Controlled Thermonuclear Fusion — Question 4

Question 4

Positive plasma gain does not by itself establish net electrical output

A hypothetical plant produces $P_f=500$ MW of fusion power with Q=10. External heating has electrical-to-plasma efficiency $\eta_h=.500$. All fusion and deposited heating power enters a thermal converter of efficiency $\eta_t=.400$. Other electrical loads total 30.0 MW.

1. Calculate gross and net electrical power.

2. At fixed fusion power and efficiencies, derive the minimum Q for positive net electrical power.

Question 4 - Solution

Positive plasma gain does not by itself establish net electrical output

(a) Method and calculation

$$P_h=P_f/Q=50\,\mathrm{MW},\quad\boxed{P_{\mathrm{gross}}=\eta_t(P_f+P_h)=220\,\mathrm{MW}}.$$$$\boxed{P_{\mathrm{net}}=220-50/.500-30=90\,\mathrm{MW}}.$$

(b) Interpretation and further calculation

$$P_{\mathrm{net}}=\eta_tP_f-P_{\mathrm{aux}}-\frac{P_f}{Q}(1/\eta_h-\eta_t)>0.$$$$\boxed{Q>\frac{P_f(1/\eta_h-\eta_t)}{\eta_tP_f-P_{\mathrm{aux}}}=\frac{800}{170}=4.70588}.$$

Physical check

The accounting explicitly recovers deposited heating as heat. Converter output is offset by heating electricity and auxiliary loads; plasma Q alone omits these costs.