# What exactly sets the scale in Fusion power plants?

In fusion power plants, larger devices are said to achieve fusion more easily, next step tokamaks like DEMO are even larger than ITER. In a quantitative way, what exactly isn't scale invariant in a fusion power plant and why?

To get a self-sustaining (burning) plasma, the triple product of plasma density $$n$$, ion temperature $$T_i$$, and energy confinement time $$\tau_E$$ needs to surpass a certain value: $$n T_i \tau_E > F$$ This triple product, which is often referred to as Lawson criterion, tells us that we have three possibilities to achieve a burning plasma, since there are three factors. Physics, however, taught us that density and temperature are both limited for various reasons (stability, optimum temperature for the fusion process). Optimum values for the Deuterium-Tritium fusion, which is the easiest to achieve, are roughly $$n \approx 10^{20}\,\mathrm{m}^{-3}, \quad T_i=15\,\mathrm{keV}.$$ Increasing those values further creates problems, so we need to get $$\tau_E$$ large. This is basically the time it takes for the energy to "leave" the plasma when the heating processes are switched-off.
Since the energy confinement time is such an important quantity in magnetic confinement fusion, scaling laws had been developed using experimental data from dozens of tokamaks across the world. Doing a regression analysis, the energy confinement scaling can be simplified to $$\tau_E \propto f_H V B^{0.8} P^{-0.6},$$ with $$V$$ the plasma volume, $$B$$ the magnetic field, $$P$$ the applied heating power, and $$f_H$$ a factor characterizing the confinement quality (this is where the so-called H-mode comes into play).