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Challenges of Future Accelerators for Particle Physics Research

For over half a century, high-energy particle accelerators have been a major enabling technology for particle and nuclear physics research as well as sources of X-rays for photon science research in material science, chemistry and biology. Particle accelerators for energy and intensity Frontier research in particle and nuclear physics continuously push the accelerator community to invent ways to increase the energy and improve the performance of accelerators, reduce their cost, and make them more power efficient. The accelerator community has demonstrated imagination and creativity in developing a plethora of future accelerator ideas and proposals. The technical maturity of the proposed facilities ranges from shovel-ready to those that are still largely conceptual. At this time, over 100 contributed papers have been submitted to the Accelerator Frontier of the US particle physics decadal community planning exercise known as Snowmass’2021. These papers cover a broad spectrum of topics: beam physics and accelerator education, accelerators for neutrinos, colliders for Electroweak/Higgs studies and multi-TeV energies, accelerators for Physics Beyond Colliders and rare processes, advanced accelerator concepts, and accelerator technology for Radio Frequency cavities (RF), magnets, targets and sources. This paper provides an overview of the present state of accelerators for particle physics and gives a brief description of some of the major facilities that have been proposed, their perceived advantages and some of the remaining challenges.

43 PARTICLE ACCELERATORS↗

Beam power scale-up in micro-electromechanical systems based multi-beam ion accelerators

We report on the development of multi-beam RF linear ion accelerators that are formed from stacks of low cost wafers and describe the status of beam power scale-up using an array of 120 beams. The total argon ion current extracted from the 120-beamlet extraction column was 0.5 mA. The measured energy gain in each RF gap reached as high as 7.25 keV. We present a path of using this technology to achieve ion currents >1 mA and ion energies >100 keV for applications in materials processing.

47 OTHER INSTRUMENTATION↗

Analysis of RF high power sources for 1MW – range, 10 MeV CW industrial accelerator.

Cobalt-60 is the dominant source of ionizing radiation for sterilizing products in the $200B/year medical device industry. Security and accessibility concerns around this radioactive material - sourced from countries including Russia and China - present national security and economic risks. There is a continued national urgency to replace such high-risk sources with low-risk alternatives such as electron or x-ray beams driven by accelerators. While e-beam sources have been in use for many years, they still represent a small portion of the market. X-ray sources are becoming economical alternatives. Meeting the processing capacity required to replace Co-60 requires a step-change in the capability, efficiency, and overall operating cost of electron accelerators to make adoption feasible. The radiofrequency (RF) power that drives accelerating cavities represents significant capital and operating costs for these accelerators. For accelerator-based systems to be a viable alternative for these applications, RF systems must be economical to manufacture, deploy, and operate.

43 PARTICLE ACCELERATORS↗

Design and Principles of Linear Accelerators and Colliders." in Particle Physics Reference Library, pp. 295-336. Springer, Cham, 2020.

Linear accelerators (linacs) use alternating radiofrequency (RF) electromagnetic fields to accelerate charged particles in a straight line. Linacs were invented about 95 years ago and have seen many significant technical innovations since. A wide range of particle beams have been accelerated with linacs including beams of electrons, positrons, protons, antiprotons, and heavy ions. Linac parameter possibilities include pulsed versus continuous wave, low and high beam powers, low and high repetition rates, low transverse emittance beams, short bunches with small energy spreads, and accelerated multiple bunches in a single pulse. The number of linacs around the world has grown tremendously with thousands of linacs in present use, many for medical therapy, in industry, and for research and development in a broad spectrum of scientific fields. Researchers have developed accelerators for scientific tools in their own right, being awarded several Nobel prizes. Moreover, linacs and particle accelerators in general have enabled many discovery level science experiments in related fields, resulting in many Nobel prizes as well.

