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Chapter Six - Derivation, cross-validation, and comparison of analytic formulas for electrostatic deflector aberrations

Here, we derived first and second order analytic aberration formulas in the horizontal transverse plane for an electrostatic deflector specified by the reference orbit radius, the central angle spanning the deflector, and its inhomogeneity coefficients. The derivation was performed using an iterative order-by-order perturbation method in a Frenet–Serret beamline coordinate system. We produced a C program edabrt for calculation of the first and second order aberrations using the formulas that we derived. The electrostatic deflector aberration formulas from Wollnik (1965) disagree with COSY INFINITY and the aberration formulas that we derived here, and they also deviate from the first and second order symplecticity conditions. The reason for this discrepancy is that the aberration formulas from Wollnik (1965) consider only motion in the main field of the deflector and do not properly account for fringe field effects, in particular the necessarily occurring change of kinetic energy due to the change in potential. The code GIOS uses electrostatic aberration formulas from Wollnik (1965) and exhibits the same discrepancy. We performed a comparison of first and second order electrostatic deflector aberrations for (1) the analytic formulas derived in this work, (2) differential-algebraic (DA) numerical integration of the equations of motion using the code COSY INFINITY, (3) the aberration formulas from Wollnik (1965), (4) aberrations computed using the code GIOS, and (5) the aberration formulas from Wollnik (1965) adjusted to account for the occurring change in potential. An electrostatic spherical deflector and an electrostatic cylindrical deflector were used as test cases for this comparison. There is excellent agreement between methods (1), (2), and (5), and these three methods satisfy the first and second order symplecticity conditions.

43 PARTICLE ACCELERATORS↗

Analysis and fringe field scaling of a legacy set of electrostatic deflector aberration formulas [Chapter Seven]

In this work we performed an analysis of the derivation of first and second order analytic aberration formulas by Wollnik (1965) for the case of electrostatic deflectors in the horizontal plane. We found that these aberration formulas are valid for the main field of the deflector; however, they do not account for any fringe field effects. To address this issue, we modified the aberration formulas from Wollnik (1965) for a hard edge fringe field by scaling the particle inclinations at the entrance and exit edges of the deflector. These modified aberration formulas fully agree with electrostatic aberration formulas derived by Valetov and Berz (2020), as well as with differential-algebraic (DA) calculations of electrostatic deflector aberrations using the code COSY INFINITY.

43 PARTICLE ACCELERATORS↗

Development of deflector mode for spin-resolved time-of-flight photoemission spectroscopy

Spin- and angle-resolved photoemission spectroscopy (“spin-ARPES”) is a powerful technique for probing the spin degree-of-freedom in materials with nontrivial topology, magnetism, and strong correlations. Spin-ARPES faces severe experimental challenges compared to conventional ARPES attributed to the dramatically lower efficiency of its detection mechanism, making it crucial for instrumentation developments that improve the overall performance of the technique. Here in this paper, we demonstrate the functionality of our spin-ARPES setup based on time-of-flight spectroscopy and introduce our recent development of an electrostatic deflector mode to map out spin-resolved band structures without sample rotation. We demonstrate the functionality by presenting the spin-resolved spectra of the topological insulator Bi2Te3 and describe in detail the spectrum calibrations based on numerical simulations. By implementing the deflector mode, we minimize the need for sample rotation during measurements, hence improving the overall efficiency of experiments on small or inhomogeneous samples.

47 OTHER INSTRUMENTATION↗

Controlled molecule injector for cold, dense, and pure molecular beams at the European x-ray free-electron laser

A permanently available molecular-beam injection setup for controlled molecules (COMO) was installed and commissioned at the small quantum systems (SQS) instrument at the European x-ray free-electron laser (EuXFEL). A b-type electrostatic deflector allows for pure state-, size-, and isomer-selected samples of polar molecules and clusters. The source provides a rotationally cold (T ≈ 1 K) and dense (ρ ≈ 10 8 cm −3 ) molecular beam with pulse durations up to 100 µs generated by a new version of the Even-Lavie valve. Here, a performance overview of the COMO setup is presented along with characterization experiments performed both with an optical laser at the Center for Free-Electron-Laser Science and with x rays at EuXFEL under burst-mode operation. COMO was designed to be attached to different instruments at the EuXFEL, in particular, the SQS and single particles, clusters, and biomolecules (SPB) instruments. This advanced controlled-molecules injection setup enables x-ray free-electron laser studies using highly defined samples with soft and hard x-ray FEL radiation for applications ranging from atomic, molecular, and cluster physics to elementary processes in chemistry and biology.

