30.2 Simple Thomson Scattering without Ray Tracing

As of FLASH4.5, we provide the a “Simple” implementation of Thomson Scattering. In the future, an implementation that employs true ray tracing may be provided.

30.2.1 Ray Tracing in the Geometric Optics Limit

In the “simple” implementation, We do not “trace” rays but “cast” them: “rays” consist of two straight-line parts, which we'll refer to as “leg 1” and “leg 2”.

30.2.2 Laser Power Deposition

The power deposited in an experiment by a probe laser may significantly alter the behavior of the physical system, by deposition energy into the system. This is usually an undesired effect. The ThomsonScattering unit does not model this effect. As a purely diagnostic unit, it has no impact on the dynamics of the physical system. However, a ThomsonScattering configuration can easily be combined with a configuration of a laser for energy deposition, provided by the EnergyDeposition unit, see Sec:EnergyDeposition. Commonly this configuration will consist of adding a laser beam, in addition to the beams already present in an experimental setup. The definitions of pulse, beam parameters, etc., for this additional beams should closely mirror the runtime parameters chosen to configure the Thomson probe laser beam.

30.2.3 Laser Energy Density

The ThomsonScattering unit will fill several variables with information about the Thomson probe laser power and its spatial distribution, if variables of the following names are defined:

• pwin - Power in, restricted to a “measurement region” that is used to calibrate the configured laser power.
• pwia - Power in, everywhere except in locations that are forbidden because the cirtical electron density is exceeded.
• pwi1 - Power in, with leg 1 attenuation applied, computed everywhere in the domain. Note that this can increase run time very significantly, since integrations along many more ray paths have to be performed than what is needed for computing scattering spectra.
• pwi2 - Power in, with leg 1 and leg 2 attenuation applied. Only computed in regions within the cone defined by a detector's opening angle.
• pwde - Total power of detectable scattered light, without attenuation.
• pwi1 - Total power of detectable scattered light, with leg 1 attenuation applied.
• pwi2 - Total power of detectable scattered light, with leg 1 and leg 2 attenuation applied.

Laser Energy Density for the probe laser can be made available for visualization in the lase variable, if an EnergyDeposition beam has been added to the configuration, es described in Sec:LASE.

30.2.4 Algorithmic Implementations of the Ray Tracing

As mentioned above, we provide the a “Simple” implementation of Thomson Scattering. Even though the code uses “raytracing” terminology in some variable names etc., realy we are “casting” rays along predetermined paths, rather than letting each ray find its own path through set-by-step integration.

30.2.5 Setting up the Probe Laser Pulse

We use runtime parameters analogous to those of the EnergyDeposition unit to configure the time behavior of the ThomsonScattering unit. Computations are only performed by this code unit at times when the probe laser pulse is nonzero. Additionally, a time-dependent probe laser power will directly affect the absolute scaling of computed spectro, so it can be useful for comparing a sequence of spectra computed at different times.

The laser's pulse contains information about the laser's energy profile and can thus be characterized by a function of laser power in terms of time $P(t)$. The curve of $P(t)$ gives the power of the laser pulse at any given simulation time. In FLASH, the form of $P(t)$ is given by a series of points, which are connected via straight lines (see Figure 18.5).

Note, that $t_1$ is the time the laser first comes into existence. In Figure 18.5 there is therefore no line connecting the origin (zero power) with $P_1$. If the user wants a gradual buildup of laser power from zero, an explicit point $P_1=0$ must be given at time $t_1$. The same consideration applies for the other end of the timescale.

Runtime parameters thsc_spectrumFileIntervalStep and thsc_spectrumFileIntervalTime can be used to limit the frequency of scattering computations, so that they won't happen at the end of every time step wile the probe laser is on.

30.2.6 Setting up the Laser Beam

Note: currently only one probe beam is supported.

The setup of each laser beam follows closely the setup of the laser beams in 18.4.6 for energy-depositing lasers. While the implementation of rays is quite different, we aim to make setting up a Thomson scattering probe laser beam very simir to setting up a beam for laser energy deposition. Lens and arget coordinates are used for directing a beam. Additional runtime parameters needed for each beam are: 1) the launching time (the beam fires once the simulation time exceeds the launching time), 2) its target detector screen and 3) the beam power. For the ThomsonScattering unit, lens and target ellipses can both be fully or partially inside or outside the simulation volume.

