Control of the energy balance in a fusion plasma

Abstract

Under appropriate simplifying assumptions, the energy balance in a fusion plasma is described by a set of seven nonlinear first-order ordinary differential equations. These are: an energy-conservation equation for the plasma; an energy-conservation equation for the plasma and the confining magnetic field together; and five particle- conservation equations, one for each ionic species in the plasma. Numerical simulation, using these equations, shows that in certain circumstances the energy balance is unstable. From the steady-state energy-balance equations, it can be shown that, for a given mixture, any equilibrium state of the plasma may be defined by the temperature, density, and volume. It can also be shown that a given set of values of magnetic-field strength, fuel flow rate and particle confinement time is associated with a unique point in temperature-density-volume space. Thus field strength, flow rate, and confinement time are a possible set of control variables. Numerical simulation shows that a proportional-control system using these control variables can stabilize the energy balance, and can transfer the plasma from one equilibrium state to another in a stable manner. Small power overshoots, and somewhat larger temperature overshoots, do occur during transitions between equilibrium states. Response times are typically measured in tens of seconds.