## B25 Specific power

By adding all the contributions coming from the above expressions it is possible to write an expression for specific power:

M{PtW" = Pfus (l/"mag + l/"s + l/"cryo + l/"rad) (Bl9)

Upon substituting all expressions derived, we obtain a(kW/kg) = [(l - F )[vd/d + Vth(l - fD)](l - fr) +fr](l + l/Q)

x {(rm/rp)2PSpec(MW/rn3)-l[km + (l - r2p/r2m)ft(t/m3)] +fn x l03(rp/rm) exp[-(rm - rp)/Xn] (B.20)

with km = 2.4(B(T)/l2.5)rm(m)-1 for the case of superconducting magnet technology and km = 2 x l0-3B(T)2 for the case of copper technology.

The simplest limiting case for the above expression is fn = 0 (aneutronic reactions) and fT = 1 (direct propulsion) which yields (with rp = rm; i.e., no shield)

Thus, to obtain specific power in the range 1 kW/kg to 10kW/kg, as specified in Section B.1, the fusion power density for aneutronic reactions must be in the range 1 MW/m3 to 10 MW/m3 times the constant km k 1.

In the case of neutron-producing reactions, it is convenient first to maximize Equation (B.20) with respect to the ratio rp/rm at fixed rm (to minimize the cryoplant plus blanket mass), and then with respect to the ratio TR/TH (assuming the Carnot expression for efficiency r) at the fixed TH, determined by structural material limitations.

Two limiting cases can be singled out, depending on whether (a) the radiator mass or (b) the fusion system mass tends to dominate.

Case a. Large radiator mass (saTR/prad < (rp/rm)2PSpec(MW/m3)/(km+Ps(t/m3))). In this limit the mass budget is dominated by the radiator, and specific power is independent of fusion power density a (kW/kg) k [saT R ]/(103Prad)[( 1 - F)[rf + rth(1 - fn)](1 - fT) +fr\(1 + 1/Q)

x[[ fn(1-rn) + (1 - rth)(1-fn)](1- fT )(1+1/Q)+(1 -raux)/(Qraux)\-1

The radiator temperature reduces to TR = 3/4TH in the limit fD ^ 1, fT ^ 1 (see [Roth, 1989]). Note that the radiator temperature can become larger than the blanket temperature TH for finite values of fT and fD: this result simply means that if the fraction of energy going directly to thrust or recovered by direct electricity conversion is large, there is no need to have thermal electricity conversion and the remaining fraction must be radiated at the highest possible temperature. For a radiator able to radiate 5kW/kg, Equation (B.22) predicts a specific power in the range 1 kW/kg (for fD = fT = 0; i.e., fusion-electric propulsion) to 9 kW/kg (for fD = fT = 0.5, in which only 25% of the power must be radiated). Specific power increases very rapidly as fD and fT increase.

It is thus apparent that fusion-electric propulsion is marginal in terms of specific power.

Note that Equation (B.22) is independent of any parameter related to plasma behavior.

Case b. Small radiator mass (saTR/prad ^ (rp/rm)2Pspec(MW/m3)/(km+ps(t/m3))). In this limit the radiator mass is negligible with respect to reactor mass a(kW/kg) k [(1 - F)mfD + rth(1 - fn )](1 - fT) +fr]

x (1 + 1/Q)(rp/rm)2PSpec(MW/m3)/(km + Ps(t/m3)) (B.23)

with rm = rp + 3A„ ln 10 - Xn ln{2(rm/rp)3(km + Ps)/[f„PSpec(MW/m3)(rp/\n + 1)]}

This solution is a generalization of Equation (B.21) that includes blanket mass. Radiator temperature can now be substantially lower than TH and high-efficiency I can be obtained. For a radiator able to radiate 5 kW/kg (as noted, a conservative value), Equation (B.23) becomes valid for

{fD(1 - ID) + (1- lth)(1- fD)](1- fT)(1 + 1/ß) + (1- raux)/(ßraux)}PSpec(MW/m3)

0 0