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This report summarizes the findings of the AF5 Topical Subgroup to Snowmass 2021, which investigated accelerators for rare processes and physics beyond colliders. The report focuses primarily on opportunities for dark sector searches and the need for coordinated development of the Fermilab experimental program for PIP-II and beyond. In addition, a number of other physics opportunities are cataloged and suggestions for synergistic R & D opportunities with various areas of technological development are discussed.

We discuss the technical feasibility, key machine parameters and major challenges of a 14 TeV c.m.e. muon-muon collider in the LHC tunnel. The luminosity of the collider is evaluated for three alternative muon sources - the PS synchrotron, one of a type developed by the US Muon Accelerator Program (MAP) and a low-emittance option based on resonant muon pair production. Project affordability is also discussed., Comment: 11 p. Version accepted by publisher

The Proton Improvement Plan-II (PIP-II) encompasses a set of upgrades and improvements to the Fermilab accelerator complex aimed at supporting a world-leading neutrino program over the next several decades. PIP-II is an integral part of the strategic plan for U.S. High Energy Physics as described in the Particle Physics Project Prioritization Panel (P5) report of May 2014 [1] and formalized through the Mission Need Statement approved in November 2015. As an immediate goal, PIP-II is focused on upgrades to the Fermilab accelerator complex capable of providing proton beam power in excess of 1 MW on target at the initiation of the Long Baseline Neutrino Facility/Deep Underground Neutrino Experiment (LBNF/DUNE) program [2], currently anticipated for the mid- 2020s. PIP-II is a part of a longer-term goal of establishing a high-intensity proton facility that is unique within the world, ultimately leading to multi-MW capabilities at Fermilab....

The Muon Ionization Cooling Experiment (MICE) will perform a detailed study of ionization cooling to evaluate the feasibility of the technique. To carry out this program, MICE requires an efficient particle-identification (PID) system to identify muons. The Electron-Muon Ranger (EMR) is a fully-active tracking-calorimeter that forms part of the PID system and tags muons that traverse the cooling channel without decaying. The detector is capable of identifying electrons with an efficiency of 98.6%, providing a purity for the MICE beam that exceeds 99.8%. The EMR also proved to be a powerful tool for the reconstruction of muon momenta in the range 100-280 MeV/$c$., 22 pages, 19 figures

The (International Design Report) IDR neutrino factory scenario for capture, bunching, phase-energy rotation and initial cooling of micro's produced from a proton source target is explored. It requires a drift section from the target, a bunching section and a -E rotation section leading into the cooling channel. The rf frequency changes along the bunching and rotation transport in order to form the 's into a train of equal-energy bunches suitable for cooling and acceleration. Optimization and variations are discussed. An important concern is rf limitations within the focusing magnetic fields, mitigation procedures are described. The method can be extended to provide muons for a micro+-micro < Collider, variations toward optimizing that extension are discussed., 6 pp. 12th International Workshop on Neutrino Factories, Superbeams and Beta beams (NuFact10) 20-25 Oct 2010: Mumbai, India

Observations are consistent with the possibility of an “ep” instability in the Los Alamos Proton Storage Ring (PSR) with both bunched and unbunched beam. The instability requires electrons to be trapped within the beam, and calculations have shown that such trapping requires leakage of beam into the interbunch gap. Observationally, leakage of beam into the gap appears necessary for the onset of the instability. In this paper we present results of studies of the longitudinal beam dynamics at PSR parameters. The studies indicate that the combined effects of the rf buncher, longitudinal space charge, and injection mismatch are sufficient to cause the observed bunch leakage. Simulation results are presented and compared with PSR observations. Variations of PSR performance parameters are considered, and methods of improving bunch confinement are suggested and studied.