Seeman, John↗

Accelerating Random Forest Classification on GPU and FPGA

Random Forests (RFs) are a commonly used machine learning method for classification and regression tasks spanning a variety of application domains, including bioinformatics, business analytics, and software optimization. While prior work has focused primarily on improving performance of the training of RFs, many applications, such as malware identification, cancer prediction, and banking fraud detection, require fast RF classification. In this work, we accelerate RF classification on GPU and FPGA. In order to provide efficient support for large datasets, we propose a hierarchical memory layout suitable to the GPU/FPGA memory hierarchy. We design three RF classification code variants based on that layout, and we investigate GPU- and FPGA-specific considerations for these kernels. Our experimental evaluation, performed on an Nvidia Xp GPU and on a Xilinx Alveo U250 FPGA accelerator card using publicly available datasets on the scale of millions of samples and tens of features, covers various aspects. First, we evaluate the performance benefits of our hierarchical data structure over the standard compressed sparse row (CSR) format. Second, we compare our GPU implementation with cuML, a machine learning library targeting Nvidia GPUs. Third, we explore the performance/accuracy tradeoff resulting from the use of different tree depths in the RF. Finally, we perform a comparative performance analysis of our GPU and FPGA implementations. Our evaluation shows that for high accuracy targets, our GPU implementation yields 5-9x speedup over CSR, and up to a 2x speedup over cuML.

FPGA, Xilinx FPGA, GPU, Random Forest classificati↗

Energy gain in a two-gap RF cavity

Velocity of a deeply non-relativistic particle can change during its acceleration inside an RF cavity significantly enough to cause a deviation of the energy gain from a linear model. This paper derives formulae for corrections to the energy gain in a two-gap RF cavity calculated by taking into account this velocity change in the next approximation. Then, the results are compared with direct particle tracking of an HWR cavity used at the PIP2IT test accelerator. The formulae significantly extend the range of parameters where analytical calculations work with a good accuracy. The approach is applied to two aspects of cavity phasing.

43 PARTICLE ACCELERATORS↗

Fast ion transport by sawtooth instability in the presence of ICRF-NBI synergy in JET plasmas

JET experiments have shown that the three-ion scenarios using waves in the ion cyclotron range of frequencies (ICRF) is an efficient way to build fast ion population through beam ion acceleration by radio frequency (RF) waves. Here, such a heating scheme is applied to plasmas with at least two thermal ion species. Analysis of mixed discharges with complex heating schemes requires a workflow that allows to model thermal and fast ion transport consistently. This paper is dedicated to modelling of a mixed plasma discharge with significant fraction of fast ions and contributes to development of fast ion transport models. For interpretive analysis with the TRANSP code a JET hydrogen-deuterium (HD) plasma discharge with neutral beam injection (NBI) and ICRF heating has been chosen. The task is complicated by NBI-ICRF synergy and plasma magnetohydrodynamic activity, like sawtooth crashes. D beam ions accelerated by RF waves form a high energy tail in fast ion distribution. Significant difference between the neutron rate computed by TRANSP and measured one is observed if the same diffusivity for electrons and ions is assumed. Sensitivity studies show that uncertainties in input plasma parameters and thermal ion transport models are crucial for modelling mixed plasma discharges and increased D transport is required to reach the plasma composition consistent with diagnostic measurements at the plasma edge. Fast ion redistribution by a sawtooth instability is characterised by non-resonant transport due to reconnection of magnetic field lines and resonant transport caused by resonance interaction between the instability and fast ions. With ORBIT simulations it has been shown that resonant interaction strongly affects fast ions of high energies, like beam ions accelerated by RF waves and fusion products. For the considered case, fast ion profiles simulated by ORBIT remain peaked after the sawtooth crashes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Design of an Integrated-System FARAD Thruster

Pulsed inductive plasma accelerators are spacecraft propulsion devices in which energy is stored in a capacitor and then discharged through an inductive coil. The device is electrodeless, inducing a current s heet in a plasma located near the face of the coil. The propellant is accelerated and expelled at a high exhaust velocity (order of 10 km/s) through the interaction of the plasma current and the induced magne tic field, The Faraday Accelerator with RF-Assisted Discharge (FARAD) thruster is a type of pulsed inductive plasma accelerator in which t he plasma is preionized by a mechanism separate from that used to for m the current sheet and accelerate the gas. Employing a separate preionization mechanism allows for the formation of an inductive current s heet at much lower discharge energies and voltages than those used in previous pulsed inductive accelerators like the Pulsed Inductive Thr uster (PIT). In this paper, we present the design of a benchtop FARAD thruster with all the subsystems (mass injection, preionization, and acceleration) integrated into a single unit. Design of the thruster follows the guidelines and similarity performance parameters presented elsewhere. The system is designed to use the ringing, RF-frequency s ignal produced by a discharging Vector Inversion Generator (VIG) to p reionize the gas. The acceleration stage operates on the order of 100 J/pulse and can be driven by several different pulsed powertrains. These include a simple capacitor coupled to the system, a Bernardes and Merryman configuration, and a pulsecompression circuit that takes a temporally broad, low current pulse and transforms it into a short, h igh current pulse. A set of applied magnetic field coils are integrated into the system to guide the preionized propellant as it spreads ov er the face of the inductive acceleration coil. The coils are operate d in a pulsed mode, and the thruster can be operated without using the coils to determine if there is a performance improvement gain realiz ed when an applied field is present.

