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This is a general information article of the ICFA Beam Dynamics Newsletter No. 81. Thus, it contains two forewords from the Editor-in-Chief and the issue editor, a workshop and conference report section, a recent Ph.D. thesis section, a forthcoming beam dynamics events section, and a section of announcements from the beam dynamics panel.
The Muon $g-2$ experiment at Fermilab (E989) aims to measure the anomalous magnetic moment of the muon with an accuracy of 140 ppb (parts per billions). This accuracy, obtained by adding in quadrature a statistical and a systematic contribution of comparable value (100 ppb), will allow to reduce the experimental uncertainty (from the previous E821 experiment at BNL \cite{bnl}) of a factor of 4, and represents one of the most precise tests of the Standard Model (SM) theory of elementary particles. The first result on the Run-1 dataset \cite{prl} was released on April 7, 2021, showing a very good agreement with the previous result from BNL experiment, with a slightly better uncertainty. The corresponding experimental average increases the significance of the discrepancy between the measured and Standard Model prediction of 4.2$\sigma$ \cite{white_paper}.\\ \noindent The measured quantity is the muon magnetic anomaly a$_\mu$=$\frac{g_\mu-2}{2}$ where g$_\mu$ is the gyromagnetic factor of the muon. Dirac's equation predicts g$_\mu$ = 2, while radiative corrections, dominated by the QED contribution due to an exchange of a virtual photon, causes a per-mille correction on this quantity. By including all the SM contributions, a$_\mu$ is known at 370 ppb. The E989 experiment measures $a_\mu$ injecting positive muons with momentum of 3.1 GeV/$c$ polarized longitudinally in bunches (called $fills$) with an average rate of 12 Hz, in a storage ring of 14 meters diameter. Due to the parity violation in the weak muon decay, high energy positrons produced are emitted preferably in the muon's spin direction. By counting the number of positrons with energy greater then 1.7 GeV in function of the time, the frequency precession of the muon spin is measured, that together with the measurement of the magnetic field, allows to extract $a_\mu$. The positrons are detected with 24 electromagnetic calorimeters, that measure the energy and the arrival time of the positrons, each made of 54 crystals of lead fluoride (PbF$_2$) read by silicon photomultipliers (SiPM). Together with calorimeters, two tracking detectors are used to make non-destructive measurements of the muon beam characteristic by reconstructing the muon decay position extrapolating backward the decay positrons. The knowledge of the beam motion inside the ring plays a fundamental role in the analysis of $a_{\mu}$, where the measured anomalous precession frequency $\omega_a$ must be corrected for four main beam dynamics effects. A first correction is associated with the presence of an electric field responsible of the vertical focusing on the storage ring, where vertical direction is orthogonal to the orbit and horizontal direction is along the storage ring radius. Due to the oscillations in the vertical direction, the so called vertical betatron oscillations, a second correction is necessary to account for an average angle associated with the muon motion off the ideal orbit. A third correction is caused by lost muons in the ring which have a different spin phase at the injection respect to the decay ones. Finally, due to the correlation between the vertical and horizontal beam motion of the muons and the acceptance of the calorimeter, a correction (called ``phase-acceptance") arises. In Run1, due to the presence of two damaged resistors in one electrostatic quadrupole, this correction had a prominent role. The replacement of the damaged resistors before Run2 decreased this effect by one order of magnitude, and a further reduction in Run-3 was provided by an improved orbit.\\ \noindent The work of this Thesis focuses on the beam dynamics corrections on $\omega_a$. Due to the prominent role in Run-1 a special attention has been put to the phase-acceptance correction\footnote{The effect of this correction on the E821 BNL measurement of the $g-2$ has been evaluated to be within the quoted systematic error.}. Chapter \ref{ch:anomalous_magnetic_moment} introduces the anomalous magnetic moment of the muon. Chapter \ref{ch:early_experiment} describes the history of the Muon $g-2$ experiments. Chapter \ref{ch:theory} discusses the Standard Model prediction and possible new physics scenario. Chapter \ref{ch:muon_g2_experiment} describes the E989 experiment, whose experimental technique and the apparatus are discussed focusing on the improvements needed to reach the final goal on $a_\mu$ measurement. The original work of the Thesis is discussed in the last 5 chapters. Chapter \ref{ch:experiment_technique} presents the analysis technique to extract $\omega_a$, Chapter \ref{ch:beam_dynamics} describes the beam dynamics in the E989 experiment, Chapter \ref{ch:beam_dynamics_correction} discusses the beam dynamics correction to $\omega_a$, and Chapter \ref{sec:pa_corr} focuses on the phase acceptance correction. Finally Chapter \ref{ch:run23_analysis_improvements} contains the Run-2/3 improvements which are expected to allow for an increased precision ons the beam dynamics co...