There exists now a large demand in better neutrino beams in particle physics community. Studying of such beams could reveal interesting and important properties of the observed neutrino oscillations. A high intensity source of a single flavor of neutrinos with reduced backgrounds, a known energy spectrum and intensity is needed for this research. Such intense source of neutrinos is supposed to be provided by the Neutrino Factory. A Neutrino Factory, as proposed, relies on formation and acceleration of ultra-large emittance muon beams with subsequent decay of the muons into a well-collimated, well-characterized neutrino beam. The muon beam creating section of the lattice is originally based on capturing, bunching and phase rotation in an expensive induction linac. A recently proposed different scheme bunches particles and reduces their energy spread in an array of high-frequency rf cavities whose rf frequency varies along the length of the channel. The cost reduction and simplicity of the proposed approach is extensive but is still not at its optimum. Different variations of the design paramaters leading to different properties of the beam and cost are possible. This work explores the approach, variations and develops an optimization scheme for rf parameters based on the underlying beam dynamics.

Novel methods of correcting dynamic nonlinearities resulting from the multipole content of a synchrotron are discussed. In simplest form, correction elements are placed at the center (C) of the accelerator half-cells as well as near the focusing (F) and defocusing (D) quadrupoles. In a first approximation, the corrector strengths follow Simpson's rule. The F, C, and D correctors permit direct control of horizontal, coupled, and vertical motion. For example, second-order sextupole nonlinearities can be corrected with F, C, and D octupoles. Generalizations and variations of the methods are described, and applications to the SCC (Superconducting Super Collider), LHC (Large Hadron Collider) AHF, and HERA (Hadron-Electron Ring Accelerator) projects are discussed. Correction by three or more orders of magnitude can be obtained, and simple solutions to a fundamental problem in synchrotrons are demonstrated. >

A method for measuring the response of a beam current monitor is described, and response and impedance measurement results for a Proton Storage Ring (PSR) wall current monitor are reported. The through-short-delay calibration method (TSD) is extended to measure the response of a current monitor embedded within hardware that interfaces to a network analyzer. Error correction parameters generated with the TSD-calibration are used to calculate the actual current present at the current monitor. The results show a marked increase in impedance due to the cables and combiners. >

In the high-intensity unbunched-beam experiments carried out in the Proton Storage Ring (PSR) at Los Alamos National Laboratory, the threshold current of the vertical transverse instability showed pronounced differences when the betatron tune varied across an integer. Experimental observations are presented, and the possible relations between the threshold current and the machine impedance are discussed. The possible effects related to the distorted closed orbit are also discussed. It was found that the behavior of the threshold current for vertical tune near the integers 2 and 3 could be related to the resistive-wall-type instability of modes n=2 to 4 together with the space-charge effect. It is conjectured that the closed-orbit distortion and a nonuniformly distributed asymmetric transverse impedance may contribute to some degree to the discontinuity of the threshold current when the vertical tune crosses an integer. >

We propose to use the curved transport line into Hall C at CEBAF to measure the beam energy. With only dipoles powered, this transport arc has a dispersion of 12 cm/%. We propose to insert pairs of wire scanners at the entrance and exit of the arc to measure beam position and direction. These measurements, together with a calibrated dipole field, obtain an absolute beam energy measurement with /spl sim/10/sup -3/ accuracy, according to error analyses. In operational mode, arc quads and sextupoles are powered to obtain a second order achromat with a dispersion of 2.1 cm/% at the arc center. A wire scanner at the arc center then obtains a relative energy measurement of /spl sim/10/sup -4/ accuracy. >

The particular properties of unstable ships force the use of nonlinear mathematical models. A first-order nonlinear model of a ship with a proportional-derivative (PD) controller used as an autopilot is investigated. Thus, a second-order closed-loop system is obtained. Stability properties of nonlinear systems are, in general, difficult to prove. The method adopted here is Lyapunov's direct method as given by W. Hahn, (1967). This method is particularly suited to second-order systems; however, normally local stability only can be proved by a Lyapunov function. In this case it is possible to find a one-parameter family that proves global asymptotic stability. As a result, the nonlinear system is stable whenever the linearized system is stable. In addition to this an estimation of the exponential decay rate is given. >

In recent operation of the Los Alamos Proton Storage Ring (PSR), the vertical and horizontal tunes have been moved closer to the integers ( nu /sub y/=2.12, nu /sub x/=3.17) to enlarge the low-loss working region. In this region, the beam can be significantly affected by space charge. The first observed effects are a nondestructive distortion of the beam profile and vertical growth of beam size sufficient to keep the shifted tunes from crossing the integer, but without large beam loss. At higher intensities, or with tunes closer to the integer, beam blow-up, accompanied by beam losses, can occur. A report is presented on recent observations of this intensity-dependent effect and implications for future PSR operation are discussed. >

In a conceptual design of the accelerating systems for a 4-TeV /spl mu//sup +/-/spl mu//sup -/ collider, three recirculating superconducting linacs (with energies reaching 70 GeV (with 350 MHz SRF), 250 GeV (800 MHz) and 2000 GeV (1300 GHz), respectively) are used. We briefly describe design concepts for the acceleration features, superconducting RF cavities, input couplers, RF control and the RF power systems.

