Since we do not expect the two codes to agree overall on the first attempt, we need to break each down into its physics components and compare them separately. DEGAS 2 has standalone test codes just for this purpose, allowing all of the results shown below to be obtained without ever running the full code. The corresponding EIRENE results were acquired by hardwiring the "input" values and writing out the required data.
Two other pages describe the first full runs of the codes and a detailed "EIRENE physics" comparison of all of the densities and plasma sources computed. Following this comparison, the differences between the two codes (in this case, the surface physics) had been minimized. A final comparison examines the impact of using "DEGAS 2 physics" on the results.
The second major section of this benchmark exercise compares the performance of these two codes.
The first and easiest thing to verify is that both codes correctly reproduce the prescribed ion flux distribution (the launch points of the Monte Carlo flights) on the target. No problem here within the error bars (I think this is for 5000 flights):
The surfaces in this problem are mirrors, molybdenum, and one exit. Because of the proximity of surface physics experts, the surface physics in the German code surpasses that of the old DEGAS and, hence, DEGAS 2. Consequently, it did not seem useful to attempt an overall comparison with different surface physics data. Below are graphs demonstrating the successful installation in DEGAS 2 of the Bateman format data for reflection of D off of Mo.
These data prescribe the reflection coefficient, the outgoing energy, and two outgoing angles as a function of the incident energy and polar angle. That the reflection coefficients computed in the codes was verified for several different parameter incident conditions. A graph was not generated in this case.
The outgoing energy distribution is compared here at a 19 eV incident energy for normal incidence. The distribution specified by the input data are provided as well:
Some features of this plot are common to others in this section. First, the data specify parameter values (in this case, the outgoing energy) at intervals of the cumulative distribution function: 0.1, 0.3, 0.5, 0.7, 0.9. One can also establish data points at each end of the distribution. E.g., a minimum energy might be the wall temperature; a maximum would be the incident energy. In DEGAS 2, I use this additional information to extrapolate beyond the ends of the data (the interpolation is logarithmic in DEGAS 2; hence, the apparent better match to the data in the lower half of the plot).
EIRENE, however, mindlessly extrapolates the data and enforces the minimum and maximum values after sampling. The result is that the sampled maximum and minimum may be noticeably different from what was expected, as is clear in this case.
The cosines of the angular distribution are sampled in an analogous way. In this case, the bounds of the sampled parameters are clearer still since they are the cosines of the angles. Here's how the codes compared with the data:
Again, close inspection reveals the interpolation differences at the endpoints. The differences in the lower plot are within the error bars (limited by the number of datapoints I can stick into KaleidaGraph comfortably). For normal incidence, both codes strictly enforce azimuthal symmetry for the outgoing velocity (the raw surface physics data may not be symmetric because of Monte Carlo noise).
To check the codes for off-normal incidence, the exercise was repeated with an incident energy of 30 eV and a polar angle of 40 degrees:
The features are similar to the above plots. The input data are not included here (the only efficient way of interpolating them is to use the code we're trying to check!).
Incident D which is not reflected (as well as all incident D2) is thermally re-emitted as D2 at the wall temperature. The velocity distribution is the normal (to the surface) velocity * a Maxwellian (called a Maxwell flux distribution). The sampled energies and velocity direction cosines are compared here:
The apparent discrepancy in the top plot is just due to using a smaller number of bins for the EIRENE data (note the log scale).
The common ancestry of EIRENE, DEGAS, and DEGAS 2 is apparent here. All three codes rely upon the molecular data in the Janev book. The reaction rates are explicitly the same in all three codes, as are the dissociation energies, and the electron energy loss rates. There are some differences, but they should not be a factor in these simulations. Note also that since the scoring of momentum transfer to the plasma in EIRENE is relatively new, its implementation is incomplete: there is no momentum transfer for the molecular dissociation processes. However, given the dominance of the other momentum sources, this shouldn't be a problem. DEGAS 2 tracks all three components of the momentum transfer in all reactions.
This version of EIRENE (with this input file anyway) uses the reaction rate for charge exchange in the Janev book. No attempt is made to ensure that the sampled background ion velocities are consistent with the charge exchange cross section (e.g., see Heifetz' article in the NATO book). Furthermore, the momentum and energy transfer expressions are correct only in the limit of sigma-v = constant. I am certain that at least Detlev does better than this; I haven't checked any of the recent Garching input files yet.
DEGAS 2's standard charge exchange uses a cross section from the 1994 Janev-Smith database, with consistently computed reaction rates, and energy and momentum transfer rates. For the first set of comparisons, these data will be used. In a subsequent run, the EIRENE data will be substituted.
Detlev and I each have our own collisional radiative codes for computing the multi-step electron-impact ionization of hydrogen. Furthermore, we've made numerous comparisons between these codes in the past. The basic difference is that his is based upon the Johnson-Hinnov cross sections. Mine uses the more recent 1994 Janev-Smith database. I believe my rates are also in good agreement with ADAS. Here's how the ionization rate in EIRENE (from the file AMJUEL) compares with that in DEGAS 2 (from the file ehr2.dat):
The collisional radiative codes also provide the energy loss rates. Those match quite well. However, because of the differences in the ionization rates at low temperature, the energy per ionization is noticeably different:
As with charge exchange, the initial comparison run will be made without modifying the DEGAS 2 physics. A later run will utilize the AMJUEL data.