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Third order aberration theory of double Wien filters
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...
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| Published in: | Review of scientific instruments 2004-11, Vol.75 (11), p.4434-4441 |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | 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. |
|---|---|
| ISSN: | 0034-6748 1089-7623 |
| DOI: | 10.1063/1.1777410 |