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DOE OSTI2021

Self-consistent PIC simulations of ultimate space charge compensation with electron lenses

Further progress of fundamental particle physics requires high intensity and high brightness of accelerated proton and ion beams. This goal is essential for the FAIR hadron beams at GSI, for the neutrino production at the facilities such as Fermilab and JPARC, and for the Large Hadron Collider luminosity at CERN. One of the most formidable obstacles toward that goal is the beam's own space charge, whose forces cause beam emittance growth, losses and lifetime degradation. Typically, such effects become intolerable when the space charge tune-shift parameter Δ QSC exceeds ~ - (0.25–0.5). To reduce these detrimental effects, it was suggested to use electron lenses to compensate the space charge forces. Furthermore, this paper reports on detailed particle-in-cell space charge and electron lens compensation simulations for extremely intense proton bunches whose space charge tune-shift parameter exceeds -1.0. Different scenarios were evaluated based on reduction in the emittance growth and particle loss at a 4σ aperture. Further, we investigate phenomena and issues related to the focusing lattice errors, importance of the transverse and longitudinal matching of the electron beam profiles to the proton ones, and vary the strength and the number of the electron lenses distributed around a circular machine to optimize the reduction of harmful space charge effects.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Extracting symplectic maps for space-charge dominated beams

Symplecticity of transfer maps is important for reliable evaluation of space-charge dominated beams in accelerators. Unfortunately, most simulation codes that include collective effects, such as space charge, do not use canonical phase-space variables and therefore are not symplectic in the presence of electromagnetic fields. In this paper, we present a numerical method to extract local linear symplectic transfer maps using particle tracking simulation code for space-charge dominated beams. We demonstrate this method for the photoinjector (113 MHz SRF gun) section of the Coherent electron Cooling (CeC) Proof of Principle (POP) experiment.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Injection simulations of space charge dominated proton beams in IOTA

A 2.5 MeV proton injector is being constructed for the IOTA ring at Fermilab to study the interaction of nonlinear integrable optics (NIO) with high space charge beams. Space charge in the transport line from the RFQ to the injection location has a significant current dependent effect on the phase space. Simulation studies to support efficient injection of intense bunches into IOTA are presented, included schemes to inject directly into NIO lattices.

Accelerator Physics↗

DOE OSTI2025

Injection simulations of space charge dominated proton beams in IOTA

Wieland, J. [Fermilab; Michigan State U.] (ORCID:0↗

DOE OSTI2021

Space Charge Effects in Low Energy Magnetized Electron Beams

Magnetized electron cooling of the ion beam is one of the major approaches towards obtaining the required high luminosity in the proposed Electron-Ion Collider (EIC). To increase the cooling efficiency, a bunched electron beam with a high bunch charge and high repetition rate is required. However, these features can combine to enhance the collective interactions, such as the space charge effect. A magnetized electron beam was successfully generated at the Thomas Jefferson National Accelerator Facility (JLab) using a compact, 300 kV DC high voltage photo-gun with an inverted insulator geometry and bi-alkali antimonide photocathode. The beam magnetization was characterized using a modest diagnostic beamline to measure beam sizes, rotation angles, and normalized transverse emittance as a function of magnetic field at the photocathode, laser spot size, and gun high-voltage. Simultaneously, simulations were performed using the A Space Charge Tracking Algorithm (ASTRA) and General Particle Tracer (GPT) programs. Further, sustained high average current magnetized beam up to 28 mA was demonstrated, and the photocathode lifetime for different magnetized electron beam currents was investigated. In the second part of the project, the space charge effect in low-energy magnetized electron beams was studied and compared with GPT simulations. The high bunch charge studies showed evidence of space charge current limitations starting at 0.3 nC and limited the maximum delivered bunch charge to 0.7 nC. To reach the high bunch charge goal of a few nC, the existing DC photo-gun design was modified using CST Studio Suite’s electromagnetic field solver, and a way to cancel the beam deflection exerted by the non-symmetric nature of the inverted insulator photo-gun geometry was discovered. This thesis presents a detailed description of the generation, characterization, and simulation of high current, high bunch charge magnetized electron beams at JLab, as well as the modified photo-gun design. Together with measurements and simulations, the purpose of this thesis is to provide a solid background on the theoretical aspects and the experimental challenges associated with magnetized electron beams for accelerator applications.