He, Lanhai↗

Energetic ion mass spectrometer

A new type of spectrometer for space application has been developed to measure separately mass/charge and the three-dimensional velocity distribution of incident ions. The instrument has relatively high resolution and allows rapid measurement of the four-dimensional set of mass/charge, speed, elevation angle, and azimuth angle. The instrument includes a sector magnet, an electrostatic deflector, microchannel plate detectors with position sensitive readout, and a set of grids with variable applied voltage.

Neugebauer, M.↗

Radionuclide measurements by accelerator mass spectrometry at Arizona

Over the past years, Tandem Accelerator Mass Spectrometry (TAMS) has become established as an important method for radionuclide analysis. In the Arizona system the accelerator is operated at a thermal voltage of 1.8MV for C-14 analysis, and 1.6 to 2MV for Be-10. Samples are inserted into a cesium sputter ion source in solid form. Negative ions sputtered from the target are accelerated to about 25kV, and the injection magnet selects ions of a particular mass. Ions of the 3+ charge state, having an energy of about 9MeV are selected by an electrostatic deflector, surviving ions pass through two magnets, where only ions of the desired mass-energy product are selected. The final detector is a combination ionization chamber to measure energy loss (and hence, Z), and a silicon surface-barrier detector which measures residual energy. After counting the trace iosotope for a fixed time, the injected ions are switched to the major isotope used for normalization. These ions are deflected into a Faraday cup after the first high-energy magnet. Repeated measurements of the isotope ratio of both sample and standards results in a measurement of the concentration of the radionuclide. Recent improvements in sample preparation for C-14 make preparation of high-beam current graphite targets directly from CO2 feasible. Except for some measurements of standards and backgrounds for Be-10 measurements to date have been on C-14. Although most results have been in archaeology and quaternary geology, studies have been expanded to include cosmogenic C-14 in meteorites. The data obtained so far tend to confirm the antiquity of Antarctic meteorites from the Allan Hills site. Data on three samples of Yamato meteorites gave terrestrial ages of between about 3 and 22 thousand years.

Jull, A. J. T.↗

Application of reversal electron attachment for ultrasensitive detection of thermal electron-attaching molecules - CCl4 and C6H5O2

A standard gas-dilution method was used to determine the selective response of the reversal electron attachment detector to carbon tetrachloride concentrations in nitrogen. Data are provided that determine the lowest concentration of sample detectable with the present instrumental configuration as being below 1.0 part per trillion by volume. The incorporation of a 90-deg electrostatic deflector with the quadrupole mass spectrometer is shown to be vital, and with it, negative-ion quadrupole mass spectrometry is used to characterize the ionization process. Observations are also made of the reversal electron attachment response to nitrobenzene. The analytical potential of reversal electron capture negative-ion mass spectrometry is examined, and areas for future development are discussed.

Bernius, Mark T.↗

Suppressing Ghost Diffraction in E-Beam-Written Gratings

A modified scheme for electron-beam (E-beam) writing used in the fabrication of convex or concave diffraction gratings makes it possible to suppress the ghost diffraction heretofore exhibited by such gratings. Ghost diffraction is a spurious component of diffraction caused by a spurious component of grating periodicity as described below. The ghost diffraction orders appear between the main diffraction orders and are typically more intense than is the diffuse scattering from the grating. At such high intensity, ghost diffraction is the dominant source of degradation of grating performance. The pattern of a convex or concave grating is established by electron-beam writing in a resist material coating a substrate that has the desired convex or concave shape. Unfortunately, as a result of the characteristics of electrostatic deflectors used to control the electron beam, it is possible to expose only a small field - typically between 0.5 and 1.0 mm wide - at a given fixed position of the electron gun relative to the substrate. To make a grating larger than the field size, it is necessary to move the substrate to make it possible to write fields centered at different positions, so that the larger area is synthesized by "stitching" the exposed fields.

