Theory
The equation for the change in radial velocity for a particle as it passes between any pair of cylinders in the lens is:
z is the axis passing through the middle of the lens. r is the direction normal to z. If the lens is constructed with cylindrical plates, the field is symmetrical around z. is the magnitude of the electric field in the radial direction for a particle at a particular radial distance and distance across the gap, the rest mass of the particle passing through the field, is the velocity of the particle and q is the charge of the particle. The integral occurs over the gap between the plates. This is also the interval where the lensing occurs.
The pair of plates is also called an electrostatic immersion lens, thus an einzel lens can be described as two or more electrostatic immersion lenses. Solving the equation above twice to find the change in radial velocity for each pair of plates can be used to calculate the focal length of the lens.
Read more about this topic: Einzel Lens
Famous quotes containing the word theory:
“The theory seems to be that so long as a man is a failure he is one of God’s chillun, but that as soon as he has any luck he owes it to the Devil.”
—H.L. (Henry Lewis)
“... the first reason for psychology’s failure to understand what people are and how they act, is that clinicians and psychiatrists, who are generally the theoreticians on these matters, have essentially made up myths without any evidence to support them; the second reason for psychology’s failure is that personality theory has looked for inner traits when it should have been looking for social context.”
—Naomi Weisstein (b. 1939)
“There never comes a point where a theory can be said to be true. The most that one can claim for any theory is that it has shared the successes of all its rivals and that it has passed at least one test which they have failed.”
—A.J. (Alfred Jules)