Polzin, K.A.↗

Laboratory-Model Integrated-System FARAD Thruster

Pulsed inductive plasma accelerators are spacecraft propulsion devices in which energy is stored in a capacitor and then discharged through an inductive coil. The device is electrodeless, inducing a plasma current sheet in propellant located near the face of the coil. The propellant is accelerated and expelled at a high exhaust velocity (order of 10 km/s) through the interaction of the plasma current with an induced magnetic field. The Faraday Accelerator with RF-Assisted Discharge (FARAD) thruster [1,2] is a type of pulsed inductive plasma accelerator in which the plasma is preionized by a mechanism separate from that used to form the current sheet and accelerate the gas. Employing a separate preionization mechanism in this manner allows for the formation of an inductive current sheet at much lower discharge energies and voltages than those found in previous pulsed inductive accelerators like the Pulsed Inductive Thruster (PIT). In a previous paper [3], the authors presented a basic design for a 100 J/pulse FARAD laboratory-version thruster. The design was based upon guidelines and performance scaling parameters presented in Refs. [4, 5]. In this paper, we expand upon the design presented in Ref. [3] by presenting a fully-assembled and operational FARAD laboratory-model thruster and addressing system and subsystem-integration issues (concerning mass injection, preionization, and acceleration) that arose during assembly. Experimental data quantifying the operation of this thruster, including detailed internal plasma measurements, are presented by the authors in a companion paper [6]. The thruster operates by first injecting neutral gas over the face of a flat, inductive acceleration coil and at some later time preionizing the gas. Once the gas is preionized current is passed through the acceleration coil, inducing a plasma current sheet in the propellant that is accelerated away from the coil through electromagnetic interaction with the time-varying magnetic field. Neutral gas is injected over the face of the acceleration coil through a fast-acting valve that feeds a central distribution manifold. The thruster is designed to preionize the gas using an RF-frequency ringing signal produced by a discharging Vector Inversion Generator (VIG). The acceleration stage consists of a multiple-turn, multiple-strand spiral induction coil (see Fig. 1, left panel) and is designed for operation at discharge energies on the order of 100 J/pulse. Several different pulsed power train modules can be used to drive current through the acceleration coil. One such power train is based upon the Bernardes and Merryman circuit topology, which restricts voltage reversal on the capacitor banks and can be clamped to eliminate current reversal in the coil. A second option is a pulse-compression-ring power train (see Fig. 1, right panel), which takesa temporally broad, low current pulse and transforms it into a short, high current pulse.

Polzin, K.A.↗

Development and Operation of PIP-II Injector Test, SSR1 Cryomodule, 325 MHz Amplifiers

The PIP-II Injector Test (PIP2IT) has successfully accelerated ionized hydrogen up to 17MeV through a superconducting, single spoke resonator (SSR1) cryomodule at Fermi National Accelerator Laboratory (FNAL). Each of the SSR1 cavities is tuned to 325MHz and requires up to 6 kW of RF power to accelerate 2mA of ionized hydrogen at the design gradients. RF power amplifiers, specialized for SRF cavity beam operations, were designed by Bhabha Atomic Research Center (BARC) and constructed in a collaboration between the BARC in Mumbai, India and the Electronics Corporation of India Limited (ECIL) in Hyderabad, India. The RF amplifiers meet the specifications and requirements mutually approved between BARC and FNAL. They operate at 325 MHz with a linear power output of 7 kW in both CW and pulse mode. The amplifiers are compatible with the FNAL accelerator personnel safety system and the cavity protection interlocks. Access to controls and internal diagnostic instrumentation are compatible with EPICS control standards. This paper gives details about RF power amplifier development within the Department of Atomic Energy (DAE), India and the operational details with PIP2IT at FNAL.