Wilson, Daniel↗

Low-Pressure, Field-Ionizing Mass Spectrometer

A small mass spectrometer utilizing a miniature field ionization source is now undergoing development. It is designed for use in a variety of applications in which there are requirements for a lightweight, low-power-consumption instrument that can analyze the masses of a wide variety of molecules and ions. The device can operate without need for a high-vacuum, carrier-gas feed radioactive ionizing source, or thermal ionizer. This mass spectrometer can operate either in the natural vacuum of outer space or on Earth at any ambient pressure below 50 torr (below about 6.7 kPa) - a partial vacuum that can easily be reached by use of a small sampling pump. This mass spectrometer also has a large dynamic range - from singly charged small gas ions to deoxyribonucleic acid (DNA) fragments larger than 104 atomic mass units - with sensitivity adequate for detecting some molecules and ions at relative abundances of less than one part per billion. This instrument (see figure) includes a field ionizer integrated with a rotating-field mass spectrometer (RFMS). The field ionizer effects ionization of a type characterized as "soft" in the art because it does not fragment molecules or initiate avalanche arcing. What makes the "soft" ionization mode possible is that the distance between the ionizing electrodes is less than mean free path for ions at the maximum anticipated operating pressure, so that the ionizer always operates on the non-breakdown side of the applicable Paschen curve (a standard plot of breakdown potential on the ordinate and pressure electrode separation on the abscissa). The field ionizer in this instrument is fabricated by micromachining a submicron-thick membrane out of an electrically nonconductive substrate, coating the membrane on both sides to form electrodes, then micromachining small holes through the electrodes and membrane. Because of the submicron electrode separation, even a potential of only 1 V applied between the electrodes gives rise to an electric field with a strength of in excess of a megavolt per meter strong enough to ionize any gas molecules passing through the holes. An accelerator grid and an electrostatic deflector focus the ions from the field ionizer into the rotating-field cell of the RFMS. The potentials applied to the electrodes of the cell to generate the rotating electric field typically range from 1 to 13 V. The ions travel in well-defined helices within this cell, after which they are collected in a Faraday cup. The mass of most of the molecules reaching the Faraday cup decreases with increasing frequency of rotation of the electric field in the cell. Therefore, the frequency of rotation of the electric field is made to vary in order to scan through a desired range of ion masses: For example, lightweight gas molecules are scanned at frequencies in the megahertz range, while DNA and other large organic molecules are scanned at kilohertz frequencies.

Hartley, Frank↗

Fusion of 12 C+ 24 Mg far below the barrier: Evidence for the hindrance effect

Background: The phenomenon of fusion hindrance may have important consequences on the nuclear processes occurring in astrophysical scenarios, if it is a general behavior of heavy-ion fusion at extreme subbarrier energies, including reactions involving lighter systems, e.g., reactions in the carbon and oxygen burning stages of heavy stars. The hindrance is generally identified by the observation of a maximum of the S-factor vs energy. Whether there is an S-factor maximum at very low energies for systems with a positive fusion Q value is an experimentally challenging question. Purpose: Our aim has been to search for evidence of fusion hindrance in 12 C+ 24 Mg which is a medium-light m system with positive Q value for fusion, besides the heavier cases where hindrance is recognized to be a general phenomenon. 12 C+ 24 Mg is very close to the 16 O + 16 O and 12 C + 12 C systems that are important for the late evolution of heavy stars. Methods: The experiment has been performed in inverse kinematics using the 24 Mg beam from the XTU Tandem accelerator of LNL in the energy range 26-52 MeV with an intensity of 4-8 pnA. The targets were 12 C evaporations 50 mu g/cm 2 thick, isotopically enriched to 99.9%. The fusion-evaporation residues were detected at small angles by a E-Delta E-ToF detector telescope following an electrostatic beam deflector. Results: Previous measurements of fusion cross section for 12 C+ 24 Mg were limited to above-barrier energies. In the present experiment the excitation function has been extended down to similar or equal to 15 mu b and it appears that the S factor develops a clear maximum vs energy, indicating the presence of hindrance. This is the first convincing evidence of an S factor maximum in a medium-light system with a positive fusion Q value. These results have been fitted following a recently suggested method and a detailed analysis within the coupled-channels model that has been performed using a Woods-Saxon potential and including the ground state rotational band of 24 Mg. The coupled-channels calculations give a good account of the data near and above the barrier but overpredict the cross sections at very low energies. Conclusions: The hindrance phenomenon is clearly observed in 12 C+ 24 Mg, and its energy threshold is in reasonable agreement with the systematics observed for several medium-light systems. The fusion cross sections at the hindrance threshold show that the highest value (sigma(s) = 1.6 mb) is indeed found for this system. Therefore it may even be possible to extend the measurements further down in energy to better establish the position of the S-factor maximum.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