Quadrupole Multiplets Research Articles

Quadrupole multiplet for medium energy beam transport for proton improvement plan −2

The Proton Improvement Plan-II (PIP-II) is a proposed upgrade for the accelerator complex at Fermi National Accelerator Laboratory, Batavia, USA. The injector experiment called the PIP-2 Injector Test (P2IT) is a 20 MeV front end comprising a warm front end and superconducting cryomodules. Quadrupole Multiplets for MEBT of P2IT are designed, developed, and qualified by Bhabha Atomic Research Centre (BARC) which is the lead laboratory for the design, development, and qualification of all warm magnets and superconducting solenoid magnets of Proton Improvement Plan – 2 under Indian Institute and Fermilab Collaboration (IIFC). Quadrupole doublets and triplets for MEBT of P2IT are beam commissioned at FNAL and went through a series of beam trials and experiments. This paper describes the design, development, qualifications, and beam experiment results of MEBT Quadrupole multiplets.

Effects of linear quadrupole fringe field overlap on transverse matching to an radio frequency quadrupole

Along many low energy beam transport (LEBT) systems transverse hadron beam matching to a subsequent radio frequency quadrupole (RFQ) is performed by magnetic quadrupole multiplets. Large apertures combined with short distances between the quadrupoles lead to overlap of individual singlet fields and significantly impact on the effective beam optics. Systematic measurements of beam transmission through an RFQ have been done and compared to beam dynamics simulations. For the latter, simplified hard-edge quadrupole fields were replaced by measured field data. It turned out that the hard-edge model is not sufficiently accurate to achieve acceptable agreement between calculated and measured beam properties.

Design of compact ultrafast microscopes for single- and multi-shot imaging with MeV electrons

Ultrafast high-energy electron microscopy, taking advantage of strong interaction of electrons with matter while minimizing space charge problems, can be used to address a wide range of grand challenges in basics energy sciences. However, MeV-electron lenses are inherently bulky and expensive, preventing them from acceptance in a broad scientific community. In this article, we report our novel design of a compact, low-cost imaging-lens system for MeV-electrons based on quadrupole multiplets, including triplet, quadruplet and quintuplet, both symmetric and asymmetric. We compare optical performance of quadrupole-based condenser, objective and projector lenses with that of the traditional round-lenses and discuss the strategy for their practical use in constructing MeV-electron microscopes for high spatial and temporal resolution single- and multi-shot imaging. Combining the compound electron-optical system with a photocathode radiofrequency (RF) gun, such a MeV electron microscope can be fit into a small-sized laboratory for ultrafast observations and measurements.

Use of a line focus of a quadrupole multiplet for irradiating millimeter length lines

We have developed a new method of irradiation suitable for uniformly irradiating long, straight lines for waveguide and channel fabrication in semiconductors and polymers. This is achieved by exciting the quadrupole lenses of a nuclear microprobe in a manner such that the beam is focused in one plane but highly defocused in the orthogonal plane. This method requires no surface mask and since the beam is not scanned, it produces uniformly-irradiated patterns. This approach has been used for rapid exposure of lines 8 mm in length with widths of about 3 μm in silicon and 1.5 μm in polymethyl methacrylate.

The use of solenoid lenses in a two-stage nuclear microprobe probe-forming system

Nuclear microprobes typically achieve a demagnification between 20 and 100 by using a single-stage quadrupole multiplet as the probe-forming system. Whilst quadrupole lenses provide the strong field necessary for focusing MeV ions, they also have higher intrinsic spherical and chromatic aberrations, and also higher parasitic aberrations than found in solenoid lenses. Given the fundamentally superior spatial resolution which is attainable using solenoids, their use in a two-stage microprobe system comprising a magnetic quadruplet and a solenoid lens as the first and second demagnifying stages respectively is studied here. Calculated results are compared with a two-stage system comprising two quadruplets and also with an existing single-stage system.

Nonlinear effects in fine focus applications with quadrupole multiplets and solenoids

Nonlinear effects are studied in proton fine focus systems consisting of electrostatic and magnetic quadrupole multiplets as well as of solenoids. Based on the investigation of aberrations induced by main and fringing fields, a suggestion is made for a fine focus lens that includes two electrostatic quadrupole doublets and one solenoid. The relative importance of various types of misalignments on the system performance is discussed.