30.2.7 Creating the Rays

The rays inside each beam are created by connecting one-to-one grid points inside the lens area with the subcell center points inside the interaction region. The ray directions inside each beam can be parallel or conically diverging or converging collinear and are not allowed to cross. The lens positions and directions at the lens are calculated using the same strategy as presented in 18.4.7.6. Rays missing the domain can either be simply ignored or directly recorded on the detector screen.

30.2.7.1 Ray Specifications

Each beam/disk ray needs to know its position $x,y,z$ and velocity $v_x,v_y,v_z$ as it traverses the domain. In addition to these 6 components it needs to know: 1) the time spent travelling in domain, 2) the current block and processor numbers, 3) a global identification tag, 4) the originating beam and target detector numbers. Screen rays on the other hand are only defined on the detector screen and hence need no specific information for domain travelling. Their information is reduced to a screen position coordinate pair $x,y$ and a detector number to which detector they are associated with.

Additionally, upon request, the Thomson scattering code is able to calculate extra magnetic diagnostic quantities ${\bf k}$ and $J$ for each beam/disk and screen ray:

$${\bf k} = \int {\bf B}\;d\ell,$$ (30.8)

$$J = \int {\bf v}_n \cdot (\nabla\times {\bf B})\;d\ell,$$ (30.9)

where $\int d\ell$ denotes path integration, ${\bf B}$ is the magnetic field vector and ${\bf v}_n$ is the unit normal velocity vector along the ray path. Transforming the path integrals into time integrals using the relation $d\ell=\vert{\bf v}(t)\vert dt$, we get the differentials:

$$\frac{d{\bf k}}{dt} = {\bf B}\vert{\bf v}(t)\vert,$$ (30.10)

$$\frac{dJ}{dt} = {\bf v}(t)\cdot (\nabla\times {\bf B}).$$ (30.11)

30.2.8 Setting up the Detectors

Note: currently only one detector is supported.

Each detector is defined as a point together with a cone of directions from which it can receive light, the latter defined by a direction and an opening angle. Thus the geometry is specified by three components: 1) the detector location ${\bf C}$, 2) the unit vector ${\bf n}$ of the direction of the cone axis, and 3) the angle $\alpha$.

30.2.8.1 Recording Rays at the Detector

Each ray that reaches the detector gets recorded. Two kinds of files can be generated at the end of ThomsonScattering processing:

1. a detector file, and/or
2. a spectrum file.

Runtime parameters thsc_spectrumFileIntervalStep and thsc_spectrumFileIntervalTime determine approximately how often these files are generated. This is only approximate because these runtime parameters do not modify the simulation time step. Currenly, generation of one kind of these files may force generation of the other one at the same time. Each detector file is currently an ascii file (formatted) and named:

$$\mbox{$<$basename$>$ThomsonDetectorFile$<$detectorID$>$\_$<$timestamp$>$}$$ (30.12)

where $<$basename$>$ is the name of the simulation, $<$detectorID$>$ is the detector number (currently limited to the range [01-99]) and (optionally) $<$timestamp$>$ is the simulation time when the file was created. Only the $(x,y)$ pairs are written (first $x$ followed by $y$ on each line) without any headers. Thus the file can be directly incorporated and read by other software for graphical output (see for example the proton imaging ASCII $->$ PGM greyscale converter). Each spectrum file is also a text file and named:

$$\mbox{$<$basename$>$ThomsonSpectrumFile$<$detectorID$>$\_$<$timestamp$>$}$$ (30.13)

where $<$basename$>$ is the name of the simulation, $<$detectorID$>$ is the detector number (currently limited to the range [01-99]) and (optionally) $<$timestamp$>$ is the simulation time when the file was created. The first two columns are wave length and detected intensity, respectively. There will normally be thsc_spectrumNpts_N lines.

30.2.9 Usage

To include the use of the Thomson Scattering unit, something like the following can be included into the setup command line:  

-unit=diagnostics/ThomsonScattering [thsc_maxBeams=<number> thsc_maxDetectors=<number> threadThomsonSc=True]

The default settings are: maximum number of beams = 6, maximum number of detectors = 1 and no use of threading during tracing of rays through the domain, which can be changed by the following three setup variables:

• thsc_maxBeams: The maximum number ray beams for the simulation.
• thsc_maxDetectors: The maximum number of Thomson scattering detectors for the simulation.
• threadThomsonSc: Enables threading during ray domain tracing.

