# HYADES

## HYADES Professional and HYADES Professional Plus

Radiation hydrodynamics simulation codes for the design and analysis of laboratory high energy-density experiments.

These codes have a proven performance for inertial fusion research, laser-plasma interaction studies, and materials processing technologies. More than fifty laboratories throughout the world are using these simulation codes.

## Table of Contents

- Who should use these codes?
- What are the HYADES codes?
- Some details of the Specific Physics Models
- Future Development Efforts
- Support
- Upgrade Policies

## Who should use these codes?

HYADES Professional is the basic radiation hydrodynamics simulation code. It contains the fundamental hydrodynamics and energy transport models for simulating the behavior of laboratory experiments. Many experimental situations can be adequately simulated with this code. The primary advantages of selecting this version are the simplicity of use as well as efficient use of computer resources. It is ideal for the academic community and especially for researchers beginning in the field of high energy-density physics.

HYADES Professional Plus (ProPlus) is the advanced version. It contains all of the physics of the Professional version, plus additional, more advanced, models of radiation transport, atomic physics, magnetic fields and material strength; it is thus able to simulate more complex experimental situations. Because of the increased complexity of the models, this version is well suited for the more advanced researcher with some experience in the field.

## What are the HYADES codes?

The HYADES Professional and Professional Plus codes solve the conservation equations of mass, momentum and energy. These equations are closed by a constitutive equation that provides the pressure and specific energy as a function of temperature and density (the equation of state). An extensive choice of energy sources are available.

HYADES Professional and Professional Plus are one dimensional, three geometry, three fluid Lagrangean hydrodynamics and energy transport simulation codes. One dimensional behavior in planar, cylindrical, or spherical geometry may be selected. Since the HYADES codes are designed for high temperature situations, where materials are significantly ionized, the three fluids are designated as the free electrons, the massive particles (ionized and neutral atoms), and the radiation field.

The electron and ion populations are treated separately in a fluid approximation and are coupled to each other via Coulomb collisions. Each fluid is in thermodynamic equilibrium, described by Maxwell-Boltzmann statistics. Energy transport for these fluids is modeled by flux limited diffusion. Radiative energy transport is treated in a single group (gray diffusion) approximation or (additionally in the ProPlus version) in a multigroup diffusion prescription; in the former, the radiation is assumed Planckian, and the latter model allows for small departures from a pure Planckian. The two models have different prescriptions for coupling the radiation field to the electron fluid. A deterministic radiation transport model will be available soon in the ProPlus version.

The hydrodynamic motion of the material is modeled using the von Neumann method of artificial viscosities. A simple model is included to estimate the effects of material strength and melting. The ProPlus version of HYADES has material strength (yield) and ?fracture? models.

The degree of ionization is determined from one of several models: Saha, Thomas-Fermi, LTE average atom, or fully stripped models; different material regions may have different ionization models. The ProPlus version includes a time-dependent nonLTE average atom ionization model. The thermodynamic and equation of state quantities are derived from realistic (Sesame or other theoretical models) tables, an in-line quotidian equation of state, or a perfect gas model.

Deposition of energy into a material may be specified in several ways: temperatures, energy depositions, pressures, velocities, lasers, and radiative fluxes. These various sources may be mixed (with some restrictions) and arbitrary time dependencies may be specified. There are a number of different laser absorption models including the standard inverse bremsstrahlung ray trace model, and/or a Helmholtz wave equation solution for plane waves. This latter feature is well suited for the sub-picosecond irradiation of solid materials by a high intensity laser.

The physics models chosen for HYADES were selected for their relevance to the conditions of interest, and their ease of use within the code, both from the perspective of accuracy and in computer requirements (memory and execution time). However, as a note of caution, since the models are relevant for specific conditions, significant departures from those regimes may cause the applicability of the models to be called into question. Small changes in the physics models may be accomplished by changing multipliers on the different processes; e.g. the electron thermal conductivity, or the electron-ion collision rate.

Output from the simulation code is provided in the form of printable tables and a binary post processor file that may be read by a number of utilities. Each version of HYADES is actually a suite of codes that consists of the simulation code itself, and a number of ancillary codes for maintaining libraries and post processing the simulation output.

The overall structure of the two codes is the same, with the additional physics of the ProPlus version added as separate modules. Thus, problems run with the Professional version will also run with the ProPlus version.

