Laser–Plasma Calculator
From laser energy, pulse duration and focal spot to a₀, critical density, self-focusing threshold and nonlinear wakefield-acceleration scalings, all in one place.
Inputs
Results
Email me this report + expert setup advice
Get a formatted copy of these results in your inbox. Reply to it and a physicist will review your planned setup for free.
Method, assumptions & references
Peak power assumes a Gaussian temporal profile (P ≈ 0.94 E/τFWHM) and peak intensity I = 2P/(πw₀²) for a Gaussian focal spot with 1/e² intensity radius w₀. The normalised vector potential is a₀ = 0.855 λ[µm] √(I/10¹⁸ W cm⁻²) for linear polarisation (÷√2 for circular). Relativistic self-focusing occurs above Pc ≈ 17 (nc/ne) GW.
The LWFA estimates use the nonlinear (blowout) scalings of Lu et al., Phys. Rev. ST Accel. Beams 10, 061301 (2007): matched spot kpw₀ = 2√a₀, dephasing length Ld = (4/3)(ω₀²/ωp²)√a₀/kp, pump depletion Lpd = (ω₀²/ωp²)cτ and energy gain ΔE ≈ (2/3)mec²(ω₀²/ωp²)a₀. They are valid roughly for 2 ≲ a₀ ≲ 6 and ne ≪ nc. Use them for orientation, not design.
Need this simulation set up, run and verified?
We handle the physics, the numerics and the HPC. You get trustworthy results.