Laser Source Setup

Laser light energy is deposited in the hydrodynamics spatial grid using one of two models:

• A Standard laser deposition model, in which the laser light is absorbed using an inverse Bremsstrahlung model
• An External Radiation Source model, in which the laser light is included as a external light source, and absorption includes contributions from free-free, bound-free, and bound-bound transitions.

The Standard laser deposition model was originally developed for the deposition of optical laser light, and has the following features:

• Energy propagating along a ray is attenuated by free-free absorption (inverse Bremsstrahlung model)
• An option is available to include additional attenuation due to bound-free and bound-bound absorption (using PROPACEOS opacity tables)
• When laser light reaches the critical surface, the remaining energy is dumped into the volume element (however, the user can specify that some fraction of the light is reflected)
• Ray tracing algorithms is governed by Snell's law with refractive index determined by the local values of electron density.

The model in which laser light is included as an External Radiation Source has the following features:

• The absorption of laser light is computed by considering the opacity of all transitions in the material (free-free, bound-free, and bound-bound). When non-LTE atomic kinetics are computed (collisional-radiative modeling in HELIOS-CR), the opacity is computed based on the non-LTE populations.
• No dump of energy at the critical surface is performed.
• The model is supported only for planar geometry and multi-angle radiation transport, and the laser beam is assumed to enter the spatial grid at normal incidence.

The Standard model is more suitable for optical lasers, while the External Radiation Source model is most often employed in simulations involving short-wavelength lasers. The External Radiation Source model is selected by checking the Include Laser Beam Radiation as External Source box in the Advanced sections.

Source Location

In HELIOS, the laser source can originate from the inner or outer boundary of the hydro grid -- i.e., R(min) or R(max) -- or at the boundary between any two spatial Regions.

For a source originating at an interface between two regions, the region name and the side at which the source originates must be specified. For example, to set up a laser source originating on the R(max) side of region "Plastic_1", select Plastic_1 for the name and R(max) for the boundary. Laser sources originating on a boundary on the R(max) side of a region propagate in the direction of R(min).

Beam Power Time-Dependence:

The time-dependence of the laser beam power can be entered into a two-column table of times and beam powers, or a Gaussian profile can be chosen.

• Table values: the beam power at a given simulation time is determined by interpolation of values in the beam power table. A multiplier can be applied to all the values.
• Gaussian profile: The profile can be specified by either the peak power or the total energy in the beam. The time at the peak and the Full Width at Half Maximum (FWHM) are also specified.

Note that in planar geometry the laser powers are entered as TW/cm², while for spherical geometry and cylindrical geometry the power is in units of TW and TW/cm, respectively.

Beam Parameters

The Beam Parameters section is used to specify:

• Laser wavelength (in microns)
• Parameters for ray-trace modeling.

For planar geometry, the Incidence Angle is entered (see top image on this page). For cylindrical and spherical geometries, the focal position, the half cone angle, and the number of angles is specified (the default for the number of angles is the number of zones in the plasma).

Advanced Modeling Parameters

Additional Laser Source modeling options can be viewed by clicking on the Advanced button. Modeling options include:

• The percentage of the laser power that is reflected at the critical surface. This may be specified by entering a number between 0 and 100.
• Treating laser light as an External Radiation Source, by checking the Include Laser Beam Radiation as External Source box. (If unchecked, the Standard model is used.)

The above options can be specified on a beam-by-beam basis in a multiple beam simulation.

When the Standard laser deposition model is employed, the following options are also available:

• The minimum mean charge used in calculating the free-free laser absorption. The default value is 0.1.
• The contribution to laser absorption from bound-bound and bound-free transitions may be included using PROPACEOS tables.

For cylindrical and spherical geometries, additional focal plane parameters, discussed below in Ray-Trace Modeling description, can be entered on the Advanced section:

Ray-Trace Modeling

The direction of laser ray propagation across the zone boundaries inside the plasma is governed by Snell's law, where the refractive index is determined by the local values of electron density. At the zone there the critical value of the electron density is reached (critical surface), a user-specified fraction of laser energy can be reflected back into the plasma. Any energy remaining in the beam is deposited. In this model, laser energy is not allowed to penetrate beyond the critical surface.

For planar geometry, the laser beam is assumed to propagate along a single ray. The angle between this ray and the normal to the zone boundaries is given by the Incidence angle.

For spherical or cylindrical geometry, a more elaborate ray tracing algorithm is utilized. This allows for a more realistic calculation of the laser energy deposited within the 1-D modeling. The following parameters define the modeling geometry:

• the position of the focus plane with respect to the plasma origin
• the half cone angle
• the spot size at the focal plane.

The default number of angles within a cone is equal to the number of zones in the problem. The number of rays for the focal spot is 1 (basically, it assumes that the laser focuses to a point). For non-zero spot size, where the number of rays for the focal spot is greater than one, the angles of incidence for each ray are recomputed. The point of origin for each ray is assumed to be sufficiently far from the plasma that the rays entering the focal plane can be treated as parallel.

The spatial profile of the laser intensity at the focal spot in spherical and cylindrical simulations can be specified to be either uniform or Gaussian. For Gaussian profile, the spot size determines the location where the laser intensity is decreased by a factor of 1/e.

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