(EX/P3-18) Scaling and Modeling Studies of High-Bootstrap-Fraction Tokamaks

**Abstract.** A steady-state tokamak reactor will depend almost entirely on
bootstrap current as a source for the poloidal magnetic field. Examination
of a model for a tokamak with plasma current arising solely from the
bootstrap current finds a steady-state solution to the coupled heat- and
poloidal-flux-diffusion equations. The model uses a gyroBohm heat
diffusivity that depends on the poloidal field, coupling heat diffusion and
poloidal field diffusion physics. The problem is cast in terms of coupled,
nondimensional ODEs and associated eigenvalues. Numerical solution of these
equations yields a rather flat relative q-profile and a triangular
temperature profile. The eigenvalues produce the scaling expressions
T(0) = 1.2^{ . }P^{0.667 . }(R/a)^{0.33} and
I_{p} = 0.23^{ . }n^{0.5 . }P^{0.33}a [P:MW, T:keV, I_{p}:MA, a:m,
n:
10^{19}m^{- 3}]. Experimental plans call for DIII-D and C-Mod
discharges heated by a source with no direct current drive
capability. Extrapolation from DIII-D discharges indicates that
= 3
(required for unity bootstrap fraction) can be attained with MHD stability
if
I_{p} 0.6 MA. *Work supported by U.S. DOE Contracts
DE-AC02-76CH03073, DE-AC03-99ER54463, W-7405-ENG-48.

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*IAEA 2003*