Plasma position control in a tokamak reactor around ignition

Abstract

Plasma position control in a tokamak reactor in the phase approaching ignition is closely related to burn control. If ignited burn corresponds to a thermally unstable situation the plasma becomes sensitive to the thermal instability already in the phase when ignition is approached so that the trajectory in the positionpressure (R, p) space becomes effectively unpredictable. -For example, schemes involving closed cycles around ignition can be unstable in the heating-cooling phases, and the deviations may be cumulative in time. -Reliable plasma control in pressure-position (p, R) space is achieved by beforehand constraining the p, R trajectory rigidly with suitable feedback vertical field stabilization, which is to be established already below ignition. -A scheme in which ignition is approached in a stable and automatic way by feedback stabilization on the vertical field is proposed and studied in detail. -The values of the gain coefficient ensuring stabilization and the associated p and R excursions are discussed both analytically, with a 0-D approximation including non-linear effects, and numerically, with a 1-D code in cylindrical geometry. Profile effects increase the excursions, in particular above ignition.

Ignition and burn control characteristics of thermonuclear plasmas

“…By varying the vertical field during a thermal runaway, the plasma can expand (or compress) adiabaticlly . [40, 41,42,43] For an expansion, the resulting state has lower n, lower T', larger R and larger a. In most circumstances the strong n,T dependence of the alpha particle heating dominates.…”

CIT burn control using auxiliary power modulation

“…The average auxiliary power heating density is defined as the total power absorbed by the plasma, P., divided by the plasma volume. Thus Finally the radiative loss due to Bremsstrahlung is given by 5.3 x 103 Zej n 2 T 1 /2 W 2t') ±= 17,18,21,22, and 23 are now substituted in Eq. 6 and the power balance becomes…”

Localizability of a toroidal burning plasma in the pressure-position space

“…Obviously, to obtain a detailed description of real situations, it is necessary to use 1-D or \\-D codes. In the present paper, as in the previous one [ 1 ], our intention is to establish analytically the conditions for a stable path of the plasma column in the pressureposition space; these conditions then can lead to proper guidelines, on one hand for implementing a stable behaviour of the system in p, R space and on the other hand for a proper formulation of the complete computational treatment of the transport equilibrium problem in the presence of alpha particles.…”

“…The problem of stabilization of the burn and position of the plasma column in an igniting tokamak involves the study of the stability of its motion along well defined trajectories in the space p, R (p being the average pressure and R the major radius of the column) [ 1 ]. In particular, the trajectories to be studied are those crossing the ignition curve p = p m (R) where equilibrium exists between the alpha heating and the losses.…”

“…In particular, the trajectories to be studied are those crossing the ignition curve p = p m (R) where equilibrium exists between the alpha heating and the losses. In the case of an autonomous system and with a zero-dimensional approximation, the problem can be reduced to the discussion of two coupled non-linear differential equations of first order [ 1 ], and the stability can easily be related with simple topological properties of the trajectories relative to the ignition curve and with the sign along the trajectory of a certain quantity, F(p, R) (see Section 2). In a stable situation (including stabilization with a suitable feedback on the vertical field) the ignition curve acts as an attractor of neighbouring states in p, R space.…”