### Ion thruster

They are a type of space propulsion rockets that use an ion beam at the motor output to generate the thrust of the ship, using the load-mass ratio of the particles emitted, according to which, for each quantity of output load There is an amount of mass issued that is what generates the thrust of the ship.

These motors provide an internal electric field that accelerates the previously ionized particles in a chamber or “ion source”. T also have a mechanism of neutralization of the total charge that consists of providing the output the excess of opposite charge so that the mass of gases that leave issued is neutral and thus the ship-gases set is neutral. This is necessary because the charged gases are very reactive and could have effects on the flight if, for example, they were found with cosmic dust, for example ..It is taken for the pushing force. The pushing force is given by the equation:

F = 2nP / gIsp.

Where n is the efficiency, P the electrical power used by the propeller (in watts) and Isp is the specific impulse in seconds and g is the acceleration of gravity.

1. It allows to achieve a specific high impulse with a lower amount of mass than would be required for any fuel.2

2. It is possible to accelerate the fuel to very high speeds, this allows that with very little mass a high specific impulse can be generated

They can develop an order of magnitude higher fuel efficiency relative to traditional rockets.They have a long lifespan.

he amount of power needed to reach a specific impulse is greater than in conventional rockets.It is restricted to very low accelerations.It is sacrificed between the specific impulse and the thrust, both being inversely proportional to a certain amount of energy. You can not have equal gain in both specific impulse and in thrust because they are inversely proportional.

Damage to the internal engine system is very frequent due to the high corrosive level of the ions.

Equation for the Force of Push (http://www.sc.ehu.es/sbweb/fisica_/dinamica/cohetes/cohete1/cohete1.html#Descripci%C3%B3n) :This is the strength experienced by the ship due to the variation of the mass that is lost during the burning of the fuel.

F = v dm / dt

We solve This equation is solved, where F is the force that the ship experiences, v is the exit velocity of the ion beam, and dm / dt is the mass variation of the ion gas per unit of time.

By a simple analysis we can see that the variation of the mass in time depends on the intensity of the particle beam, I, which comes out of the rocket, the mass of each ionic particle of the beam, mp, and its charge, q, according to the relationship

dm / dt = I m_p / q

The speed with which the beam particles move depends on the difference in accelerating potential, V, between the source, S, and the electrode, B. Assuming

that the ions at the source start with zero velocity, their velocity, v, when you get to the ring, B, it will be

v = √ (2Vq / m_p)

The formula of the pushing force is

F = I√ ((2m_p V) / q)

The electrical power consumed (energy per unit time) is the product of the intensity of the ion beam, I, by the accelerating potential I.P = I.V

Finally, we express xpresamos the thrust force in terms of engine power, P, is expressed by:

F = √ ((2m_p) / qV)     For a given power P of the motor.