Hmm. What is the correct shape?
The "correct" shape for an implosion bomb is usually a sphere, this is dictated by basic solid geometry. With a sophisticated implosion lens system other shapes can be collapsed sufficiently quickly for a chain reaction; some artillery shell delivered fission weapons use a teardrop shaped pit
1.
Usually the pit is constructed by casting or machining Plutonium elements and assembling them
2 into a hollow sphere which is surrounded by the implosion lenses, carefully machined pieces of explosives that are detonated in a sequence to compress the pit sufficiently so that neutrons released by spontaneous fission will tend to strike other nuclei and induce fission, leading to an uncontrolled chain reaction.
Really, the basic idea isn't difficult a bright undergraduate could work out the details.
How much of fissile material is needed?
Depends on the material used, its purity and the sophistication of the design. For Pu
239 containing less than 7% Pu
240 about 5.5kg without tamping or boosting. With a good design less than one kilogram.
There are many other fissile (as opposed to fissionable) isotopes;
Pu
241, U
233, Pu
238, U
235, Pu
240, Np
237, Cm
243, Pu
242, Cf
251, Am
241
All the whilst avoiding predetonation.
Only generally a problem with gun-barrel designs; spherical implosion designs require a complex series of actions to occur, in sequence, to function.
What is the relationship between the required velocity of the bullit/implosion, the rate of spontanious fission , the ambient neutron level and the likelyhood of predetonation?
This again depends on the materials or mix of materials used in the pit and is generally complex.
For example a Plutonium gun-barrel bomb is possible but not practical as the presence of Pu
240 as an impurity at any significant level leads to too great a level of spontaneous fission and thus would cause a pre-detonation ('fizzle'). However using Uranium this is less of a problem as the most common impurity in HEU (U
238) isn't fissile using thermal neutrons. Nor is this a significant concern with implosion designs.
On a related note, how can we ensure that the chain reaction starts at the moment of maximum supercriticallit?. What device is needed to achieve that?
I'm not sure what you mean by this.
What is the required precission in symmetry for an implosion type of device? How do we achieve such a level of symmetry?
The fissile material is imploded by a number (typically 32 to ~120) of lenses made from explosives with different detonation velocities and detonated either simultaneously or at microsecond intervals depending o the design.
Methinks making a nuclear weapon is quite a bit more difficult than that is popularly believed.
No not really. As I said a bright undergrad with access to a good library and CAD software could to better than the Manhattan project; the science has been done.
You'd need specific engineering skills for working with the Plutonium (and Beryllium and Polonium is used) and the explosives.
1 The US W48 for example. This "linear implosion" allows for smaller diameter weapons.
2 Carefully. Very, very carefully.