Wikipedia 10K Redux by Reagle from Starling archive. Bugs abound!!!

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There are many different types of ways to accelerate craft in space.
Below is a summary of some of the more popular, proven technologies.

''' Solid '''

The first rockets made by the Chinese used gunpowder, and
until this century all rockets used some form of solid or
powdered propellant. Solid rockets are considered to be safe and
reliable; these kinds of rockets have been used for so long that
engineers have a very good understanding of them.

One of the many drawbacks to solid rocket systems is that once
they've been ignited, they can't be turned off. That is why they
aren't commonly used in satellites; satellites need rockets that
can be fired multiple times (or ''pulsed''.)

''' Hybrid '''

A hybrid propulsion system is composed of solid fuel and liquid or gas
oxidizer, typically.  These systems are superior to solid propulsion
systems because of safety, throttling, restartability, stability,
and environmental cleanliness.  Hybrid systems are more complex than
solids, though, and more expensive.  

''' Monoprop '''

Most familiar combustible chemicals (gasoline, alcohol, wood, natural gas) 
require oxygen to ignite and burn, but there are some unique chemical compounds that
burn by themselves - no oxygen required! This is because the combined chemicals, when energized, "reduce," or change in ionic state by reacting with each other, as opposed to an outside oxidant.  The most commonly used monopropellant is ''hydrazine'' (N2H4), a chemical which is characterized as "strongly reducing".

Rocket scientists long ago realized the usefulness of monopropellant
chemicals for satellite propulsion. Because only one chemical is
used, the system is very simple, and thus very cheap.
Unfortunately, monopropellants are not nearly as efficient as the
other propulsion technologies. Engineers choose monopropellant
systems when the satellite's propulsion needs are not very great.
If the propulsion system is going to be heavily used, such as on
a geosynchronous satellite or an interplanetary spacecraft, other
technologies are used.

''' Biprop '''

Systems that use both a propellant and an oxidizer are called
bipropellant systems. Bipropellant systems are more efficient
than monopropellant systems, but they tend to be more complicated
because of the extra hardware components needed to make sure the
right amount of propellant gets mixed with the right amount of
oxidizer (this is known as the ''mixture ratio''.) 

''' Dual mode propulsion '''

Dual mode propulsion systems combine the high efficiency of biprop with
the reliability and simplicity of monoprop systems.  Dual mode systems
are either hydrazine/N2O4, or MMH/peroxide (the former is much more
common).  Typically, this system works as follows:  During the initial
high-impulse orbit-raising manuevers, the system operates in a
bipropellant fashion, providing high thrust at high efficiency; when it
arrives on orbit, it closes off either the fuel or oxidier, and conducts
the remainder of its mission in a simple, predictable monopropellant

''' Resistojet '''

A resistojet can be thought of as a "space heater attached to a water
hose".  Of course, it's much more sophisticated than that!  But it is a
good analogy, because it emphasizes the two characteristic parts of the
system:  A source of heat produced by electricity through some sort of a
resistor, and a source of (typically non-reactive) fluid.

Resistojets have been flown in space, and do well in situations where
energy is much more plentiful than mass, and where propulsion efficiency
needs to be reasonably high but low-thrust is acceptable.

''' Arcjet '''

Arcjets are a form of electric propulsion, whereby an electrical
discharge (arc) is created in a flow of propellant (typically hydrazine
or ammonia).  This imparts additional energy to the propellant, so that
one can extract more work out of each kilogram of propellant, at the
expense of increased power consumption and (usually) higher cost.  Also,
the thrust levels available from typically used arcjet engines are very
low compared with chemical engines.

''' Hall Effect Thrusters (HETs) '''

Also known simply as ''plasma thrusters'', HETs use the
Hall Effect to accelerate ions to produce thrust. A varient
called stationary plasma thruster (SPT) has been used by the
Russians for stationkeeping for many years and will be used on
Western satellites soon. 

One problem with HETs is that their plumes diverge quickly and
thus can impinge on other spacecraft parts leading to thermal and
contamination problems.

''' Ion Thruster '''

Of all the electric thrusters, ion engines have been the most
seriously considered commercially and academically. Ion engines
use accelerated beams of ions for propulsion. 

Ion engines are best used for missions requiring very high
delta-V's (the overall change in velocity, taken as a single value), interplanetary missions, for example. This is because
the more performance required of the propulsion system, the
faster a high efficiency system like ion engines will pay off.

NASA has developed an ion engine called NSTAR for use in their
interplanetary missions. Hughes has developed the XIPS (Xenon Ion
Propulsion System) for performing stationkeeping on geosynchronous

''' Magnetoplasmadynamic (MPD) Thrusters '''

Thrusters that use the Lorentz force (a force exerted on charge particles by magnetic and electrical fields in combination) are called magnetoplasmadynamic (or MPD) thrusters. MPD thruster technology has been explored academically, but commercial interest has been

MPD thrusters can be run in a steady state fashion or in a
pulsed mode.

''' Pulsed plasma thruster (PPT) '''

Pulsed plasma thrusters use an arc of electric current through a
solid propellant (almost always teflon), to produce a quick and highly
efficient and dependable burst of impulse.  PPT's are great for attitude
control, and for main propulsion on particularly small spacecraft (those
in the hundred-kilogram or less category).  

-- Added above article.  BryceHarrington