The coupling between radial motion and temperature fluctuations of an ignited D-T tokamak plasma is studied in terms of a one-dimensional transport model. The energy balance equations are linearized about the thermal equilibrium (i.e. ignition) point and an eigenvalue analysis is used to determine the growth rate of perturbations. If the density dynamics is relatively slow, it is found that there is, at most, one growing eigenmode. The growth rate of temperature perturbations and the extent of radial movement depend upon a parameter ηr which describes the elasticity of radial motions (ηr = T/R dR/dT, where R is the major radius and T is the plasma temperature) . A simple MHD model is used to determine the dependence of ηr upon the vertical field index (η = - R/BvdBv/dR) and the poloidal beta. The implications of different empirical scaling laws for the electron energy confinement time are examined. Similar values of ηr (ηr ∼ 0.2) can be obtained for representative ETF/INTOR and ignition test reactor (ITR) parameters. For ηr ∼ 0.2 the effect of radial motion is to reduce the central ion temperature needed for thermal stability from ∼ 50 to ∼ 35 keV if the electron energy confinement time scales as τe ∼ na2; at lower temperatures (central ion temperatures ∼ 10 – 20 keV) , the thermal runaway time is increased by a factor ∼ 2 to 3. It is pointed out that if the plasma edge is determined by some type of limiter at the midplane, small temperature fluctuations can significantly change the plasma minor radius; active burn control may be needed in some reactor designs to prevent unacceptably large radial movement in addition to providing constant plasma pressure and temperature.
Energy balance instability of a plasma in the thermonuclear reactor