T. J. M. Zouros

The hemispherical deflector analyser revisited. I. Motion in the ideal 1/r potential, generalized entry conditions, Kepler orbits and spectrometer basic equation

Abstract We re-examine the orbits of non-relativistic charged particles in a hemispherical deflector analyser (HDA) assuming an ideal 1/r potential. The particles start their trajectory within the HDA at the arbitrary entry radius r0, within a circular entry aperture centered at R0 at an arbitrary potential V0=V(R0). We present a vector treatment of the trajectories deriving many useful relations expressed as a function of the launching angle α. Refraction at the potential boundary at the entry of the HDA (modelled by an idealized step potential) is also considered and found to be important when V0≠Vp, where Vp is the plate voltage used for preretardation. We derive the analyser’s generalized basic equation for deflection through 180° for which the principal reference ray is an ellipse rather than a circle as in the conventional HDA treatment. Both the conventional HDA, for which R 0 = R and V0=Vp, as well as the paracentric HDA for which R 0 ≠ R and V0≠Vp, where R is the mean radius, are thus described as special cases of the same trajectory equation. Our results are expected to be of interest to all fields of electron spectroscopy, but particularly to those utilizing modern spherical sector analysers with sizeable interradial separation for accommodating large area position-sensitive detectors. This investigation is part of a concerted effort to investigate the refocusing properties of the paracentric HDA recently reported by Benis and Zouros [Nucl. Instr. & Meth. A 440 (2000) 462].

Improving the energy resolution of a hemispherical spectrograph using a paracentric entry at a non-zero potential

Abstract We demonstrate by ray tracing analysis that the focusing properties of a hemispherical spectrograph depend critically on the placement of the electron entrance position R 0 and the value of the potential V 0 at R 0 . Improvements over conventional spectrographs using R 0 = R , the mean radius and V 0 =0 are predicted for particular combinations of R 0 and V 0 . A spectrograph with R =101.6 mm and an entrance at R 0 =82.55 mm using a zoom lens and a two-dimensional position sensitive detector (2D-PSD) with 40 mm multichannel plates and resistive anode encoder has been used to confirm the predicted qualitative behaviour. These results suggest that improvement in energy resolution may be attained without the use of fringing field correctors.

Optimal energy resolution of a hemispherical analyzer with virtual entry

For an ideal hemispherical deflector analyzer (HDA) utilizing a virtual entry aperture whose size is controlled by an injection lens, the “slit” and angular contributions to the overall base resolution RB are not independent, but constrained by the Helmholtz–Lagrange law. Thus, RB becomes a function of the linear lens magnification ∣ML∣ and has a minimum, RBo¯≡RB(∣ML∣o), at the optimal magnification ∣ML∣=∣ML∣o. RBo¯ and ∣ML∣o are shown to be analytic expressions of basic experimental parameters. RBo¯ is thus the ultimate resolution that can be attained in this case. The generality and simplicity of this result should be very helpful in the efficient design and performance evaluation of any modern HDA.

Novel and traditional fringing field correction schemes for the hemispherical analyser : comparison of first-order focusing and energy resolution

Strong fringing fields at the entry and exit of a real hemispherical deflector analyser (HDA) significantly degrade the 180° first-order focusing conditions, one of the central advantages of the ideal-field HDA. Over the past 50 years, traditional approaches to cure this problem have primarily sought to suppress these fields by improving field termination conditions typically requiring the unwieldy use of additional electrodes. Recently, Zouros et al (2006 Meas. Sci. Technol. 17 N81–N86) have shown in simulation that a simple repositioning of the HDA entry when appropriately biased results in the effective utilization of the intrinsic lensing properties of these fields to restore and even improve first-order focusing. Here, we investigate in simulation the efficacy of the new controlled lensing approach and compare it to the traditional Herzog and Jost field corrector approach. HDA focusing properties and energy resolution are reported as a function of entry angle, source extent and hemispherical interelectrode separation. For all cases considered, HDAs using controlled lensing always came out ahead demonstrating superior focusing along the 180° deflection plane and improved energy resolution.

High resolution RTE measurements at 0° using a hemispherical analyser with lens and 2-D PSD

Abstract First high resolution measurements using a new electron spectrograph at 0° to the beam direction are reported. The new apparatus consists of a hemispherical analyser with a mean radius of 101.6 mm, a 4-element focusing lens and 40 mm diameter 2-D position sensitive detector (PSD). Electrons are decelerated and focused in the lens prior to analysis to improve the energy resolution. As a test of the apparatus in deceleration mode, we measured the differential cross section of the F 7+ (2p 2 ) 1 D state produced by Resonance Transfer Excitation (RTE) in collisions of 21.78 MeV F 8+ + H 2 . An effective energy resolution of 0.25% was obtained using a deceleration factor of 4. Good agreement with known cross section values was found. Presently, our spectrograph with a maximum count rate of about 4 kHz (limited by dead-time considerations) is more than 15 times faster than the conventional tandem zero-degree spectrometer at Kansas State University, while using a factor of 20 lower intensity beams.

