Fig 3 - uploaded by Daniele Spiga
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a rough schematization of the hysteresis cycle of a magnet. The greyed region is the regime where permanent magnets operate.
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Scope of this document is to report some details on the activities performed in the phase A of the SIMBOL-X project to develop a magnetic diverter (MD), aimed at reducing the background due to the funnelling of high-energy (100 keV and above), charged particles, chiefly protons and electrons.
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Citations
... The magnetic field computation of an assembly of uniformly magnetized, rectangular blocks was already described in detail in [RD1]. The solution was subsequently extended to uniformly magnetized wedges [RD2]. ...
... When attempting to calculate the B field in the same way used in [RD1], one finds integrals involving elliptic integrals already at the integration over the 2 nd coordinate. We therefore regard the ring as a double loop of current: this is possible, because the magnetization is uniform and purely axial, so the bulk current density reads J = Ñ´M = 0. ...
... So Ar = 0, and the sole azimuthal component remains. It is convenient to firstly perform the integration in the z´ variable, which can be carried out by substitution [RD1]: ...
In this brief report, we develop the computation of the magnetic induction B vector generated by magnetized elements with curvilinear geometry, i.e. segments of rings (with rectangular radial section, not toroidal), or segments of cylindrical shells.
... 27 A known countermeasure can be a magnetic diverter, i.e. an arrangement of permanent magnets generating a magnetic field that deflects charged particles far from detectors. A possible magnetic diverter geometry for ATHENA is the Halbach array: unlike previous magnetic diverters located near the optics (e.g. for SWIFT-XRT or SIMBOL-X 28,29 ), this equipment -already present in the ATHENA CDF, and under study also by Thales Alenia Space -generates a powerful magnetic field within a small volume, with minimal escape field and without obstructions of focused X-rays. For proper operation, the ring has to be compact, and therefore needs to be located quite close (a few meters) to the focal plane. ...
The ATHENA X-ray observatory is a large-class ESA approved mission, with launch scheduled in 2028. The technology of silicon pore optics (SPO) was selected as baseline to assemble ATHENA’s optic with hundreds of mirror modules, obtained by stacking wedged and ribbed silicon wafer plates onto silicon mandrels to form the Wolter-I configuration. In the current configuration, the optical assembly has a 3 m diameter and a 2 m2 effective area at 1 keV, with a required angular resolution of 5 arcsec. The angular resolution that can be achieved is chiefly the combination of i) the focal spot size determined by the pore diffraction, ii) the focus degradation caused by surface and profile errors, iii) the aberrations introduced by the misalignments between primary and secondary segments, iv) imperfections in the co-focality of the mirror modules in the optical assembly. A detailed simulation of these aspects is required in order to assess the fabrication and alignment tolerances; moreover, the achievable effective area and the angular resolution depend on the mirror module design. Therefore, guaranteeing these optical performances requires: a fast design tool to find the most performing solution in terms of mirror module geometry and population, and an accurate point spread function simulation from local metrology and positioning information. In this paper, we present the results of simulations in the framework of ESA-financed projects (SIMPOSiuM, ASPHEA, SPIRIT) to prepare the ATHENA X-ray telescope: we deal with a detailed description of diffractive effects in an SPO mirror module, show ray-tracing results including mirror module misalignments, study in detail diffractive effects in different configurations, and assess the focal spot correspondence in X-rays and in the UV light, an important aspect to perform the mirror module alignment and integration. We also include a proton tracing simulation through a magnetic diverter in Halbach array configuration.
... In practice, a cylindrical layout with continuously varying magnetization orientation is very difficult to achieve and a good approximation is represented by a set of trapezoidal magnets. However, our simulation codes have so far implemented only the analytical formulae for rectangular rods[4,5]or disks with axial magnetization[6]. Satisfactory results can be also obtained assembling a Halbach array with rectangular rods (Fig. 1): in this case, the rotation of the magnetization vector M is obtained either rotating the magnetic bars or – whenever M is not normal to any face of the rod – superposing rods with different orientations of M and appropriate magnitude. ...
... It can be seen fromFig. 1that the B field is quite parallel and uniform in the array bore, assuming an uniform magnetization magnitude of 1.3 T[4]. We show inFig. ...
