IBS - Intra Beam Scattering¶
C++ Library with PYBIND11 Python wrapper for IBS calculations, including an ODE model simulation.
Free software: MIT license
Documentation: https://ibslib.readthedocs.io.
Tutorial on Binder¶
Visit the link below for a live jupyter notebook with the turorial.
https://mybinder.org/v2/gh/tomerten/ibs/main?filepath=IBS%2Fdocs%2Fnotebooks%2FTutorial.ipynb
Requirements¶
For the installation:
CMake >= 3.10.2
GCC compiler
Python >= 3.7.1
Git - for the submodules
For the docs (see docs/requirements.txt - except doxygen):
doxygen
breathe
sphinx-click
click
cookiecutter
semantic-version
matplotlib
ipython
nbsphinx
ipykernel
pandoc
Quick start¶
If you do not want to go through the trouble of installing everything on your local system, you can also use either Docker or Singularity containers.
$ git clone https://github.com/tomerten/IBS.git
$ cd IBS
$ docker build -t ibslib:latest .
$ sudo singularity build ibslib.sim ibslib.sdef
For quick access to the runode simulations (make sure input file and Twiss file are in the run directory):
$ ./ibslib.sim JSON_SIM_INPUT_FILE
For using docker have a look at the docker documentation on how to mount folders for using files from your local system. One interesting feature is running jupyter from within the container, giving you direct access to the tutorial notebook.
$ docker run -it --user 1000 -v DIR_TO_MOUNT:/home -p 8889:8888 ibslib:latest jupyter notebook --ip=0.0.0.0 --no-browser --allow-root
After this, open a browser and go to localhost:8889, copy the token from the terminal window and you
are good to go. For the turorial navigate to IBS/docs/notebooks/Tutorial.ipynb. In the above case
files from the DIR_TO_MOUNT directory will be in the home directory in the container. If you create
a notebook and save it there it will also appear on your local (host) system.
Source Installation¶
The sources for ibs can be downloaded from the Github repo.
We recommend to install everything in a dedicated Conda environment.
$ conda create python=3.8 --name=ibslibenv
$ conda activate ibslibenv
$ conda install pip
$ pip install poetry
Clone the public repository and run the build_all.sh script:
$ git clone git://github.com/tomerten/ibs
$ cd ibs
$ bash build_all.sh
For more details see the installation guidelines on Installation documentation.
Build Docs¶
Building of the documentation is based on this article making use of Cmake, Doxygen, Breathe and Sphinx. It can be build locally by the following command:
$ bash build_docs.sh
To install Doxygen in a Conda environment:
$ conda install -c conda-forge doxygen
Features¶
Read MADX Twiss module
Numeric Functions Lib necessary for the IBS calculations, including necessary constants.
Coulomb Log module
Radiation Damping module
Integration methods module (Simpson, Simpson Decade, Simpson Decade with scaling)
IBS models
ODE simulation module with CLI interface
Current Supported Models¶
Piwinski smooth lattice approximation
Piwinski Lattice element by element weighted
Piwinski Lattice Modified taking some vertical effects into account
Nagaitsev’s high-energy approximation (standard Coulomb Log and with Tailcut)
Bjorken-Mtingwa (standard Coulomb Log and with Tailcut)
Conte-Martini (standard Coulomb Log and with Tailcut)
Zimmerman (Madx - CERN note AB-2006-002) using TWINT and SIMPSONDECADE methods to perform the integration (standard Coulomb Log and with Tailcut).
Coublomb Log methods¶
twclog - uses element by element twiss data
twclogtail - uses element by element twiss data
CoublombLog - uses ring averages
TailCutCoulombLog - uses ring averages
Integration methods¶
Simpson (standard implementation)
SimpsonDecade - Simspon per decade for covering large spread in integration ranges (ususally 50 orders of magnitude difference between low and high)
TWINT, SimsponDecade with scaling method
Radiation Damping¶
Radiation Damping using smooth lattice approximation
Radiation Damping element by element
Equilibrium from pure radiation damping and exitation (taux, tauy, taus, exinf, eyinf, sigeoe2, sigsinf, jx, jy)
Radiation losses per turn
Critical omega, theta, photon energy
Numeric Functions¶
Method to calculate standard accelerator quantities.
