1. Project for Unit 1 Calculate the beam ellipse at the exit of an element

2. A very Important Property of linear transformation x´ x (x,x´) x´ x (x,x´) An ellipse is transformed into another ellipse under linear transformation and the area of the ellipse is conserved

3. Procedure Load in SIMION an Einzel lens PA file from the SIMION ‘examples’ directory Choose a number of particles (x,x’) on the perimeter of a phase space ellipse located close to the entrance of the Enzel lens Record the coordinates of the particles (x,x’) at the exit of the Einzel lens. Plot the phase space coordinates and determine the orientation of the ellipse generated by these coordinates