Problem A Solar Sailing to Mars

Light exerts a pressure equal to twice its energy density when reflected from a surface.  Therefore, a large, lightweight reflective surface known as a solar sail allows radiation from the sun to propel a spacecraft.    Assume that the sail is made of material of mass 7 g/m²; a rocket will launch a total mass of 2,000 kg (sail plus payload) to escape velocity from Earth.  Determine the size of the sail and a flight plan for the solar sail spacecraft from Earth to Mars.  Assume that the Earth and Mars are at their closest approach at the time of launch and that the spacecraft and Mars must have a relative velocity of no more than 9 km/s for safe landing.  Optimize the flight plan to maximize the payload and reduce transit time.

Problem B Ion Thrusters

Ion thrusters can be an effective means for propelling space probes through our solar system.  Gridded electrostatic ion thrusters begin by ionizing their propellant, accelerating the positively charged ions using a potential difference between two or more grids, and then neutralizing the exhaust by firing a beam of electrons into it.  A research team is working on a prototype Xenon ion thruster, 35 cm in diameter, with a specific impulse of 5,100 seconds and a thrust of 350 millinewtons.  However they find that ions exit the final grid at a wide range of angles.  A member of the team proposes that you could generate a magnetic field that would affect the trajectories of ions out of the final grid, before the ions are neutralized, to direct their velocities into a more uniform exit direction.  Evaluate this proposal.  Would it be practical to generate such a magnetic field, and if so, how?