Mössbauer investigation of rare earth sites in europium containing glasses

Samples of crystalline and amorphous trivalent europium metaphosphate were examined by 151Eu Mössbauer spectroscopy. The disorder of the lanthanide sites in the glass has been investigated by comparing the glass to the corresponding crystalline material. In the crystalline and amorphous samples, the rare earth is accommodated in a site on average distorted with respect to cubic symmetry; this site has no threefold or fourfold symmetry axis. In the glass, the structural disorder has been evaluated by broadening the Lorentzian component of the quadrupole multiplet with respect to the crystal. The spectrum of the amorphous sample was also analysed using a convolution method, which reproduces the distribution of the quadrupole interaction parameter due to the structural disorder.

Manipulation of ion channeling patterns using magnetic quadrupole lenses

This letter demonstrates that ion channeling patterns, produced by the passage of 3 MeV protons through a 0.5 μm thick [001] silicon crystal, can be transported and manipulated to produce enlarged or reduced area patterns using magnetic quadrupole lenses. The different effects on the ion channeling patterns obtained by using single quadrupole lenses and quadrupole multiplets are shown. The maximum attainable magnification under present conditions is investigated and a fundamental limitation to this process is identified as being the energy spread gained by the proton beam as it passes through the crystal.

Achromatic quadrupole focusing systems for use with liquid metal ion sources

We discuss the use of achromatic quadrupole lenses to overcome the limitation due to the energy spread of ions from liquid metal ion sources as they are currently focused with axially symmetric electrostatic lenses. Achromatic quadrupoles require both magnetic and electrostatic focusing elements. Each lens acts to focus in one plane and defocus in the other so that multiplet focusing systems are required to form an image of the source. Lens acceptance angles are limited by the bore of the electrostatic elements which in turn is limited by the necessary magnetic gradients required of the magnetic elements. The coefficients relating image distance to lens excitation of some of the elements of the quadrupole multiplets are found to be much larger than those in an axially symmetric electrostatic system. These factors are discussed in terms of the stability requirements of lens power supplies for a particular achromatic triplet system which is undergoing initial test.

Anticipated performance of achromatic quadrupole focusing systems when used with liquid metal ion sources

Current focusing systems for producing finely focused ion beams from liquid metal ion sources (LMIS) using axially symmetric electrostatic lenses are limited by chromatic aberration due to the relatively high (∼10 eV) energy spread inherent in LMIS. The highest current densities achievable are in the range of 1–5 A/cm2 at energies above 20 keV. In this paper, we discuss the use of achromatic quadrupole lenses to overcome the limitation due to energy spread. These lenses require both magnetic and electrostatic focusing elements. Lens acceptance angles are limited by the electrode positions and by the necessary magnetic gradients. The coefficients relating image distance to lens excitation of some of the elements in the quadrupole multiplet are found to be much larger than in electrostatic systems. These factors combine to require excitation stabilities as high as 1 part per million in order to achieve current densities more than 10 A/cm2, although such performance can be expected at beam energies of 5 keV or below.

Electric Field Gradient and Magnetic Hyperfine Interaction at Eu Nuclei in Ferromagnetic EuS

The NMR spectra of 151 Eu and 153 Eu nuclei with the nuclear spin I =5/2 were observed in ferromagnetic EuS using a single-crystal sphere by the cw method in fields up to 21 kOe below 4.2 K. In fields above magnetic saturation the 153 Eu spectrum consists of quadrupole-split five lines whose relative intensities depend on field direction. The central-line frequency which gives a hyperfine field at nuclei exhibits a small anisotropy in good agreement with the previous results, but the frequency separation Δν q between the quadrupole multiplets is isotropic, which is determined to be 0.358±0.005 MHz at 4.2 K. The temperature dependence of Δν q is rapid compared with that of the Eu magnetic moment. A linear extrapolation to absolute zero gives a value of Δν q =0.422±0.005 MHz which yields a quadrupole coupling of e 2 q Q /h=2.81±0.03 MHz. The 151 Eu spectrum is a single line even in magnetic fields.

Spectroscopic quadrupole moments from muonic atoms: Nuclear polarizability correction

In extracting spectroscopic quadrupole moments from the quadrupole hyperfine structure of intermediate orbits of muonic atoms nuclear polarizability is an important theoretical correction. Whilst the electric quadrupole polarizability is fairly well understood, this is not so for the electric dipole polarizability. We show that the latter yields a center-of-gravity shift δ 0 of the quadrupole multiplet and a shift δA 2 of the quadrupole hyperfine constant. The quantity δ 0 is evaluated using nuclear sum rules and is found to be in good agreement with existing numerical studies. The shift δA 2 is very small due to strong cancellations in the nuclear matrix elements. This cancellation is studied and proven in a number of nuclear models.