Various methods related to RF calculations to derive longitudinal quantities necessary for the IBS algorithms.
Numeric functions used by specific IBS models (fmohl, rds).
ODE¶
The tables below show examples of the output of the ODE method, applied to the BESSY II design lattice. For the examples below the stability threshold set to 1e-3 written to a csv file.
t |
ex |
ey |
sigs |
|---|---|---|---|
0 |
7.5e-09 |
1e-09 |
0.005 |
0.00199509 |
6.70356e-09 |
5.00852e-10 |
0.00306037 |
0.00399018 |
6.30713e-09 |
2.50877e-10 |
0.00307313 |
0.00598527 |
6.11027e-09 |
1.25688e-10 |
0.00308823 |
0.00798035 |
6.01344e-09 |
6.29943e-11 |
0.00310801 |
0.00997544 |
5.96714e-09 |
3.15986e-11 |
0.00313478 |
0.0119705 |
5.94682e-09 |
1.5878e-11 |
0.00317109 |
0.0139656 |
5.94045e-09 |
8.00908e-12 |
0.0032197 |
0.0159607 |
5.94228e-09 |
4.07412e-12 |
0.00328328 |
0.0179558 |
5.94964e-09 |
2.1118e-12 |
0.00336386 |
0.0199509 |
5.96124e-09 |
1.14043e-12 |
0.00346161 |
0.021946 |
5.97612e-09 |
6.68309e-13 |
0.00357279 |
0.0239411 |
5.99276e-09 |
4.47683e-13 |
0.00368685 |
0.0259362 |
6.00853e-09 |
3.51024e-13 |
0.00378611 |
0.0279312 |
6.02077e-09 |
3.11398e-13 |
0.00385566 |
0.0299263 |
6.0287e-09 |
2.9561e-13 |
0.00389519 |
0.0319214 |
6.03326e-09 |
2.89252e-13 |
0.00391462 |
0.0339165 |
6.03572e-09 |
2.86635e-13 |
0.00392341 |
0.0359116 |
6.037e-09 |
2.85538e-13 |
0.00392724 |
0.0379067 |
6.03766e-09 |
2.85073e-13 |
0.00392886 |
0.0399018 |
6.038e-09 |
2.84875e-13 |
0.00392955 |
t |
ex |
ey |
sigs |
|---|---|---|---|
0 |
7.5e-09 |
1e-09 |
0.005 |
0.00199509 |
6.70593e-09 |
5.00852e-10 |
0.00305871 |
0.00399018 |
6.31454e-09 |
2.50877e-10 |
0.00306793 |
0.00598527 |
6.12357e-09 |
1.25689e-10 |
0.00307902 |
0.00798035 |
6.0344e-09 |
6.29949e-11 |
0.00309374 |
0.00997544 |
5.99846e-09 |
3.15995e-11 |
0.0031139 |
0.0119705 |
5.99228e-09 |
1.58796e-11 |
0.00314152 |
0.0139656 |
6.00505e-09 |
8.01161e-12 |
0.00317883 |
0.0159607 |
6.03224e-09 |
4.0781e-12 |
0.00322806 |
0.0179558 |
6.0723e-09 |
2.11785e-12 |
0.00329096 |
0.0199509 |
6.12447e-09 |
1.1492e-12 |
0.00336782 |
0.021946 |
6.18669e-09 |
6.80275e-13 |
0.00345562 |
0.0239411 |
6.2531e-09 |
4.62741e-13 |
0.00354548 |
0.0259362 |
6.31324e-09 |
3.6824e-13 |
0.00362286 |
0.0279312 |
6.35764e-09 |
3.29534e-13 |
0.00367636 |
0.0299263 |
6.38497e-09 |
3.13888e-13 |
0.00370659 |
0.0319214 |
6.39998e-09 |
3.07412e-13 |
0.00372152 |
0.0339165 |
6.40776e-09 |
3.04652e-13 |
0.00372837 |
0.0359116 |
6.4117e-09 |
3.03451e-13 |
0.0037314 |
