A.6 Why bigger tokamaks with larger plasma current are better at fusion?

As is mentioned in Sec. A.4, the beta limit study on JET tokamak shows that the maximal β_t obtained is proportional to I_p∕aB_t0. This means the maximal plasmas pressure obtained is proportional to I_p∕a, i.e.,

(541)

The total plasma energy is given by E ≈⟨p⟩2πRπa², where R is the major radius of the device. Using Eq. (541), we obtain

(542)

Since fusion power is proportional to the plasma energy, the above relation indicates, to obtain larger fusion power, we need bigger tokamaks with larger plasma current.

The reason why larger plasma current is desired can also be appreciated by examining an empirical scaling of the the energy confinement time τ_E given by

(543)

which is proportional to I².

Another fundamental reason for building larger tokamaks is that the energy confinement time τ_E ∼ a²∕χ increases with the machine size, where χ is the heat diffusitivity. In addition, the heat diffusitivity χ decreases with increasing machine size if the diffusitivity satisfies the gyro-Bohm scaling, which is given by

(544)

which is inverse proportional to the machine size a. However, if the diffusitivity satisfies the Bohm scaling, which is given by

(545)

then, the diffusitivity is independent of the machine size. The Bohm diffusitivity χ_B is a∕ρ_s times larger than the gyro-Bohm diffusitivity χ_GB, where ρ_s is the gyro-radius. Heat diffusitivity scaling in the low confinement operation (L mode) in present-day tokamaks is observed to be Bohm or worse than Bohm.