Magnetic einzel lens satisfying anastigmatic and achromatic conditions

Starting from the rigorous treatment on a magnetic einzel lens given by the field distribution along the optical axis z; H(z)= H o (z/a) m-1 / [1+(z/a) 2m ], where m is the parameter depending on the double gap pole- piece geometry and the magnetic flux concentration, the lens model is the simple einzel lens whose solution of paraxial ray paths can be obtained in the hypergeometric function. For m=2, it corresponds to the permanent einzel lens introduced by Lenz(1956). Based on this solution, the important optical quantities and third order aberrations for the practical lens representing the true field distribution which is classified by m=3, as shown in Fig.1 , are analytically formulated. Anastigmatic and achromatic lenses satisfying the anastigmatic and achromatic conditions are presented at the view-point of lens design. 1] Field distribution and paraxial ray paths The paraxial differential equation for a magnetic field of rotational symmetry is, u"+K 2 u=0; K=K o f(z/a), and K o 2 =(e/m)H o 2 /(8)Φ (1), where H o is the maximum value of the field,(e/m) the specific charge of the electron, Φ the accelerating potential and f(z/a) expresses the function of the field distribution along the axis z/a.