A xenon ion rocket of 5 N thrust at a specific impulse of 5000 s is to be built within the...

A xenon ion rocket of 5 N thrust at a specific impulse of 5000 s is to be built within the following two limitations: (a) minimum electrode space = 5 mm, (b) maximum average gradient between electrodes = 105 V/cm. Assuming the acceleration region to behave as a simple space-charge-limited plane diode, what beam area is required?

To reduce the beam area, it is proposed to increase the current density by first accelerating through a larger potential difference. The ions are subsequently decelerated to the proper exhaust speed (see diagram). What is the minimum beam area and the corresponding acceleration potential?