Radiation¶
The spectrally resolved far field radiation of charged macro particles.
Our simulation computes the Lienard Wiechert potentials to calculate the emitted electromagnetic spectra for different observation directions using the far field approximation.
Details on how radiation is computed with this plugin and how the plugin works can be found in [Pausch2012]. A list of tests can be found in [Pausch2014] and [Pausch2019].
Variable 
Meaning 

\(\vec r_k(t)\) 
The position of particle k at time t. 
\(\vec \beta_k(t)\) 
The normalized speed of particle k at time t. (Speed divided by the speed of light) 
\(\dot{\vec{\beta}}_k(t)\) 
The normalized acceleration of particle k at time t. (Time derivative of the normalized speed.) 
\(t\) 
Time 
\(\vec n\) 
Unit vector pointing in the direction where the far field radiation is observed. 
\(\omega\) 
The circular frequency of the radiation that is observed. 
\(N\) 
Number of all (macro) particles that are used for computing the radiation. 
\(k\) 
Running index of the particles. 
Currently this allows to predict the emitted radiation from plasma if it can be described by classical means. Not considered are emissions from ionization, Compton scattering or any bremsstrahlung that originate from scattering on scales smaller than the PIC cell size.
External Dependencies¶
The plugin is available as soon as the libSplash and HDF5 libraries are compiled in.
.param files¶
In order to setup the radiation analyzer plugin, both the radiation.param and the radiationObserver.param have to be configured and the radiating particles need to have the attribute momentumPrev1
which can be added in speciesDefinition.param.
In radiation.param, the number of frequencies N_omega
and observation directions N_theta
is defined.
Frequency range¶
The frequency range is set up by choosing a specific namespace that defines the frequency setup
/* choose linear frequency range */
namespace radiation_frequencies = linear_frequencies;
Currently you can choose from the following setups for the frequency range:
namespace 
Description 


linear frequency range from 

logarithmic frequency range from 


All three options require variable definitions in the according namespaces as described below:
For the linear frequency scale all definitions need to be in the picongpu::plugins::radiation::linear_frequencies
namespace.
The number of total sample frequencies N_omega
need to be defined as constexpr unsigned int
.
In the subnamespace SI
, a minimal frequency omega_min
and a maximum frequency omega_max
need to be defined as constexpr float_64
.
For the logarithmic frequency scale all definitions need to be in the picongpu::plugins::radiation::log_frequencies
namespace.
Equivalently to the linear case, three variables need to be defined:
The number of total sample frequencies N_omega
need to be defined as constexpr unsigned int
.
In the subnamespace SI
, a minimal frequency omega_min
and a maximum frequency omega_max
need to be defined as constexpr float_64
.
For the filebased frequency definition, all definitions need to be in the picongpu::plugins::radiation::frequencies_from_list
namespace.
The number of total frequencies N_omega
need to be defined as constexpr unsigned int
and the path to the file containing the frequency values in units of \(\mathrm{[s^{1}]}\) needs to be given as constexpr const char * listLocation = "/path/to/frequency_list";
.
The frequency values in the file can be separated by newlines, spaces, tabs, or any other whitespace. The numbers should be given in such a way, that c++ standard std::ifstream
can interpret the number e.g., as 2.5344e+16
.
Note
Currently, the variable listLocation
is required to be defined in the picongpu::plugins::radiation::frequencies_from_list
namespace, even if frequencies_from_list
is not used.
The string does not need to point to an existing file, as long as the filebased frequency definition is not used.
Observation directions¶
The number of observation directions N_theta
is defined in radiation.param, but the distribution of observation directions is given in radiationObserver.param)
There, the function observation_direction
defines the observation directions.
This function returns the x,y and z component of a unit vector pointing in the observation direction.
DINLINE vector_64
observation_direction( int const observation_id_extern )
{
/* use the scalar index const int observation_id_extern to compute an
* observation direction (x,y,y) */
return vector_64( x , y , z );
}
Note
The radiationObserver.param
set up will be subject to further changes.
These might be namespaces that describe several preconfigured layouts or a functor if C++ 11 is included in the nvcc.
Nyquist limit¶
A major limitation of discrete Fourier transform is the limited frequency resolution due to the discrete time steps of the temporal signal. (see NyquistShannon sampling theorem) Due to the consideration of relativistic delays, the sampling of the emitted radiation is not equidistantly sampled. The plugin has the option to ignore any frequency contributions that lies above the frequency resolution given by the NyquistShannon sampling theorem. Because performing this check costs computation time, it can be switched off. This is done via a precompiler pragma:
// Nyquist low pass allows only amplitudes for frequencies below Nyquist frequency
// 1 = on (slower and more memory, no Fourier reflections)
// 0 = off (faster but with Fourier reflections)
#define __NYQUISTCHECK__ 0
Additionally, the maximally resolvable frequency compared to the Nyquist frequency can be set.
namespace radiationNyquist
{
/* only use frequencies below 1/2*Omega_Nyquist */
const float NyquistFactor = 0.5;
}
This allows to make a save margin to the hard limit of the Nyquist frequency.
By using NyquistFactor = 0.5
for periodic boundary conditions, particles that jump from one border to another and back can still be considered.
Form factor¶
The form factor is a method, which considers the shape of the macro particles when computing the radiation. More details can be found in [Pausch2018] and [Pausch2019].
One can select between different macro particle shapes. Currently eight shapes are implemented. A shape can be selected by choosing one of the available namespaces:
/* choosing the 3D CIClike macro particle shape */
namespace radFormFactor = radFormFactor_CIC_3D;
Namespace 
Description 


