## Lawson Diagram For Selfsustaining Fusion Burns

Figure B.3. Lawson criterion. j Inptil power (riot 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 + ^th(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)(l - fD )](1 - fr )(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 = [(l - F )[Vd/D + Vth(l - fD)](l - fr) +fr](l + l/Q)Pfus (B.10)

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