# Lawson Diagram For Selfsustaining Fusion Burns

Figure B.3. Lawson criterion. Figure B.4. Generic fusion rocket geometry (from [Santarius and Logan, 1998]).

j Inptil power (not Indeed In mode!) '

Figure B.4. Generic fusion rocket geometry (from [Santarius and Logan, 1998]).

efficiency vd) or by thermal conversion (for the remaining part) with an efficiency vth into electrical power Pel = [vd/d + Vth(1 -/d)](1 - fr)(Pfus + Paux).

A certain fraction of this power must be used for auxiliary systems. If the efficiency for auxiliary power generation is vaux, such a fraction is given by Paux/vaux = FPel, with F being the re-circulating power fraction. Figure B.5. Idealized power flow in a fusion rocket.

FPel

Figure B.5. Idealized power flow in a fusion rocket.

The fusion gain Q can then be related to F, vth, and vaux by

The waste power to be radiated to space is therefore

Prad = f (1 - Vd) + (1 - Vth)(1 - fD )](1 - fT )(Pfus + Paux) + (1 - Vaux) Paux/Vaux

If the reactor is self-sustaining (Paux = 0) then the re-circulating fraction vanishes. In practice this does not even occur for Paux = 0, since part of the electric power must feed the control system, the cryogenic system, and so on. Assuming the realistic value F = 20% and 50% for both efficiencies, values of Q in the range Q = 20-30 are necessary for efficient energy production.

From the above expressions the power available for thrust is finally

Pthrust = [(1 - F)[vDfD + Vth(1 - fD)](1 - fT) + M1 + 1/Q)Pfus (B.10) 