43 PARTICLE ACCELERATORS↗

Operational Characteristics and Plasma Measurements in a Low-Energy FARAD Thruster

Pulsed inductive plasma accelerators are spacecraft propulsion devices in which energy is stored in a capacitor and then discharged through an inductive coil. The device is electrodeless, inducing a plasma current sheet in propellant located near the face of the coil. The propellant is accelerated and expelled at a high exhaust velocity (order of 10 km/s) through the interaction of the plasma current with an induced magnetic field. The Faraday Accelerator with RF-Assisted Discharge (FARAD) thruster is a type of pulsed inductive plasma accelerator in which the plasma is preionized by a mechanism separate from that used to form the current sheet and accelerate the gas. Employing a separate preionization mechanism in this manner allows for the formation of an inductive current sheet at much lower discharge energies and voltages than those found in previous pulsed inductive accelerators like the Pulsed Inductive Thruster (PIT). In this paper, we present measurements aimed at quantifying the thruster's overall operational characteristics and providing additional insight into the nature of operation. Measurements of the terminal current and voltage characteristics during the pulse help quantify the output of the pulsed power train driving the acceleration coil. A fast ionization gauge is used to measure the evolution of the neutral gas distribution in the accelerator prior to a pulse. The preionization process is diagnosed by monitoring light emission from the gas using a photodiode, and a time-resolved global view of the evolving, accelerating current sheet is obtained using a fast-framing camera. Local plasma and field measurements are obtained using an array of intrusive probes. The local induced magnetic field and azimuthal current density are measured using B-dot probes and mini-Rogowski coils, respectively. Direct probing of the number density and electron temperature is performed using a triple probe.

Polzin, K. A.↗

On the Life Expectancy of High-Power CW magnetrons for Superconducting Accelerators*

Utilization of the high-power CW magnetrons as RF sources in SRF accelerators was proposed in a number of works, e.g., [1, 2]. But typically, the CW high-power magnetrons are designed as RF sources for industrial heating, and the lifetime of the tubes is not the first priority as it is required for high-energy accelerators. The high-power CW magnetrons use cathodes made of pure tungsten. The emission properties of the tungsten cathodes are not deteriorated much by electron and ion bombardment, but the latter causes sputtering of the cathode in the magnetron crossed fields. The sputtered cathode material covers the magnetron interior. That leads to sparks and discharges in a magnetron limiting its lifetime. Thus, the life expectancy estimates are highly important for application of CW magnetrons in SRF accelerator projects.

43 PARTICLE ACCELERATORS↗

Degradation of Poly- and Perfluoroalkyl Substances (PFAS) in Water via High Power, Energy-Efficient Electron Beam Accelerator

