Date Awarded


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)




Allen H Boozer


A fundamental requirement for the successful operation of a tokamak is the maintenance of a toroidal electric current within the tokamak plasma itself. Maintaining this internal plasma current can be a very difficult technological problem. In this work, a well-known but non-standard method for maintaining the tokamak current called the bootstrap effect is discussed. The bootstrap effect occurs when a fusion plasma is near thermonuclear conditions, and allows the tokamak to greatly amplify its electric current.;Because the bootstrap effect amplifies but does not create a plasma current, it has long been argued that a completely bootstrapped tokamak is not possible. That is, it has been argued that some fraction of the tokamak current must be created externally and injected into the plasma for a bootstrap amplification to occur. This injection of current is not desirable, however, since current-drive schemes are difficult to implement and are only marginally efficient.;An important but largely unexplored implification of the bootstrap effect is that the effect, by itself, creates hollow (outwardly peaked) tokamak current profiles. Hollow tokamak current profiles are known to lead to tearing modes, which are resistive (non-ideal) magnetohydrodynamic (MHD) plasma instabilities. Although usually characterized as harmful for plasma confinement, it turns out that tearing modes may actually be beneficial for the tokamak bootstrap effect.;In this work, a new theoretical approach based on a helicity conserving mean-field Ohm's law is used to examine the interaction between the bootstrap effect and tearing modes. Magnetic helicity is a topological quantity which is conserved even in turbulent plasma. Computer simulation results of the mean-field Ohm's law are presented which suggest that a completely bootstrapped tokamak may indeed be possible. In a completely bootstrapped tokamak, the tokamak self-maintains its electric current by amplifying an intrinsic internal plasma current due to the tearing modes.



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