3D CloudInCell shape 

3D Triangular shaped density cloud 

3D Quadratic spline density shape (Piecewise Cubic Spline assignment function) 

CloudInCell shape in ydirection, dot like in the other directions 

symmetric Gauss charge distribution 

Gauss charge distribution according to cell size 

forces a completely incoherent emission by scaling the macro particle charge with the square root of the weighting 

forces a completely coherent emission by scaling the macro particle charge with the weighting 
Reducing the particle sample¶
In order to save computation time, only a random subset of all macro particles can be used to compute the emitted radiation.
In order to do that, the radiating particle species needs the attribute radiationMask
(which is initialized as false
) which further needs to be manipulated, to set to true for specific (random) particles.
Note
The reduction of the total intensity is not considered in the output. The intensity will be (in the incoherent case) will be smaller by the fraction of marked to all particles.
Note
The radiation mask is only added to particles, if not all particles should be considered for radiation calculation. Adding the radiation flag costs memory.
Note
In future updates, the radiation will only be computed using an extra particle species. Therefore, this setup will be subject to further changes.
Gamma filter¶
In order to consider the radiation only of particles with a gamma higher than a specific threshold, the radiating particle species needs the attribute radiationMask
(which is initialized as false
).
Using a filter functor as:
using RadiationParticleFilter = picongpu::particles::manipulators::FreeImpl<
GammaFilterFunctor
>;
(see Bunch or Kelvin Helmholtz example for details) sets the flag to true is a particle fulfills the gamma condition.
Note
More sophisticated filters might come in the near future. Therefore, this part of the code might be subject to changes.
Window function filter¶
A window function can be added to the simulation area to reduce ringing artifacts due to sharp transition from radiating regions to nonradiating regions at the boundaries of the simulation box. This should be applied to simulation setups where the entire volume simulated is radiating (e.g. KelvinHelmholtz Instability).
In radiation.param
the precompiler variable PIC_RADWINDOWFUNCTION
defines if the window function filter should be used or not.
// add a window function weighting to the radiation in order
// to avoid ringing effects from sharp boundaries
// 1 = on (slower but with noise/ringing reduction)
// 0 = off (faster but might contain ringing)
#define PIC_RADWINDOWFUNCTION 0
If set to 1
, the window function filter is used.
There are several different window function available:
/* Choose different window function in order to get better ringing reduction
* radWindowFunctionRectangle
* radWindowFunctionTriangle
* radWindowFunctionHamming
* radWindowFunctionTriplett
* radWindowFunctionGauss
*/
namespace radWindowFunctionRectangle { }
namespace radWindowFunctionTriangle { }
namespace radWindowFunctionHamming { }
namespace radWindowFunctionTriplett { }
namespace radWindowFunctionGauss { }
namespace radWindowFunction = radWindowFunctionTriangle;
By setting radWindowFunction
a specific window function is selected.
More details can be found in [Pausch2019].
.cfg file¶
For a specific (charged) species <species>
e.g. e
, the radiation can be computed by the following commands.
Command line option 
Description 


Gives the number of time steps between which the radiation should be calculated.
Default is 

Period, after which the calculated radiation data should be dumped to the file system.
Default is 

If set, the radiation spectra summed between the last and the current dumptimestep are stored. Used for a better evaluation of the temporal evolution of the emitted radiation. 

