A First Look at 
Fusion-Reactor Control 
A “black-box” approach to the fusion reactor 
predicts over-all control characteristics 
resembling those of a conventional fission reactor 
By M. A. SCHULTZ 
Westinghouse Electric Corporation, Pittsburgh, Pennsylvania 
THE FUSION REACTOR concept has been 
developed to the point where there is 
now enough information to enable dis- 
cussion of some of the associated engi- 
neering problems. For instance, R. F. 
Post’s article ‘‘Controlled Fusion Re- 
search” (1) provides an excellent back- 
ground for speculation as to what a con- 
trolled fusion reactor might eventually 
look like and how it might be expected 
to behave. Although the basic con- 
ceptual problems outlined by Post ap- 
pear to be most formidable, it is quite 
clear that the succeeding engineering 
problems will easily match them in 
complexity. 
Attempts to understand these prob- 
lems can begin by comparing some of 
the problems with currently understood 
fission-reactor problems. The reactor 
control engineer in particular can begin 
to be interested in questions of stability, 
control, and speed of response. 
Reactor stability, in the mind of the 
control engineer, concerns the reactor 
as a whole and as a component in the 
complete plant. Detailed effects, such 
as neutron-flux spatial variations in the 
fission reactor or plasma oscillations in 
the fusion reactor, are of little concern. 
Problems of plasma instabilities that 
affect the basic feasibility of a fusion- 
reactor design [for example, the type 
predicted by Kruskal and Schwarz- 
child (2)] will presumably have been 
solved before the engineer is required to 
design a control and protective system. 
These considerations lead to the 
“‘black-box’’ approach to over-all re- 
actor stability in which no geometry 
need be specified and the performance 
of the ‘‘box” as a controlled power 
generator is given by kinetic equations 
in terms of a few variables. 
Fission-Reactor Example 
The approach used to analyze the 
kinetic behavior of a conventional fis- 
sion reactor is a familiar example of the 
black-box method. The ‘‘black-box”’ 
picture of a simple fission reactor is 
shown in Fig. 1. The kinetic perform- 
ance of such a reactor without tempera- 
ture coefficient is mathematically de- 
scribed by the following well-known 
equations: 
6 
dn bk 8B . 
on pat Mets (1) 
a = By n— VAC (2) 
a 
Neutron 
leakage 
Neutron 
source 5 — 7} BASS 
Reactivity 
control Multiplication| 
FIG. 1. Black-khox representation of 
fission-reactor control problem. k_ is 
reactivity, n is neutron flux and S is 
neutron source 
ee Ton 
—~ leakage 
Fuel 2 Neutrons 
injection He oti] 
Bremsstrahlung 
Magnetic 
tield loss 
FIG. 2. Black-box representation of 
fusion-reactor control problem. a(T)n” 
is reaction rate, T is reaction tempera- 
ture, B is magnetic field and S is fuel 
injection rate 
Equation 1 is a neutron-balance equa- 
tion, and Eq. 2 describes the time be- 
havior of delayed emitter concentra- 
tions. It will be noted that there is no 
concern about time variations in the 
spatial distributions of neutron flux or 
emitter concentrations. The equa- 
tions are concerned rather with how 
the entire box responds as a unit with 
time. From these equations the fre- 
quency response or transfer function, 
relating output to input, can be de- 
rived. An examination of the transfer 
function then allows prediction about 
the stability of the reactor and gives in- 
sight into the general characteristics 
required of an external control system. 
This gross handling of a complex, de- 
tailed subject has been most successful 
for the fission reactor and consequently 
leads one to attempt a similar approach 
for the fusion reactor (see Fig. 3). 
Fusion-Reactor Black Box 
The corresponding ‘‘black box”’ for 
a fusion reactor in which the reaction 
is presumed to be confined by a mag- 
netic field might be that of Fig. 2. 
Several other configurations of black 
boxes can also be made, but at this 
stage it seems more important to illus- 
trate the approach rather than present 
all of the specific concepts. The equa- 
tions and constants describing this box 
follow Post’s notation and graphs. 
Two equations of roughly the same 
form as the fission equations can be 
written for a simple confined plasma 
system: 
— = lenov)ave W 
K p,nkT 
— 0.54 X 10-927”? — 
7(T) 
(3) 
41 
