Position, Energy, and Transit Time Distributions in a Hemispherical Deflector Analyzer with Position Sensitive Detector

Figure 2

Elliptical orbits with the same kinetic energy for ° (a), ° (b), and ° (c) with (red) and (blue). The field is central with center at O, one of the foci of the ellipse. The electron enters at the point P with radius and angle and exits at point M after going through a full 180°. All orbits with are always outer and therefore are always longer in both space and time with corresponding eccentricity vector lying in the opposite lower half plane. As decreases the corresponding eccentricity vectors rapidly rotate towards the positive -axis coalescing for , in which case the orbits exactly overlap. The angular momentum and eccentricity are even functions of and are conserved in the ideal field. Therefore orbits with the same have identical shape but a slightly different, but symmetric, tilt around the nodal line POM as shown. Due to this symmetry orbits with and are complementary giving rise to the condition of (31).

(a)

(b)

(c)