## Some Details of the Specific Physics Models

## Hydrodynamics

The central physics package of HYADES is the modeling of the hydrodynamic motion of the material. It is based on a fluid dynamics model, but has numerous extensions of importance to plasmas and to the solid state. Basically, the law of conservation of momentum is solved by calculating mesh accelerations from pressure gradients. From this information, the velocity and positions of the mesh points are found with a leap frog algorithm. Since the formulation is Lagrangean, mass is automatically conserved. The numerical method is due to vonNeumann, where shock fronts are modeled with artificial viscosities. Real viscosities are available to the user, but the quadratic artificial viscosity is usually sufficient to describe the frictional heating. Stability of the hydro equations is governed by the speed of sound across a computational zone (Courant condition); the sound speed is derived from the equation of state data. The Lindemann melt model or a Cowan model is included to affect a transition between solid and liquid phases of a material. Multiple vacuum gaps between material layers are allowed that may collapse during the motion.

## Thermal Energy Transport

Energy transported by the electrons and ions is modeled in the diffusion approximation for each fluid. The flux of energy of each species is limited to its free streaming value. The temperature of each species is advanced according to Fourier's law, with the specific heat being determined by the thermodynamic derivatives from the selected EOS model. The heat flux depends upon the thermal conductivity of each species (electrons or ions); the transport coefficients for the ions are essentially those of Spitzer/Braginskii, while the transport coefficients for the electrons are Spitzer/Braginskii modified to include electron degeneracy effects. The electron thermal conductivity is further modified to include high density effects and melting at low temperatures. At lower temperatures, the electron thermal conductivity model may be supplemented by the user in a generalized form.

Coupling between the electron and ion fluids is modeled by collisions between the two populations using Spitzer's model with the electron-ion collision rate being modified to include electron degeneracy effects. The electron-ion collision time may be altered by the user to include the effects of phonon coupling and interband electron transitions when near-free electron metals are specified.

## Equation of State

The simulation of the motion and thermal energy transport in a material depends upon the microscopic properties of the specific material. The change in internal energy requires information about the specific heats of the material, while the hydrodynamic response requires information about the pressure. HYADES' models for these processes use mass density and temperature as the independent variables. The dependent variables are pressure and specific energy, and their derivatives with respect to the independent variables.

Because different materials experience widely different behavior for similar conditions, it is impossible to include sophisticated in-line EOS models, so HYADES depends upon material tables constructed by more elaborate physics packages. The most common source of these tables is the Los Alamos Sesame Library. Since not all materials are available in tabular form, HYADES has an in-line quotidian EOS model that may be used instead. It is based on a multiphase EOS combining Debye, Gruneisen, Lindemann, and fluid scaling laws for the ion component, and a Thomas-Fermi model for the electrons. In addition, an option is included for using a perfect gas model with a user-selectable gamma (ratio of specific heats).

## Ionization

The distribution of an atomic species among its various stages of ionization is determined by the elemental constituents, the density of the material, the electron temperature, and the radiation temperature or radiation energy distribution as a function of photon energy. The familiar Saha model is based upon the generalization of the Boltzmann thermal equilibrium model, and is the default model in HYADES. It is appropriate for many materials including gases.

A second ionization model comes from the generalized Thomas- Fermi model of the atom based on Fermi-Dirac statistics, which includes degeneracy effects. Hence, this model is particularly good for metals. In the limit of high temperature and low density, the Thomas-Fermi results agree with the Saha model.

Both the Saha and Thomas-Fermi models have been extended to include excitation levels within a particular ionization stage. This information is needed to calculate the multi-frequency xray absorption coefficients (see below).

The third ionization model, and the one most relevant to dense plasmas where the radiation energy density is appreciable (but small), is the average-atom model. Its purpose is to extend the thermodynamic equilibrium Saha model to include non Planckian radiation. The "average atom" is a term used to describe a single "average" ionization stage in which the atomic states may have fractional number of bound electrons in each level; this is in contrast to a detailed atomic model in which information about every possible configuration is considered. The distribution of bound electrons within and between ion stages are based upon statistical equilibrium since the distribution of electrons is assumed to be Maxwellian, and the electron-ion collision rates are fast enough to dominate the photon field. In the limit of high temperature and low density, the LTE average-atom results agree with those of the Saha model.

An extension of the LTE average-atom model is to the time-dependent, nonLTE conditions which relax many of the assumptions made above. Generally speaking, the conditions of importance are when the collision rates are not high enough to dominate the photon field, rather than the electron distribution not being Maxwellian. This package, which solves the complete set of rate equations, can be computational expensive, thus the user may define only those material regions in which to use this model.

When using one of the laser deposition models (see below) a model of impact ionization and/or multiphoton ionization may be activated for those zones where laser energy is present. This model gives the electron density based upon a rate equation whose coefficients depend upon the specific material, the laser intensity and wavelength; these coefficients are supplied by the user.

Many of the physics models in HYADES require the ionization potential energies for successive stages of ionization; these are included in tabular form for all elements of the periodic table.

## Radiation Transport

The transport of radiation within plasma may play an important role in the hydrodynamic response of a material. The plasma's temperature may be altered far from the heat source by radiative energy being absorbed by the electrons, and thus its pressure being increased; in an inverse fashion, the plasma may loose energy to the vacuum by radiation, thus cooling the plasma and decreasing its pressure. The interplay with hydrodynamics, thermal energy transport and radiation transport is quite complex.

