Controlled Thermonuclear Fusion — Question 9

Question 9

Pulse energy gain must be combined with repetition and electrical costs

A hypothetical pulsed experiment releases 1.00 GJ of fusion energy per pulse and consumes .200 GJ of electrical driving energy per pulse. Pulses repeat every 20.0 s. A converter captures only fusion energy at efficiency .400; continuous auxiliary loads are 5.00 MW.

1. Calculate average fusion power and average gross electrical output.

2. Find average net electrical output and the longest pulse interval allowing positive net output if per-pulse energies remain fixed.

Question 9 - Solution

Pulse energy gain must be combined with repetition and electrical costs

(a) Method and calculation

$$\boxed{\overline P_f=1.00\,\mathrm{GJ}/20.0\,\mathrm s=50.0\,\mathrm{MW},\quad\overline P_{\mathrm{gross}}=20.0\,\mathrm{MW}}.$$$$\boxed{\overline P_{\mathrm{drive}}=.200\,\mathrm{GJ}/20.0\,\mathrm s=10.0\,\mathrm{MW}}.$$

(b) Interpretation and further calculation

$$\boxed{\overline P_{\mathrm{net}}=20.0-10.0-5.00=5.00\,\mathrm{MW}}.$$$$\frac{.400(1.00)-.200}{\Delta t}\,\mathrm{GJ}>5.00\,\mathrm{MW}\Rightarrow\boxed{\Delta t<40.0\,\mathrm s}.$$

Physical check

The driving energy is already electrical input; no extra driver-efficiency factor belongs here. A pulse energy ratio is insufficient without repetition rate and continuous loads.