Wijethunga, W M Sajini↗

DOE OSTI2023

A numerical solver for investigating the space charge effect on the electric field in liquid argon time projection chambers

This paper reports the development of a numerical solver aimed to simulate the interaction between the space charge (i.e. ions) distribution and the electric field in liquid argon time projection chamber (LArTPC) detectors. The ion transport equation is solved by a time-accurate, cell-centered finite volume method and the electric potential equation by a continuous finite element method. The electric potential equation updates the electric field which provides the drift velocity to the ion transport equation. The ion transport equation updates the space charge density distribution which appears as the source term in the electric potential equation. The interaction between the space charge distribution and the electric field is numerically simulated within each physical time step. The convective velocity in the ion transport equation can include the background flow velocity in addition to the electric drift velocity. The numerical solver has been parallelized using the Message Passing Interface (MPI) library. Numerical tests show and verify the capability and accuracy of the current numerical solver. It is planned that the developed numerical solver, together with a Computational Fluid Dynamics (CFD) package which provides the flow velocity field, can be used to investigate the space charge effect on the electric field in large-scale particle detectors.

42 ENGINEERING↗

DOE OSTI2024

Proton Beam Dynamics in Bare IOTA with Intense Space-Charge

We are commissioning a 2.5~MeV proton beam for the Integrable Optics Test Accelerator at Fermilab, allowing experiments in the strong space-charge regime with incoherent betatron tune shifts nearing 0.5. Accurate modelling of space-charge dynamics is vital for understanding planned experiments. We compare anticipated emittance growth and beam loss in the bare IOTA configuration using transverse space-charge models in Xsuite, PyORBIT, and MAD-X simulation codes. Our findings reveal agreement within 30\% in core phase-space density predictions up to 100~synchrotron periods at moderate beam currents, while tail distributions and beam loss show significant differences.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Proton beam dynamics in bare IOTA with intense space-charge

We are commissioning a 2.5-MeV proton beam for the Integrable Optics Test Accelerator at Fermilab, allowing experiments in the strong space-charge regime with incoherent betatron tune shifts nearing 0.5. Accurate modelling of space-charge dynamics is vital for understanding planned experiments. We compare anticipated emittance growth and beam loss in the bare IOTA configuration using transverse space-charge models in Xsuite, PyORBIT, and MADX simulation codes. Our findings reveal agreement within a factor of 2 in core phase-space density predictions up to 100 synchrotron periods at moderate beam currents, while tail distributions and beam loss show significant differences.

43 PARTICLE ACCELERATORS↗

DOE OSTI2026

Numerical Investigation of Fluid Flow and Space Charge in Liquid Argon Time Projection Chamber (LArTPC) Detectors

Overview This project focused on developing a high-fidelity numerical framework to simulate the multiphysics environment within Liquid Argon Time Projection Chamber (LArTPC) detectors. The primary objective was to characterize the complex interplay between ion transport, background fluid dynamics, and electric field distortions—a critical factor for the calibration and sensitivity of next-generation High Energy Physics experiments, such as DUNE. Technical Achievements The research successfully yielded a hybrid numerical space-charge solver utilizing a Cell-Centered Finite Volume Method (FVM) for ion transport coupled with a Finite Element Method (FEM) for electric potential. Key accomplishments include: • Verification & Validation: The 3-D solver was rigorously verified against 1-D analytical solutions, demonstrating high numerical accuracy in predicting space-charge-induced field deviations. • Field Distortion Analysis: 3D simulations revealed that space charge effects introduce significant non-uniformities in the electric field. Critically, the research identified that background LAr flow velocities, when comparable to ion drift velocities, markedly exacerbate these distortions. • Technology Transfer: The resulting source code and comprehensive user manuals were successfully transferred to collaborators at Fermilab, providing a portable computational tool for the broader scientific community. Challenges and Future Directions While the space-charge solver achieved all performance metrics, the integrated fluid dynamics modeling encountered convergence challenges stemming from the extreme 200-fold disparity in length scales between the detector's 37 mm inlet pipes and the 8-meter global domain. To address this, the project has identified a clear technical pivot toward Hierarchical Geometric Adaptive Mesh Refinement (HG-AMR). By implementing an h-type refinement strategy with hanging nodes, future iterations of this solver will be capable of resolving localized high-gradient inlet flows without the prohibitive computational costs of regular grids. This advancement, combined with data-driven uncertainty quantification based on MicroBooNE-style calibration, will enable the precise modeling of detector responses in large-scale cryogenic environments where direct measurement remains difficult. Impact The computational tools developed under this award provide a foundation for enhancing the energy resolution and spatial reconstruction of noble liquid detectors. By bridging the gap between theoretical fluid dynamics and experimental field calibration, this work supports the DOE’s mission to advance the frontiers of neutrino physics and dark matter detection.

