You can read all about the (unclassified) details of their internal construction and mechanism here.
Occasionally you will find a fusion weapon referred to as a "Solar-Phoenix" or a "Bethe-cycle" weapon. This is a reference to the nuclear scientist Hans Bethe and the Bethe-Weizsäcker or carbon-nitrogen cycle which powers the fusion reaction in the heart of stars heavier than Sol.
 A "neutron bomb" is what you call an "enhanced radiation bomb". They are specially constructed so more of the bomb's energy is emitted as neutrons instead of x-rays. This means there is far less blast to damage the buildings, but far more lethal neutron radiation to kill the enemy troops. Conventional nuclear warheads typically release 5% of the energy as neutrons, but in neutron bombs it is more like 40%. Neutron energy is higher as well: 14 MeV instead of the conventional 1 to 2 MeV.
A 1 kiloton neutron bomb will irradiate anybody unfortunate enough to be at a range of 900 meters with 80 Grays of neutrons. According to dosages set by the US military, this is high enough to instantly send the victim into a coma, with certain death to follow within 24 hours due to damage to the central nervous system. The LD50 dose is at a range of between 1350 and 1400 meters.
- Neutron activation of the steel girders of buildings would render them unsafe. Which was one of the selling points of neutron bombs: the buildings could be immediately used by an advancing army, once you removed all the dead enemy soliders.
- Armored fighting vehicles provide enemy soldiers with a surprisingly high protection of neutron radiation, and can be easily increased. Since all spacecraft include radiation shielding from solar storms and galactic cosmic rays, this will drastically reduce the effect of neutron bombs. Spacecraft with nuclear propulsion will try to aim their shadow shields at the neutron bomb for added protection.
- Enemy soldiers can also find high amounts of protection by sheltering inside buildings with 12 inch concrete walls and ceiling, or in a cellar under 24 inches of damp soil. Both will reduce the radiation exposure by a factor of 10.
- Neutron bomb ordinance requires maintenance, since one of the components is Tritium with its annoyingly short half-life of 12.32 years. This means that every few years the neutron bombs will have to be opened up and have their tritium replaced.
You will also occasionally find references to a nasty weapon called a "cobalt bomb". This is technically termed a "salted bomb". It is not used for spacecraft to spacecraft combat, it is only used for planetary bombardment. They are enhanced-fallout weapons, with blankets of cobalt or zinc to generate large quantities of deadly radioactive cobalt or zinc isotope dust. The warhead proper will probably be a neutron bomb: since the more neutrons emitted by the warhead, the more of the blanket will be transmuted into radioactive isotopes.
Please note the difference between a "salted bomb" and a "dirty bomb".
A dirty bomb is an ordinary chemical explosive in a small bag of ground-up radioactive material. The chemical explosion merely sprays the powdered plutonium or whatever all over the city block. Strictly a terrorist weapon, it is pretty worthless as a military weapon.
A salted bomb is a nuclear warhead designed to make a nuclear explosion that will spread millions of bagfulls of fallout that is thousands of times more radioactive that mere powdered plutonium over a quarter of a continent.
Term comes from metaphor "sowing the Earth with salt".