A truly accurate model of radiation transport within HYADES is precluded for a variety of reasons that include both computer time and available memory. HYADES, therefore, uses simple models based upon diffusion theory. The basic model is that of a single group, or gray, diffusion model. The formulation is quite similar to that of the electron (or ion) thermal transport (see above), but now the radiative specific heat is a strong function of temperature. The xray absorption coefficients (diffusion coefficients) are obtained from tables whose independent variables are density and electron temperature (similar to the EOS tables).

In moderately dense plasmas, the radiation distribution function yields photon mean free paths that vary from very short to very long (compared to the scale length of the plasma), and the gray diffusion model is inappropriate. The second model is to divide the radiation distribution function into a number of spectral groups (in photon energy space), and solve the transport equation for each group. This is done in a manner similar to that for gray diffusion, but now the frequency dependent absorption coefficients are derived from the particular ionization model selected. At low temperatures, where the material's optical properties approximate those at room temperature, tabular cold opacities are used.

In many cases, the in-line opacities are insufficient for simulating dense plasmas. This is particularly true for medium to high atomic number materials. Accurate calculation of the absorption spectrum requires sophisticated computer codes that cannot be incorporated into HYADES. Hence, provision is made to generate the required information externally, in the form of a table that can be read by HYADES.

## Magnetic fields

Certain laboratory experiments, such as Z-pinches, incorporate magnetic fields. These may be externally generated, or formed self-consistently; an example of the latter might be the thermoelectric effect arising from the two dimensional nature of orthogonal gradients of temperature and density near the margin of a laser beam. Because of the one dimensional nature of HYADES, only a limited set of magnetic field effects are included. In cylindrical geometry only, either azimuthally directed (B?) or axially directed (Bz) fields may be included.

The hydrodynamic response of the material is altered due to the magnetic field's pressure and if there is an externally applied current, the j ? B force. The magnetic field may increase/decrease due to hydrodynamic compression/ expansion. A magnetic induction equation is used to account for the field changing due to a number of processes, including the Nernst effect. Magnetic fields effect the transport of thermal energy (both the electron and ion species) by modifying the collision times resulting from changes in the mean-free-paths due to cyclotron motion. Additional thermal source terms arise from the Nernst effect and from j ? E, when an external current is specified.

## Laser Deposition

The primary method of energy deposition in HYADES is via laser-plasma interactions. The basic approach is a ray trace algorithm that deposits energy locally along the ray's trajectory using the standard inverse bremsstrahlung model. If the ray reaches the critical density or turning point for non normal incidence, energy may be deposited either by an angle dependent resonance absorption model (for P polarization), or by a user-defined fraction. Normally, the laser is assumed to be a plane wave and thus has an infinite focal point. A variation on this model is to allow focused laser sources in cylindrical or spherical geometry. The inverse bremsstrahlung absorption coefficient is found from an electron-ion collisional model; the collision rate may be specified by the user to cover those cases where the degree of ionization is too small to be useful in the normal inverse bremsstrahlung model.

A class of laser-material interaction experiments address the response of a material to ultra short, high intensity laser irradiation. These situations are characterized by the laser energy being deposited within a few skin depths on a time scale short compared to any hydrodynamic motion. Hence, the laser energy is deposited only in a thermal component, and the local temperature can be quite high. The usual inverse bremsstrahlung model is not appropriate here since there may be no underdense plasma, and the density gradient at the critical density may be steep. To simulate these ?short pulse? situations, HYADES solves the Helmholtz wave equation for S or P polarization (in planar geometry only) to describe the local energy deposition. Again, the user may alter the electron-ion collision rate to more accurately describe the laser absorption properties of the material. In addition, the user may specify the refractive and absorptive indices of the material.

## Material Strength

Lasers have been used to explore the properties of materials under less extreme conditions than those that create plasma. The rapid deposition of laser energy creates a high pressure that may drive a shock wave through a material and thus causing very high strain and/or strain rate. HYADES has an elastic-plastic wave propagation model in conjunction with a user selected yield model (stress- strain relationship); models for both low strain rate and high strain rate are available. In addition, simple models for spallation are provided. Future efforts will include a more elaborate crack nucleation and growth model. At present, the models primarily address ductile materials.

## Sources

In addition to the laser deposition packages (see above), energy may be added to the plasma by specifying temperatures (electron, ion, radiation), specific energy deposition rates for each fluid, pressures or velocities. These sources may be specified at any location with in the material, and have a complex time dependence; multiple sources are allowed.

In addition, the user may specify an external radiation flux or a time and frequency dependent xray flux or deposition profile.

