How hot should the plasma be for nuclear fusion? Regularly we can read success stories like "physicists obtained
a 100 million Celsius plasma and held it for 102 seconds". (These are recent data from the EAST tokamak.)
But what are their aims? What are estimated temperatures and discharge durations for the industrial use of fusion?
 A: One of the major challenges of a fusion reactor will be to generate the conditions for a burning plasma. A burning (self-heated) plasma must generate enough heat from fusion reactions to balance the heat lost through radiation, turbulence, and collisions. This requirement is known as the Lawson criterion and is met when
\begin{equation}
n T \tau_E \geq \frac{12 k_B T^2}{E_{\text{ch}} \langle \sigma v \rangle} \,,
\end{equation}
where $n$ is the plasma density, $T$ is the ion temperature, $E_{\text{ch}}$ is the energy of charged fusion products (e.g. 3.5 MeV for alpha particles from Deuterium-Tritium fusion), $\langle \sigma v \rangle$ is the reactivity, and $\tau_E$ is the so-called energy confinement time (not to be confused with discharge duration). The threshold value of this "triple product" is plotted as a function of temperature below for Deuterium-Tritium (DT) and other fusion reactions (data from Bosch & Hale, Nucl. Fusion, 1992).

For Deuterium-Tritium fuel, the conditions for a burning plasma are most easily met at a temperature of $\mathbf{157}~$million Kelvin (or 13.5 keV). This temperature corresponds to a minimum in the triple product of
\begin{equation}
n T \tau_e \approx 2.79 \times 10^{15}\text{ keV s/cm}^3\,.
\end{equation}
The desired discharge duration is more than 600 seconds for pulsed operation (likely requiring more than one nuclear reactor per plant), or about 1 year for steady-state operation (requiring only one fusion reactor per plant). This shows that the recent results from superconducting tokamaks KSTAR (100 million Kelvin, 20 seconds) and EAST (120 million Kelvin, 102 seconds) are important steps towards a burning plasma. However, the above equation shows that the density $n$ and energy confinement time $\tau_E$ are also needed to determine how close we are to a burning plasma. The highest triple product was achieved in the JT-60 tokamak at $1.53 \times 10^{21} \text{ keV s/cm}^3$ (50% of Lawson). Future devices such as ITER and SPARC plan to achieve burning plasmas.
