EDITRON: EDM Simulation Software

• EDITRON is an advanced computational toolkit for EDM experiments that offers exact symplectic tracking of both orbital and spin dynamics.
• It reconstructs historical electric storage rings like the AGS Electron Analogue ring, enabling rigorous benchmarking of beam behavior and lattice dynamics.
• Its high-fidelity simulation results validate long-duration spin coherence necessary for precision EDM measurements and guide next-generation experiment design.

EDITRON is an advanced computational approach and software toolkit for planning and simulating electric dipole moment (EDM) experiments using all-electric storage rings, with particular emphasis on high-precision modeling of both orbital and spin dynamics of polarized charged particles. Developed in the context of the Unified Accelerator Libraries (UAL), EDITRON centers around the ETEAPOT module, enabling the reconstruction and virtual operation of historical accelerator designs (most notably the AGS Electron Analogue ring) for the computational evaluation and optimization of EDM experiments. Its core functionality addresses the stringent requirements of EDM physics measurements, such as maintaining frozen spin states and ensuring symplectic tracking over extremely long timescales.

1. ETEAPOT Code Architecture and Core Functionality

ETEAPOT forms a dedicated module within UAL, designed specifically for electric- rather than magnetic-bending storage rings. Its key distinction is exact symplectic integration of charged particle trajectories subject to electric fields, including arbitrary quadrupole, sextupole, and higher-order multipole elements. The code supports both “real” and “virtual” multipoles and can model fringe field effects using linear ramps over electrode gaps as opposed to hard-edged field approximations.

The principal innovation is in the coupled tracking of orbital and spin degrees of freedom. Spin evolution is computed in accordance with the Thomas-BMT equation:

$$\dot{\mathbf{S}} = \boldsymbol{\Omega} \times \mathbf{S}$$

where $\mathbf{S}$ is the spin vector and $\boldsymbol{\Omega}$ is the spin precession vector determined by local electromagnetic field values. ETEAPOT enforces constancy in the norm of the spin vector $|\mathbf{S}|$ to guarantee exact symplecticity.

The module supports long-duration spin tracking, with explicit monitoring of transverse spin components ($S_x$, $S_y$) and the synchrotron tune (notably $\sim 1/59$ for the AGS Analogue lattice). Lattice functions such as Twiss parameters $(\alpha, \beta, \gamma)$ are recovered using FFT and model-independent analysis.

2. Historical Reconstruction of the AGS Electron Analogue Ring

The AGS Electron Analogue ring, constructed in 1954 at Brookhaven National Laboratory, is unique as the only relativistic accelerator employing pure electric bending and as the earliest implementation of alternating gradient focusing. Its historical value lies in its suitability for electron EDM studies and as a prototype for more costly proton EDM machines.

Due to the physical loss of the appliance and its engineering archives, the ring has been resurrected by reconstructing its lattice from archival documents—a 1953 funding proposal, a 1991 Plotkin report, and unpublished Courant notes. This process resulted in detailed lattice description files (e.g., in .sxf format) compatible with UAL/ETEAPOT, enabling rigorous computational reenactment of beam and spin behavior per original machine specifications.

The resurrection serves dual functions: validating EDITRON methodologies against historical data, and providing a cost-efficient model for exploration of electron and proton EDM measurement strategies.

3. Simulation Results and Comparison to Historical Machine Studies

ETEAPOT’s predictions were benchmarked against historic AGS Electron Analogue ring data. Key diagnostics include tune-plane resonance diagrams, which display loss and disruption at integer and half-integer resonances, as well as stop bands induced by the ring’s eightfold lattice symmetry.

Simulation results demonstrate high fidelity to historical measurements (e.g., as reported by Courant in 1955 and Plotkin in later years). In the context of the AGS Analogue ring, modifications from magnetic to electric bending produce minimal perturbation (with nominal tunes around 6.5), while planned proton EDM ring designs will experience greater variance.

Spin evolution under electron EDM measurement conditions (requiring a $\sim 1.5$ times higher bending field for “magic energy” operation at 15 MeV) exhibits consistent behavior in simulated results. For protons, ETEAPOT tracks 33 million turns, confirming that $S_x, S_y$ undergo only minute oscillatory excursions, an indicator of robust spin coherence critical for EDM sensitivity.

4. Modeling Lattice Optics and Field Effects

ETEAPOT enables precise modeling of lattice optics, including the emulation of orbital tunes and resonance structures via the reconstructed AGS Analogue lattice. Fringe field effects are directly modeled by linearly ramped field profiles, capturing real physical transitions across electrode gaps. This detail is essential for resolving minute effects in orbital dynamics and systematic errors associated with beam loss and resonance crossings.

Extensive simulation runs confirm absence of spurious damping or growth in beam and spin parameters over millions of turns, indicating suitability for high-fidelity EDM measurement planning.

5. Long-term Spin Tracking and EDM Measurement Implications

The module's capacity for proton spin tracking is exemplified by the simulation of 33 million turns in a prototype all-electric 230 MeV ring. Initial conditions with tangentially aligned spin ($S_z = 1$) remain stable over the full trajectory, with transverse polarization showing only small oscillatory variation tied to betatron and synchrotron effects.

Sinusoidal fits to early-turn $S_x$ data affirm consistent oscillatory frequency and amplitude, persisting undamped across the simulation timespan. The absence of drift or artificial decoherence substantiates the exact symplectic nature of ETEAPOT's tracking algorithm.

Such tracking stability is paramount: anticipated EDM measurements demand preservation of spin polarization across experimental lifetimes (ca. $10^9$ betatron oscillations, equivalent to $\sim 10^3$ s). ETEAPOT’s performance indicates that systematic errors—especially due to geometric phases or residual field effects—can be constrained within the rigorous requirements of contemporary and next-generation EDM experiments.

6. Prospects for Precision EDM Experiment Design

EDITRON’s demonstrated accuracy in replicating historical ring behavior and innovating detailed spin tracking provides a foundation for future EDM experiment design. The insights gained into spin coherence time (SCT) and systematic effects inform critical design choices for storage ring architectures, electric field supply, and data acquisition strategies.

A plausible implication is that high-fidelity computational modeling via EDITRON could supplant many prototype hardware validation steps, streamlining development and reducing cost and risk. Furthermore, the approach enables systematic assessment and mitigation of experimental errors related to polarization, geometric phase shifts, and unwanted field perturbations, thereby supporting the stringent sensitivities demanded by EDM searches in both electron and proton systems.

In summary, EDITRON (via ETEAPOT) establishes a computational paradigm for EDM experiment planning, marked by exact symplectic tracking, successful resurrection and modeling of historical electric storage rings, and robust, scalable simulations informing the architecture and performance of future precision measurement campaigns.