Materials for high vacuum technology, an overview

In modern accelerators stringent requirements are placed on materials of vacuum systems. Their physical and mechanical properties, machinability, weldability or brazeability are key parameters. Adequate strength, ductility, magnetic properties at room as well as low temperatures are important factors for vacuum systems of accelerators working at cryogenic temperatures, such as the Large Hadron Collider (LHC) under construction at CERN. In addition, baking or activation of Non-Evaporable Getters (NEG) at high temperatures impose specific choices of material grades of suitable tensile and creep properties in a large temperature range. Today, stainless steels are the dominant materials of vacuum constructions. Their metallurgy is extensively treated. The reasons for specific requirements in terms of metallurgical processes are detailed, in view of obtaining adequate purity, inclusion cleanliness, and fineness of the microstructure. In many cases these requirements are crucial to guarantee the final leak tightness of the vacuum components

On the distribution of the order and index for the reductions of algebraic numbers

Let $\alpha_1,\ldots,\alpha_r$ be algebraic numbers in a number field $K$ generating a subgroup of rank $r$ in $K^\times$. We investigate under GRH the number of primes $\mathfrak p$ of $K$ such that each of the orders of $(\alpha_i\bmod\mathfrak p)$ lies in a given arithmetic progression associated to $\alpha_i$. We also study the primes $\mathfrak p$ for which the index of $(\alpha_i\bmod\mathfrak p)$ is a fixed integer or lies in a given set of integers for each $i$. An additional condition on the Frobenius conjugacy class of $\mathfrak p$ may be considered. Such results are generalizations of a theorem of Ziegler from 2006, which concerns the case $r=1$ of this problem

Physics and measurements of magnetic materials

Magnetic materials, both hard and soft, are used extensively in several components of particle accelerators. Magnetically soft iron-nickel alloys are used as shields for the vacuum chambers of accelerator injection and extraction septa; Fe-based material is widely employed for cores of accelerator and experiment magnets; soft spinel ferrites are used in collimators to damp trapped modes; innovative materials such as amorphous or nanocrystalline core materials are envisaged in transformers for high-frequency polyphase resonant convertors for application to the International Linear Collider (ILC). In the field of fusion, for induction cores of the linac of heavy-ion inertial fusion energy accelerators, based on induction accelerators requiring some 107 kg of magnetic materials, nanocrystalline materials would show the best performance in terms of core losses for magnetization rates as high as 105 T/s to 107 T/s. After a review of the magnetic properties of materials and the different types of magnetic behaviour, this paper deals with metallurgical aspects of magnetism. The influence of the metallurgy and metalworking processes of materials on their microstructure and magnetic properties is studied for different categories of soft magnetic materials relevant for accelerator technology. Their metallurgy is extensively treated. Innovative materials such as iron powder core materials, amorphous and nanocrystalline materials are also studied. A section considers the measurement, both destructive and non-destructive, of magnetic properties. Finally, a section discusses magnetic lag effects.Comment: 25 pages, presented at the CERN Accelerator School CAS 2009: Specialised Course on Magnets, Bruges, 16-25 June 200

On the order of the reductions of algebraic numbers

Let K be a number field, and let G be a finitely generated and torsion-free subgroup of K*. For almost all primes p of K, we consider the order of the cyclic group (G mod p), and ask whether this number lies in a given arithmetic progression. The density of primes for which this condition holds exists (this generalizes a result of Ziegler from 2006) and it is, under certain assumptions, a computable positive rational number. We also present a uniformity property concerning some special cases. This is a joint work with A. Perucca

Vacuum for accelerators: introduction to materials and properties

In modern accelerators, stringent requirements are placed on the materials used for vacuum systems. Their physical and mechanical properties, machinability, weldability and brazeability are key parameters. Adequate strength, ductility, magnetic properties at room as well as low temperatures are important factors for vacuum systems of accelerators working at cryogenic temperatures. In addition, components undergoing baking or activation of Non-Evaporable Getters (NEG) or directly exposed to the beam impose specific choices of material grades for suitable outgassing and mechanical properties in a large temperature range. Today, stainless steels are the dominant materials of vacuum systems. The reasons for specific requirements in terms of metallurgical processes are detailed for obtaining adequate purity, inclusion cleanliness and fineness of the microstructure. In many cases these requirements are crucial to guarantee the final leak tightness of the vacuum components. Innovative manufacturing and material examination technologies are also treated.Comment: 30 page

Effects of Thermocapillary Forces during Welding of 316L-Type Wrought, Cast and Powder Metallurgy Austenitic Stainless Steels