Internal Rotation of Molecules with Two Inequivalent Methyl Groups: The Microwave Spectrum of N-Methylethylidenimine

The microwave spectra of two isotopic species of trans-N-methylethylidenimine (CH3CH=NCH3) were recorded between 8 and 40 GHz. The rotational transitions clearly demonstrate the coupling with the internal motions of the two methyl groups, which are inequivalent in this molecule. The theory for the over-all and internal rotation was extended to molecules with two inequivalent symmetric internal rotors. The internal axis method (IAM) was used to calculate the internal rotors' splittings of the rotational transitions. They were split into five components according to the different irreducible representations of the symmetry group. In addition to this, the spectra were further complicated by the nuclear quadrupole multiplets of the nitrogen. A least squares analysis of the measured transition frequencies yielded the following rotational and quadrupole coupling constants for CH3CH=NCH3: A=38258.627± 0.048 MHz, B=4078.1354± 0.0058 MHz, C=3862.7391± 0.0072 MHz, χaa=1.578± 0.039 MHz, χbb=−4.601± 0.037 MHz, χcc=3.023± 0.041 MHz; and for CH3CD=NCH3: A=32982.409± 0.050 MHz, B=4076.6142± 0.0066 MHz, C=3799.5528± 0.0079 MHz, χaa=1.551± 0.038 MHz, χbb=−4.595± 0.023 MHz, χcc=3.044± 0.036 MHz. The mean values for the barriers of the two methyl groups were found to be 1642± 19 cal/mole for the C–CH3 top and 2109± 84 cal/mole for the N–CH3 top. A dipole moment of 1.499± 0.007 D was determined from the measured Stark splittings.

Nuclear resonance in crystals

In crystals, the nuclear spin-lattice relaxation time, t 1, is generally very long while the spin-spin relaxation time, t 2, is very short. In very few instances, however, is t 1 as long as it ought to be in a perfect crystal. Usually the dominant relaxation process involves not the lattice vibrations but internal molecular or ionic rotations, or possibly paramagnetic impurities. The temperature dependence of t 1 gives considerable information about internal rotation. Experiments on a number of crystals, including the ammonium halides, are described, and the relation of these studies to line-shape investigations is discussed. The coupling of a nuclear electric quadrupole to a vibrating lattice can be much stronger than the dipole effect. Pound has found examples in which this effect is dominant at room temperature, and has identified the mechanism as quadrupole coupling by selectively saturating one line of a quadrupole multiplet while observing the intensity of another. The relaxation time is not far from that predicted by Waller's theory, adapted to this case. The availability of crystals with a long relaxation time at room temperature has led to studies of the persistence of nuclear polarization when the crystal is removed from the magnet — in effect, “adiabatic demagnetization” from room temperature. It is possible to reserve the field in the crystal quickly, without reversing the polarization; the spin temperature is then negative, and the crystal emits, rather than absorbing, at resonance. These experiments raise a number of interesting questions about the state of the system when H 0 is comparable to, or less than, the internal fields, and make possible resonance studies in this new region.

The Interaction of Nuclear Electric Quadrupole Moments with Molecular Rotation in Asymmetric-Top Molecules. I

The theory of the interaction of nuclear electric quadrupole moments with molecular rotation is extended to asymmetric-top molecules containing one or two quadrupolar nuclei. The first-order theory is developed in detail, and in a form which makes use of published numerical tables of line strengths of asymmetric-top pure rotation transitions, and involves the second derivatives of the electrostatic potential $V$ taken along the three principal axes of inertia. Only two of these are independent, and ($\frac{{\ensuremath{\partial}}^{2}V}{\ensuremath{\partial}{z}^{\ensuremath{'}2}}$) and $(\frac{{\ensuremath{\partial}}^{2}V}{\ensuremath{\partial}{x}^{\ensuremath{'}2}})\ensuremath{-}(\frac{{\ensuremath{\partial}}^{2}V}{\ensuremath{\partial}{y}^{\ensuremath{'}2}})$ are a convenient choice of the parameters of the problem. A general formulation of the theory, which includes higher order effects, is given. In case a molecule contains only one quadrupolar nucleus, the structure of the quadrupole multiplets should be sufficient to identify pure rotation transitions.