Main Quadrupole Research Articles

Transductors for Current Sensing in the Dipole and Quadrupole Magnet Circuits of the Fermilab Main Ring

Transductors are used as current measuring devices in the main accelerator quadrupole power supply feedback loop and as monitors in the dipole circuit. The development of these transductors is described, starting with the basic series - connected (Kraemer) transductor circuit, and adding the features of biasing and a voltage follower to obtain improved linearity and high slewing rate.

Peak tails produced by elastic scattering in mass spectra of tandem mass spectrometers

The elastically scattered ion current distributions are given for tandem mass spectrometers including magnetic and electrostatic deflectors with circular main paths, Wien filters and quadrupoles. To compute the distributions for mass spectrometer geometry and the first order radial matrix formalism and the graphs included in the work must be used.

Modification of LINDA to Treat the Grain Orientation Effect

An approximate method of dealing the grain orientation effect has been investigated. This has been applied to the field computation of the main ring quadrupole magnet of KEK-PS.

Proton Inelastic Scattering from the Five Stable, Even-Mass Isotopes of Molybdenum

Elastic and inelastic scattering of 15-MeV protons, accelerated by the 90-in. cyclotron at Lawrence Radiation Laboratory, Livermore, from isotopically enriched targets of $^{92,94,96,98,100}\mathrm{Mo}$ were studied with an over-all resolution of 50 keV (full width at half maximum). The experimental angular distributions were analyzed using a coupled-channel calculation. The collective vibrational model was employed to describe the states of the nucleus. Fifty angular distributions of scattered particles were measured and all but three were fitted with theoretical curves. The results for $^{92}\mathrm{Mo}$, which has a closed neutron shell associated with the magic number $N=50$, are discussed separately. All the inelastic scattering to levels in $^{92}\mathrm{Mo}$ were fitted with single-step processes. The other even-mass isotopes of molybdenum were analyzed first by considering the main quadrupole and octupole vibrational states and then considering the states that can be described as possible mixtures of one- and two-quadrupole phonons. A high degree of single-phonon admixture was found to be present. Finally the weaker states were considered with the simple ${0}^{+}\ensuremath{-}{I}^{\ensuremath{\pi}}$ coupling scheme. Electromagnetic transition rates inferred from the deformabilities deduced in the present experiment. The results are compared with other experiments.

Meson channel design and performance for the SREL synchrocyclotron

A pion-muon channel has been designed for internally generated mesons from the NASA Space Radiation Effects Laboratory 600 MeV synchrocyclotron. The channel, similar to those at CERN and Chucago, consists of three sections: a main section containing 24 identical 11” bore quadrupole magnets, an inout matching section consisting of a quadrupole doublet for matching to the meson emittance from the cyclotron, and an output bending magnet. Computer programs using quadrupole transfer matrices including linear magnetic fringe field effects have been used to optimize the meson flux. The main section quadrupoles have terraced pole tips and achieve a gradient of 2.4 kG/in. Movable channel mounting has been incorporated with pillared shielding to facilitate reorientation of the channel with respect to the cyclotron to change the mean pion momentum entering the channel. 740 stopped μ − per gram sec and 1.500 stopped π − per gram sec were observed into a 6″ × 6″ target.

Sensitive Detection of Nuclear Quadrupole Interactions in Solids

The pure nuclear quadrupole resonance of a low-abundance spin species in zero field is observed for molar concentrations as low as one part in ${10}^{7}$ by the application of a nuclear-double-resonance method. The quadrupole resonance is measured in terms of a decrease in the magnetic order of abundant nuclei which are dipolar-coupled to the low-abundance nuclear species. The double-resonance process is analyzed from the point of view of two energy reservoirs coupled by a dipolar perturbation, and spin diffusion among abundant nuclei is included phenomenologically. Radio-frequency power, which causes the main quadrupole transitions of rare spins, is frequency-modulated to provide saturation in the rotating frame and to enable identification of unknown spin transitions. The pure nuclear quadrupole resonance of Na and Cl nuclei near impurities and imperfections in NaCl is measured. Particular attention is given to the resonances associated with ${\mathrm{K}}^{+}$ and ${\mathrm{Br}}^{\ensuremath{-}}$ ions injected as impurities into the NaCl lattice. An unsuccessful search in zero field has been made for the naturally abundant 0.0156% deuterium quadrupole resonance in CaS${\mathrm{O}}_{4}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O and ${\mathrm{C}}_{10}$${\mathrm{H}}_{8}$, where the proton resonance is monitored as the abundant nuclear species. The proton dipolar absorption in zero magnetic field is anomalously broad and overlaps too much with the deuterium quadrupole resonance to permit independent observation of the latter. A narrowing of proton dipolar absorption in zero field is observed for strong radio-frequency fields larger than internal dipole fields.

Zero-Field Nuclear Quadrupole Spin-Lattice Relaxation in the Rotating Frame

Nuclear quadrupole spin-lattice relaxation rates in different frames of reference for pure electric quadrupole coupling are evaluated in terms of spectral density functions of lattice vibrations. The rate is determined in each of three important reference frames defined with respect to (1) the axial crystalline field in the laboratory, (2) a strong rotating radiofrequency field, and (3) internal dipolar fields following adiabatic demagnetization in the rotating frame. For spin states established by pure quadrupole coupling, modification of the relaxation behavior in the different frames does not conform to the behavior obtained from spins bound in pure magnetic Zeeman states. The density-matrix perturbation formalism is applied. In order to transform the total Hamiltonian into the interaction representation of the main quadrupole interaction, a convenient representation is devised for quadratic exponential unitary operators which do not directly carry out simple rotations. The transformation permits an approach to the rigorous analysis of dynamic nuclear quadrupole resonance phenomena which usually have been qualitatively described by comparison with analogous phenomena in pure magnetic resonance. The new representation is presented explicitly for spin $I=\frac{3}{2}$. Experimental measurements of ${\mathrm{Cl}}^{35}$ pure quadrupole spin-lattice relaxation times in chlorate salts in the three reference frames are compared with the theoretically determined relaxation rates.