A special radiation leak ?source? allows the user to specify a time dependent loss of radiation from other than the outer boundary(s) of the simulation.

Input/output and code control:

Input to the HYADES simulation code is accomplished by constructing an input file that describes the dimensions and composition of the problem, along with the choice of physics models and their modifications (if any), and specifications for the source terms. The user may specify the type of output desired and other code control parameters as necessary.

Output from HYADES consists of a printable tabular form containing user-defined "snapshots" of the progress of the simulation. In addition, the user may specify a history file of selected quantities that then may be post processed with a variety of tools (see below).

A limited amount of active code control is provided via the user?s computer keyboard. The user may halt the calculation to change selected physics or code control parameters, insert an edit into the output file, set the restart flag, or terminate the calculation.

In some instances, the user may wish to stop the calculation, examine the results, and then restart it for another period. A restart file may be created, and then upon restarting, selected model information may be altered.

Numerical stability of the calculation is a critical component of any simulation. Selection of time steps for the different physical processes is determined automatically. However, the user may alter these time steps via various multipliers.

## Future Development Efforts

There is a continuing effort to improve and extend the physics models in HYADES. The selection of packages to be developed depends upon the research initiatives of the high energy-density physics community. For example, the construction of NIF at the Lawrence Livermore National Laboratory will be used for many aspects of high energy-density physics. Having identified some of those experimental plans, the relevant physics is tentatively identified, and the development of improved and/or additional physics modules is initiated.

There are several physics packages currently under development, with several more on the ?wish? list. Those actively being developed are:

A deterministic multigroup radiation transport model based upon the discrete ordinates approximation. This effort should be completed in the spring of 2005.

A non local electron transport model is being considered. While code development has yet to be initiated, the favored approach to this problem will be a multigroup diffusion model. Initially, a modified kernel to the transport model will be developed. A mid-2005 time frame is anticipated for completion.

A significant effort is being started to update and extend the post processor capability. This will include a more flexible HYADPLOT package, as well as the development of ?instrument specific? simulation utilities.

## Support

HYADES is licensed on a one-time basis. This means that you may use the specific version of the code indefinitely, subject to the license agreement(s). The compiled application comes with documentation on how to use the code, extensive documentation on the physics in HYADES, sample input files, and numerous test problems.

Telephone/email support is provided ?indefinitely?, at a reasonable level of use. The HYADES Code Suite

Both the Professional and Professional Plus versions of HYADES include the simulation code and five post processor utilities as well as three ancillary utilities. The post processor utilities are:

HYADPLOT - A simple plotting package for a "quick" look at the results,

HYADPOST - An extraction utility to generate an ASCII file for subsequent use in a more sophisticated plotting package,

PPF2NCDF - A file conversion utility to convert the HYADES post processor file format to the industry standard netCDF format; this file may be read by a number of commercially available computer programs*,

PPF2IDL - A series of IDL? procedures to read the HYADES post processor file,

PPF2FLY - Extracts time history information from the HYADES post processor file for input to the FLY Atomic Kinetics code.

The ancillary utilities are:

HYADLIBM - The EOS and opacity libraries maintenance utility,

APOP - A stand-alone driver for the average-atom atomic physics package; provides detailed information about the atomic level energies and their electronic populations, and the frequency dependent absorption coefficients (xray opacities),

HUGONIOT - A stand-alone utility that calculates the principal Hugoniot for a selected EOS table or QEOS model. * Not available for all computer platforms.

## Computer Platforms Supported

Both HYADES Professional and Professional Plus are available on the following computers:

IBM-compatible PCs running MSDOS or MS Windows IBM-compatible PC running Linux Macintosh G3/G4 PCs running OS 8.6-9.2 HP9000 under HPUX Sun/SPARC under Solaris DEC Alpha Compaq Tru64

A version for the Mac OS X systems will be available in mid-2005. For availability on other computer platforms, contact Cascade Applied Sciences, Inc.

## Upgrade Policies

HYADES users often wish to try the entry-level version (Professional version) before committing to the more complex ProPlus version. Hence, licensees of the Professional version of HYADES who wish to upgrade to the Professional Plus version may do so within six months from the license purchase date of the Professional version. A credit of 1/2 of the Professional version base license fee will be applied towards the license fee of the ProPlus version.

Licensees of a previous version of ProPlus may upgrade to the current version of ProPlus. Licensees of the version just previous to the current one are credited with 1/2 of the base license fee of the previous version and that is applied towards the current version. Those with a version two back are credited 1/4 of the base license fee of that version.

Cascade Applied Sciences, Inc. also produces a version of HYADES (the Research version) with specialized physics packages. A two-dimensional version of HYADES (known as h2d) is under-going "beta" testing. For information about either of these products, specialized code development, or consulting and/or training services, please contact Cascade Applied Sciences, Inc.