The Large Hadron Collider (LHC) is now under construction at the European Organization for Nuclear Research (CERN). This 27 km long accelerator requires 1248 superconducting dipole magnets operating at 1.9 K. The cold mass of the dipole magnets is closed by a shrinking cylinder with two longitudinal welds and two end covers at both extremities of the cylinder. The end covers, for which fabrication by welding, casting or Powder Metallurgy (PM) was considered, are dished-heads equipped with a number of protruding nozzles for the passage of the different cryogenic lines. Structural materials and welds must retain high strength and toughness at cryogenic temperature. AISI 316L-type austenitic stainless steel grades have been selected because of their mechanical properties, ductility, weldability and stability of the austenitic phase against low-temperature spontaneous martensitic transformation. 316LN is chosen for the fabrication of the end covers, while the interconnection components to be welded on the protruding nozzles will be fabricated from forged 316L or 316LN, and welded 316L tubes. Autogenous welds between the nozzles and the interconnection components will be performed by the automatic orbital TIG technique. Several thousands of welds are foreseen. When welding together grades of slightly different composition, or grades issued from different fabrication methods (cast, PM, cold or hot rolled, forged...), phenomena such as variable weld penetration, "off-centre welding" and "arc wander" may possibly appear, resulting in uncontrolled formation of non axisymmetric welds. Such deflections of the weld pool are difficult to correct for an automatic process and may affect the soundness of the weld. A large and systematic campaign of welding tests associated with video recording of the melt pool has been carried out. Hot metal deflections have been precisely quantified. The results are interpreted in terms of the different content of soluble surface-active elements of the various steel batches and the directions of the thermocapillary flow arising from these different contents. This interpretation gives a quantitative prevision of the hot metal deflections. Possible corrections applicable to automatic welding processes are discussed

Phase stability of high manganese austenitic steels for cryogenic applications

The aim of this work is to study the austenitic stability against a' martensitic transformation of three non-magnetic austenitic steels : a new stainless steel X2CrMnNiMoN 19-12-11-1 grade, a traditional X8CrMnNiN 19-11-6 grade and a high manganese X8MnCrNi 28-7-1 grade. Measurements of relative magnetic susceptibility at room temperature are performed on strained tensile specimens at 4.2 K. A special extensometer for high precision strain measurements at low temperature has been developed at CERN to test specimens up to various levels of plastic strain. Moreover, the high precision strain recording of the extensometer enables a detailed study of the serrated yield phenomena associated with 4.2 K tensile testing and their influence on the evolution of magnetic susceptibility. The results show that high Mn contents increase the stability of the austenitic structure against a' martensitic transformation, while keeping high strength at cryogenic temperature. Moreover, proper elaboration through primary and possibly secondary melting maintains high levels of low temperature ductility

Prime divisors of ℓ\ell-Genocchi numbers and the ubiquity of Ramanujan-style congruences of level ℓ\ell

Let $\ell$ be any fixed prime number. We define the $\ell$-Genocchi numbers by $G_n:=\ell(1-\ell^n)B_n$, with $B_n$ the $n$-th Bernoulli number. They are integers. We introduce and study a variant of Kummer's notion of regularity of primes. We say that an odd prime $p$ is $\ell$-Genocchi irregular if it divides at least one of the $\ell$-Genocchi numbers $G_2,G_4,\ldots, G_{p-3}$, and $\ell$-regular otherwise. With the help of techniques used in the study of Artin's primitive root conjecture, we give asymptotic estimates for the number of $\ell$-Genocchi irregular primes in a prescribed arithmetic progression in case $\ell$ is odd. The case $\ell=2$ was already dealt with by Hu, Kim, Moree and Sha (2019). Using similar methods we study the prime factors of $(1-\ell^n)B_{2n}/2n$ and $(1+\ell^n)B_{2n}/2n$. This allows us to estimate the number of primes $p\leq x$ for which there exist modulo $p$ Ramanujan-style congruences between the Fourier coefficients of an Eisenstein series and some cusp form of prime level $\ell$.Comment: 27 page

Influence of coating temperature on niobium films

The coating of niobium on copper is the technology successfully used for the production of LEP accelerating cavities. A good understanding of the influence of the different coating parameters on the f ilm properties can contribute to improve the RF performance of such cavities. Several copper samples were coated with a 1.5 mm thick niobium film in a cylindrical magnetron sputtering system, using a rgon as discharge gas. To study the effect of the coating temperature only, a 500 MHz cavity was equipped with three sample-holders on the equatorial region. The latter were kept at different temperat ures during the baking and the simultaneous coating (150ºC, 250ºC and 35ºC). The films were characterised by measuring the RRR, critical temperature, total Ar content and lattice parameter. Films depo sited at higher temperatures show higher RRR and lower Ar content. The film lattice parameter and, consequently, the critical temperature change with the coating temperature. The results are interpret ed in terms of the film bombardment during the growth, of higher niobium surface mobility at higher temperature and of the different thermal expansion coefficients between the niobium film and the sub strate