Particle accelerators use powerful and complex magnetic fields to turn, shape, and eventually collide beams of near-light-speed particles, yet the fundamental magnetic principles behind the accelerator magnets can be understood by undergraduate students. In this paper we use small-scale accelerator magnet analogs in a multi-faceted, low-cost exploration of the magnetic field exterior to accelerator magnets. These fields are best understood using the multipole expansion of the field. If we assume that the magnetic field is created by ideal magnetic dipoles, we can derive a theoretical model that shows that each accelerator magnet configuration is dominated by a single multipole moment and obeys $B \propto 1/r^{l+2}$, where $l$ is the multipole order (with $l = 1, 2, 3, 4$ for the dipole, quadrupole, octopole, and hexadecapole moments, respectively). Using commercially available NdFeB magnets and the magnetic field sensor inside a smartphone, we experimentally verify the power-law dependence of the accelerator magnet configurations. Finally, we use the open-source Python library Magpylib to simulate the magnetic field of the permanent magnet configurations, showing good agreement between theory, experiment, and simulation.
This lecture note describes how to set up and what is behind a magnetodynamic field simulation for an accelerator magnet. The relevant formulation of Maxwell's equations is derived. The formulation is discretized in space by the finite-element method and in time by a standard time integration method. The steps for setting up the accelerator-magnet model are described. An exemplary simulation of the GSI SIS-100 magnet is given as illustration. Finally, some extensions to the standard FE method, dedicated to accelerator magnets, are discussed.
KEK cryogenics science center is developing superconducting magnet technology for future accelerator science. Three major technological categories are focused; 1) high precision 3D magnetic field technology based on the g-2/EDM magnet developments, 2) rad-hard superconducting magnet technology based on the COMET magnet developments, and 3) high magnetic field superconducting magnet technology for future colliders based on the LHC MQXA and HL-LHC D1 magnet developments. Extensive studies including Nb3Sn conductor and magnet developments for high field magnets and HTS for rad-hard superconductin…
Muon acceleration using a radio-frequency accelerator was recently demonstrated for the first time. Measurement of the muon anomalous magnetic moment and electric dipole moment at Japan Proton Accelerator Research Complex is the first experiment using accelerated muon beams, and construction will begin soon. The radio-frequency accelerator used in the experiment and the first muon acceleration are described in this paper.
Among various long-standing standing problems in superconducting accelerator magnet development, training is one of the oldest and well-known issues affecting magnet performance. Understanding physics behind the training process is crucial for proper mitigation and elimination of this phenomenon in new magnet designs. This paper discusses application of acoustic emission (AE) diagnostics to localization and classification of transient mechanical events in superconducting magnets and characterization of transient energy releases responsible for premature quenching, memory effects and, ultimatel…
Four decades ago development of high-current superconducting NbTi wire cables revolutionized the magnet technology for energy frontier accelerators, such as Tevatron, RHIC and LHC. The NbTi based magnets offered advantage of much higher fields B and much lower electric wall plug power consumption if operated at 4.5 K but relatively small ramping rates dB/dt << 0.1 T/s. The need for the accelerators of high average beam power and high repetition rates have initiated studies of fast ramping SC magnets, but it was found the AC losses in the low-temperature superconductors preclude obtaining the r…
The next generation high energy physics accelerators will require magnetic fields at ~20 T. HTS coils will be an essential component of future accelerator magnets and several efforts are currently dedicated on designing 20 T HTS- LTS hybrid magnets. Among the existing challenges, there is the lack of a robust quench detection system for hybrid magnet technology. Another big challenge is represented by the high number of training quenches required by Nb3Sn magnets to reach performance level. In this framework it is important to find a tool that allow local real-time monitoring of magnet strain …
The Snowmass community exercise started in April 2020 to identify and document a scientific vision for the future of particle physics in the US and international partners. The AF7-Magnets working group was charged to a) address the potential contributions of magnet technology to future HEP facilities, b) evaluate the R\&D required to enable these opportunities, c) estimate the time and cost scales of these efforts, and d) assess the needs for associated fabrication infrastructure and test facilities. This report addresses the working group charge, summarizes the status of accelerator and detec…
