Some more on the gun type design and how it may possibly fit into the NASR, who's payload is rated at 400 KG. Although an SRBM its dimensions are very close to a 300 mm tube artillery.
18.104.22.168 Gun Assembly
This was the first technique to be seriously proposed for creating fission explosions, and the first to be successfully developed. The first nuclear weapon to be used in war was the gun-type bomb called Little Boy, dropped on Hiroshima. Basic gun assembly is very simple in both concept and execution. The supercritical assembly is divided into two pieces, each of which is subcritical. One of these, the projectile, is propelled into the other, called the target, by the pressure of propellant combustion gases in a gun barrel. Since artillery technology is very well developed, there are really no significant technical problems involved with designing or manufacturing the assembly system.
The simple single-gun design (one target, one projectile) imposes limits on weapon, mass, efficiency and yield that can be substantially improved by using a "double-gun" design using two projectiles fired at each other. These two approaches are discussed in separate sections below. Even more sophisticated "complex" guns, that combine double guns with implosion are discussed in Hybrid Assembly techniques.
Gun designs may be used for several applications. They are very simple, and may be used when development resources are scarce or extremely reliability is called for. Gun designs are natural where weapons can be relatively long and heavy, but weapon diameter is severely limited - such as nuclear artillery shells (which are "gun type" weapons in two senses!) or earth penetrating "bunker busters" (here the characteristics of a gun tube - long, narrow, heavy, and strong - are ideal).
Single guns are used where designs are highly conservative (early US weapon, the South African fission weapon), or where the inherent penalties of the design are not a problem (bunker busters perhaps). Double guns are probably the most widely used gun approach (in atomic artillery shells for example).
22.214.171.124.1 Single Gun Systems
We might conclude that a practical limit for simple gun assembly (using a single gun) is a bit less than 2 critical masses, reasoning as follows: each piece must be less than 1 critical mass, if we have two pieces then after they are joined the sum must be less than 2 critical masses.
Actually we can do much better than this. If we hollow out a supercritical assembly by removing a chunk from the center like an apple core, we reduce its effective density. Since the critical mass of a system is inversely proportional to the square of the density, we have increased the critical mass remaining material (which we shall call the target) while simultaneously reducing its actual mass. The piece that was removed (which will be called the bullet) must still be a bit less than one critical mass since it is solid. Using this reasoning, letting the bullet have the limiting value of one full critical mass, and assuming the neutron savings from reflection is the same for both pieces (a poor assumption for which correction must be made) we have:
M_c/((M - M_c)/M)^2 = M - M_c
where M is the total mass of the assembly, and M_c is the standard critical mass. The solution of this cubic equation is approximately M = 3.15 M_c. In other words, with simple gun assembly we can achieve an assembly of no more than 3.15 critical masses. Of course a practical system must include a safety factor, and reduce the ratio to a smaller value than this.
The weapon designer will undoubtedly surround the target assembly with a very good neutron reflector. The bullet will not be surrounded by this reflector until it is fired into the target, its effective critical mass limit is higher, allowing a larger final assembly than the 3.15 M_c calculated above.
Looking at U-235 critical mass tables for various candidate reflectors we can estimate the achievable critical mass ratios taking into account differential reflector efficiency. A steel gun barrel is actually a fairly good neutron reflector, but it will be thinner and less effective than the target reflector. M_c for U-235 (93.5% enrichment) reflected by 10.16 cm of tungsten carbide (the reflector material used in Little Boy) is 16.5 kg, when reflected by 5.08 cm of iron it is 29.3 kg (the steel gun barrel of Little Boy was an average of 6 cm thick). This is a ratio of 1.78, and is probably close to the achievable limit (a beryllium reflector might push it to 2). Revising Eq. 126.96.36.199.1-1 we get:
M_c/((M - (1.78 M_c))/M)^2 = M - (1.78 M_c)
which has a solution of M = 4.51 M_c. If a critical mass ratio of 2 is used for beryllium, then M = 4.88 M_c. This provides an upper bound on the performance of simple gun-type weapons.
Some additional improvement can be had by adding fast neutron absorbers to the system, either natural boron, or boron enriched in B-10. A boron-containing sabot (collar) around the bullet will suppress the effect of neutron reflection from the barrel, and a boron insert in the target will absorb neutrons internally thereby raising the critical mass. In this approach the system would be designed so that the sabot is stripped of the bullet as it enters the target, and the insert is driven out of the target by the bullet. This system was apparently used in the Little Boy weapon.
