Some Schemes for Nuclear Propulsion, Part I:
With C. Longmire (LAMS-2186, March 1958)
Part I of this report is a discussion of the proposals made in the preceding report. (Author's note).*
It is intended to present here a qualitative description of certain schemes for nuclear propelled rockets. The ideas sketched in the sequel stem from the schemata proposed by some of us in the past. Various details and technical points were discussed in a Rocket Group which meets weekly in our Laboratory.
The scheme discussed here might be considered as intermediate between the one outlined in report 71 and the ones where the idea is to propel a nuclear rocket by having a gaseous fission reactor operating inside the vehicle.2
C. Longmire and S. Ulam-Internal Explosions
Briefly speaking, we imagine a great number N of very mild explosions taking place in succession. These explosions involve bomb-like assemblies of either metal surrounded by a small amount of high explosive and essentially hydrogenous material or UDk cores. Each of these explosions is supposed to heat the total mass involved only to
* Only Part I is reproduced here, as Part II is by F. Reines. (Eds.)
very moderate temperatures. To fix the ideas we consider temperatures of the order of 3/4 ev, i.e., 9,000°C, although temperatures up to a few ev may be useful. Each of these explosions will involve only several kilograms of active material and several tens of kilograms of hydrogenous material, and therefore the total yield of the order of a few hundreds of kilograms (sic!) of TNT equivalent. These explosions are, properly speaking, "fizzles" resembling burning rather than a true nuclear detonation. One imagines a large chamber with steel walls of roughly paraboloidal shape with the "explosions" taking place at its focus. The chamber may be considered, for the purpose of this discussion, as being evacuated except for the material to be exploded. The linear dimensions of the chamber are large compared to the assembly which is exploding. For orientation, we may assume the diameter of the chamber to be of the order of 4 meters, whereas the diameter of the bomb, together with the enclosing hydrogen, is say of the order of 40 cm. Each of our bombs should be thought of as being in a liquid or solid state before the explosion. This explosion will convert its whole mass into gas which will expand and fill the chamber with high velocity particles impinging on the walls and ultimately escaping from the chamber.
The "bombs" are brought in in rapid succession from a storage chamber and brought to the "nozzle" chamber where they are exploded. Compared to the proposals made in the preceding report the present scheme differs in the following respects: The explosions are of smaller yield. Their number is greater by a factor of 10 or 20. They will be of longer duration and lesser violence, and therefore, by order of magnitude, the individual accelerations given to the body of the rocket in each push will be smaller. Secondly, they are made internally, which allows a greater fraction of mass to be used in imparting the momentum. This, of course, is more than counter-balanced by the greater number of supercritical assemblies that one has to employ. Let
us say from the beginning that the total amount of fissionable material expended will be of the order of a few tons, at least for a first design. This makes it appear, offhand, that the primary use of such rocket motors would be to have large satellites and vehicles for interplanetary travel, rather than for stockpiling in large numbers.
We shall employ the following notations:
N = total number of exploding assemblies Ei i=1 ... N = the energy release in the i-th explosion Mi = the total amount of material exploded mi = the mass of fissionable material in the i-th "bomb" R = the diameter of the nozzle chamber Pi = the pressure on the wall of the nozzle d = the thickness of the wall Ve = the velocity of propellant mass escaping the chamber p = mean molecular weight of the bomb material Ti = the temperature to which the mass Mi is brought as a result of the nuclear reaction Ww = weight of the walls of the paraboloid Wp = weight of the propellant Wa = weight of the structure of housing of the bombs, and injecting mechanisms, instruments and "payload" W = W, + Wp + Ww total weight.
We now give a tentative set of values in c.g.s. units for our quantities. N = 103 mi = ml = 5.104 gms R = 2.102 cm T = 3/4 ev d = 3cm / = 3.
The effective volume V of our paraboloid with a length of 300 cm would be V - R2t = 3.14 x (2.102)2 . 3.102 ~ 4.107 cc. W, -~ 27rRdp =6.3 x 2.102 .3.102 x 3 x 8 -10 tons Wp ~ 103 x 5.104 - 50 tons Wa ~ 10 tons W ~ 70 tons.