0.0379067 |
6.41367e-09 |
3.02922e-13 |
0.00373271 |
0.0399018 |
6.41466e-09 |
3.02687e-13 |
0.00373328 |
t |
ex |
ey |
sigs |
|---|---|---|---|
0 |
7.5e-09 |
1e-09 |
0.005 |
0.00199509 |
6.70588e-09 |
5.00852e-10 |
0.00305869 |
0.00399018 |
6.31437e-09 |
2.50877e-10 |
0.00306787 |
0.00598527 |
6.12325e-09 |
1.25689e-10 |
0.00307891 |
0.00798035 |
6.03389e-09 |
6.29948e-11 |
0.00309357 |
0.00997544 |
5.99771e-09 |
3.15994e-11 |
0.00311366 |
0.0119705 |
5.99121e-09 |
1.58794e-11 |
0.00314119 |
0.0139656 |
6.00354e-09 |
8.01139e-12 |
0.00317838 |
0.0159607 |
6.03017e-09 |
4.07776e-12 |
0.00322746 |
0.0179558 |
6.06954e-09 |
2.11736e-12 |
0.00329021 |
0.0199509 |
6.12085e-09 |
1.14849e-12 |
0.00336691 |
0.021946 |
6.18207e-09 |
6.79323e-13 |
0.00345459 |
0.0239411 |
6.24746e-09 |
4.61536e-13 |
0.00354443 |
0.0259362 |
6.30673e-09 |
3.6684e-13 |
0.00362195 |
0.0279312 |
6.35053e-09 |
3.28024e-13 |
0.00367567 |
0.0299263 |
6.37751e-09 |
3.12331e-13 |
0.00370609 |
0.0319214 |
6.39232e-09 |
3.05837e-13 |
0.00372114 |
0.0339165 |
6.4e-09 |
3.0307e-13 |
0.00372806 |
0.0359116 |
6.40388e-09 |
3.01867e-13 |
0.00373112 |
0.0379067 |
6.40583e-09 |
3.01337e-13 |
0.00373245 |
0.0399018 |
6.4068e-09 |
3.01101e-13 |
0.00373302 |
t |
ex |
ey |
sigs |
|---|---|---|---|
0 |
7.5e-09 |
1e-09 |
0.005 |
0.00199509 |
6.70641e-09 |
5.00852e-10 |
0.00305891 |
0.00399018 |
6.31624e-09 |
2.50877e-10 |
0.00306886 |
0.00598527 |
6.12706e-09 |
1.25688e-10 |
0.00308136 |
0.00798035 |
6.04081e-09 |
6.29944e-11 |
0.00309872 |
0.00997544 |
6.00958e-09 |
3.1599e-11 |
0.0031235 |
0.0119705 |
6.01075e-09 |
1.58793e-11 |
0.00315867 |
0.0139656 |
6.03454e-09 |
8.01214e-12 |
0.00320763 |
0.0159607 |
6.07752e-09 |
4.08044e-12 |
0.00327364 |
0.0179558 |
6.13893e-09 |
2.12371e-12 |
0.00335865 |
0.0199509 |
6.21798e-09 |
1.1611e-12 |
0.00346214 |
0.021946 |
6.31056e-09 |
7.01185e-13 |
0.00357776 |
0.0239411 |
6.40554e-09 |
4.94521e-13 |
0.00369019 |
0.0259362 |
6.48563e-09 |
4.0963e-13 |
0.00377859 |
0.0279312 |
6.53939e-09 |
3.76947e-13 |
0.00383246 |
0.0299263 |
6.56968e-09 |
3.64316e-13 |
0.0038591 |
0.0319214 |
6.58529e-09 |
3.59257e-13 |
0.00387079 |
0.0339165 |
6.59307e-09 |
3.57173e-13 |
0.00387563 |
0.0359116 |
6.59691e-09 |
3.56298e-13 |
0.00387758 |
0.0379067 |
6.59881e-09 |
3.55927e-13 |
0.00387836 |
0.0399018 |
6.59975e-09 |
3.55768e-13 |
0.00387866 |
t |
ex |
ey |
sigs |
|---|---|---|---|
0 |
7.5e-09 |
1e-09 |
0.005 |
0.00199509 |
6.70613e-09 |
5.00852e-10 |
0.00305875 |
0.00399018 |
