Case study of a magnetic system for low-energy machines

The extra low-energy antiproton ring (ELENA) is a CERN particle decelerator with the purpose to deliver antiprotons at lowest energies aiming to enhance the study of antimatter. The hexagonal shaped ring with a circumference of about 30 m will decelerate antiprotons from momenta of 100 to $13.7\mathrm{MeV}/\mathrm{c}$. In this paper, the design approach for a magnet system for such a machine is presented. Due to the extra-low beam rigidity, the design of the magnet system is especially challenging because even small fields, arising for example from residual magnetization and hysteresis, have a major impact on beam dynamics. In total, seven prototype magnets of three different magnet types have been built and tested. This paper outlines challenges, describes solutions for the design of the magnet system and discusses the results of the prototypes.

Figure 1

Sketch of the ELENA ring.

Figure 2

Design options for dipole magnets.

Figure 3

Sketch of a sector coil generating an approximate dipole field.

Figure 4

Picture of ELENA preseries magnet during magnetic measurements.

Figure 5

Cross section and pole profile of ELENA dipole magnet.

Figure 6

Picture of prototype. Two geometrically identical prototype magnets have been built, one with a diluted and one with a nondiluted yoke.

Figure 7

Average permeability of steel I for different iron fractions by using measurement results performed with mixed samples.

Figure 8

Normalized center transfer function of LHeC dipole prototypes ($\lambda =0.33$) and LEP dipoles ($\lambda =0.27$) over iron field $B_{\mathrm{pole}}=B_{\mathrm{gap}}/\lambda$ [42].

Figure 9

Normalized center transfer function of ELENA diluted prototype ($\lambda =0.33$) over iron field $B_{\mathrm{pole}}=B_{\mathrm{gap}}/\lambda$. Measurements from [42].

Figure 10

Sketch of quadrupole magnet.

Figure 11

Hysteresis cycle for M140-35 S from two different suppliers A and B.

Figure 12

Picture of quadrupole prototype during magnetic measurement.

Figure 13

Comparison of measurement and simulation of the normalized transfer function of a diluted quadrupole with no end plates. Measurements are from [42].

Figure 14

Picture of a conventional $\mathrm{H}/\mathrm{V}$ corrector magnet used to measure remanent field and field quality at very low fields.

Figure 15

Sketch of $\mathrm{H}/\mathrm{V}$ corrector magnet.

Figure 16

Cross section of $\mathrm{H}/\mathrm{V}$ corrector magnet. The inner aperture has a diameter of 124 mm.

Figure 17

Picture of the coil-dominated corrector prototype.

Figure 18

Measurement and fit of the coercive force versus angle in polar coordinates at $J\approx 1.6\mathrm{T}$ for two NGO steel grades.

Figure 19

Measurement and fit of the coercive force versus angle in polar coordinates at $J\approx 1.4\mathrm{T}$ for two GO steel grades.

Figure 20

Coefficient of determination $R^2$ for different steel grades over excitation values.