Subject: Applied Physics 2

Topic: Motion Of Charged Particles In Electric And Magnetic Fields

Difficulty: High

Electrostatic Focusing:

The electron path is bent at each equipotential surface in the same way as light ray is bent at an optical boundary. A simple electrostatic lens consist of to coaxial short cylindrical metal tubes T1 and T2 separated by small distance. They are held at different potential say V 1 and V2 respectively. Assume $V_2$ › $V_1$ .A nonuniform electric field is produced in the gap between the tubes as a result of different potentials applied to the tubes.Figure below shows a schematic diagram of a simple electrostatic lens where in electric field lines and equipotential surface are depicted. Field lines are perpendicular to equipotential surface.

Consider bundles of electron rays entering from T 1 to T2 . electron labelled 1 on reaching equipotential surface, experience an electric force acting along the axis in forward direction. The electron is therefore accelerated towards T2 without deviation from initial path. Electron labelled 2, on reaching equipotential surface experiences a force acting at an angle to the direction of motion. So, it can be resolved into two components. F-parallel and F -perpendicular. F-parallel acts parallel to axis while F-perpendicular acts normal to the axis. Because of F-perpendicular, electron is deflected towards the axis and also accelerated forward because of F-parallel. Similarly, electron labelled 3 are deflected upward and simultaneously accelerated forward. Thus, all the off-axis electron tends to converge toward axis. However, on crossing midplane, electron encounters a concave shape. Here F- perpendicular component is directed away from axis and F-parallel is directed forward. As a result, electrons are accelerated but tends to diverge. The first half of gap acts like convex lens and tends to converge and second half acts like a concave lens which defocusses the ray. But since V2 › V1 , electron will spend more time in first half so converging action will be stronger. So, the net effect is to focus the electron beam.

Magnetostatic focusing:

Magnetic fields which are axially symmetric have focusing effect on an electron beam passing through them. The axially symmetrical magnetic fields are produced by short solenoids. By encasing the coils in hollow iron shield, the magnetic fields are concentrated and improved focusing action is obtained. Such solenoid is called magnetic lenses.

We know that an electron travelling at an angle ϴ into the field describes a helical path. The motion is resultant of translational motion along field direction and circular motion in a plane perpendicular to the field, The radius of the path described is R = mvsinϴ/Be

From the above equation, it is seen that radius of the loop goes on decreasing as the electron moves into stronger field. In the similar way, while travelling through the solenoidal field, the helical path of electron is twisted into tighter loops and turns become smaller and smaller and ultimately electron comes to a point focus. With the adjustment of current through the solenoid and initial accelerating voltage of electron the focal distance of magnetic lens can be adjusted