Calculator inputs
Use the responsive grid below. It displays three columns on large screens, two on smaller screens, and one on mobile.
Example data table
| Parameter | Example value | Unit |
|---|---|---|
| Particle type | Proton–proton | — |
| Dipole field per beam | 8.33 | T |
| Bending radius per beam | 2804 | m |
| Rest mass energy | 0.938272 | GeV/c² |
| Charge state | 1 | |q/e| |
| Ring circumference | 26658.883 | m |
| Particles per bunch | 1.15e11 | particles |
| Bunch count | 2808 | bunches |
| Crossing angle | 0.59 | mrad |
| Approximate beam energy | 7002.35 | GeV |
| Approximate collider √s | 14004.70 | GeV |
Formula used
1) Magnetic rigidity and momentum
p ≈ 0.299792458 × B × ρ × |q/e|
Here, p is momentum in GeV/c, B is dipole field in tesla, and ρ is bending radius in meters.
2) Relativistic total energy
E = √(p² + m²)
Rest mass energy m is entered in GeV/c², so the calculator works in practical high-energy natural units.
3) Kinetic energy, gamma, and beta
K = E - m
γ = E / m
β = p / E
4) Revolution frequency and beam current
frev = βc / C
I = e × |q/e| × Nparticles × frev
where C is ring circumference and Nparticles is total particles stored in the beam.
5) Stored beam energy
U = Nparticles × E × 10⁹ × e
The result is reported in megajoules for machine-protection and beam-dump context.
6) Center-of-mass energy with crossing angle
s = m₁² + m₂² + 2(E₁E₂ + p₁p₂ cos α)
√s = √s
Here, α is the crossing angle in radians. Setting α = 0 gives the head-on case.
7) Synchrotron radiation loss per turn
U₀ ≈ 88.5×10⁻⁶ × (me/m)⁴ × E⁴ / ρ GeV/turn
This is extremely important for leptons and usually tiny for hadrons.
How to use this calculator
- Select a preset particle for each beam, or choose Custom and enter your own rest mass and charge state.
- Enter dipole field and bending radius for each beam. These two values drive the magnetic rigidity and momentum estimate.
- Provide particles per bunch, bunch count, and ring circumference to estimate revolution frequency, current, and stored beam energy.
- Set the crossing angle in mrad. Use zero for ideal head-on operation or a small nonzero value for practical collider geometry.
- Press the calculate button. The result block appears above the form, followed by CSV export, PDF export, and the Plotly graph.
FAQs
1) What does this calculator estimate?
It estimates beam momentum, total energy, kinetic energy, gamma, beta, magnetic rigidity, revolution frequency, beam current, stored energy, synchrotron loss, and collider center-of-mass energy.
2) Why is bending radius used instead of only circumference?
Beam momentum in a circular machine is controlled by magnetic rigidity, which depends directly on dipole field and local bending radius. Circumference mainly affects revolution frequency and current.
3) Can I model asymmetric colliders?
Yes. Turn off the mirror switch and enter different fields, radii, masses, charges, bunch patterns, or particle types for Beam 1 and Beam 2.
4) Does synchrotron loss matter for proton machines?
Usually it is very small because synchrotron radiation scales strongly with inverse particle mass to the fourth power. It becomes much more important for electrons and positrons.
5) What units should I enter?
Use tesla for dipole field, meters for bending radius and circumference, GeV/c² for rest mass energy, mrad for crossing angle, and particles or bunches as plain counts.
6) Does a crossing angle lower center-of-mass energy?
Yes. A nonzero crossing angle slightly reduces the effective center-of-mass energy compared with a perfect head-on geometry, though the reduction is usually modest for very small angles.
7) Can I use this for ions or custom particles?
Yes. Choose Custom or a preset ion and enter the correct rest mass energy and charge state. The rigidity and energy relations remain valid for those inputs.
8) Is this a full accelerator design code?
No. It is a strong engineering calculator for first-pass estimates. It does not replace detailed lattice, optics, RF, collective-effects, or beam-beam simulation software.