Name of the folder, in which the summed spectra for the simulation time between the last dump and the current dump are stored.
Default is 

If set the spectra summed from simulation start till current time step are stored. 

Folder name in which the total radiation spectra, integrated from the beginning of the simulation, are stored.
Default 

Time step, at which PIConGPU starts calculating the radiation.
Default is 

Time step, at which the radiation calculation should end.
Default: 

If set, each GPU additionally stores its own spectra without summing over the entire simulation area. This allows for a localization of specific spectral features. 

Name of the folder, where the GPU specific spectra are stored.
Default: 

If set, the hdf5 output is compressed. 
Memory Complexity¶
Accelerator¶
each energy bin times each coordinate bin allocates one counter (float_X
) permanently and on each accelerator.
Host¶
as on accelerator.
Output¶
Depending on the command line options used, there are different output files.
Command line flag 
Output description 


Contains ASCII files that have the total spectral intensity until the timestep specified by the filename.
Each row gives data for one observation direction (same order as specified in the 

has the same format as the output of totalRadiation.
The spectral intensity is only summed over the last radiation 

Same output as totalRadiation but only summed over each GPU. Because each GPU specifies a spatial region, the origin of radiation signatures can be distinguished. 
radiationHDF5 
In the folder 
Textbased output¶
The textbased output of lastRadiation
and totalRadiation
contains the intensity values in SIunits \(\mathrm{[Js]}\). Intensity values for different frequencies are separated by spaces, while newlines separate values for different observation directions.
In order to read and plot the textbased radiation data, a python script as follows could be used:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm
# frequency definition:
# as defined in the 'radiation.param' file:
N_omega = 1024
omega_min = 0.0 # [1/s]
omega_max = 5.8869e17 # [1/s]
omega = np.linspace(omega_min, omega_max, N_omega)
# observation angle definition:
# as defined in the 'radiation.param' file:
N_observer = 128
# as defined in the 'radiationObserver.param' file:
# this example assumes one used the default Bunch example
# there, the theta values are normalized to the Lorentz factor
theta_min = 1.5 # [rad/gamma]
theta_max = +1.5 # [rad/gamma]
theta = np.linspace(theta_min, theta_max, N_observer)
# load radiation textbased data
rad_data = np.loadtxt('./simOutput/lastRad/e_radiation_2820.dat')
# plot radiation spectrum
plt.figure()
plt.pcolormesh(omega, theta, rad_data, norm=LogNorm())
# add and configure colorbar
cb = plt.colorbar()
cb.set_label(r"$\frac{\mathrm{d}^2 I}{\mathrm{d} \omega \mathrm{d} \Omega} \, \mathrm{[Js]}$", fontsize=18)
for i in cb.ax.get_yticklabels():
i.set_fontsize(14)
# configure xaxis
plt.xlabel(r"$\omega \, \mathrm{[1/s]}$", fontsize=18)
plt.xticks(fontsize=14)
# configure yaxis
plt.ylabel(r"$\theta / \gamma$", fontsize=18)
plt.yticks(fontsize=14)
# make plot look nice
plt.tight_layout()
plt.show()
HDF5 output¶
The hdf5 based data contains the following data structure in /data/{iteration}/DetectorMesh/
according to the openPMD standard:
Amplitude (Group):
Dataset 
Description 
Dimensions 


real part, xcomponent of the complex amplitude 
( 

imaginary part, xcomponent of the complex amplitude 
( 

real part, ycomponent of the complex amplitude 
( 

imaginary part, ycomponent of the complex amplitude 
( 

real part, zcomponent of the complex amplitude 
( 

imaginary part, zcomponent of the complex amplitude 
( 
Note
Please be aware, that despite the fact, that the SIunit of each amplitude entry is \(\mathrm{[\sqrt{Js}]}\), the stored unitSI
attribute returns \(\mathrm{[Js]}\).
This inconsistency will be fixed in the future.
Until this inconstincy is resolved, please multiply the datasets with the square root of the unitSI
attribute to convert the amplitudes to SI units.
DetectorDirection (Group):
Dataset 
Description 
Dimensions 


xcomponent of the observation direction \(\vec n\) 
( 

ycomponent of the observation direction \(\vec n\) 
( 

zcomponent of the observation direction \(\vec n\) 
( 
DetectorFrequency (Group):
Dataset 
Description 
Dimensions 