42 ENGINEERING↗

DOE OSTI2024

A variational method for the sheath potential of hypersonic leading edges with space-charge limitations

Electron transpiration cooling for the leading edges (LE) of hypersonic aircraft utilizes thermionic emission; however, space-charge effects limit the electron emission rate, potentially diminishing the efficiency of this cooling mechanism. We develop a variational weak form of the Poisson equation that describes the sheath potential and then numerically solve it using the finite element method. This formulation has two main benefits: (1) the space-charge limit condition can be incorporated as a constraint and (2) it allows for the analysis of three-dimensional geometries with complex boundary conditions. We demonstrate that the current emitted from the surface of an LE is generally a small fraction of the Child–Langmuir limit due to space charge. We then propose several methods to enhance the emitted current from the surface and to boost the cooling effect of thermionic emission. These include increasing the plasma density, applying a negative surface potential, and using fringe fields under suitable geometric conditions. For a LaB6 emitting LE, the total emitted current is shown to be minimal and independent of the temperature of a surface with floating potential. However, when a negative potential is applied and the surface is heated, the emitted current follows the Richardson–Dushman relationship up to a critical temperature, beyond which it remains constant. At an applied surface potential of −5 V, the critical temperature is around 1700 K.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Experiments on Electron Cooling and Intense Space-Charge at IOTA

The Integrable Optics Test Accelerator at Fermilab will explore beam dynamics in a ring with intense space-charge using 2.5~MeV proton beams with an incoherent tune shift approaching -0.5. We will use this machine to explore the interplay between electron cooling, intense space-charge, and coherent instabilities. In this contribution, we describe the machine setup including the design of the electron cooler and the lattice, list specific experiments and discuss the results of numerical simulations which include the effects of electron cooling and transverse space-charge forces.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

EXPERIMENTS ON ELECTRON COOLING AND INTENSE SPACE-CHARGE AT IOTA

The Integrable Optics Test Accelerator at Fermilab will explore beam dynamics in a ring with intense space-charge using 2.5 MeV proton beams with an incoherent tune shift approaching -0.5. We will use this machine to explore the interplay between electron cooling, intense space-charge, and coherent instabilities. In this contribution, we describe the machine setup including the design of the electron cooler and the lattice, list specific experiments and discuss the results of numerical simulations which include the effects of electron cooling and transverse space-charge forces.

Banerjee, N.↗

DOE OSTI2023

Experiments On Electron Cooling and Intense Space-charge at IOTA

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Description of longitudinal space charge effects in beams and plasma through dielectric permittivity

We develop a universal framework which allows quickly solve a wide class of problems for longitudinal space charge effects in beams and plasmas in cylindrical geometry. We introduce the longitudinal dielectric permittivity for the beam of charged particles, which describes its collective space charge response. The analysis yields an effective plasma frequency, which depends on the transverse geometry of the system. This dielectric permittivity mirrors the dielectric permittivity of plasma and matches the one dimensional (1D) expression once the transverse size of the beam is large. Several particle species can be included as additive terms describing susceptibility of each specie. The developed approach allows to study stability criteria for collective beam-beam and beam-plasma instabilities for arbitrary transverse distributions in particle densities.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Proposal for a proton-bunch compression experiment at IOTA in the strong space-charge regime

The longitudinal compression of intense proton bunches with strong space-charge force is an essential component of a proton-based muon source for a muon collider. This paper discusses a proton-bunch compression experiment at the Integrable Optics Test Accelerator (IOTA) storage ring at Fermilab to explore optimal radio frequency (RF) cavity and lattice configurations. IOTA is a compact fixed-energy storage ring that can circulate a 2.5-MeV proton beam with varying beam parameters and lattice configurations. The study will aim to demonstrate a bunch-compression factor of at least 2 in the IOTA ring while examining the impact of intense space-charge effects on the compression process.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Proposal for a Proton-Bunch Compression Experiment at IOTA in the Strong Space-Charge Regime

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Space-Charge Aberrations in Single-Shot Time-Resolved Transmission Electron Microscopy

In this paper, we discuss effects of space-charge fields on imaging performance in a single-shot time-resolved transmission electron microscope. Using a Green’s function perturbation method, we derive analytical estimates for the effects of space-charge nonlinearity on the image formation process and the associated aberration coefficients. The dependence of these coefficients on the initial beam phase space distribution is elucidated. The results are validated by particle tracking simulations and provide fundamental scaling laws for the trade-off between temporal and spatial resolutions in single-shot time-resolved transmission electron microscopy.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Dimensional analysis on microscale gas breakdown with electric field nonuniformity and positive space charge effects

A dimensional method was employed to evaluate the microscale gas breakdown characteristics at atmospheric pressure, resulting in a universal breakdown curve applicable to different types of gases (e.g., Ar, Xe, Ne, and N2). As the gap distance decreases, the breakdown mode transitions from ion-induced secondary electron emission to the field emission regime. In the field emission regime, the positive space charge effect becomes more significant. We discovered that incorporating the positive space charge effect in the field emission regime can be achieved by modifying the local electric field enhancement factor β. Consequently, we propose an effective electric field enhancement factor, βeff, which scales linearly with β, to accurately reproduce the breakdown curve while considering the positive space charge effect. This proposed approach significantly simplifies the numerical model. Additionally, we examined the effects of gas pressure, gap distance, cathode properties (e.g., work function and secondary electron emission coefficient), and electric field nonuniformity.

Physics↗