Using the M_c for 93.5% enriched U-235, the ratio M/M_c for Little Boy was (64 kg)/(16.5 kg) = 3.88, well within the limit of 4.51 (ignoring the hard-to-estimate effects of the boron abosrbers). It appears then that the Little Boy design (completed some six months before the required enriched uranium was available) was developed with the use of >90% enrichment uranium in mind. The actual fissile load used in the weapon was only 80% enriched however, with a corresponding WC reflected critical mass of 26.5 kg, providing an actual ratio of 64/26.5 = 2.4.
The mass-dependent efficiency equation shows that it is desirable to assembly as many critical masses as possible. Applying this equation to Little Boy (and ignoring the equation's limitations in the very low yield range) we can examine the effect of varying the amount of fissile material present:
1.05 80 kg
1.1 1.2 tons
1.2 17 tons
1.3 78 tons
1.4 220 tons
1.5 490 tons
1.6 930 tons
1.8 2.5 kt
2.0 5.2 kt
2.25 10.5 kt
2.40 15.0 kt LITTLE BOY
2.5 18.6 kt
2.75 29.6 kt
3.0 44 kt
If its fissile content had been increased by a mere 25%, its yield would have tripled.
The explosive efficiency of Little Boy was 0.23 kt/kg of fissile material (1.3%), compared to 2.8 kt/kg (16%) for Fat Man (both are adjusted to account for the yield contribution from tamper fast fission). Use of 93.5% U-235 would have at least doubled Little Boy yield and efficiency, but it would still have remained disappointing compared to the yields achievable using implosion and the same quantity of fissile material.
188.8.131.52.2 Double Gun Systems
Significant weight savings a possible by using a "double-gun" - firing two projectiles at each other to achieve the same insertion velocity. With all other factors being the same (gun length, projectile mass, materials, etc.) the mass of a gun varies with the fourth power of velocity (doubling velocity requires quadrupling pressure, quadrupling barrel thickness increases mass sixteen-fold). By using two projectiles the required velocity is cut by half, and so is the projectile mass (for each gun). On the other hand, to keep the same total gun length though, the projectile must be accelerated in half the distance, and of course there are now two guns. The net effect is to cut the required mass by a factor of eight. The mass of the breech block (which seals the end of the gun) reduces this weight saving somewhat, and of course there is the offsetting added complexity.
A double gun can improve on the achievable assembled mass size since the projectile mass is divided into two sub-critical pieces, each of which can be up to one critical mass in size. Modifying Eq. 184.108.40.206.1-1 we get:
M_c/((M - 2M_c)/M)^2 = M - 2M_c
with a solution of M = 4.88 M_c.
Taking into account the effect of differential reflector efficiency we get mass ratios of ratios of 3.56 (tungsten carbide) and 4 (beryllium) which give assembled mass size limits of M = 7.34 M_c and M = 8 M_c respectively.
Another variant of the double gun concept is to still only have two fissile masses - a hollow mass and a cylindrical core as in the single gun - but to drive them both together with propellant. One possible design would be to use a constant diameter gun bore equal to the target diameter, with the smaller diameter core being mounted in a sabot. In this design the target mass would probably be heavier than the core/sabot system, so one end of the barrel might be reinforced to take higher pressures. Another more unusual approach would be to fire the target assembly down an annular (ring shaped) bore. This design appears to have been used in the U.S. W-33 atomic artillery shell, which is reported to have had an annular bore.
These larger assembled masses give significantly more efficient bombs, but also require large amounts of fissile material to achieve them. And since there is no compression of the fissile material, the large efficiency gains obtainable through implosive compression is lost. These shortcomings can be offset somewhat using fusion boosting, but gun designs are inherently less efficient than implosion designs when comparing equal fissile masses or yields.
220.127.116.11.3 Weapon Design and Insertion Speed
In addition to the efficiency and yield limitations, gun assembly has some other significant shortcomings:
First, guns tend to be long and heavy. There must be sufficient acceleration distance in the gun tube before the projectile begins insertion. Increasing the gas pressure in the gun can shorten this distance, but requires a heavier tube.