frequency \(\omega\) of virtual detector bin 
(1, 
Please be aware that all datasets in the hdf5 output are given in the PIConGPUintrinsic unit system. In order to convert, for example, the frequencies \(\omega\) to SIunits one has to multiply with the datasetattribute unitSI.
import h5py
f = h5py.File("e_radAmplitudes_2800_0_0_0.h5", "r")
omega_handler = f['/data/2800/DetectorMesh/DetectorFrequency/omega']
omega = omega_handler[0, :, 0] * omega_handler.attrs['unitSI']
f.close()
In order to extract the radiation data from the HDF5 datasets, PIConGPU provides a python module to read the data and obtain the result in SIunits. An example python script is given below:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm
from picongpu.plugins.data import RadiationData
# access HDF5 radiation file
radData = RadiationData("./simOutput/radiationHDF5/e_radAmplitudes_2820_0_0_0.h5")
# get frequencies
omega = radData.get_omega()
# get all observation vectors and convert to angle
vec_n = radData.get_vector_n()
gamma = 5.0
theta_norm = np.arctan(vec_n[:, 0]/vec_n[:, 1]) * gamma
# get spectrum over observation angle
spectrum = radData.get_Spectra()
# plot radiation spectrum
plt.figure()
plt.pcolormesh(omega, theta_norm, spectrum, norm=LogNorm())
# add and configure colorbar
cb = plt.colorbar()
cb.set_label(r"$\frac{\mathrm{d}^2 I}{\mathrm{d} \omega \mathrm{d} \Omega} \, \mathrm{[Js]}$", fontsize=18)
for i in cb.ax.get_yticklabels():
i.set_fontsize(14)
# configure xaxis
plt.xlabel(r"$\omega \, \mathrm{[1/s]}$", fontsize=18)
plt.xticks(fontsize=14)
# configure yaxis
plt.ylabel(r"$\theta / \gamma$", fontsize=18)
plt.yticks(fontsize=14)
# make plot look nice
plt.tight_layout()
plt.show()
There are various methods besides get_Spectra()
that are provided by the python module.
If a method exists for _x
(or _X
) it also exists for _y
and _z
(_Y
and _Z
) accordingly.
Method 
Description 


get frequency \(\omega\) of virtual detector bin in units of \(\mathrm{[1/s]}\) 

get observation direction \(\vec{n}\) 

get spectrum \(\mathrm{d}^2 I / \mathrm{d} \omega \mathrm{d} \Omega\) in units of \(\mathrm{[Js]}\) 

get spectrum but only for polarization in xdirection 

get xcomponent of complex amplitude (unit: \(\mathrm{[\sqrt{Js}]}\)) 

the iteration (timestep) at which the data was produced (unit: PICcycles) 
Note
Modules for visualizing radiation data and a widget interface to explore the data interactively will be developed in the future.
Analyzing tools¶
In picongp/src/tools/bin
, there are tools to analyze the radiation data after the simulation.
Tool 
Description 


Reads ASCII radiation data and plots spectra over angles as color plots.
This is a python script that has its own help.
Run 

Reads ASCII radiation data and statistically analysis the spectra for a user specified region of observation angles and frequencies.
This is a python script that has its own help. Run 
smooth.py 
Python module needed by 
Known Issues¶
The plugin supports multiple radiation species but spectra (frequencies and observation directions) are the same for all species.
References¶
 Pausch2012
Pausch, R. Electromagnetic Radiation from Relativistic Electrons as Characteristic Signature of their Dynamics Diploma Thesis at TU Dresden & HelmholtzZentrum Dresden  Rossendorf for the German Degree “DiplomPhysiker” (2012) https://doi.org/10.5281/zenodo.843510
 Pausch2014
Pausch, R., Debus, A., Widera, R. et al. How to test and verify radiation diagnostics simulations within particleincell frameworks Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 740, 250–256 (2014) https://doi.org/10.1016/j.nima.2013.10.073
 Pausch2018
Pausch, R., Debus, A., Huebl, A. at al. Quantitatively consistent computation of coherent and incoherent radiation in particleincell codes — A general form factor formalism for macroparticles Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 909, 419–422 (2018) https://doi.org/10.1016/j.nima.2018.02.020
 Pausch2019(1,2,3)
Pausch, R. Synthetic radiation diagnostics as a pathway for studying plasma dynamics from advanced accelerators to astrophysical observations PhD Thesis at TU Dresden & HelmholtzZentrum Dresden  Rossendorf (2019) https://doi.org/10.5281/zenodo.3616045