One type of rockets used by spacecrafts to steer in space uses motion of ions in

Question

One type of rockets used by spacecrafts to steer in space uses motion of ions in electric fields for generating the thrusts. These are Xenon ions, which are nearly 132 times more massive than protons(Mp=1.67x10-27kg). Take their mass to be mxe for now. Charge on Xenon ions is +e.

1. If the electric fields in the thruster are uniform and of the order of E=1000N/C, what is the time required for the ion to clear the acceleration stage? This stage consists of two parallel plates separated by a distance d=2mm with holes to allow for the entry and exit of the ions through them. Express the time in terms of the variables assume initial velocity is v=1m/s.

2. During this time what is the force acting on the ions? Is there a force acting  on the plates too? What is its magnitude and direction?

3. Indicate the sings of the charges on the plates so that the Xe ions get accelerated.

4. The impulse is defined as change in momentum in a given time t. p=impulse=force x t. Calculate the impulse in terms of the quantities . This impulse per unit time is the force. If the thrusters needs to produce a force  of FT, how many Xe ions does Nxe need to pass throught it per unit time? This can be found by recognizing that Nxe=FT/P

Explanation / Answer

General description Ion thrusters use beams of ions (electrically charged atoms or molecules) to create thrust in accordance with momentum conservation. The method of accelerating the ions varies, but all designs take advantage of the charge/mass ratio of the ions. This ratio means that relatively small potential differences can create very high exhaust velocities. This reduces the amount of reaction mass or fuel required, but increases the amount of specific power required compared to chemical rockets. Ion thrusters are therefore able to achieve extremely high specific impulses. The drawback of the low thrust is low spacecraft acceleration because the mass of current electric power units is directly correlated with the amount of power given. This low thrust makes ion thrusters unsuited for launching spacecraft into orbit, but they are ideal for in-space propulsion applications. Various ion thrusters have been designed and they all generally fit under two categories. The thrusters are categorized as either electrostatic or electromagnetic. The main difference is how the ions are accelerated. Electrostatic ion thrusters use the Coulomb force and are categorized as accelerating the ions in the direction of the electric field. Electromagnetic ion thrusters use the Lorentz force to accelerate the ions. Power supplies for ion thrusters are usually solar panels, but at sufficiently large distances from the Sun, nuclear power is used. In each case the power supply mass is essentially proportional to the peak power that can be supplied, and they both essentially give, for this application, no limit to the energy.

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