Third order aberration theory of double Wien filters

• Published in: Review of scientific instruments 2004-11, Vol.75 (11), p.4434-4441
• Main Authors: Ioanoviciu, D., Tsuno, K., Martinez, G.
• Format: Article
• Language: English
• ISSN: 0034-6748; 1089-7623
• DOI: 10.1063/1.1777410

The second and the third order aberration theory for a double Wien filter have been analytically developed. A new second order aberration-free condition is found at the image plane of the second filter. This condition is met when b 2 =−1/4 , e 2 =−1/2 , and b 3 −e 3 =−1/8 , where b 2 =B 2 R/B 1 , e 2 =E 2 R/E 1 , b 3 =B 3 R 2 /B 1 , and e 3 =E 3 R 2 /E 1 . Here, R is the cyclotron radius and E 1 , B 1 , E 2 , B 2 , E 3 , and B 3 are the dipole, quadrupole, and hexapole components of electric and magnetic fields, respectively. This condition is different from the second order aberration-free condition for a single Wien filter, which is satisfied when b 2 =−3/4 , e 2 =−1 , and b 3 −e 3 =−3/8 . The geometrical second order aberration-free condition has also been found, and requires that e 3 −b 3 =(m−1)/8 , e 2 =−m/4 , and b 2 =(1−m)/4 . This last set is sufficient to satisfy the above two sets of conditions as well. Residual third order aberrations are calculated for various m . The third order aberrations at the second focus are very small when the new aberration-free condition is fulfilled.