Using Thomson scattering runtime parameters in the flash.par file, the user can set up the proper ray imaging configuration for his specific needs. The following list of runtime parameters is currently available for the user.

30.2.9.1 Thomson Scattering Beams Runtime Parameters

The following are some runtime parameters for the Thomson scattering beams. The _n at the end of each runtime parameter characterizes the beam number, hence replace _n by _1 for the first beam, _n by _2 for the second beam, etc.

See Beam Runtime Parameters for a more complete list of beam parameters.

• thsc_numberOfBeams: The number of Thomson scattering beams that are going to be used.
• thsc_beamLens[X,Y,Z]_n: The global 3D components of the lens center position vector ${\bf C}$.
• thsc_beamTarget[X,Y,Z]_n: The global 3D components of the target position vector ${\bf T}$.
• thsc_beamDetector_n: The detector number, where the rays of the beam should be recorded. This should be set to 1 as long as only one detector is used.
• thsc_maxRayCount: Maximum total number of rays. Rays may be dropped if this number is exceeded.

Note: only configurations with one beam have been tested as of FLASH4.5.

30.2.9.2 Thomson Scattering Detectors Runtime Parameters

The following are some runtime parameters for the Thomson scattering detectors. In most of them, the _n at the end of each runtime parameter characterizes the detector number, usually “1”. See Detector Runtime Parameters for a more complete list of detector parameters.

• thsc_numberOfDetectors: The number of Thomson scattering detectors that are going to be used.
• thsc_detectorCenter[X,Y,Z]_n: The global 3D components of the detector center position vector ${\bf C}$.
• thsc_detectorTarget[X,Y,Z]_n: The local 3D components of the center of the target area to which the detector is oriented.
• thsc_detectorTargetRadius_n: The radius of a circular area perpendicular to the detector-target connecting line, from which the detector receives scattered radiation. This is converted to an equivalent opening angle and used if thsc_detectorApertureAngle_n is not specified.
• thsc_detectorApertureAngle_n: The conical full aperture angle, specified directly.
• thsc_detectorSideLength_n: The side length (cm) of the detector square screen.

Note: currently only one detector is supported.

30.2.9.3 Thomson Scattering General Runtime Parameters

• thsc_detectorFileNameTimeStamp: If set to true, a time stamp will be added to each detector file name. This allows for time splitting of detectors.
• thsc_detectorXYwriteFormat: Controls formatted ascii output of the ray $(x,y)$ pairs on the detector screens (default 'es20.10').
• thsc_detectorDGwriteFormat: Controls formatted ascii output of the magnetic diagnostic quantities $k_x,k_y,k_z,J$ on the detector screens (default 'es15.5').
• thsc_maxRayCount: The maximum number of beam/disk rays that can be created/read-in on one processor per batch in the domain.
• thsc_printPulses: If true, it prints detailed information about the laser pulses to a file with name $<$basename$>$ThomsonPulsesPrint.txt, where $<$basename$>$ is the base name of the simulation.
• thsc_printBeams: If true, it prints detailed information about the ray beams to a file with name $<$basename$>$ThomsonBeamsPrint.txt, where $<$basename$>$ is the base name of the simulation.
• thsc_printDetectors: If true, it prints detailed information about the ray detectors to a file with name $<$basename$>$ThomsonDetectorsPrint.txt, where $<$basename$>$ is the base name of the simulation.
• thsc_printMain: If true, it prints general information regarding the ray imaging setup to a file with name $<$basename$>$ThomsonScatteringMainPrint.txt, where $<$basename$>$ is the base name of the simulation.
• thsc_recordOffScreenRays: If true, rays not hitting their target detector screen are also recorded on the detector files. These rays will have screen coordinate pairs $(x,y)\notin [0,1]$.
• thsc_screenRayBucketSize: Sets the bucket size for flushing screen rays out to disk.
• thsc_screenRayDiagnostics: If true, the magnetic diagnostic quantities $k_x,k_y,k_z,J$ are evaluated for each ray and recorded on the detector screens.
• useThomsonScattering: If false, no Thomson scattering will be performed, even if the code was compiled to do so. Bypasses the need to rebuild the code.

30.2.10 Example Setup

A version of the laser Slab setup with an added Thomson scattering diagnostic is provided, see Sec:LaserSlabThc for a description.