R.A. Hartmann

Optimal neutron Larmor precession magnets

Spectroscopic techniques based on Larmor precession of particle spins require that for all trajectories of a diverging beam the path integral of the modulus of the magnetic field must be a constant. The amount of precession performed by each spin is then a function of the particle energy only. For cylinder magnets this homogeneity condition can be expressed as a variational problem. An analytical solution is presented for this variation problem. This solution describes the optimal field shape (OFS) to obtain the best possible homogeneity for a given magnet length. In practice the ideal shape can be obtained by superposing a series of solenoids of different lengths but the homogeneity is generally not good enough so that in-beam correction coils are needed that include corrections for the line integral differences caused by the finite-beam divergence. The solution is presented together with a method to implement it in practice using discrete in-beam current distributions. The resulting magnet has a homogeneity of 10/sup -6/, so that the Larmor precession angle is still well defined after 10/sup 4/ turns. >

Numerical solutions of the current distribution in superconducting cables

Superconducting cables are described by current sheets using the continuum model of W. Carr Jr. [1] and assuming an anisotropic conductivity. Two different situations are considered: a) finite length of cable in spatially independent magnetic field; b) infinitely long cable in a periodical magnetic field.

Hysteresis losses in hollow superconductors

Flux penetration into a hollow superconducting filament in a time-varying transverse magnetic field is determined numerically. The magnetization of the filaments is calculated for field variations below and above the penetration field of the filament. The influence of the inner radius of the superconducting filament on the magnetization and the hysteresis losses in the filament is shown. The critical current density is taken to be constant during the external field cycle and depends within the superconducting filament on the local magnetic field, which is the sum of the externally applied field and the field induced by the local screening currents. Calculations based on the theory presented here show good agreement with experimental results. >

Numerical solution of the transverse resistivity of superconducting cables under AC conditions

The authors develop a numerical method for calculating the transverse resistivity of superconducting cables. A superconducting cable consists of a twisted bundle of strands with a nonconducting inner region. If such a cable is placed in an external magnetic field, the induced currents will not merely flow in the axial direction, but also around the center, in the plane of the cross section. It is shown that the transverse transport current, which is induced by external fields acting on the cable, can saturate most of the filaments of the superconducting layer. This results in a smaller maximal value of a longitudinal transport current and small coupling losses. >

Calculations on the current density and the voltage-current relation under a.c. conditions of filaments

Technical applications of multifilamentary wires indicate that filaments are used in complex magnetic fields (a combination of non-parallel a.c./d.c. transverse and rotating fields) carrying an a.c./d.c. transport current of various frequency. Furthermore, due to technical manufacturing processes the filaments are heavily distorted. Therefore, a numerical model is developed to compute the current density of a filament of arbitrary shape in any external transverse field carrying an a.c./d.c. transport current. The great flexibility of the model is shown in several examples.

Construction of optimized superconducting spin precession magnets for neutron spectroscopy

The design and construction of a superconducting magnet system for a high-resolution neutron spin echo spectrometer. The principal solution for the field shape of optimal precession magnets is B/sub 0/cos/sup 2/( pi z/L). In practical precession magnets, this field shape is approximated by 30 superimposed concentric solenoids with a bore of 80 mm. The required field integral of 1 Tm, providing 10/sup 4/ precession turns, is achieved in a magnet with a length of about 1.5 m. The field in the center is 1.5 T maximum. The relative line integral inhomogeneity of about 10/sup -3/ obtained with such a coil is improved to less than 10/sup -6/ by two in-beam correction coils. The advanced homogeneity level means that after 10000 precession turns the precession angle remains still well defined without using tedious correction procedures. >

NUMERICAL SOLUTIONS OF THE CURRENT DISTRIBUTION IN SUPERCONDUCTING RECTANGULAR CABLES

Cables are used in several technical applications such as accelarators, SMES and fusion projects. In all of these applications we find that a cable is placed in a combination of a transverse and a longitudinal applied field. Furthermore, we can define the problem periodical along the axis of the cable, because of the solinoidal or toroidal shape of the magnet. We will derive a simple numerical method for calculating the current distribution in a rectangular cable, where a cable is approximated by a small layer of wires with a nonconducting inner region, where the internal structure of the wire is neglected. A general outline for the unsaturated stationairy problem is given, but the described method can also be applied for instationary situations or cases were saturated regions may be expected.

An experiment on interstrand coupling currents in soldered cables

The effective frequency-dependent transverse resistivity experienced by coupling currents in superconducting cables was studied experimentally. The results extend the theory regarding the effective transverse resistivity of soldered strands to the whole AC domain. An accompanying magnetic effect due to the twist of the filaments has been measured and qualitatively explained by a simple model of the filament layer in the strands. It is seen that the coupling current experiences maximum resistivity if the strands are almost untwisted. >