We discuss possible acceleration scenarios and methods for a /spl mu//sup +/-/spl mu//sup -/ collider. The accelerator must take the beams from /spl sim/100 MeV to 2 TeV energies within the muon life-time (2.2/spl times/10/sup -6/E/sub /spl mu///m/sub /spl mu// /spl mu/S), while compressing bunches of /spl sim/10/sup 12/ muons from m to cm bunch lengths. A linac, recirculating linac, and very rapid-cycling synchrotron approaches are studied. A multiple recirculating linac approach is matched to the muon lifetime and appear readily feasible. Rapid-cycling approaches require innovations in magnet designs and layouts, but could be much more affordable.

Muon acceleration is one of the most difficult stages to develop for a Neutrino Factory or a Muon Collider. The large transverse and longitudinal admittances which must be designed into the system, and the rapidity with which acceleration must take place because of muon decay preclude the use of conventional synchrotron design. The current baseline approach employs recirculating linacs (RLAs) with separate, fixed-field arcs for each acceleration turn. Here a 3-11 GeV RLA will be described along with sophisticated optical codes and tools developed specifically to accurately track, physically describe, and assist in designing this complex system.

The successful design of a high luminosity muon collider requires that the six dimensional phase-space of the muon beam generated by pion decay be reduced by a factor of /spl sim/(10/sup 5/-10/sup 6/) before it enters the collider. This "beam cooling" has to take effect in a time scale comparable to the lifetime of the muon. Because of this time limitation, Ionization Cooling is the preferred option for the muon collider. In this paper we discuss the design issues for an Ionization Cooling channel based on lithium lenses and solenoid transport channels and we present simulation results obtained using a detailed tracking code with a complete model of muon-atom interactions. Cooling results for a minimal configuration of two lithium lenses and one matching section are presented, for beams with a normalized transverse emittance of 0.0067 m-rad. The cooling factor obtained is /spl sim/1.5.

We propose a very simple method for tracking and disturbance rejection, when the reference and disturbance signals are superpositions of finitely many sinusoids (including constants). The internal model is a convex combination of partial internal models for the individual frequencies of interest. The stabilizing compensator is designed by solving a weighted sensitivity H∞ problem, which is independent of the frequencies involved, or of their number. The results remain valid for infinite-dimensional plants. We comment also on the robustness properties of such control systems.

A rule-based control system for coal combustion on a chain-grate stoker is presented. The objectives of the controller were to permit, automatically, continuous running of the process at different load levels while achieving high efficiency and maintaining permitted emissions levels. Its achievement of these goals has been demonstrated in plant trials on a 1 MW stoker and test results are presented.

The accelerators must take the muon beams from -100 MeV to 2 TeV energies within the muon lifetime for a 4 TeV energy muon collider. These constraints plus the muon decay heating seriously challenge the designs of the superconducting RF (SRF) cavities and magnets in the accelerators and collider ring. The multiple superconducting recirculation linac and the very rapid-cycling superconducting synchrotron approach are both studied. We briefly introduce the technical considerations and preliminary designs of the SRF systems and magnets.

An expert rule-based control system is presented which has been applied to a 1 MW coal-fired chain-grate stoker. The goal of the control scheme is to achieve efficient carbon burnout while meeting a specified load demand schedule and simultaneously achieving statutory emissions levels in the face of random disturbances to the feed and quality of both the coal and the air supply.

