Magnetic Quadrupole Lenses Research Articles

Polarization transfer coefficients for 3He(p, p)3He elastic scattering below 11 MeV

Abstract The polarization transfer coefficients K x x ′ , K z x ′ , and K y y ′ for 3 He(p, p) elastic scattering (Wolfenstein parameters R , A and D ) were measured at incident energies of 6.82, 8.82 and 10.77 MeV at up to four angles. Polarized protons scattered by a liquid nitrogen cooled 3 He cell were focussed by a magnetic quadrupole lens into a high pressure polarimeter filled with 4 He. The measured values compare satisfactorily with values calculated from previously determined phase shifts, from an R -matrix analysis of p- 3 He scattering and from microscopic calculations based on an approximate nucleon-nucleon potential.

Analysis of the lateral distribution of trace elements in biological and other materials by proton-induced X-ray fluorescence using a microbeam scanner

A proton microbeam facility for trace multi-element analysis has been built at the Bochum Dynamitron Tandem Laboratory. A proton beam of 4 MeV is collimated by a diaphragm of 200 μm diameter and then focused by four magnetic quadrupole lenses; thus a beam spot of 60 × 40 μm 2 size and 120 nA intensity is produced at the target position. Using the technique of X-ray fluorescence analysis, investigation of cooperative cellular colonies in the biological microstructure has been started. First lateral distributions of several trace elements are presented.

Ion orbits in quadrupole lenses

An exact expression for the ion orbits in the main field of an electric quadrupole lens with hyperbolic electrodes is given. For the magnetic quadrupole lens with pole pieces of hyperbolic or slightly deviating (e.g. circular) shapes, as well as for the electric quadrupole lens with slightly deviating electrode shapes, fifth-order approximations of the orbits are given.

Unbound isobaric analog states inMn53: The reactionsCr52(He3,d)Mn53andCr52(He3,dp)Cr52

The $^{52}\mathrm{Cr}(^{3}\mathrm{He},d)^{53}\mathrm{Mn}$ reaction investigated at 25 MeV incident energy with a split pole spectrometer was used to populate highly excited analog states in $^{53}\mathrm{Mn}$. Fifty-two levels between 6.9 and 12.0 MeV excitation energy were observed in $^{53}\mathrm{Mn}$. The main components of the ${T}_{>}2{p}_{\frac{3}{2}}$, $2{p}_{\frac{1}{2}}$, $1{f}_{\frac{5}{2}}$, and $1{g}_{\frac{9}{2}}$ single-particle strengths were identified. Angular distributions of transitions to 38 unbound-levels in $^{53}\mathrm{Mn}$ have been extracted and analyzed with distorted-wave Born approximation and Gamov functions (as form factors for the transferred proton) to yield the absolute spectroscopic strength. An appreciable amount of the missing $2{p}_{\frac{3}{2}}$, $2{p}_{\frac{1}{2}}$, and $1{f}_{\frac{5}{2}}$ proton ${T}_{<}$ strengths is observed in $^{53}\mathrm{Mn}$ between 7.0 and 8.5 MeV whereas a small fraction of the $1{g}_{\frac{9}{2}}$ and $2{d}_{\frac{5}{2}}$ single-particle orbitals appears between 7.0 and 12 MeV excitation energy. The $^{52}\mathrm{Cr}(^{3}\mathrm{He},dp)^{52}\mathrm{Cr}$ reaction was performed at 24 MeV incident energy using a triplet of magnetic quadrupole lenses. The angular correlations of the emitted protons were measured in coincidence using method II of Litherland and Ferguson with zero degree detection of deuteron groups. Spins, population parameters, and branching ratios of proton partial widths to the ground and excited states of the target were determined for 14 unbound levels in $^{53}\mathrm{Mn}$ from the analysis of the angular correlation data. These two experiments provide a rather complete description of the spectroscopic properties of the analog of the levels of $^{53}\mathrm{Cr}$ up to 5.0 MeV excitation energy. A comparison is made with the previous ($^{3}\mathrm{He},d$), ($p,\ensuremath{\gamma}$), ($p,p$), and ($d,p$) results on the same target. Components of the $^{53}\mathrm{Cr}$ parent states which consist of a neutron coupled to an excited state of the $^{52}\mathrm{Cr}$ nucleus are also determined.NUCLEAR REACTIONS $^{52}\mathrm{Cr}(^{3}\mathrm{He},d)$, $E=25$ MeV; measured $\ensuremath{\sigma}({E}_{d},\ensuremath{\theta})$, $^{52}\mathrm{Cr}(^{3}\mathrm{He},dp)$, $E=24$ MeV; measured $\ensuremath{\sigma}({E}_{d},{E}_{p},{\ensuremath{\theta}}_{p})$. $^{53}\mathrm{Mn}$ deduced IAS, $L$, $J$, $\ensuremath{\pi}$, $S$, ${\ensuremath{\Gamma}}_{p}$, proton branching. $^{53}\mathrm{Cr}$, $^{53}\mathrm{Mn}$ analog pairs deduced Coulomb displacement energies. DWBA analysis using Gamov functions as form factors. Natural targets.

