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DOE OSTI2025

Symplectic machine learning model for fast simulation of space-charge effects

Symplectic simulation of space-charge effects is crucial for the design and operation of high-intensity particle accelerators. Traditional methods for simulating these effects are often computationally expensive, resulting in significant overhead. In this work, we introduce a generative model based on a U-Net architecture within a generative adversarial network framework to efficiently simulate space-charge effects. The model is trained to predict the transverse multiparticle space-charge Hamiltonian, which can be physically computed using a gridless spectral method. The one-step symplectic transverse transfer map for the particles is then obtained by differentiating the predicted Hamiltonian. Benchmarking results demonstrate that this generative model achieves an order of magnitude higher computational efficiency compared to the spectral method, providing a highly efficient alternative for simulating space-charge effects with a large number of particles. By maintaining symplecticity, the model effectively preserves the phase-space structure and mitigates nonphysical errors in long-term simulations. This model has been integrated into jutrack, a novel autodifferentiable accelerator modeling code developed in the julia programming language.

Beam code development & simulation techniques↗

DOE OSTI2025

IOTA Experiment for Proton Pulse Compression at Extreme Space-Charge

The longitudinal compression of high-intensity, space-charge-dominated proton bunches is a critical requirement for future proton-driven muon colliders. We propose a proton bunch compression experiment at the Integrable Optics Test Accelerator (IOTA) storage ring at Fermilab to investigate optimal radio-frequency (RF) cavity parameters and lattice configurations. IOTA is a compact, fixed-energy storage ring dedicated to beam physics Research and Development and capable of circulating a 2.5 MeV proton beam under extreme space-charge conditions. Using the ImpactX code with its 3D space-charge solver, simulations indicate that the bunch length can be rapidly reduced by at least a factor of two without appreciable degradation of transverse beam quality--even in the strong space-charge regime. However, longitudinal defocusing due to the space-charge remains a significant challenge in short-pulsed intense proton bunches, and the optimization of compression under these conditions is discussed.

Simons, B. D. [Northern Illinois U.]↗

DOE OSTI2025

A two-and-a-half dimensional symplectic space-charge solver

The nonlinear space-charge effect plays a significant role in high-intensity accelerators and has been extensively studied using multi-particle tracking methods. In this paper, we present a novel 2.5- dimensional symplectic space-charge solver specifically designed for long beam bunches. We begin by detailing its application to a transverse Gaussian density distribution under open boundary conditions in a straight system, where a semi-analytical expression is derived. We then demonstrate the solver’s adaptation to arbitrary distributions in open space, as well as within rectangular and round conducting pipes. Finally, we discuss the extension of this solver to circular accelerator systems. This study shows that the fast 2.5-dimensional solver can be a good approximation to the fully three-dimensional solver for long bunches in large circular accelerators.

Beam code development & simulation techniques↗

DOE OSTI2025

Injection simulations of space charge dominated proton beams in IOTA

Injection simulations of space charge dominated proton beams in IOTA ABSTRACT = A 2.5 MeV proton injector has been 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.

Wieland, J. [Fermilab]↗

DOE OSTI2026

Space charge studies on strong hadron cooler energy recovery linac

An Energy Recovery Linac (ERL) based cooler, using Coherent electron Cooling (CeC) is being designed for cooling hadron beams of the Electron-Ion Collider (EIC). The ERL design utilizes highcurrent, high-brightness electron beams with low emittance and a uniform longitudinal distribution for efficient hadron cooling. This is designed to operate in two modes to accommodate cooling requirements for hadron bunches at 100 GeV and 275 GeV, each with an average current of 100 mA and 1 nC bunch charge. With these parameters, the space charge effects become significant in this ERL design due to the low beam energy and high beam current. In this paper, we discuss strategies for including space charge effects in the optics design and implementation of an interface for space charge dominated and non-dominated regions of this ERL lattice.