The beam transport system for the CEBAF Industrial FEL includes a two-pass transport of the beam with acceleration from injector to wiggler, followed by energy recovery transport from wiggler to dump. From that context, the authors discuss the general problem of multi-pass energy-recovery beam transport for FELs. Tunable, nearly-isochronous, large-momentum-acceptance transport systems are required. The entire transport must preserve beam quality, particularly in the acceleration transport to the wiggler, and have low losses throughout the entire system. Various possible designs are presented, and results of dynamic analyses are discussed.

Recently, it has been suggested that improved technology and reduced costs in remotely-drilled small-diameter tunnels, coupled with improvements in robotic technology, may make the original concept of the ``desertron`` more realistic and affordable. In this concept, a long, small-diameter tunnel is drilled (

We review quasi‐achromatic magnetic focussing elements which collect pions produced in a target for transport into a π→μ decay channel, with features appropriate to the development of high energy muon colliders. We discuss how the collection and target requirements of a muon collider are different from and similar to existing secondary particle collection systems. We briefly discuss target technology issues.

Ionization cooling may play an important role in reducing the phase space volume of muons for a future muon‐muon collider. We describe a possible experiment to demonstrate transverse emittance cooling using a muon beam at the AGS at Brookhaven National Laboratory. The experiment uses device dimensions and parameters and beam conditions similar to what is expected in an actual muon‐muon collider.

The combustion of coal on a chain-grate stoker presents a complex problem to the control engineer. Although such rigs can operate continuously with a minimum of supervision emission requirements and the need for greater fuel efficiency are leading to a review of operating practice. The principal problems that are being addressed are the variation in the coal feed quality and distribution, and unscheduled secondary air. The variations that these cause in both the heat and emissions output of the boiler are in need of regulation. In an attempt to bring modern control theory to the problem a new general control system is being designed for chain-grate stoker rigs in a collaborative project between Exeter University and CRE Group Ltd. The control of chain-grate stokers is made difficult by the imbalance between the complex and distributed process on the one hand, and the relatively few measurements available on commercial plants on the other. The control system must reflect this. However it is both expensive and possibly hazardous to carry out this development on-line. Another vehicle on which to develop the control system is required. (7 pages)

A high‐intensity CW photocathode electron injector test stand has been designed and is being built for a 200 MeV two‐pass recirculating CW superconducting accelerator. The accelerator is being designed to drive a high average power (1 kW) UV free‐electron laser (FEL). This FEL requires beam emittances as small as 11 mm mrad for the transverse normalized rms emittance and 30 deg‐keV for the longitudinal rms emittance. The electrons contained in a 135 pC charged bunch are compressed from an initial bunch length of 90 ps (6σ) at the photocathode down to 1.2 ps (a factor of 75 compression) at the wiggler. In this paper, we present our studies on the space charge effects that determine the magnitude of beam emittance growth during the various stages of beam transport from the injector through the driver accelerator to the wiggler.

We report the discussions and some preliminary results from the sessions of the 200×200 GeV μ+−μ− Collider working group. The physics motivation for such a ‘‘medium‐energy’’ collider is discussed. Possible parameters for such a system are described, and compared with higher‐energy systems. Relatively‐high luminosities (L∼1033 cm−2s−1) appear possible. Modifications of existing facilities to obtain medium‐energy μ+−μ− collisions are discussed. Other discussion topics (μ‐p colliders, low‐energy μ sources, etc.) are summarized.

The control of coal combustion on chain-grate stokers is a complex problem which is of importance to environmental concerns. Producing efficient combustion in spite of material and feed disturbances is a difficult task, allying this to the meeting of stringent emissions criteria even more so. A mathematical model has been used to develop a control scheme, some simulation results of which are shown.

The use of the Hall C achromatic arc line as an energy analyser is proposed. It has a dispersion of 12cm/% with all the quadrupoles, sextupoles, and beam correctors switched off. The transverse position and the angle of the beam at the entrance of the arc is precisely measured by a pair of wire scanners spaced by 2.5 m, and the transverse position of the outgoing beam is measured by another pair of wire scanners at the exit of the arc. After the absolute beam energy is measured, the arc will be turned into normal achromat mode by energizing all the elements and the beam position probe located at the mid-point of the arc is used to monitor the beam energy in the operational mode. A complete error analysis shows that an absolute beam energy measurement with 10{sup {minus}3} accuracy can be achieved. Relative energy measurements at the 10{sup {minus}4} level are also obtainable.

