Star Trek fans will quickly point out that Enterprise and Voyager are propeled using engines fueled by antimatter. Far from being unrealistic, research at Penn state University and NASA Advanced Space Transportation Program (ASTP) is ongoing in order to create the next generation of thrusters utilizing antimatter.

To date, the highest amount of energy can be produced by annihilating antimatter with matter. Chemical reactions at best can provide 1x10^7 joules/kg, nuclear fision 8x10^13 j/kg, and nuclear fusion 3x10^14 j/kg. Matter antimatter annihilation yields 9x10^16 j/kg.

There are many technical obstacles to be addressed. First, the amount of available antimatter in production is not enough, particle accelerators such as the ones found in Fermilab, close to Chicago, and CERN, in Switzerland, produce somewhere between 1 to 10 nanograms of antimatter annually. The process of production typically involve accelerating protons near the speed of light and slamming it into a metal, such as tungsten. Various subatomic particles are produced by this collision, including antiprotons, the simplest form of antimatter. 71 milligrams of antimatter would provide an equal amount of energy that is provided by space shuttle external tank.

The second obstacle is storage. Antimatter can not be stored in normal containers because it will instantly annihilate once antimatter makes contact with matter. One solution is using Penning Trap, a super cold vacuum using electro magnets in order to suspend particles of antimatter. Antielectrons are difficult to store because of their mass, however, antiprotons are stored much more easily. Antimatter storage reaps several benefits, one of which is O15 production, a radioisotope used for Positron Emission Tomography (PET) of the human brain.

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References:

http://www.engr.psu.edu/antimatter/introduction.html
http://science.nasa.gov/headlines/y2000/ast29may%5F1m.htm
http://science.nasa.gov/newhome/headlines/prop12apr99_1.htm