Ion Propulsion: A story of the Conservation of Momentum

     Behind every theory for future forms of spacecraft propulsion lies a terrible truth. They are all either too costly, to difficult, too dangerous, or too inefficient for practical use today for reaching towards the planets. But what if there were a form of propulsion for which the fuel would cost 33 times less than traditional fuel? What if there were a fuel that was non-toxic, non-volatile, and unlikely to cause an explosion or other catastrophic failure? What if there were an engine that had an average efficiency rating of 70%? And what if it were available and ready to launch today? Ladies and gentlemen, this is the truth behind the xenon ion propulsion drive.

     The ion thruster is a feasible solution for space travel in the not-so-distant future. The truth is, it has already been done. In 1998, NASA launched Deep Space 1, a probe designed to do a close flyby of an asteroid. What was supposed to be a fairly short, straightforward mission turned much more complicated when they realized that Deep Space 1 also had the opportunity to study the attributes of passing comet Borrelly first hand. Though the encounter with the asteroid was only considered a partial success, the information gathered from Deep Space One's flyby of comet Borrelly turned out to be a huge success. And it was all thanks to the highly efficient and decently cheap ion propulsion system mounted on board.

     The theory behind an ion drive is actually quite simple. Xenon atoms are initially stored in a containment unit. Since xenon has a full valence shell of electrons, it is non-volatile and non-toxic. This also means that xenon is very easy to ionize. Ionization is a process where a stream of electrons are shot at regular atoms in such a way that electrons get knocked loose from the atom, creating a net positive charge on the atom. Since positive charges are attracted to negative charges, these ions are then subjected to two powerful charged plates, the one behind the ions being positive, and the one in front of them being negative. As the positive plate forces the ions away from the craft, the negative plate pulls the ions out into space. The potential difference accelerates these positive ions out of the exhaust tube at speeds upwards of 40 kilometers per second! Since leaving a trail of positive ions behind the spacecraft can induce a charge upon the spacecraft, which can be dangerous, a stream of electrons is shot into outgoing ions to neutralize them so they have no net charge.

Theory Behind an Ion Drive

     However, at this point you may have noticed the problem. Though the exhaust velocity is 40 kilometers per second, we can only accelerate a few atoms of xenon at a time. This makes acceleration a very difficult and tedious process. It would be like instead of pressing the gas pedal to accelerate your car to work, you threw grains of sand at extreme velocities to slowly accelerate your car to its top speed. Granted, you would save gas money, and your car would actually achieve a higher speed (neglecting friction), but it would take you hours or days to even get your car to go a modest speed. An ion powered spacecraft would either need to be constructed in space, or blasted into orbit via chemical rockets. This is the only major downfall of ion propulsion.

     The ion propelled thruster works on a very simple level. The law of conservation of momentum states that the mass multiplied by the velocity of one object which exerts its energy upon a second object is equal to the other mass multiplied by the other velocity. In simpler terms:

m1v1 = m2v2

     Where m1 and v1 are the mass and velocity of the xenon atoms, and m2 and v2 are the mass and velocity of the spacecraft. We know that the mass of one xenon atom is 2.18*10^-25 kg, and that they are being expelled from the spacecraft at 40 km/s, or 40,000 m/s. Let's say that we wanted to launch a 500 kg probe to Mars. How much xenon would we need. Well:

m1 = 2.18E-25

v1 = 40,000

m2 = 500

v2 = ?

(2.18E-25)*(40,000) = (500)*(v2)

v2 = 1.74E-23 m/s

     Let's say we want our top velocity to reach 20,000 m/s, about 5 times the speed of a conventional rocket:

(20,000)/(1.74E-23) = 1.15E27 xenon atoms = 250.7 grams.

     This mass of xenon will get the craft to 20,000 m/s. The craft will then coast at that speed until it is time for it to begin to slow down to arrive at its destination. This does mean, however, that it will need another 250.7 grams of xenon to slow back down to starting velocity, bringing the total amount of fuel to about 502 grams. But how fast can we get up to this speed? Let's say that our engine has a diameter of half a meter. This will give it an output of about .044 Newtons of thrust. For our 500 kg craft, this is equal to an acceleration of  8.8*10^-5 m/s^2. This means that, starting from 0 m/s, it would take upwards of 6 hours to reach our desired speed of 20,000 m/s. So time is the only sacrifice of the ion engine.

     But what about the benefits? The cost of 501 grams of xenon fuel for a 500 kilogram spacecraft would cost just proud of $600. Compare that to the $20,000 of liquid fuel that it would take to get a space vessel from low Earth orbit to Mars's orbit. And even with all that expensive fuel, it would still only be able to achieve a peak net velocity of around 4000 m/s, though it may only take a few minutes to get there. This is only a fraction of the top speeds achievable by the ion drive. Plus, with no explosive or volatile chemicals on board, the journey would be much less prone to accidents. The far future may hold the keys of space exploration in nuclear and antimatter drives, but getting us to our celestial neighbors today may be much more feasible by means of the xenon ion drive.