Calculations and measurements for a magnetic quadrupole lens with a large aperture and a bell-shaped field distribution

A magnetic quadrupole lens of an aperture radius of 12.5 cm and a physical over-all length of 12 cm is described. The fringe field is linearized by means of rounded-off pole pieces and parallel end plates. The distribution of the transverse field components along the axis is nearly bell-shaped. The field strength necessary to focus parallel incoming electrons of an energy of 20 keV has been measured. The effect of the field distribution on the motion of electrons through the quadrupole lens has been calculated in first order theory using a hard-edge and a bell-shaped model. The bell-shaped model gives 4 and 3% larger fields than the hard-edge model, respectively, for two different focal lengths. There is a good agreement between measurement and bell-shaped model calculations for paraxial rays. For beams crossing the axis at large angles the fringe field linearization reduces the third order aberration by a factor of 4 compared to a pure bell-shaped quadrupole field. Moreover, the focusing fields were obtained by a stepwise numerical integration of the trajectory equations using the measured field distribution. The agreement with the measurements is satisfactory. Finally the stigmatic focusing of parallel beams by a quadrupole doublet consisting of two of these lenses has been considered. The bell-shaped model yields better results than the hard-edge model as is shown by numerically calculated trajectories using the measured field distributions and the field gradients obtained by the models.

Coupled lenses and their combinations

Electric or magnetic quadrupole lenses and their thin lens analogues, or coupled lenses, are examined for double focusing. The compatibility conditions for double focusing are similar to the stability conditions of betatron oscillations. When the double-focusing conditions are satisfied, a quadrupole lens doublet or a pair of coupled thin cylindrical lenses is equivalent to a single thick converging lens with unequal focal lengths in two orthogonal meridian planes. Specific double-focusing examples are given and a nomogram is developed for facilitating the calculations when combinations of coupled lenses are considered.

Third order transfer matrices for the fringing field of magnetic and electrostatic quadrupole lenses

Third order transfer matrices are derived for the fringing field of magnetic and electrostatic quadrupole lenses. All ion optical effects of the fringing field are reduced to a simple transformation at the ideal field boundary. The dominant third order elements are independent of the distribution of the fringing field. The other third order and the first order elements can be evaluated using the distribution function of the field gradient. The calculations are done in an effective fourth order approximation under the assumption that the extension of the fringing field is of about the same size as the beam diameter.

Comparison of calculated third-order aberrations of a magnetic quadrupole lens

Discrepancies between expressions for third-order aberration coefficients of a magnetic quadrupole lens of uniform gradient calculated by Smith 1) and by Lee-Whiting 2) are traced to an algebraic error in the former.

The Unilac Ion Source and Injection System

The design of the UNILAC injector was particularly governed by aspects of maintenance and reliable performance. Thus an open air 254 kV high gradient single gap acceleration was chosen for Uranium 11+ particles, corresponding to an injection energy of 11.7 keV/amu and a charge-to-mass ratio of 0.046. This allows fast ion source changes because only a short time for tube conditioning is required and takes into account the lifetime of present sources for multiply-charged heavy ions. Two independent Faraday-rooms, symmetrically arranged to the axis of the main accelerator, are housing each a 300 kV oil-insulated Cockcroft-Walton generator, a duoplasmatron and a Penning source with the associated equipment. Hereby a fast switch over to the stand-by source in case of an ion source failure is provided. Magnetic quadrupole lenses focus and match the beam through a magnetic deflection system, a 50 Hz chopper and a double drift buncher into the linac.

Superconducting magnetic quadrupole lens

Superconducting magnetic quadrupole lens

A quadrupole lens reaction products spectrometer system

The use of the momentum aberration inherent in magnetic quadrupole lenses is studied as the basis for constructing low resolution nuclear reaction product spectrometers and magnetic rigidity band pass filters. An operational system utilizing a quadrupole doublet is described. The system provides a solid angle of 1.8 mrs, a variable momentum acceptance range up to a mass energy product of 100 amu MeV, and a range of laboratory scattering angles from 0 to ± 80°. Data from representative experiments taken with the system are presented to demonstrate its capabilities.

