Scaling dimensionally similar tokamak discharges to ignition

The tokamak operates in a variety of confinement regimes suggesting there may be several transport mechanisms in combination. The detailed parametric dependence of each is likely to be very complicated. However, it can be argued that all plasma diffusion mechanisms can be divided into the extremes of gyro-Bohm (gB) or Bohm (B) types depending on their scaling with ion gyroradius rho sub s relative to the minor radius a: rho sub s a. These correspond to turbulent diffusion processes with short or long step sizes scaled to rho sub s or a, respectively. The local diffusivities and confinement times can be written as D sub gB = (c sub s/a) rho sub s sup 2 F sub gB or D sub B = c sub s rho sub s F sub B and tau sub gB = B sup -1 (rho sub s/a) sup -3 bar F sub gB or tau sub B = B sup -1 (rho sub s/a) sup -2 bar F sub B, respectively. The form factors are possibly complicated functions of the dimensionless parameters associated with geometry, atomic and profile parameters, and the plasma parameters collisionality (cflx nu) (proportional to) nu a/c sub s and beta. Discharges with all these dimensionless parameters including rho sub s/a the same would have tau (proportional to) B sup -1 and could be called dimensionally identical in their transport properties. It is well known that isolating the dependence on the dimensionless variables imposes a single constraint on the scaling of tau with respect to machine variables. It is observed that while dimensionally identical discharges cannot be scaled to ignition, existing and proposed ignition regime tokamak discharges can have all these dimensionless parameters the same except rho sub s/a. Such discharges are called dimensionally similar and focus on the scalings with respect to rho sub s/a.