The goal of the 2-year workplan was to see if electron beam (EB) could be used to break down a sub-set of the larger chemical family of per and polyfluoroalkylated substances (PFAS) in an energy efficient and economical manner when compared to conventional water treatment technologies. Year one (Y1) work focused on sample EB treatment work in the Fermi National Accelerator Laboratory’s (FNALs) Accelerator Applications Demonstration and Development (A2D2) EB accelerator. While there are reportedly thousands of types of PFAS, for the point of most of the work herein, a small subset was examined, typically perfluorooctane sulfonate (PFOS) and perfluorooctanoate (PFOA). PFOA and PFOS are two of the most well studied PFAS and are studied for baseline evaluations and are considered most useful. The work from Y1 provided information about the optimal operating parameters and additives to use when treating PFOS and PFOA via EB. The data were then used to see where in a water treatment system an EB accelerator would be best suited to treat PFAS. A conventional water treatment technology, GAC, was then compared to e-beam treatment technology with respect to energy and costs for treatment. In year two (Y2), several conventional e-beam accelerator designs, and FNAL’s developmental compact SRF accelerator design, were evaluated for their suitability in PFAS treatment, from an energy efficiency and cost standpoint. Several EB parameters were evaluated and optimized for the removal of PFOA and PFOS from water at normal pressure and temperature, measured as total PFAS removal. Under the optimized test conditions both PFOA showed complete destruction to inorganic fluoride, and PFOS to inorganic fluoride and sulfate, with mass balance. The effect on PFAS removal relative to solution pH, total EB dose, EB dose rate, dissolved oxygen concentration (DO), temperature, and initial PFAS concentration were evaluated. In general, PFOA was easier to destroy than PFOS. Degradation products, typically observed under less-than-optimal EB conditions, provided insight to degradation mechanisms. Products were identified to rule out possible deleterious biproduct formation. The water radiolysis radical reaction kinetics with PFOS and PFOA were not dependent on the initial concentration over 5-orders of magnitude from 2 μg/L to 20 mg/L. This is thought to be because there was an overabundance of the reactive water radiolysis radicals relative to PFAS molecules and largely attributed to aqueous electrons. The reaction rates appeared to be diffusion limited. Testing at higher concentrations (100-200 mg/L) showed a decrease in removal efficiency, suggesting alternative kinetics, possibly second order rates, at higher concentrations. In all, we successfully defined a set of optimal EB parameters to treat PFOA and PFOS at concentrations of 20 mg/L in water with destruction efficiencies near 100%. We further tested the optimized EB parameters with other types of PFAS, including shorter and longer fluorocarbon chain homologs of PFOA and PFOS, and PFAS with alternative functional groups such as sulfonamides. Based on our results EB can be optimized as an effective destructive technology for removing PFAS from water. The conditions optimized for PFOA and PFOS were less effective with ultra-short fluorocarbon compounds like TFMS, PFES, PFPS and PFBS, and likely require re-optimization of parameters to them. In all, it was determined that from a cost and energy efficiency standpoint, EB would be best applied to waste streams with relatively high concentrations of PFOS and PFOA and is not as cost effective as GAC treatment for removing low concentrations of PFAS from water. Higher concentrations of PFAS can be found in the wastewater of conventional treatment processes such as RO and IE and therefore EB may be used to supplement such treatment technologies. Some real-world IE regeneration wash water and RO reject water containing higher concentrations of PFAS and obtained from pilot scale industrial wastewater treatment system at a fluorochemical manufacturing facility, showed that EB could remove PFAS from such types of wastewaters. The IE regenerant wash water appeared to be the most efficient of the two types of wastewaters tested. However, some further optimization of the EB parameters for the specific PFAS types present in those wastewaters may be required. Also, the effects of co-present TOC and mineral salts should be considered during such optimization efforts. From the experimental Y1 results it was seen that the aqueous electron drives degradation of the PFAS. In a hypothetical water treatment skid using EB for PFAS destruction the parameters of the system should be optimized to promote aqueous electron production. Before EB treatment, the PFAS should be preconcentrated when possible, the pH should be raised to pH 10 or higher to enhance aqueous electron production, and the water should be nitrogen purged to remove dissolved oxygen to minimize aqueous electron scavenging. An excel spreadsheet was created that calculates optimal conditions based on inlet PFAS concentration and desired outlet concentration, by optimizing the accelerator power, dose rate, water treatment rate, pH and dissolved oxygen levels to reach the desired endpoint. Given this information on accelerator operating conditions five different EB accelerator systems were compared. One EB system was a continuous-wave, linear superconducting accelerator being designed at Fermilab. Three other EB systems (IMPELA at 5% and 25% duty factor and the ILU-14) were normal conducting pulsed linear accelerators. The fifth system was an IBA Rhodotron which is a normal conducting, circular, continuous-wave accelerator. The accelerator efficiency (% of the incoming power that is used in water treatment) was the dominating factor in accelerator choice. The radio frequency (RF) power supply and the accelerator design (superconducting versus warm technology) drive the accelerator efficiency. The IBA Rhodotron was seen to be the most energy efficient commercially available technology with a wall-plug (total) power efficiency of 43% at 400 kW. The Fermilab design, with a prototype for a different application currently being fabricated, was the most energy efficient at 55% when driven by a Klystron RF power supply and as high as 77% when powered by a magnetron. As the Fermilab design was the most energy efficient by approximately 10-30%, further design work was done on the accelerator and beam delivery system specific to the destruction of PFAS in water. The Fermilab design is unique from industrial accelerators in that is superconducting. Superconducting technology allows for the acceleration of electrons without losses. The accelerator must be cooled to below the point where it is superconducting and is operated around 4 degrees Kelvin. The bulk of the design work for the accelerator is on making the accelerator as energy efficient as possible so that it does not require liquid helium and can be cooled with conduction cooling via cryocoolers. Final design work resulted in an EB accelerator that would operate at minimally 200 kW and 10 MeV. Prototype construction would cost $\$ $7.8 million dollars when driven by a Klystron power supply. A second version of the same accelerator would cost $\$ $5.5 million dollars when driven by a magnetron that is still under development. The commercially available 300 kW IBA Rhodotron cost was estimated at approximately $\$ $9 million. While it is hard to directly compare, an operational GAC system used by 3M for groundwater treatment capital cost (2022 dollars) was estimated to cost $\$ $3.3 million. While the capital expense of the EB accelerator systems was higher than GAC, the accelerator EB treatment would result in destruction of the PFAS and not just sequestration of PFAS to form a new waste stream that requires further treatment or disposal. The operating cost to destroy the PFAS via 400 kw EB system was less than $\$ $1000/kg of PFAS destroyed when treating at a 20 mg/L PFAS concentration, compared to GAC with operating costs that calculated at $\$ $27,530 per kg of PFAS sequestered when treating 100 μg/L PFOA and PFOS combined concentration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Plasma Measurements in an Integrated-System FARAD Thruster