Second, gun assembly is slow. Since it desirable to keep the weight and length of the weapon down, practical insertion velocities are limited to velocities below 1000 m/sec (usually far below). The diameter of a core is on the order of 15 cm, so the insertion time must be at least a 150 microseconds or so.
In fact, achievable insertion times are much longer than this. Taking into account only the physical insertion of the projectile into the core underestimates the insertion problem. As previously indicated, to maximize efficiency both pieces of the core must be fairly close to criticality by themselves. This means that a critical configuration will be achieved before the projectile actually reaches the target. The greater the mass of fissile material in the weapon, the worse this problem becomes. With greater insertion distances, higher insertion velocities are required to hold the probability of predetonation to a specified value. This in turn requires greater accelerations or acceleration distances, further increasing the mass and length of the weapon.
In Little Boy a critical configuration was reached when the projectile and target were still 25 cm apart. The insertion velocity was 300 m/sec, giving an overall insertion time of 1.35 milliseconds.
Long insertion times like this place some serious constraints on the materials that can be used in the bomb since it is essential to keep neutron background levels very low. Plutonium is excluded entirely, only U-235 and U-233 may be used. Certain designs may be somewhat sensitive to the isotopic composition of the uranium also. High percentages of even-numbered isotopes may make the probability of predetonation unacceptably high.
The 64 kg of uranium in Little Boy had an isotopic purity of about 80% U-235. The 12.8 kg of U-238 and U-234 produced a neutron background of around 1 fission/14 milliseconds, giving Little Boy a predetonation probability of 8-9%. In contrast to the Fat Man bomb, predetonation in a Little Boy type bomb would result in a negligible yield in nearly every case.
The predetonation problem also prevents the use of a U-238 tamper/reflector around the core. A useful amount of U-238 (200 kg or so) would produce a fission background of 1 fission/0.9 milliseconds.
Gun-type weapons are obviously very sensitive to predetonation from other battlefield nuclear explosions. Without hardening, gun weapons cannot be used within a few of kilometers of a previous explosion for at least a minute or two.
Attempting to push close to the mass limit is risky also. The closer the two masses are to criticality, the smaller the margin of safety in the weapon, and the easier it is to cause accidental criticality. This can occur if a violent impact dislodges the projectile, allowing it to travel toward the target. It can also occur if water leaks into the weapon, acting as a moderator and rendering the system critical (in this case though a high yield explosion could not occur).
Due to the complicated geometry, calculating where criticality is achieved in the projectile's travel down the barrel is extremely difficult, as is calculating the effective value of alpha vs time as insertion continues. Elaborate computation intensive Monte Carlo techniques are required. In the development of Little Boy these things had to be extrapolated from measurements made in scale models.
Once insertion is completed, neutrons need to be introduced to begin the chain reaction. One route to doing this is to use a highly reliable "modulated" neutron initiator, an initiator that releases neutrons only when triggered. The sophisticated neutron pulse tubes used in modern weapons are one possibility. The Manhattan Project developed a simple beryllium/polonium 210 initiator named "Abner" that brought the two materials together when struck by the projectile.
If neutron injection is reliable, then the weapon designer does not need to worry about stopping the projectile. The entire nuclear reaction will be completed before the projectile travels a significant distance. On the other hand, if the projectile can be brought to rest in the target without recoiling back then an initiator is not even strictly necessary. Eventually the neutron background will start the reaction unaided.
A target designed to stop the projectile once insertion is complete is called a "blind target". The Little Boy bomb had a blind target design. The deformation expansion of the projectile when it impacted on the stop plate of the massive steel target holder guaranteed that it would lodge firmly in place. Other designs might add locking rings or other retention devices. Because of the use of a blind target design, Little Boy would have exploded successfully without the Abner initiators. Oppenheimer only decided to include the initiators in the bomb fairly late in the preparation process. Even without Abner, the probability that Little Boy would have failed to explode within 200 milliseconds was only 0.15%; a delay as long as one second was vanishingly small - 10^-14.
Atomic artillery shells have tended to be gun-type systems, since it is relatively easy to make a small diameter, small volume package this way (at the expense of large amounts of U-235). Airbursts are the preferred mode of detonation for battlefield atomic weapons which, for an artillery shell travelling downward at several hundred meters per second, means that initiation must occur at a precise time. Gun-type atomic artillery shells always include polonium/beryllium initiators to ensure this.