Inputs
Example data table
These sample runs illustrate typical ranges for quick checks.
| Mode | Particle | Input K₀ (MeV) | Key settings | Typical outcome |
|---|---|---|---|---|
| Linear | Proton | 10 | E=20 MV/m, L=15 m, η=90% | ~280 MeV gain, relativistic β rises |
| Cyclotron | Proton | 5 | R=20 m, B=1.6 T, Vrf=0.3 MV | Energy capped by rigidity; T_rev shortens |
| Synchrotron | Electron | 50 | R=100 m, B=1.2 T, Vrf=1.0 MV | Orbit near ring size; γ increases strongly |
Formulas used
This simulator uses standard accelerator relationships in a simplified form.
- Energy gain (linac): ΔK = |q|·E·L·η
- Energy gain per turn (ring): ΔK_turn = |q|·V_rf·sin(φ)·η
- Relativistic factors: γ = (K + mc²)/mc², β = √(1 − 1/γ²)
- Momentum–energy: E² = (pc)² + (mc²)²
- Orbit radius: r = p / (|q|·B)
- Rigidity limit: p_max = |q|·B·R
- Cyclotron frequency: ω = |q|·B / (γm), f = ω/2π
All outputs are approximate and intended for learning and quick design intuition.
How to use this calculator
- Select an accelerator type matching your scenario.
- Choose a particle preset, or enter custom mc² and z.
- Set injection energy K₀, then fill linac or ring settings.
- Click Simulate to compute energy, orbit, and timing.
- Review warnings about limits, then refine parameters.
- Export your run as CSV or a compact PDF report.
Tip: For ring modes, keep r close to R without exceeding it.
Technical article: interpreting the particle accelerator simulator
1) Purpose and scope
This simulator is designed for fast, first‑pass accelerator estimates. It models energy gain from an accelerating field (linac) or RF voltage per turn (ring) and then converts energy to relativistic motion. The goal is design intuition: how changing voltage, field strength, or ring geometry shifts energy, speed, and time scales.
2) Inputs that dominate performance
For linacs, the main lever is the effective gradient and active length. Practical gradients commonly span 5–30 MV/m for many normal‑conducting structures, while high‑gradient concepts can push higher under specialized conditions. For rings, the product B·R sets a hard momentum scale, while RF voltage and phase determine how quickly you approach it.
3) Linac energy gain with a numeric example
The linac model uses ΔK ≈ |q|·E·L·η. With z=+1, E=20 MV/m, L=15 m, and η=90%, the integrated voltage is 300 MV and the net gain is about 270 MeV. Starting from K₀=10 MeV, the run ends near 280 MeV, and β rises toward relativistic values as γ increases.
4) RF gain per turn and turn‑count scaling
Ring acceleration uses ΔKturn ≈ |q|·Vrf·sin(φ)·η. With Vrf=0.5 MV, φ=30°, and η=85%, a z=+1 particle gains roughly 0.2125 MeV per turn. Over 2000 turns this is ~425 MeV, which is easy to validate by changing turns and watching the output scale linearly.
5) Magnetic rigidity and the energy ceiling
The rigidity limit follows pmax=|q|·B·R. For z=+1, B=1.5 T, and R=100 m, the momentum scale is about 45 GeV/c, corresponding to proton energies in the tens of GeV range. Doubling B or R doubles the reachable momentum; increasing |z| raises it proportionally for higher charge states.
6) Orbit radius, frequency, and timing
The orbit radius is r=p/(|q|B). If r approaches your chosen ring radius, you are operating near the aperture limit. The revolution frequency is f≈|q|B/(2πγm), so f decreases with γ even though v approaches c. This is why high‑energy rings can have nearly constant orbit time per turn despite increasing energy.
7) Using limits and warnings professionally
The limit fields do not block computation; they flag questionable parameter sets. If “orbit radius exceeds ring radius” appears, increase B, reduce energy gain per turn, or enlarge R. If “phase yields zero net RF gain” appears, move φ into a range where sin(φ) is positive and sized for your ramp strategy.
8) Choosing a mode for realistic workflows
Use the linac mode to estimate injector or pre‑accelerator sections, where gradient and length dominate. Use the cyclotron mode for fixed‑field scenarios and quick checks of rigidity‑limited energy. Use the synchrotron mode when you want RF ramping with a geometry‑driven momentum ceiling. Effects like synchrotron radiation, space charge, and lattice optics are intentionally excluded here.
FAQs
1) Does the simulator include synchrotron radiation losses?
No. The model assumes net RF gain without radiation damping or energy loss. For electrons at high energy, radiation can dominate and would require a dedicated synchrotron‑radiation model and lattice parameters.
2) Why does the final energy stop increasing in ring modes?
The calculation enforces a rigidity ceiling using pmax=|q|BR. Once the ideal RF gain would exceed that momentum, the final kinetic energy is capped to match the ring’s B and radius.
3) What does “RF phase” change physically?
The synchronous phase sets the effective accelerating component via sin(φ). Small positive phases give gentle, stable acceleration, while phases near 90° maximize gain. Negative or zero sin(φ) yields no net acceleration.
4) How should I pick efficiency values?
Use efficiency as a combined factor for capture, phasing, and effective voltage seen by the beam. For quick studies, 70–95% is typical. Lower values emulate mismatch, beam loading, or conservative design margins.
5) Why can orbit radius exceed the ring radius?
If momentum grows faster than B·R allows, r=p/(|q|B) becomes larger than your ring radius. Increase B, increase R, reduce turn gain, or lower the target energy to bring r back inside the ring.
6) Can I simulate heavy ions?
Yes. Choose “Custom” and enter the ion’s rest energy mc² and charge state z. Higher |z| boosts acceleration and rigidity, while larger mc² reduces β at the same kinetic energy.
7) What should I export, CSV or PDF?
Use CSV for comparing many parameter scans in a spreadsheet. Use PDF for quick sharing, documentation, or lab notes. Both exports capture the same run values shown in the result panel.