6.31537e-09 |
2.50876e-10 |
0.00306835 |
0.00598527 |
6.12549e-09 |
1.25688e-10 |
0.00308044 |
0.00798035 |
6.03829e-09 |
6.2994e-11 |
0.00309726 |
0.00997544 |
6.00576e-09 |
3.15983e-11 |
0.00312131 |
0.0119705 |
6.00513e-09 |
1.58782e-11 |
0.00315551 |
0.0139656 |
6.02644e-09 |
8.01037e-12 |
0.00320322 |
0.0159607 |
6.06614e-09 |
4.07767e-12 |
0.00326771 |
0.0179558 |
6.12336e-09 |
2.11949e-12 |
0.00335101 |
0.0199509 |
6.19741e-09 |
1.1549e-12 |
0.00345287 |
0.021946 |
6.28466e-09 |
6.92582e-13 |
0.00356743 |
0.0239411 |
6.37503e-09 |
4.83552e-13 |
0.00368009 |
0.0259362 |
6.45235e-09 |
3.9702e-13 |
0.00377019 |
0.0279312 |
6.50506e-09 |
3.63579e-13 |
0.00382615 |
0.0299263 |
6.53506e-09 |
3.50678e-13 |
0.00385424 |
0.0319214 |
6.5506e-09 |
3.45531e-13 |
0.00386668 |
0.0339165 |
6.55836e-09 |
3.43416e-13 |
0.00387186 |
0.0359116 |
6.56219e-09 |
3.42531e-13 |
0.00387396 |
0.0379067 |
6.56408e-09 |
3.42156e-13 |
0.00387479 |
0.0399018 |
6.56501e-09 |
3.41996e-13 |
0.00387512 |
t |
ex |
ey |
sigs |
|---|---|---|---|
0 |
7.5e-09 |
1e-09 |
0.005 |
0.00199509 |
6.70657e-09 |
5.00852e-10 |
0.00305911 |
0.00399018 |
6.31677e-09 |
2.50877e-10 |
0.00306952 |
0.00598527 |
6.12803e-09 |
1.25688e-10 |
0.0030826 |
0.00798035 |
6.04237e-09 |
6.29945e-11 |
0.00310076 |
0.00997544 |
6.01196e-09 |
3.15993e-11 |
0.00312663 |
0.0119705 |
6.01428e-09 |
1.58798e-11 |
0.00316332 |
0.0139656 |
6.03962e-09 |
8.01294e-12 |
0.0032143 |
0.0159607 |
6.08462e-09 |
4.08176e-12 |
0.00328288 |
0.0179558 |
6.14851e-09 |
2.12579e-12 |
0.0033709 |
0.0199509 |
6.23042e-09 |
1.1642e-12 |
0.00347762 |
0.021946 |
6.32588e-09 |
7.05538e-13 |
0.00359615 |
0.0239411 |
6.42315e-09 |
5.00076e-13 |
0.00371046 |
0.0259362 |
6.50441e-09 |
4.15992e-13 |
0.00379932 |
0.0279312 |
6.55845e-09 |
3.83673e-13 |
0.00385278 |
0.0299263 |
6.5887e-09 |
3.71172e-13 |
0.00387893 |
0.0319214 |
6.60425e-09 |
3.66163e-13 |
0.00389032 |
0.0339165 |
6.61199e-09 |
3.64099e-13 |
0.00389501 |
0.0359116 |
6.61582e-09 |
3.63234e-13 |
0.00389689 |
0.0379067 |
6.61771e-09 |
3.62867e-13 |
0.00389763 |
0.0399018 |
6.61864e-09 |
3.6271e-13 |
0.00389792 |
t |
ex |
ey |
sigs |
|---|---|---|---|
0 |
7.5e-09 |
1e-09 |
0.005 |
0.00199509 |
6.70628e-09 |
5.00852e-10 |
0.00305895 |
0.00399018 |
6.31586e-09 |
2.50876e-10 |
0.00306899 |
0.00598527 |
6.12638e-09 |
1.25688e-10 |
0.00308164 |
0.00798035 |
6.03973e-09 |
6.29941e-11 |
0.00309923 |
0.00997544 |
6.00797e-09 |
3.15986e-11 |
0.00312435 |
0.0119705 |
6.0084e-09 |
1.58786e-11 |
0.00316003 |