... 2the magnetic induction field intensity in the mid-plane of the diverter: in the central region, the field is intense but much less than predicted by Eq. 1 (5000 G) because the field lines tend to bend along the two sides of the z-axis. Additional nonuniformities come, however, from the missing junctions between rods that cannot be correctly simulated with the formulae derived so far for the cuboidal[4]and the ring-like geometries[6]. In order to include these missing parts, we would just need to add some wedge-shaped magnets with appropriate orientation of the M vector. ...
In this short note, we complete the simulation of the Halbach array deriving the analytical expressions of the magnetic field H generated by a magnet in the shape of a wedge.
... The magnetic field computation (details are reported elswhere 38 ) show that in the test configuration adopted here the magnetic field intensity in the space between magnets (i.e., in the regions where protons can be reflected) takes on values close to 0.1 T or higher, more or less between the yellow and the orange contours in Fig. 20b. Inside the magnetic material, the B-H variation is perfectly superposed to the nominal hysteresis cycle of the material. ...
The ATHENA X-ray observatory is a large-class ESA approved mission, with launch scheduled in 2028. The technology of silicon pore optics (SPO) was selected as baseline to assemble ATHENA’s optic with more than 1000 mirror modules, obtained by stacking wedged and ribbed silicon wafer plates onto silicon mandrels to form the Wolter-I configuration. Even if the current baseline design fulfills the required effective area of 2 m2 at 1 keV on-axis, alternative design solutions, e.g., privileging the field of view or the off-axis angular resolution, are also possible. Moreover, the stringent requirement of a 5 arcsec HEW angular resolution at 1 keV entails very small profile errors and excellent surface smoothness, as well as a precise alignment of the 1000 mirror modules to avoid imaging degradation and effective area loss. Finally, the stray light issue has to be kept under control. In this paper we show the preliminary results of simulations of optical systems based on SPO for the ATHENA X-ray telescope, from pore to telescope level, carried out at INAF/OAB and DTU Space under ESA contract. We show ray-tracing results, including assessment of the misalignments of mirror modules and the impact of stray light. We also deal with a detailed description of diffractive effects expected in an SPO module from UV light, where the aperture diffraction prevails, to X-rays where the surface diffraction plays a major role. Finally, we analyze the results of X-ray tests performed at the BESSY synchrotron, we compare them with surface finishing measurements, and we estimate the expected HEW degradation caused by the X-ray scattering.
... Also unexpected were the interaction of particles with the focusing optics, which were also operating as proton concentrators [RD3]. The problem of designing a proton diverter for the XEUS telescope, which would have had an even larger collecting area and be well far out of the Earth magnetosphere (more exactly in the L2 Lagrangian point), was early considered by M. Turner [RD1] and subsequently analyzed for the case of the SIMBOL-X telescope [RD4], [RD5], always by means of permanent magnets. To date, the proposal of ATHENA to the ESA call compels us to re-consider the design of a magnetic diverter based on either 1) permanent magnets, 2) electromagnets, or 3) electrostatic grids. ...
... The two magnetic bars are 10 cm x 10 cm x 30 cm sized, with centers 538 mm distant. If the magnetic material is a rare earth one, like a Neodymium-Iron-Boron, we can assume a N52 magnetization degree (corresponding to a measured magnetic dipole density of about 1.36 T [RD5]). The total magnet mass is 45 kg. ...
... The next step consists in computing the magnetic field in the region traversed by the protons. This can be done analytically [RD5], and we obtain the maps of magnetic field intensity in the MD mid-plane (the xy plane) and in a transverse section in the xz plane (Fig. 2). We can note that the magnetic field reaches up to 0.5 T at the magnets' surface but rapidly decays in the aperture region. ...
... The magnetic field computation of an assembly of uniformly magnetized, rectangular blocks was already described in detail in [RD6]. The core problem was the calculation of the magnetic field generated by a single rectangular magnet, which was not difficult to solve [RD6] in Cartesian coordinates. ...
... The magnetic field computation of an assembly of uniformly magnetized, rectangular blocks was already described in detail in [RD6]. The core problem was the calculation of the magnetic field generated by a single rectangular magnet, which was not difficult to solve [RD6] in Cartesian coordinates. However, in this case we have to deal with a problem with axial symmetry, so it is convenient to adopt a reference frame in cylindrical coordinates (Fig. 1). ...
... The magnetic energy density B×H/2 is zero inside and outside the ring. When attempting to calculate the B field in the same way used in [RD6], one finds integrals involving elliptic integrals already at the integration over the 2 nd coordinate. We therefore regard the ring as a double loop of current: this is possible because the magnetization is uniform, so the current in the volume is zero. ...
