1. Initial field
Waveguide startup uses a PEC reference. With an open longitudinal entrance, waveguide starts with the bunch field in the entrance cross-section, before the structure, as in a PEC waveguide. For a beam travelling at the speed of light (β = 1), this initial field has Ex = 0. A longitudinal PEC entrance instead starts with zero field.
Finite-conductivity walls then respond to the bunch field. Their material history starts at zero; the initial field does not include a pre-existing conductive-wall response. A longitudinal field and a startup transient can therefore appear even in a geometrically closed entrance pipe. In that region, transverse PML is not the cause of this response.
2. Explicit dispersion-free stepping
Use the explicit dispersion-free method for both stationary and moving calculations. Stability constrains the mesh because the dispersion-free time step is
c Δt = hx(1)
Equal transverse steps
For hy = hz = h⊥, choose
hx = h⊥ / 1.5(2)
Unequal transverse steps
Use the transverse stability criterion with the implemented safety factor:
hx ≤ 1 / [1.05 √(hy−2 + hz−2)](3)
Use the automatic time-step setting (scaled_time_step: auto). Reducing the time step independently is not the intended way to satisfy this mesh criterion.
Studio Mesh Setup
Select Dispersion-free and Explicit first. The three buttons then set the steps:
| Button | Steps |
|---|---|
| Recommended Steps from σ | hx = σ / 5; hy = hz = 1.5 hx |
| Y/Z from X | keeps hx and sets hy = hz = 1.5 hx |
| X/Z from Y | keeps hy, sets hz = hy and hx = hy / 1.5 |
These buttons provide a starting mesh. Small apertures, material interfaces and other geometric features may require finer steps. Stability alone does not establish wake accuracy.
3. Implicit dispersion-free stepping
Use implicit dispersion-free stepping when explicit stepping encounters stability problems. First check the explicit mesh criterion (3). Implicit stepping removes that transverse step restriction, while retaining c Δt = hx.
Allow roughly twice the calculation time compared with explicit stepping as a practical planning estimate. The actual ratio depends on the case, mesh and execution settings.
4. Stationary FDTD
Use stationary FDTD primarily to calculate long-range wake tails. Longitudinal numerical dispersion makes the wake near the bunch less accurate and can distort its shape and amplitude. Dispersion-free stepping is the preferred choice there.
If FDTD is nevertheless used near the bunch, use more than ten mesh intervals per RMS bunch length:
hx < σ / 10(4)
This is a resolution recommendation, not a universal accuracy guarantee. Compare the wake after further refinement.
FDTD uses its own three-dimensional CFL time step; the dispersion-free relation c Δt = hx does not apply to FDTD.
5. FDTD beam self-wake correction
For a stationary FDTD wake near the bunch, Studio offers Enable beam self-wake correction. Its case-file setting is field_solver..
The option subtracts an auxiliary reference-field residual. Restrict its recommended use to a PEC background; other backgrounds require independent qualification. This is an applicability recommendation, not an input restriction enforced by the software.
The correction is off by default and is generally not recommended as the route to an accurate near-bunch wake. Prefer explicit dispersion-free stepping and a mesh-convergence check. The option is inactive for dispersion-free methods and is separate from indirect wake integration.
6. Before starting a calculation
- Select the method and stationary or moving execution.
- Set the bunch length and use the matching Mesh Setup buttons.
- Check the mesh criterion and resolve important geometric features.
- Compare the wake on a finer mesh before relying on its quantitative values.
See the Studio User Guide for controls and the Physics Guide for wake definitions and interpretation.