0.0139656 |
6.03117e-09 |
8.01109e-12 |
0.00320972 |
0.0159607 |
6.07275e-09 |
4.07887e-12 |
0.00327673 |
0.0179558 |
6.13232e-09 |
2.12139e-12 |
0.00336302 |
0.0199509 |
6.20908e-09 |
1.15776e-12 |
0.0034681 |
0.021946 |
6.29909e-09 |
6.96623e-13 |
0.00358562 |
0.0239411 |
6.3917e-09 |
4.88756e-13 |
0.00370027 |
0.0259362 |
6.47022e-09 |
4.03034e-13 |
0.00379093 |
0.0279312 |
6.52325e-09 |
3.6997e-13 |
0.00384653 |
0.0299263 |
6.55323e-09 |
3.57209e-13 |
0.00387414 |
0.0319214 |
6.56871e-09 |
3.52114e-13 |
0.00388627 |
0.0339165 |
6.57643e-09 |
3.50021e-13 |
0.00389129 |
0.0359116 |
6.58025e-09 |
3.49146e-13 |
0.00389331 |
0.0379067 |
6.58213e-09 |
3.48776e-13 |
0.00389411 |
0.0399018 |
6.58306e-09 |
3.48618e-13 |
0.00389442 |
t |
ex |
ey |
sigs |
|---|---|---|---|
0 |
7.5e-09 |
1e-09 |
0.005 |
0.00199509 |
6.70592e-09 |
5.00852e-10 |
0.00305914 |
0.00399018 |
6.31442e-09 |
2.50877e-10 |
0.00306961 |
0.00598527 |
6.12324e-09 |
1.25688e-10 |
0.00308278 |
0.00798035 |
6.03382e-09 |
6.29945e-11 |
0.00310109 |
0.00997544 |
5.99757e-09 |
3.15992e-11 |
0.00312728 |
0.0119705 |
5.99094e-09 |
1.58797e-11 |
0.0031646 |
0.0139656 |
6.0029e-09 |
8.0127e-12 |
0.00321691 |
0.0159607 |
6.02849e-09 |
4.08115e-12 |
0.00328826 |
0.0179558 |
6.06533e-09 |
2.12435e-12 |
0.00338183 |
0.0199509 |
6.11143e-09 |
1.1612e-12 |
0.0034988 |
0.021946 |
6.16299e-09 |
6.99951e-13 |
0.00363414 |
0.0239411 |
6.21264e-09 |
4.9115e-13 |
0.00377133 |
0.0259362 |
6.25081e-09 |
4.03944e-13 |
0.00388415 |
0.0279312 |
6.27298e-09 |
3.69532e-13 |
0.00395635 |
0.0299263 |
6.28294e-09 |
3.55913e-13 |
0.00399412 |
0.0319214 |
6.28657e-09 |
3.50372e-13 |
0.00401181 |
0.0339165 |
6.2876e-09 |
3.48075e-13 |
0.00401971 |
0.0359116 |
6.28774e-09 |
3.47115e-13 |
0.00402317 |
0.0379067 |
6.28764e-09 |
3.46713e-13 |
0.00402467 |
0.0399018 |
6.28751e-09 |
3.46545e-13 |
0.00402533 |
t |
ex |
ey |
sigs |
|---|---|---|---|
0 |
7.5e-09 |
1e-09 |
0.005 |
0.00199509 |
6.70657e-09 |
5.00852e-10 |
0.00305912 |
0.00399018 |
6.31678e-09 |
2.50877e-10 |
0.00306953 |
0.00598527 |
6.12806e-09 |
1.25688e-10 |
0.00308264 |
0.00798035 |
6.04244e-09 |
6.29945e-11 |
0.00310084 |
0.00997544 |
6.01215e-09 |
3.15992e-11 |
0.00312686 |
0.0119705 |
6.01475e-09 |
1.58796e-11 |
0.00316391 |
0.0139656 |
6.04077e-09 |
8.01257e-12 |
0.00321576 |
0.0159607 |
6.08732e-09 |
4.0809e-12 |
0.00328631 |
0.0179558 |
6.15455e-09 |
2.12387e-12 |
0.0033785 |
0.0199509 |
6.24298e-09 |
1.16027e-12 |
0.0034932 |
0.021946 |
6.34966e-09 |
