Shrey,
Low Z materials work well as elastic reflectors, graphite, beryllium (cough).
Presumably these are relatively cool neutrons?
More energetic neutrons will be better scattered by denser metals, tungsten, steels, etc.
What sort of energies are you getting?
For thermal neutrons, the lowest cost reflector is simply water-- but since your fusor produces high-energy neutrons, I suggest lead (bricks, or melted and then caste into a cylinder/sphere around your fusor) as the lowest cost option. If you have a large budget, tungsten is probably the most effective reflector for high energy neutrons that you can reasonably get your hands on. Pure tungsten is 19 grams/cc, the densest metal you can find at reasonable cost (pure uranium metal is also 19 g/cc but you won't be able to get that unless you work at a weapons lab or a national lab with special security). Usually you would use Densalloy, a mixture of mostly tungsten with a small fraction of other metals alloyed to make it (sort of) machineable. Pure tungsten is almost impossible to cut or machine, whereas Densalloy is merely extremely difficult/expensive to cut or machine. They euphemistically call Densalloy "machineable" tungsten... well, good luck finding one of the few machinists in the country who knows how to work with that stuff. Osmium, Iridium, gold and platinum are denser than Densalloy but they are not cost-effective, obviously.
For a mid-budget range between lead and tungsten, you might consider a heavy metal reflector made of pure bismuth metal. The melting point of bismuth is 100 celsius lower than lead (260 Celsius vs 360 Celsius). Bismuth is slightly less dense than lead, but it may have a higher (N,2N) neutron production rate at your fusor energy (I assume you are using deuterium-deuterium reaction to produce 2.5 MeV neutrons?) than lead, which could be useful if you want to maximum neutron flux.
As you know, the best possible reflector only reflects 50% of neutrons, unless you are talking about a "grazing incidence" neutron reflector (neutron mirror) for a monoenergetic cold neutron beam-- not something you are likely to produce from a fusor source.
Also, it is definitely cost-effective to have someone model your reflector options with a Monte Carlo code such as MCNPX before you invest several thousand dollars in a lead reflector (or about 10x as much for a tungsten reflector) to see what neutron flux improvement you will get at what cost. I could do that for you...
I think, that the alternative way is a lead - graphite gives good result at the least cost.
Is it possible to use layers of boron or boronised steel for the absorption of the neutrons, after they have been moderated?
Nikolaos, If you have a laboratory fast neutron source (for example, radium-beryllium source, proton-beam+lithium source, or deuterium-deuterium fusion source) and you want to shield users or equipment from neutron radiation, the usual procedure for inexpensive shielding is to combine boron within a thick layer of inexpensive moderator material, then wrap the neutron source and boron+moderator in a thin layer of dense shielding to stop gamma rays. For example 2.5 MeV D-D fusion neutrons are easily attenuated by a 10-cm-thick layer of polyethylene (or water) doped with 5% boron by mass, surrounded by a layer 4mm thick of lead or 1 cm thick of steel to stop the 477 keV gamma rays produced when the boron captures the moderated neutrons. You can buy 5% borated polyethylene from several neutron shielding suppliers, there are at least two in the United States and probably at least two in Europe or the UK. Or you can make your own borated moderator by dissolving boric acid at 5% concentration in water-- be careful! make sure your container has a corrosion-resistant interior surface! Alternatively, I have heard of a colleague who mixed a dry boron compound (perhaps Borax soap/bleach?) into several hundred liters of Paraffin Wax to make an inexpensive borated moderator. Of course Borax does not dissolve in Paraffin, so it was difficult to achieve good uniformity, but it was much cheaper than buying the borated polyethylene and safer than using boric acid dissolved in water.
If your budget is larger, you can suppress most of the 477 keV gamma rays by using lithium instead of boron. The safest form of lithium available in large quantities is lithium fluoride salt, though it is expensive. On of the two natural lithium isotopes has a large thermal neutron capture cross-section, and releases very few gamma rays when capturing a neutron. This way you can avoid some of the lead/steel shielding and/or reduce the gamma ray background radiation. Since natural lithium has on average a smaller cross-section than boron, you will need a higher density of the lithium and probably a thicker moderator than the borated polyethylene which is usually used for neutron shielding.
You can use nuclear grade beryllium fluoride, lithium fluoride, sodium fluoride.... for the forth generation Molten salt reactor.
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