| dc.description |
A study is presented of all quasi-electrostatic instabilities that are inevitable in a confined, inhomogeneous high-temperature plasma.The basic equation for electrostatic waves (E = ∇<sub>χ</sub>) is established starting from the Vlasov equations, by a perturbation method in phase space. Since the domain of stable states is bound by a frontier where the wave growth-rate is zero (marginal modes), the stability problem is reduced to obtaining the marginal modes.A systematic search for the marginal modes has been done both analytically and numerically for the case of a plasma where convective instabilities due to steep temperature gradients are excluded; thus, the plasma distribution function is assumed monotonically decreasing with energy f<sub>0</sub>/U ≤ 0. The only anisotropies considered are those due to a current in the plasma, either diamagnetic or ohmic. The adopted method has the advantage of defining, parametrically, the entire stability domain. The influence on stability of all relevant effects for a high-temperature, low-`beta' plasma, has been studied; favourable or unfavourable curvature of the magnetic lines, finite Larmor radii, electron-ion temperature ratio, ion-cyclotron harmonics, the presence of shear in the magnetic lines of force, the presence of a plasma around the unstable layer, etc.It is found that in a plasma with a sufficient number of Larmor radii in its thickness the instabilities disappear when the shear, defined by a characteristic length L<sub>s</sub>, is sufficiently strong to have everywhereL<sub>s</sub>(∇P<sub>e</sub>/P<sub>i</sub> + P<sub>e</sub>) < 3if the stabilizing effect of the plasma surrounding the unstable layer is not taken into account. Otherwise, the shear required to stabilize the plasma is weaker:L<sub>s</sub>a<sub>i</sub>(∇p/2p)<sup>2</sup> < 1.6(T<sub>i</sub>/T<sub>s</sub>)These conditions are in fact so severe that it appears practically impossible to obtain a plasma both perfectly confined and completely stable; in all configurations a residual turbulence is to be expected. The ensuing anomalous diffusion (pump-out) has been calculated for a hard-core configuration on appropriate phenomenological basis; the expected lifetime for the plasma can be deduced and is found to be the one corresponding to Bohm diffusion, reduced by a factor which is determined by the shape of the marginally stable pressure profile. |