Impulse approximation treatment of electron-electron excitation and ionization in energetic ion-atom collisions

Abstract The effect of electron-electron interactions between projectile and target electrons observed in recent measurements of projectile K-shell excitation [T.J.M. Zouros et al., Phys. Rev. Lett. 62 (1989) 2261] and ionization [T.J.M. Zouros et al., Nucl. Instr. and Meth. B56/57 (1991) 107 and D.H. Lee et al., Phys. Rev. A46 (1992) 1374] using 0° projectile Auger electron spectroscopy are analysed within the framework of the impulse approximation (IA) [D. Brandt, Phys. Rev. A27 (1983) 1314]. The IA formulation is seen to give a good account of the threshold behavior of both ionization and excitation, while providing a remarkably simple intuitive picture of such electron-electron interactions in ion-atom collisions in general. Thus, the applicability of the IA treatment is extended to cover most known processes involving such interactions including resonance transfer excitation, binary encounter electron production, electron-electron excitation and ionization.

EUV-photon-induced multiple ionization and fragmentation dynamics: from atoms to molecules

Multiple ionization (MI), induced by a few EUV photons at energies of 28.2 eV, 38 eV and 44 eV from FLASH (the free-electron laser at Hamburg), has been studied for atoms (He, Ne, Ar) and N2 molecules utilizing our multi-hit coincident technology?the reaction microscope. At comparably low intensities of I 1011?1013 W cm?2 we find the non-sequential (NS) MI mechanism dominating Ar3+ and Ar4+ production. Inspecting recoil ion and electron momentum distributions evidence is provided (i) for preferential back-to-back emission of electrons for NS double ionization of He and (ii) for angular entanglement between two outgoing electrons in sequential ionization (SI). In contrast to atoms, SI is observed to be most effective for MI of N2 molecules at an intensity of ~1013 W cm?2 leading, among others, to N2+2 ? N+ + N+, N3+2 ? N2+ + N+, N4+2 ? N2+ + N2+ Coulomb explosion channels. Fragment ion momentum distributions are investigated and are demonstrated to allow tracing SI pathways.

Resonant Transfer and Excitation Associated with Auger Electron Emission

Resonance Transfer and Excitation1–4(RTE) is a correlated two-electron process, mediated by the electron-electron interaction, involving the transfer of a loosely bound target electron to the projectile with the simultaneous excitation of a projectile electron, giving rise to doubly-excited projectile states. These projectile states relax by photon emission or Auger electron emission and are therefore investigated by low resolution x-ray - ion coincidences (RTEX), x-ray—x-ray coincidences (RTEXX), or by high resolution Auger electron spectroscopy (RTEA) measurements, respectively.5,6 In recent years, RTE has received considerable attention since it can provide direct information on electron-electron interaction phenomena7presently of great interest in atomic physics. In this presentation we focus on the status of recent state—selective RTEA measurements and their analysis within the impulse approximation.3

Electron emission in collisions of slow, highly charged ions with gases and solid surfaces

Abstract We measured electron spectra produced in O 6+ + He collisions and by N 6+ , O 7+ , Ne 9+ , and Ar q + ( q = 9, 13, 14 and 16) incident on solid surfaces of Cu and C under 10 ° with energies from 10 q to 20 q keV. Auger electrons were detected at various emission angles including 0° and 180° with respect to the incident beam. For the He gas target the angular distribution of oxygen L-Auger electrons is found to be isotropic between 10 ° and 140 ° but enhanced at 0 °. In ion-surface collisions, multiple electron capture is studied. By analyzing the Doppler shift of the projectile Auger electrons, the L-Auger electrons of argon were found to be emitted from ions incident on the surface and the K-Auger electrons of neon were observed to be emitted from reflected ions.

Using the fringing fields of a hemispherical spectrograph to improve its energy resolution

The energy resolution of a hemispherical deflector analyser (HDA) can be substantially improved by using its entry fringing fields advantageously, rather than trying to eliminate them—the traditional approach. The intrinsic lensing properties of these fringing fields, as shown in simulations, are able to not only restore, but even improve first-order focusing at the 180° deflection plane in a controlled way, without the use of any additional field correction electrodes. This is accomplished by changing the entry radius R0 and bias from their conventional values of , the mean radius and to new values with or with . An HDA with , ΔR = R2 − R1 = 58.4 mm and maximum entry angle αmax = 2° demonstrates the impressive resolution gains that can be attained, 34 for a point entry (Δr0 = 0) and 4.2 for an aperture diameter of Δr0 = 1 mm, over corresponding conventional entry conditions.