Plasma Power Balance
The accounting of heating and loss terms that determines whether a plasma sustains its temperature.
The global balance
At steady state, the power flowing into the plasma equals the power flowing out. Written per unit volume and integrated over the plasma, the balance is:
P_alpha + P_aux + P_ohmic = P_transport + P_brems + P_cyclotron + P_lineOn the left, alpha-particle self-heating (charged fusion products), external auxiliary heating, and ohmic heating from the plasma current. On the right, conducted and convected transport losses, plus radiation: bremsstrahlung, cyclotron, and impurity line radiation.
The transport term
The dominant loss is usually transport, written as the stored thermal energy W divided by the confinement time: P_transport = W / tau_E. This links power balance directly to confinement scaling and to the Lawson criterion.
The gain factor Q
The fusion gain Q is total fusion power divided by external heating power. Ignition (Q infinite) is when alpha heating alone balances losses. Break-even is Q = 1. The Hyperion breeder design targets a plasma Q of 3.424 with 88.7 MW of fusion power at its design point.
How it is solved numerically
- Couple the balance to the radial transport equations so profiles and losses are self-consistent
- Evaluate radiation terms from local n, T, and impurity fractions
- Iterate auxiliary power until the target temperature or Q is reached
The alpha-heating term makes the system nonlinear and potentially thermally unstable: more temperature yields more fusion yields more heating. Operating points must sit on a stable branch, which is checked by the sign of the derivative of net power with respect to temperature.