Accelerators magnets must have minimal magnetic field imperfections for reducing particle-beam instabilities. In the case of coils made of high-temperature superconducting (HTS) tapes, the field imperfections from persistent currents need to be carefully evaluated. In this paper we study the use of superconducting screens based on HTS tapes for reducing the magnetic field imperfections in accelerator magnets. The screens exploit the magnetization by persistent currents to cancel out the magnetic field error. The screens are aligned with the main field components, such that only the undesired f…
We report results of the experimental test of the High Temperature Superconductor based fast cycling prototype accelerator magnet capable to operate up to about 300 Tesla per second field ramping rate with some 0.5 T field in the magnet gap. The measured upper limit for the cryogenic cooling power required to support magnet conductor operation at high ramping rates indicates great potential for such types of magnets in rapid cycling synchrotrons for neutrino research or muon acceleration. The test magnet design, construction, and supporting cryogenic and power systems are briefly described. Th…
Development of energy-efficient fast cycling accelerator magnets is critical for the next generation of proton rapid cycling synchrotrons (RCS) for neutrino research and booster accelerators of future muon colliders. We see a unique opportunity for having such magnets to be built on base of High Temperature Superconductors (HTS). Besides being superconducting at relatively high temperatures, rare-earth HTS tapes have shown very small AC losses compared to low-temperature NbTi superconductor cables. Recent tests of the HTS-based 0.5 m long two-bore superconducting accelerator magnet have shown …
We take a comprehensive look at conductors used in superconducting magnets for the accelerator sector and explore the ramifications of the present marketplace for supply of conductor to future accelerator facilities. While there are thousands of superconductors, many of which have promising properties for applications, we outline the journey a promising material must take to become a magnet conductor that is manufactured at the scale needed for an accelerator facility. Among the few materials that actually reach this scale, Nb$_{3}$Sn is arguably the workhorse conductor for the next generation…
This note describes an extended exercise on the finite-element (FE) simulation of an accelerator magnet. The students construct and simulate a magnet model using the FEMM freeware. They get the opportunity to exercise on the theory of FEs, including Maxwell equations, magnetoquasistatic formulation, weighted residual approach, choice of appropriate FE shape functions and algebraic system of equations, thereby guided by fill-in sheets. They are invited to implement the most crucial parts of a simple FE solver. Finally, the own software is used to simulate the magnet once more and to develop som…
In this paper a general approach to reconstruct three dimensional field solutions in particle accelerator magnets from distributed magnetic measurements is presented. To exploit the locality of the measurement operation a special discretization of the Laplace equation is used. Extracting the coefficients of the field representations yields an inverse problem which is solved by Bayesian inversion. This allows not only to pave the way for uncertainty quantification, but also to derive a suitable regularization. The approach is applied to rotating coil measurements and can be extended to any othe…
Business models to assure availability of advanced superconductors for the accelerator sector and promote stewardship of superconducting magnet technology for the US economy
The most effective way to achieve very high collision energies in a circular particle accelerator is to maximize the field strength of the main bending dipoles. In dipole magnets using Nb-Ti superconductor the practical field limit is considered to be 8-9 T. When Nb3Sn superconductor material is utilized, a field level of 15-16 T can be achieved. To further push the magnetic field beyond the Nb3Sn limits, High Temperature Superconductors (HTS) need to be considered in the magnet design. The most promising HTS materials for particle accelerator magnets are Bi2212 and REBCO. However, their outst…
The scope of the proposal outlined in this white paper is the development and demonstration of the technology needed for next generation of Nb_3Sn accelerator magnets in the 12-14 T range. The main goal is to cut magnet cold-mass cost by a factor 2 or higher with respect to the Nb_3Sn magnets produced by the US Accelerator Upgrade Project (AUP) for the High-Luminosity Large Hadron Collider (HL-LHC). This goal will be achieved by significant reduction of labor hours, higher operating point, and improved performance uniformity. A key factor will be automation that will be achieved through indust…