6.98237e-13 |
0.00362507 |
0.0239411 |
6.46289e-09 |
4.88268e-13 |
0.00375769 |
0.0259362 |
6.56178e-09 |
3.99703e-13 |
0.00386577 |
0.0279312 |
6.63052e-09 |
3.64084e-13 |
0.00393418 |
0.0299263 |
6.67058e-09 |
3.49592e-13 |
0.00396944 |
0.0319214 |
6.69192e-09 |
3.43491e-13 |
0.00398563 |
0.0339165 |
6.70288e-09 |
3.40857e-13 |
0.00399267 |
0.0359116 |
6.70844e-09 |
3.39703e-13 |
0.00399566 |
0.0379067 |
6.71124e-09 |
3.39193e-13 |
0.00399692 |
0.0399018 |
6.71266e-09 |
3.38965e-13 |
0.00399743 |
t |
ex |
ey |
sigs |
|---|---|---|---|
0 |
7.5e-09 |
1e-09 |
0.005 |
0.00199509 |
6.70628e-09 |
5.00852e-10 |
0.00305895 |
0.00399018 |
6.31587e-09 |
2.50876e-10 |
0.003069 |
0.00598527 |
6.12641e-09 |
1.25688e-10 |
0.00308167 |
0.00798035 |
6.0398e-09 |
6.29941e-11 |
0.00309931 |
0.00997544 |
6.00815e-09 |
3.15985e-11 |
0.00312457 |
0.0119705 |
6.00884e-09 |
1.58785e-11 |
0.00316059 |
0.0139656 |
6.03223e-09 |
8.01076e-12 |
0.0032111 |
0.0159607 |
6.07526e-09 |
4.07808e-12 |
0.00328 |
0.0179558 |
6.13793e-09 |
2.11964e-12 |
0.0033703 |
0.0199509 |
6.22079e-09 |
1.15415e-12 |
0.00348311 |
0.021946 |
6.32136e-09 |
6.89875e-13 |
0.00361367 |
0.0239411 |
6.42918e-09 |
4.77746e-13 |
0.00374647 |
0.0259362 |
6.52476e-09 |
3.87693e-13 |
0.00385656 |
0.0279312 |
6.59225e-09 |
3.5138e-13 |
0.00392758 |
0.0299263 |
6.63201e-09 |
3.36635e-13 |
0.00396471 |
0.0319214 |
6.65329e-09 |
3.30447e-13 |
0.00398191 |
0.0339165 |
6.66423e-09 |
3.27782e-13 |
0.00398943 |
0.0359116 |
6.66978e-09 |
3.26617e-13 |
0.00399264 |
0.0379067 |
6.67258e-09 |
3.26103e-13 |
0.00399398 |
0.0399018 |
6.674e-09 |
3.25874e-13 |
0.00399454 |
t |
ex |
ey |
sigs |
|---|---|---|---|
0 |
7.5e-09 |
1e-09 |
0.005 |
0.00199509 |
6.70657e-09 |
5.00852e-10 |
0.00305911 |
0.00399018 |
6.31677e-09 |
2.50877e-10 |
0.00306952 |
0.00598527 |
6.12803e-09 |
1.25688e-10 |
0.0030826 |
0.00798035 |
6.04237e-09 |
6.29945e-11 |
0.00310076 |
0.00997544 |
6.01196e-09 |
3.15993e-11 |
0.00312663 |
0.0119705 |
6.01428e-09 |
1.58798e-11 |
0.00316332 |
0.0139656 |
6.03962e-09 |
8.01294e-12 |
0.0032143 |
0.0159607 |
6.08462e-09 |
4.08176e-12 |
0.00328288 |
0.0179558 |
6.14851e-09 |
2.12579e-12 |
0.0033709 |
0.0199509 |
6.23042e-09 |
1.1642e-12 |
0.00347762 |
0.021946 |
6.32588e-09 |
7.05538e-13 |
0.00359615 |
0.0239411 |
6.42315e-09 |
5.00076e-13 |
0.00371046 |
0.0259362 |
6.50441e-09 |
4.15992e-13 |
0.00379932 |
0.0279312 |
6.55845e-09 |
3.83673e-13 |
0.00385278 |
0.0299263 |
6.5887e-09 |
3.71172e-13 |
0.00387893 |
0.0319214 |
