A linear oscillator (Linac) is a device which accelerates charged particles in a straight line by means of oscillating electric field. S is a source of ion, emitting ions along a straight line (marked as axis) with negligible kinetic energy. The particles travel along a series of co-axial metallic cylindrical electrodes 1, 2, 3, etc. These electrodes are called drift tubes. These tubes are connected to a high frequency oscillator so that alternate tubes have opposite polarities. Thus in one half cycle if tubes 1, 3, 5… are negative then the source (S), tube 2, 4, 6… are positive. After every half cycle the polarities reverse. Assume that there is no electric field inside the metallic tube and the charged particles maintain a straight line trajectory. Find the ratio of lengths of the tubes x1 : x2 : x3... for the device to work

Answer

`1:sqrt2:sqrt3: ....`