Linear accelerators containing the sequence of independently phased cavities with constant geometrical velocity along each structure are widely used in practice. The chain of cavities with identical cell lengths is utilized within a certain beam velocity range, with subsequent transformation to the next chain with higher cavity velocity. Design and analysis of beam dynamics in this type of accelerator are usually performed using numerical simulations. A full theoretical description of particle acceleration in an array of independent phased cavities has not been developed. In the present paper, we provide an analytical treatment of beam dynamics in such linacs employing Hamiltonian formalism. We begin our analysis with an examination of beam dynamics in an equivalent traveling wave of a single cavity, propagating within accelerating section with constant phase velocity. We then consider beam dynamics in arrays of cavities, utilizing an effective traveling wave propagating along with the whole accelerator with the velocity of synchronous (reference) particle. The analysis concluded with the determination of the matched beam conditions. Finally, we present a beam dynamics study in 805 MHz Coupled Cavity Linac of the LANSCE accelerator facility.
A series of beam dynamic studies were performed in 2020-2021 at the PIP-II Injector Test Facility (PIP2IT) that has been built to validate the concept of the front-end of the PIP-II linac being constructed at Fermilab. PIP2IT is comprised of a 30-keV H- ion source, a 2 m-long Low Energy Beam Transport (LEBT), a 2.1- MeV CW RFQ, followed by a 10-m Medium Energy Beam Transport (MEBT), 2 cryomodules accelerating the beam to 16 MeV and a High-Energy Beam Transport (HEBT) bringing the beam to a dump. This paper presents beam dynamics - related measurements performed at PIP2IT such as the Twiss parameters with Allison scanners, beam envelopes along the injector, and transverse and longitudinal rms emittance reconstruction. These measurements are compared with predictions from the beam dynamics code Tracewin.
Beam Dynamics Challenges of a Far-Future ERL-Based Collider - The Ghost Collider In a recent paper, Valery Telnov proposed a linear collider based on twin axis cavities [1]. In a subsequent presentation, Erk Jensen proposed a modification with intra-bucket energy recovery [2], which eliminates higher order mode excitation. Interestingly, this means that there is no need for large aperture SRF cavities and high-power HOM couplers. The Ghost Collider adopts these ideas, and adds the concept of four-beam collisions (initially proposed by Joel LeDuff [3]) to remove beam-beam interactions and disruption. This concept brings up a series of new beam dynamics problems which make optimization of the parameters difficult. The presentation will describe the concept, which has a series of beam-dynamics challenges to be solved before the concept can advance. [1] V.I. Telnov, JINST 16 (2021) no.12, P12025 [2] E. Jensen https://indico.cern.ch/event/1040671/?view=nicecompact [3] Status Report on D. C. I, The Orsay Storage Ring Group, IEEE Transactions on Nuclear Science, Vol. NS-26, No.3, June 1979
Beam dynamics in the Medium-Energy Beam Transfer (MEBT) after the new proton RFQ for the LANSCE injector is modeled with the CST Particle Studio PIC solver. The modeling uses the CST-calculated 3D EM fields of MEBT elements, which is important because (i) the beam size in MEBT is large, comparable to the beam-pipe aperture, and (ii) the fields of neighboring MEBT elements overlap. Our results indicate significant beam emittance growth not predicted by traditional beam dynamics codes.
A test stand is under construction at CERN to study high perveance electron guns, electron beam dynamics, and electron beam diagnostics for electron lenses. It will be used to test electron guns for the Hollow Electron Lenses under consideration for beam halo control for High Luminosity LHC (CERN), and for the Space Charge Compensation at SIS18 (GSI) in the frame of the EU funded ARIES project. In order to prepare for this test stand, simulations will be presented and compared with experiments undertaken at the Fermilab (FNAL) electron lens test stand. These were conducted using a hollow electron gun, with the magnetic field configuration and beam current varied to study their effect. The impact of imperfections on the beam dynamics and overall quality of the electron beam will be discussed. A method for comparing experimental data with simulation is also presented to allow bench-marking of the computer models and simulation tools that will later be applied to the analysis of measurements performed at CERN.