Accelerator Physics↗

DOE OSTI2026

IOTA experiment for proton pulse compression at extreme space-charge

The longitudinal compression of intense proton bunches with strong space-charge force is an essential component of a proton driver for a muon collider. We propose 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 dedicated to beam physics R&D that can circulate a 2.5-MeV proton beam with extreme space-charge. Using ImpactX and its 3D space-charge solver, simulations indicate that bunch length can be rapidly reduced by a factor of at least two, without appreciable degradation in transverse beam quality, even under strong space-charge conditions. However, longitudinal defocusing presents a large effect in short-pulsed proton beams, and the optimization of bunch compression under such conditions is discussed.

Simons, Benjamin [Northern Illinois U.; Fermilab]↗

DOE OSTI2025

The Implications of Collisions on the Spatial Profile of Electric Potential and the Space-Charge-Limited Current

The space-charge-limited current (SCLC) in a vacuum diode is given by the Child-Langmuir law (CLL), whose electric potential ϕ(x) ∝ (x/D) 4/3 , where x is the spatial coordinate across the gap and D is the gap separation distance. For a collisional diode, SCLC is given by the Mott-Gurney law (MGL) and ϕ(x) ∝ (x/D) 3/2 . Here, we apply a capacitance argument for SCLC and use the transit time from a recent exact solution for collisional SCLC to show that ϕ(x) ∝ (x/D)ξ for a general collisional gap, where 4/3 ≤ ξ ≤ 3/2 . Furthermore, ξ is strictly a function of νT, where ν is the collision frequency and T is the electron transit time. Using this definition of ξ, we estimate the spatial dependence of the electron velocity and use the gap capacitance to derive an analytic equation for collisional SCLC that agrees within ~4.5% of the exact solution that requires solving parametrically through T. This analytic equation for general ξ asymptotically recovers the CLL as ν → 0 and the MGL as ν → ∞. As a result, matching these limits shows that ξ ≈ 1.40 and V ∝ D 2 ν 2 at the transition from a vacuum to a collisional diode for any device condition.

Anodes↗

DOE OSTI2026

Calculating the space-charge-limited current density for nonplanar geometries by simulating the charge-free electric field

Calculating the space-charge-limited-current density (SCLCD) for a complicated diode geometry often requires computationally expensive particle-in-cell (PIC) codes. Here, this paper addresses this issue by using the charge-free electric field $E_0$ calculated using COMSOL Multiphysics to determine local and global SCLCD. The SCLCD obtained by using the surface average of $|E_0|^2$ on the cathode recovers theoretical results for one-dimensional (1D) planar, cylindrical, and tip-to-tip geometries in appropriate limits. We next compared tip-to-tip calculations with the SCLCD obtained using the PIC code Empire. The SCLCD calculated using COMSOL agreed well with Empire for flatter 1D tip-to-tip geometries and diverged with increasing sharpness. Physically, Empire predicts lower SCLCD than COMSOL because the electrons spread due to concentrated space-charge at the tip, whereas theory assumes that the electrons follow the charge-free electric field lines. We further assess the behavior of the SCLCD for tips protruding from the centers of flat, circular plates of various areas. Larger plate areas with constant tip size recover the 1D planar SCLCD globally and 1D tip-to-tip SCLCD locally, while reducing the difference between Empire and COMSOL calculations since larger plates capture more of the emitted electrons, reducing SCLCD suppression due to beam spreading. These results show that charge-free electric field simulations can be used to determine the SCLCD without needing to simulate particle dynamics in PIC.

Wright, Jack K. [Purdue Univ., West Lafayette, IN ↗

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 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

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 OSTI2025

Single-Bunch Instabilities Driven by Space Charge During Low-Energy Cooling at Injection in the EIC Hadron Storage Ring

This paper presents a simulation-based study of single-bunch dynamics at the injection energy of 23.8 GeV for protons in the EIC hadron storage ring, focusing on the impact of space-charge–driven instabilities. The analysis demonstrates that at this energy, the proton bunch experiences significant transverse space-charge forces, which can reduce the stability margin in the presence of the geometric and resistive wall impedance. Various collective effects were considered, with particular attention to the nonlinear nature of the transverse space charge. To stabilize the beam, high chromaticity and octupoles were introduced and their effects analyzed using the ELEGANT code. The results provide a quantitative assessment of the stability thresholds and offer guidance for the machine design and operational strategy at injection.

43 PARTICLE ACCELERATORS↗