Pulsed inductive plasma accelerators are spacecraft propulsion devices in which energy is stored in a capacitor and then discharged through an inductive coil. The device is electrodeless, inducing a current sheet in a plasma located near the face of the coil. The propellant is accelerated and expelled at a high exhaust velocity (order of 10 km/s) through the interaction of the plasma current and the induced magnetic field. The Faraday Accelerator with RF-Assisted Discharge (FARAD) thruster[1,2] is a type of pulsed inductive plasma accelerator in which the plasma is preionized by a mechanism separate from that used to form the current sheet and accelerate the gas. Employing a separate preionization mechanism allows for the formation of an inductive current sheet at much lower discharge energies and voltages than those used in previous pulsed inductive accelerators like the Pulsed Inductive Thruster (PIT). A benchtop FARAD thruster was designed following guidelines and similarity performance parameters presented in Refs. [3,4]. This design is described in detail in Ref. [5]. In this paper, we present the temporally and spatially resolved measurements of the preionized plasma and inductively-accelerated current sheet in the FARAD thruster operating with a Vector Inversion Generator (VIG) to preionize the gas and a Bernardes and Merryman circuit topology to provide inductive acceleration. The acceleration stage operates on the order of 100 J/pulse. Fast-framing photography will be used to produce a time-resolved, global view of the evolving current sheet. Local diagnostics used include a fast ionization gauge capable of mapping the gas distribution prior to plasma initiation; direct measurement of the induced magnetic field using B-dot probes, induced azimuthal current measurement using a mini-Rogowski coil, and direct probing of the number density and electron temperature using triple probes.

Polzin, K. A.↗

“Snowmass’21 Discussions on Future HEP Facilities in the US

The US particle physics community planning exercise (a.k.a. “Snowmass”) is organized every 7 to 9 years to provide a forum for discussions among the entire particle physics community to develop a scientific vision for the future of particle physics in the U.S. and its international partners. The Snowmass'21 Accelerator Frontier activities include discussions on high-energy hadron and lepton colliders, high-intensity beams for neutrino research and for “Physics Beyond Colliders”, accelerator technologies, science, education and outreach as well as the progress of core accelerator technologies, including RF, magnets, targets and sources. Here we summarize the Snowmass'21 discussions on future HEP accelerator facilities.

43 PARTICLE ACCELERATORS↗

Snowmass 21 Discussions on Future Accelerator HEP Facilities

The US particle physics community planning exercise (a.k.a. Snowmass) is organized every 7 to 9 years to provide a forum for discussions among the entire particle physics community to develop a scientific vision for the future of particle physics in the U.S. and its international partners. The Snowmass 21 Accelerator Frontier activities include discussions on high-energy hadron and lepton colliders, high-intensity beams for neutrino research and for Physics Beyond Colliders, accelerator technologies, science, education and outreach as well as the progress of core accelerator technologies, including RF, magnets, targets and sources. Here we summarize the Snowmass 21 discussions on future HEP accelerator facilities.

43 PARTICLE ACCELERATORS↗