Modern particle accelerator optimization requires sophisticated computational methods to address the inherently stochastic nature of beam dynamics. This research develops a framework applying AD to SDEs that specifically addresses beam dynamics challenges in particle accelerators, focusing on accurately modeling and optimizing beam behavior in regimes dominated by stochastic processes. By incorporating key physical phenomena such as synchrotron radiation, wakefield effects, and quantum excitation, the framework aims to provide auto differentiation on the figure of merit of the phase space evolution and beam dynamics. The methodology will enable effective optimization method in a dynamic system with stochastic process.
Hadron beams develop intensity-dependent transverse-longitudinal correlations within radio-frequency quadrupole (RFQ) accelerating structures. These correlations are only visible in six-dimensional phase space and are destroyed by reconstructions from low-dimensional projections. In this work, we estimate the effect of artificial decorrelation on the beam dynamics in the Spallation Neutron Source (SNS) linac and Beam Test Facility (BTF). We show that the evolution of a realistic initial distribution and its decorrelated twin converge during the early acceleration stages; thus, low-dimensional projections are probably sufficient for detailed predictions in high-power linacs.
This is a general information article of the ICFA Beam Dynamics Newsletter No. 83. It contains two forewords from the Editor-in-Chief and the issue editor, a workshop and conference report section, a recent doctoral theses section, and lastly, a forthcoming beam dynamics events section.
A high-fidelity finite difference approximation of the dynamic beam equation is derived. Different types of well-posed boundary conditions are analysed. The boundary closures are based on the summation-by-parts (SBP) framework and the boundary conditions are imposed using a penalty (SAT) technique, to guarantee linear stability. The resulting SBP–SAT approximation leads to fully explicit time integration. The accuracy and stability properties of the newly derived SBP–SAT approximations are demonstrated for both 1-D and 2-D problems.
A dual energy storage ring designed for beam cooling consists of two closed rings with significantly different energies: the cooling and damping rings. These two rings are connected by an energy recovering superconducting RF structure that provides the necessary energy difference. In our design, the RF acceleration has a main linac and harmonic cavities both running at crest that at first accelerates the beam from low energy E_{L} to high energy E_{H} and then decelerates the beam from E_{H} to E_{L} in the next pass. The purpose of the harmonic cavities is to extend the bunch length in a dual energy storage ring as such a longer bunch length may be very useful in a cooling application. Besides these cavities, a bunching cavity running on zero-crossing phase is used outside of the common beamline to provide the necessary longitudinal focusing for the system. In this paper, we present a preliminary lattice design along with the fundamental beam dynamics study in such a dual energy storage ring.
Here, we introduce Linac_Gen, a tool developed at Fermilab, which combines machine learning algorithms with Particle-in-Cell methods to advance beam dynamics in linacs. Linac_Gen employs techniques such as Random Forest, Genetic Algorithms, Support Vector Machines, and Neural Networks, achieving a tenfold increase in speed for phase-space matching in Linacs over traditional methods, through the use of genetic algorithms. Crucially, Linac_Gen's adept handling of 3D field maps elevates the precision and realism in simulating beam instabilities and resonances, marking a key advancement in the field. Benchmarked against established codes, Linac_Gen demonstrates not only improved efficiency and precision in beam dynamics studies but also in the design and optimization of Linac systems, as evidenced in its application to Fermilab's PIP-II Linac project. This work represents a notable advancement in accelerator physics, marrying ML with PIC methods to set new standards for efficiency and accuracy in accelerator design and research. Linac_Gen exemplifies a novel approach in accelerator technology, offering substantial improvements in both theoretical and practical aspects of beam dynamics.