6.60425e-09 |
3.66163e-13 |
0.00389032 |
0.0339165 |
6.61199e-09 |
3.64099e-13 |
0.00389501 |
0.0359116 |
6.61582e-09 |
3.63234e-13 |
0.00389689 |
0.0379067 |
6.61771e-09 |
3.62867e-13 |
0.00389763 |
0.0399018 |
6.61864e-09 |
3.6271e-13 |
0.00389792 |
t |
ex |
ey |
sigs |
|---|---|---|---|
0 |
7.5e-09 |
1e-09 |
0.005 |
0.00199509 |
6.70628e-09 |
5.00852e-10 |
0.00305895 |
0.00399018 |
6.31586e-09 |
2.50876e-10 |
0.00306899 |
0.00598527 |
6.12638e-09 |
1.25688e-10 |
0.00308164 |
0.00798035 |
6.03973e-09 |
6.29941e-11 |
0.00309923 |
0.00997544 |
6.00797e-09 |
3.15986e-11 |
0.00312435 |
0.0119705 |
6.0084e-09 |
1.58786e-11 |
0.00316003 |
0.0139656 |
6.03117e-09 |
8.01109e-12 |
0.00320972 |
0.0159607 |
6.07275e-09 |
4.07887e-12 |
0.00327673 |
0.0179558 |
6.13232e-09 |
2.12139e-12 |
0.00336302 |
0.0199509 |
6.20908e-09 |
1.15776e-12 |
0.0034681 |
0.021946 |
6.29909e-09 |
6.96623e-13 |
0.00358562 |
0.0239411 |
6.3917e-09 |
4.88756e-13 |
0.00370027 |
0.0259362 |
6.47022e-09 |
4.03034e-13 |
0.00379093 |
0.0279312 |
6.52325e-09 |
3.6997e-13 |
0.00384653 |
0.0299263 |
6.55323e-09 |
3.57209e-13 |
0.00387414 |
0.0319214 |
6.56871e-09 |
3.52114e-13 |
0.00388627 |
0.0339165 |
6.57643e-09 |
3.50021e-13 |
0.00389129 |
0.0359116 |
6.58025e-09 |
3.49146e-13 |
0.00389331 |
0.0379067 |
6.58213e-09 |
3.48776e-13 |
0.00389411 |
0.0399018 |
6.58306e-09 |
3.48618e-13 |
0.00389442 |
t |
ex |
ey |
sigs |
|---|---|---|---|
0 |
7.5e-09 |
1e-09 |
0.005 |
0.00199509 |
6.70657e-09 |
5.00852e-10 |
0.00305911 |
0.00399018 |
6.31677e-09 |
2.50877e-10 |
0.00306952 |
0.00598527 |
6.12804e-09 |
1.25688e-10 |
0.0030826 |
0.00798035 |
6.04239e-09 |
6.29943e-11 |
0.00310076 |
0.00997544 |
6.01202e-09 |
3.15989e-11 |
0.00312663 |
0.0119705 |
6.01442e-09 |
1.58793e-11 |
0.00316332 |
0.0139656 |
6.03997e-09 |
8.01225e-12 |
0.0032143 |
0.0159607 |
6.0855e-09 |
4.08087e-12 |
0.00328288 |
0.0179558 |
6.15061e-09 |
2.12468e-12 |
0.00337091 |
0.0199509 |
6.23507e-09 |
1.16289e-12 |
0.00347762 |
0.021946 |
6.33522e-09 |
7.04072e-13 |
0.00359614 |
0.0239411 |
6.43947e-09 |
4.98527e-13 |
0.0037104 |
0.0259362 |
6.52853e-09 |
4.14409e-13 |
0.00379909 |
0.0279312 |
6.58901e-09 |
3.8205e-13 |
0.00385226 |
0.0299263 |
6.62354e-09 |
3.69501e-13 |
0.00387811 |
0.0319214 |
6.64163e-09 |
3.64449e-13 |
0.00388928 |
0.0339165 |
6.65081e-09 |
3.62355e-13 |
0.00389383 |
0.0359116 |
6.65542e-09 |
3.61471e-13 |
0.00389562 |
0.0379067 |
6.65773e-09 |
3.61093e-13 |
0.00389632 |
0.0399018 |
6.65889e-09 |
3.60929e-13 |
0.00389658 |