The exit velocity ve of the propellant will be sensibly higher than the thermal velocity of our material at the temperature obtained in the nuclear explosion. This is so because of the effects of the recombination of the molecules and ions. If T = 3/4 ev, , = 3, the thermal velocity v is about 6 km/sec., and the final ve about 10 km/sec. The energy Ei of each explosion is then given by E ~ 1/2 mv2 = 1/2 x 5 x 104 1012 = 2.5 x 1016 ergs, about 500 kgs of TNT equivalent. The pressure on the walls will be of the order of P (y - 1) E/V = (.4x2.5x 1016)/(4x 107) ~ 2.5x108 ~250 atmospheres ~4000 lbs/sq.in.
In the first discussion we shall assume that the quantities are independent of i, that is to say, each assembly and explosion have constant characteristics.
The numerical data above represent merely an order of magnitude orientation about the scheme and are, of course, in no way optimal. There are many degrees of freedom in this scheme. Obviously, most of the fissionable material is "wasted" and we could choose our yields Ei within a very wide range of values-also the composition of the hydrogenous material surrounding the bomb and its mass in proportion to the mass of U235 is at our disposal, in a large measure. The geometries of the chamber, etc., seem not to be limited from above by the numbers adopted here.
Speaking qualitatively, the possible advantages of our scheme are as follows:
1. If we admit that the temperature of the material heated by the nuclear explosion is of the order of 1/2 -1 ev, the expansion of this material in the vacuum of the nozzle chamber will convert most of the energy released and initially present in the form of thermal energy to kinetic energy of the particles with the corresponding cooling of the gas. The velocity of the escape of the propellant will be therefore of the order of 10 kilometers per second, that is to say, the velocity of a satellite. For the velocity of the final "payload" to be of this order, one needs only a ratio e between the mass of the propellant and the mass of the installation and instruments, etc.
2. We mentioned a ratio of about 10 between the linear dimensions of the nozzle chamber and those of the exploding assembly. The density of the gas which will fill the chamber before impinging on the walls will be therefore 1/1000 of the original density. This means that the pressure of the wall will be moderate. The tensile strength of the wall of a fixed thickness depends, inversely, linearly on the inner diameter. If we assume that the pressure on the wall is given by the
Bernoulli formula P = 1/2 p (v2 ) --since p depends inversely on the cube of the linear expansion there is obviously a gain by having the walls of given tensile strength far apart. This gain obtains as long as the total weight of the propellant, auxiliary equipment, and the "payload" exceeds sensibly the weight of the walls of the chamber where the explosions take place. Heating by neutrons and gammas becomes even less of a problem when, with the weight of the payload and equipment essentially constant, the chamber is large.
Considerable computational and experimental work seems necessary to provide a design of the above sort. First of all one should try to calculate individual explosions which are to heat the material to be reproducible and as precise as possible. This should be done with the greatest possible economy of the fissionable material. Probably experiments have to be made with actually exploding such assemblies in order to learn about their characteristics. The action of the expanding gas on steel or tungsten covered structures has to be studied in order to understand the erosion of the material by successive explosions of this sort. The velocity of the propellant leaving the chamber has to be calculated--possible benefits from shaping the exit of the nozzle should be studied. One should discuss the possibilities of cooling of the walls by "sweating" if that should be necessary. We have not discussed the problem of "pumping" individual assemblies at a sufficiently fast rate and the concomitant engineering difficulties. At any rate, the problem here involves a shoving in of masses of the order of 50 kilograms each in intervals of about 1/10 sec. The problem of neutron heating should be calculated in detail, also the problem of the residual gas remaining after the (i - 1)th explosion at the time when the i-th explosion is to take place, etc.
It seems likely that a shock absorber between the thrust chamber and the remainder of the missile is desirable, to spread the sharp impulses out over time as well as possible. The number of g's that the main structure has to stand can thus be reduced to a small number.
It appears that steel of average 3 cm thickness will, for our choice of the radius of the wall, contain 4000 lbs/sq.in.
The wall can be coated with tungsten to resist the temperature of the gas accumulating on its surface. The contact of the gas with the wall is of extremely short duration-in a case like the one illustrated above about I millisecond for each explosion, so that heating by conduction is seemingly negligible.
Materials other than steel could be considered for confining the exploding gas, with greater strength for weights than steel.
The main problem is the construction of "economic" bombs giving yields of ~1 ton of TNT equivalent.
We had the benefit of conversation with George Bell on this problem and C. B. Mills is in the process of calculating critical masses and "alphas" for such UDk assemblies.
1. On a Method of Propulsion of Projectiles by Means of External Nuclear Explosions, Part I, Everett and Ulam, September, 1955.
2. T-821, Nuclear Chinese Rockets, C. Longmire, May, 1956.