Minimum Chromatic Aberrations of Magnetic Quadrupole Objective Lenses

Orthogonal magnetic quadrupole lens systems that could serve as electron microscope objectives are treated theoretically. After certain constraints are placed on the quadrupole field strength, the calculus of variations is applied to obtain systems with minimum chromatic aberrations. A digital computer was used to calculate optimum orthomorphic and anamorphotic objective type systems. The resulting orthomorphic systems have four lenses while the corresponding anamorphotic systems have three. The chromatic aberration only varies by a factor of 2 in this study indicating its relative insensitivity to choice of lens systems. It is found that the optimum quadrupoles have about 3.6 times as much chromatic aberration as round lenses with comparable fields and dimensions.

The use of a phase space representation for the design of a beam transport system with doubly achromatic and dispersive modes of operation

The beam transport system for the Eindhoven AVF-cyclotron is described. Phase space representation is applied to yield dispersive properties and beam envelopes. The analysis is restricted mainly to a 90° deflecting subsystem composed of two 45° magnets and three magnetic quadrupole lenses. This system allows either a doubly achromatic or a highly dispersive mode of operation. The analysed beam will have an energy spread of 0.5% fwhm with entrance and exit slits of 1 mm width. Currents of 10 μA analysed beam are expected. The total width of the beam does not exceed 20 mm, except horizontally at the position of the two 45° magnets in the dispersive mode. The inner diameter of the beam pipes is 45 mm.

Third-order aberrations of a magnetic quadrupole lens

General expressions for the aberration coefficients are derived in a form in which derivatives of the magnetic gradient do not appear. Specializations to a segment of the optic axis on which the gradient is uniform and to the rectangular model are given. A segment on which the gradient varies is treated by expansion in a power series; the expansion coefficients depend on form-factors similar to those occurring in the first-order theory. Momentum-dependent aberrations and the transit-time are handled in the same way. In all cases laws are given for combining the effects of two adjacent segments. The calculations do not support the idea that hyperboloidal pole-ends result in reduced aberrations.

The floating wire method for determining the useful aperture of a magnetic quadrupole lens

The floating wire method is applied to determine the useful aperture of a magnetic quadrupole lens. Within the useful aperture nonlinear behaviour corresponding to spherical aberration does not exceed a specified value. The optical distance between two points upon the axis of a (thin) lens is considered. It is, mainly, a quadratic function of the distance between a particular trajectory and the optical axis in the lens. The nonlinearity results from a sixth degree term. Dependent upon the sign of the quadratic function three cases are distinguished. The behaviour of the floating wire confirms the theoretical considerations. For the measured quadrupole lens (geometrical length 15 cm, aperture radius 2.75 cm) the aberration, expressed as a fraction of the paraxial lens strength, is smaller than 1 × 10 −3 within 80% of the radius.

Focusing properties of electric and magnetic quadrupole lenses

Expressions for focusing coefficients applicable to the interior regions (transverse fields) of electric and magnetic quadrupole lenses have been derived through third order. Also, a simple procedure for computing the first-order contributions of the fringing fields in realistic lenses is discussed. Relativistic effects are taken fully into consideration. These results are applied to the specific problem of a medium-length magnetic quadrupole lens. The second-order contributions vanish in the interior as a result of the quadrupole symmetry, and the third-order terms are found to be considerably smaller than the first-order terms. It is concluded that the focusing properties of a quadrupole lens are governed almost entirely by the strength and axial variation of the transverse field gradient. These lens properties can be measured quite easily.

Aligning Magnetic Quadrupole Lenses by the ``Grove Effect''

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Beam handling behind an electromagnetic isotope separator

Beam handling using two magnetic quadrupole lenses behind a double focusing isotope separator yields a line-focus with a width of 0.6 mm. A spot-focus can be obtained too. With this technique it is possible to take a beam of radioactive ions out of the collector-chamber to a measuring-facility. Beamscanners proved to be very useful for measuring the beam profile and the position of the beam in the transport-tube. A focus can be shifted in the beam direction over a distance of 30 cm by moving the quadrupole lenses, without serious defocusing.

828. Mass spectrometer with two-dimensional magnetic prism and quadrupole lenses: T Ya Fishkova et al, Zh tekh fiz, 38 (2), Feb 1968, 375–377 ( in Russian).

828. Mass spectrometer with two-dimensional magnetic prism and quadrupole lenses: T Ya Fishkova et al, Zh tekh fiz, 38 (2), Feb 1968, 375–377 ( in Russian).

Ein Biprisma-Interferometer f�r 100 keV Elektronen und seine Anwendung

A biprism-interferometer for 100 keV electrons working with magnetic quadrupole lenses is described. With this instrument the mean inner potentials φ of Cu and Au were measured. Values of φ=(20,2± 0,7) V for Cu and φ=(16,8± 1,0) V for Au were found.