TraTT

TraTT is a time-dependent Takagi–Taupin solver. It computes what an X-ray rocking curve of a perfect crystal looks like while a GHz sound wave is still entering the crystal, before the wave has filled it: how the acoustic satellites of the Bragg peak build up between the moment the wave is launched and its transit time $t_{\mathrm{tr}}=L/v_s$. For each time it freezes the lattice displacement, solves the two-beam Takagi–Taupin equations through the crystal for every rocking angle, and stacks the rocking curves into a map $I(\eta ,t)$. Every result is an analysis of such maps.

The results so far are calculations only; no experiment has been compared yet. They were presented as poster P2.17 at the KPS 2026 Fall Meeting. The README's Results section lists them with the notebook entries that hold the numbers: the formation time of each satellite, the overshoot under a gradual turn-on, where the independent-satellite approximation holds, and a first-order transfer function between the strain spectrum and the reflectivity.

Work toward a paper (the transfer function in more detail, its dependence on the measurement window, and the conditions a real beam's divergence and bandwidth put on it) is on the branch research/paper-viability, TraTT#16. It is a draft and its conclusions are being verified; they are not summarized on this site.

Install

Python 3.12 or later.

uv venv
uv pip install tratt

pip install tratt works as well. The README's Setup section covers a clone with the analysis scripts and tests.

First run

Satellite $n$ of a Laue crystal, read at its centre ${\eta }_n=nq$, grows like a crystal of thickness $v_{s}t$ with its coupling reduced by $|J_n(S)|$: $I_n={\sin }^2(\pi \alpha |J_n(S)|\tilde{t})$ (README, result 1). This compares the full solver with that law for the first satellite:

import numpy as np
from scipy.special import jv

from tratt import Drive, rocking

alpha = 0.5  # crystal thickness L in Pendelloesung lengths
drive = Drive(S=1.5, alpha_ac=10.0)  # modulation strength, L in acoustic wavelengths
eta1 = drive.eta_channel(1)  # centre of the first satellite on the eta axis

print("  t/t_tr   satellite 1   sin^2(pi alpha |J1(S)| t)")
for t in (0.25, 0.5, 0.75, 1.0):
    intensity = rocking(alpha, eta1, phi=drive.phi(t), geometry="laue", n_z=2048)
    predicted = np.sin(np.pi * alpha * abs(jv(1, drive.S)) * t) ** 2
    print(f"  {t:6.2f}   {float(intensity):11.4f}   {predicted:11.4f}")

Output with tratt 0.1.0 from PyPI (Python 3.13):

  t/t_tr   satellite 1   sin^2(pi alpha |J1(S)| t)
    0.25        0.0489        0.0472
    0.50        0.1789        0.1800
    0.75        0.3744        0.3733
    1.00        0.5891        0.5905

drive.phi(t) is the frozen phase profile at time $t/t_{\mathrm{tr}}$: the sound wave of strength $S$ fills the depth $\zeta <t$ and the rest of the crystal is still at rest. The two columns differ by at most 0.002 here, where the acoustic wavelength is 0.05 Pendellösung lengths; the README's result 3 says how the difference grows with that ratio.

Where to go next

• Equations, on this site: the Laue and Bragg equations, the drive and the satellite channels as the solver implements them.
• DESIGN.md: the physics conventions, every assumption and what it discards, and the analytic limits used as tests.
• Lineage, on this site: where TraTT came from, which script produced which notebook entry, and which claims stand or were withdrawn.
• The lab notebook, notes/lab_notebook.md, holds every entry the results cite.
• The Python API page lists the public functions and classes of the tratt package with their docstrings.