Here, we introduce Linac_Gen, a tool developed at Fermilab, which combines machine learning algorithms with Particle-in-Cell methods to advance beam dynamics in linacs. Linac_Gen employs techniques such as Random Forest, Genetic Algorithms, Support Vector Machines, and Neural Networks, achieving a tenfold increase in speed for phase-space matching in linacs over traditional methods through the use of genetic algorithms. Crucially, Linac_Gen's adept handling of 3D field maps elevates the precision and realism in simulating beam instabilities and resonances, marking a key advancement in the field. Benchmarked against established codes, Linac_Gen demonstrates not only improved efficiency and precision in beam dynamics studies but also in the design and optimization of linac systems, as evidenced in its application to Fermilab's PIP-II linac project. This work represents a notable advancement in accelerator physics, marrying ML with PIC methods to set new standards for efficiency and accuracy in accelerator design and research. Linac_Gen exemplifies a novel approach in accelerator technology, offering substantial improvements in both theoretical and practical aspects of beam dynamics.
The Muon $g\textrm{-}2$ Experiment (E989) at Fermilab aims to measure the muon anomalous magnetic moment $a_{\mu}$ with unprecedented precision, potentially uncovering physics beyond the Standard Model of particle physics. The result based on Runs 1-3, released in 2023, achieved a precision of 0.20 ppm. The experiment circulates muons in a storage ring, measuring $a_{\mu}$ from decay positron time and energy measurements collected with calorimeters. To achieve the required accuracy, it is crucial to measure and control the magnetic field in the ring with high precision. Beam dynamics corrections are necessary for muons not orbiting exactly in the midplane, for their oscillations, and for electric field effects. Highly accurate beam dynamics simulations are instrumental for quantifying and validating the beam dynamics corrections, ultimately improving the precision of the $a_{\mu}$ measurement and facilitating the achievement of the ambitious $70\:\mathrm{ppb}$ systematic uncertainty goal. The measured field data was incorporated into models for simulations using three codes: \texttt{gm2ringsim} (an internal Geant4-based code), \textit{COSY INFINITY}, and \textit{BMAD}. The advantages of \texttt{gm2ringsim} include using CAD-based geometry and modelling the detector effects. \textit{COSY INFINITY} is a highly accurate and efficient code that uses high-order differential-algebraic transfer maps, precise fringe field calculations, and advanced symplectification methods. Symplectification is important for maintaining the physical correctness of the muon beam behaviour with high precision over the storage time, ensuring conservation of phase space volume and preventing artificial damping or excitation of particle motion. The experiment completed its final Run 6 in July 2023, collecting 21 times more data than the previous BNL experiment. Analyses of data from Runs 4-6 are ongoing, with results planned for release in 2025, potentially resolving the current tension between experiment and theory.
The Electron-Ion Collider (EIC), presently under construction at Brookhaven National Laboratory, will collide polarized high-energy electron beams with hadron beams, achieving luminosities up to 1 × 1034 cm¿2 s¿1 in the center-of-mass energy range of 20-140 GeV. To achieve such high luminosity, we adopt high bunch intensities for both beams, small and flat transverse beam sizes at the interaction point (IP), a large crossing angle of 25 mrad, and a novel strong hadron cooling in the Hadron Storage Ring (HSR) to counteract intra-beam scattering (IBS) at the collision energy. In this talk, we will review the beam dynamics challenges in the design of the EIC, particularly the single-particle dynamic aperture, polarization maintenance, beam-beam interaction, impedance budget and instabilities. We will also briefly mention some technical challenges associated with beam dynamics, such as strong hadron cooling, multipoles and noises of crab cavities, power supply current ripples, and the vacuum upgrade to existing beam pipes of the Hadron Storage Ring of the EIC.
This paper presents the results of electron beam tracking simulations for a 10 MeV on axis, biperiodic, coupled cavity standing wave electron linac for industrial purposes. For the pulsed mode operation of the present linac preferential operation parameters have been determined from the results of beam dynamics studies. (author)
We report on the beam dynamics studies and optimization methods for a high repetition rate (1 MHz) photoinjector based on a VHF normal conducting electron source. The simultaneous goals of beamcompression and reservation of 6-dimensional beam brightness have to be achieved in the injector, in order to accommodate a linac driven FEL light source. For this, a parallel, multiobjective optimization algorithm is used. We discuss the relative merits of different injector design points, as well as the constraints imposed on the beam dynamics by technical considerations such as the high repetition rate.