An alternative representation for the vector potential of the nonlinear magnetic insert for the Integrable Optics Test Accelerator (IOTA), first described in Sec. V.A. of the paper of Danilov and Nagaitsev, is determined from first principles using standard complex variable methods. In particular, it is shown that the coupled system consisting of the 2D Laplace equation and the Bertrand-Darboux equation is equivalent to a single ordinary differential equation in the complex plane, and a simple solution is constructed. The results are consistent with the paper of Danilov and Nagaitsev, and this…
LHC still does not operate at full energy due to training features in magnets. Higher field practical superconductors (Nb3Sn) show much worse training behavior than NbTi. Most magnet performance issues relate to quenching, and it is this phenomenon and its dependencies that need to be understood for us to succeed addressing them in magnets. For pragmatic and scientific reasons underlying mechanisms are hard to investigate in real magnets. Available data suggest that emulating local conditions at quench location may be enough to arrive at a good understanding of what drives observed behavior. "…
The single stretched-wire method is commonly used to measure the magnetic field strength and magnetic axis in an accelerator magnet. The integrated voltage at the connection terminals of the wire is a measure for the flux linked with the surface traced out by the displaced wire. The stretched wire can also be excited with an alternating current well below the resonance frequency. It is thus possible to measure multipole field errors by making use of the linear relationship between the wire-oscillation amplitude, integrated field, and current amplitude. This technique is a good example for solv…
Developing HTS dipole inserts producing fields larger than 5 T within 15 T Nb3Sn outserts is necessary to generate 20 T or higher fields for future high energy colliders. Dipole inserts based on the cos-theta coil geometry with various stress management concepts and Bi2212 superconducting strand and cable are being developed at Fermilab both within and beyond the U.S.-MDP effort. The ultimate goal is to develop coil technology and an approach to manage azimuthal and radial strains of high temperature superconductor inserts when integrated within Nb3Sn outserts as a hybrid magnet system. This w…
The lower conduction power losses and the positive temperature coefficient that favours parallel connections, make Silicon Carbide (SiC) metal oxide semiconductor field-effect transistors (MOSFETs) to be an excellent replacement of existing Silicon insulated gate bipolar transistors (IGBTs) technology. These characteristics combined with high switching frequency operation, enables the design of high-accuracy DC-DC converters with minimised filtering requirements. This paper investigates the design for a converter with high-accuracy current (0.9ppm) supplying a 0.05H electromagnetic load, aimin…
The European Laboratory Directors Group (LDG) was mandated by CERN Council in 2021 to oversee the development of an Accelerator R&D Roadmap. To this end, a set of expert panels was convened, covering the five broad areas of accelerator R&D highlighted in the ESPPU. The High Field Magnet (HFM) Panel is proposing a programme to demonstrate Nb3Sn magnet technology for large-scale deployment and to investigate the suitability of high temperature superconductors (HTS) for accelerator magnet applications. A summary of this programme is presented here.
Creation of high energy/intensity bremsstrahlung by a multitarget and focusing of the scattered electrons by small-angle backscatter at a cone wall and a magnetic field II - Enhancement of the outcome of linear accelerators in radiotherapy
A techniques, describing electron dynamics for magnetic models closed to cyclical accelerators, is developed and applied to the analysis of electromagnetic radiation emitted by charged particles. Formulas for the angular characteristics of synchrotron emission, which take into account the electron vibrations in the lattices of accelerators and storage rings are derived. It is shown that both the degree of photon polarization, as well as the spectral and angular distributions of radiation intensity, exhibit an observable dependence on the vertical betatron oscillations.
Vertical excursion fixed-field alternating gradient accelerators can be designed with tunes that are invariant with respect to momentum and trajectories that are scaled images of each other displaced only in the vertical direction. This is possible using guiding fields that have a vertical exponential increase, with a skew quadrupole component in the magnet body and a solenoid component at the magnet ends. Because of the coupling this introduces, orbit and optics calculations and optimisation of parameters need to be performed numerically. In this paper, idealised magnetic fields are calculate…