The basic design for the SSC started at Snowmass in the summer of 1982. The premise is that a superferric SSC has the potential to be simple, reliable, inexpensive and provide future flexibility. A concentrated effort began in March of 1984 when the Texas Accelerator Center was formed. The Texas Accelerator Center is a group of about 50 people divided into three areas of research, a calculations group working on beam dynamics, an R and D group working on superconducting magnets, and an R and D group working on new accelerator ideas including a proton linac and a plasma-laser accelerator. This paper will emphasize the work on the superferric magnet R and D.

The capability and performance of the SSC can be substantially improved by adding a third ring. In this design two collider rings operate at fixed energy to provide colliding beams. The third ring is used to accelerate beam to collision energy and transfer it into each collider ring. This separation of functions results in three important improvements for the SSC. First, the collider magnets can be simplified in design and reduced in size since they need not service injection at low energy and acceleration. Second, the accelerator ring can be used to maintain peak luminosity in the collider continuously and indefinitely. Third, the accelerator ring can also be used to service a dedicated fixed-target physics program without conflict with the collider program. Using the superferric magnet design, the collider magnets can be reduced in size and all three magnets can be housed in a common cryostat. The accelerator and collider rings can be made operationally independent (quench isolation, magnetic fields, experimental bypass). The estimated additional cost to the SSC project is ~10%.

We study the plasma fiber accelerator concept by simulation and theory. An outgrowth of the laser beat-wave accelerator concept, the plasma fiber accelerator, sets the phase velocity of the beat plasma wave at the speed of light (or any value desired) by allowing each laser light to have a specific transverse wavenumber (or structure). Two-dimensional slab duct structures with laser beams of both transverse electric and transverse magnetic polarizations are explored. Accelerated beam dynamics in fiber beat-wave is discussed.

Possible choices for SSC lattices are developed and their properties are discussed. The effects of cell length and phase and superperiodicity on lattice parameters are discussed. Comments on beam separation, tune and tuning are presented and the effects of nonlinearities are introduced in a discussion of systematic sextupole effects. Sample lattices for SSC beam dynamics studies are presented.

The theory of betatron osciallations in cyclic accelerators is reviewed. The emission of synchrotron radiation is also considered. (AIP)

The LAMPF II accelerator will require sufficient vacuum to prevent beam loss or beam blowup within the time the beam is in the accelerator. Because this time is quite short (tau < 0.03 s), the vacuum requirements should be somewhat less strict than for the long-time storage machines, such as the ISR (tau greater than or equal to 10/sup 5/ s). In this note, we catalog various vacuum limitations for LAMPF II and outline vacuum-system parameters that meet these limitations. The pressure P less than or equal to 10/sup -7/ T should be adequate for LAMPF II, and a fairly simple vacuum system should obtain P less than or equal to 10/sup -8/ T.

The rapidly changing magnetic fields of the LAMPF II rapid-cycling synchrotron will induce electric fields that will induce ohmic heating by wall currents in a beam pipe placed within these rapidly changing fields. A conducting beam pipe is required to remove high-frequency collective instabilities. Some compromise in design is required so that a beam pipe with low conductivity at the LAMPF II cycling frequency (f = 30 to 60 Hz) and high conductivity at high frequencies (f greater than or equal to 10 to 100 MHz) is obtained.

An instability in the Proton Storage Ring (PSR) is observed as fast loss of beam during accumulation and storage when the injected beam current exceeds a threshold value. Instabilities are observed during both coasting-beam and bunched-beam operation. Large coherent transverse oscillations occur prior to and during the beam loss. The growth times are rapid, typically in the range 10-100 mu s. The instability threshold is observed to depend strongly upon RF voltage, beam size, injected momentum spread, and nonlinear fields. Weaker dependences upon betratron tune, vacuum pressure, and stripping-foil bias voltage have also been observed. A possible e-p oscillation component of the unbunched beam instability is suggested. Growth times suggest a significant Re(Z/sub perpendicular to /) of approximately 0.2-0.5 M Omega /m; the source of this is not yet precisely identified. >