less than that in the large-scale and the quasilinear approximation is expected to hold, the back-reaction of the growing magnetic field on the flow will lead to a near-cancellation between the alpha- and beta -effect of the conventional kinematic theory, leaving "hyperresistivity" as the only remnant for the electromotive force. We then give a quasilinear calculation for hyperresistivity by using the MHD model. This result poses a critical challenge for the kinematic dynamo theory of magnetic field of some astrophysical plasmas. Secondly, we consider applications of dynamo theory to laboratory plasmas. We calculate the hyperresistivity by using neoclassical MHD equations in Chapter 3. Thus, the theory of a self-sustained bootstrapped tokamak by resistive MHD tearing dynamo is extended to the neoclassical regime which is more relevant for present -day tokamaks. A model giving the steady-state solutions of a complete bootstrapped tokamak is proposed. The hyperresistivity is calculated by using kinetic theory in Chapter 4, motivated by the debate on the role of kinetic and MHD dynamo in the reversed-field-pinch (RFP) experiments. A unified theory is given. The effect of density and temperature gradients of plasma on mean Ohm's law is also considered. Finally, since the electromotive force (dynamo field) in mean Ohm's law depends on the spectrum of turbulence, we develop a formal turbulent clump theory for the spectrum. We restrict our consideration, in particular, to the current density relaxation problem of well-confined tokamak plasmas. In this theory, due to the clump effect, the local fluctuations can be generated under the action of turbulent mixing of mean configuration. This turbulent mixing process is caused by the electromotive force associated with the fluctuations.
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