^{1}

^{1}

^{2}

^{2}

Study of atmospheric remnants in the low Earth orbit region (~200 km altitude) using Global Models, with application to electric thrusters of in situ resources utilization type.

Knowledge of the Earth Atmospheric Remnants (AtR) composition at altitudes from 180 km to 240 km is of paramount importance for the development of air-breathing technology which is of interest here, mainly addressing needs of Low Earth Orbits (LEO). Hall Effect Thruster (HET) and Radio-frequency Ionization Thruster (RIT) devices are expected to be used in this case. More generally, atmosphere composition is also important for satellite drag and re-entry studies.

The altitudes we are interested in belong to the thermosphere part of the atmosphere. A considerable number of studies has been made on the thermosphere composition. A general introduction on the subject, including an extended references list, can be found in [^{−9} Pa at 200 km altitude. Ultra Violet (UV) solar radiation constitutes the main contributor to the thermosphere heating. Under the influence of the Earth magnetic field most of the charged particles coming from the Sun are deflected, but a considerable fraction of them still enters in the polar regions. As far as UV solar radiation is concerned, activity cycles are observed which last about 11 years. Moreover, the Earth magnetic field is subject to sudden geomagnetic storms, which are short- lived events. Both of these phenomena result to big variations. Additionally, diurnal and seasonal variations are observed depending on the Sun-Earth geometry, set aside semi-annual variations of which the origin is unclear. The aforementioned Solar and Geomagnetic (S & G) activities, have a direct influence on the temperature in the thermosphere and consequently on the present species total densities and compositions.

Important experiments have been realized and adequate models developed to study and to characterize the thermosphere, beginning at the end of the last century. These are briefly addressed in the following Section 2. Main compendia of recommended data concerning the thermosphere are discussed in Section 3. These include results coming from DEDALOS Ltd. code 4CGM. Global Model (GM) support of air-breathing technology is addressed in Section 4. Conclusions are given in Section 5.

The main approach of the thermosphere study consists in empirical modeling. An extensive description of the subject can be found in Chap. 2 of [

α The Jacchia type models, using observations of orbital motions of satellites under the influence of drag. Recently, Jacchia-Bowel (JB) improved codes were developed by US Air Force including additional variations and activity data. On this subject, see [

β Density effects on Drag and Temperature Models (DTM), based on observation of satellite drag results and temperature of the neutral atmosphere. However, they use a more generalized model formulation, see [

γ Mass Spectrometer and Incoherent Scatter Extended (MSISE) models, initially based solely on mass spectrometer and incoherent scatter radar observations. The two most recent versions of such models are:

● MSISE-90 code, see [

● NRL-MSISE-00 code, now developed by Naval Research Laboratory, see [

The same parameters which are used in the MSISE codes are also used for HWM models for the horizontal wind evaluation. Wind influence is not addressed here, as it is not so important in our case.

The European Standard of 2000, [

Empirical models have been reported to be in agreement with the available experimental results even if some discrepancies exist [_{2} (A band) and the 630 nm line of atomic oxygen for lower and higher thermosphere respectively [_{2}/O amounts present at these altitudes.

Measurements of the Sun radiations are recorded on ground in various observatories around the Earth and are combined to make global data in “near-real time”. Those data may be included in various empirical models to obtain better results. Moreover, density observations derived from satellite dynamics can contribute to the empirical density models. This procedure is known as “model calibration”. Such implementation and calibration techniques were developed recently in the frame of ESA contracts, see [

In addition to the three types of models mentioned previously, we mention:

δ Models based on calibrations techniques, as is the case of the Near-Real Time Calibration Model (NRTCM) funded by ESA, developed by Doornbos. This model had already adjusted the NRL-MSISE-00 model to reduce the model error up to 30%, [

ε The 4CGM, a Four Components Global Model type code [_{2} and N/N_{2}, are the most present species in the aforementioned altitudes region.

The main parameters of interest here are temperature (T_{GAS}), mass (ρ) and number (n) densities and pressure (p). Composition of the thermosphere and percentages of the four main constituents (O, O_{2}, N, N_{2}) are investigated elsewhere [

Variations of the thermosphere composition as a function of the altitude from 180 km up to 240 km for low S & G activities are illustrated in _{2} (blue lines), O_{2} (red lines), N (blue lines), He (black lines), Ar (green lines) and H species (orange lines) are included. Also, total density is represented by a magenta line. The total density is calculated by us, summing the densities of the main seven species as they are given in the literature. We observe in _{2} for all the

Low S & G activities (see | ||||
---|---|---|---|---|

n_{O} | n_{N2} | n_{O2} | n_{N} | n_{TOT} |

4.93E9 | 4.75E9 | 3.72E8 | 2.81E7 | 1.01E10 |

2.73E9 | 1.80E9 | 1.28E8 | 2.11E7 | 4.70E9 |

1.60E9 | 7.17E8 | 4.35E7 | 1.52E7 | 2.38E9 |

9.43E8 | 2.93E8 | 1.61E7 | 1.08E7 | 1.26E9 |

Mean S & G activities (see | ||||

n_{O} | n_{N2} | n_{O2} | n_{N} | n_{TOT} |

7.24E9 | 7.01E9 | 4.15E8 | 5.04E7 | 1.47E10 |

4.66E9 | 3.29E9 | 1.67E8 | 4.54E7 | 8.16E9 |

3.05E9 | 1.62E9 | 7.14E7 | 4.03E7 | 4.78E9 |

2.08E9 | 8.37E8 | 3.28E7 | 3.08E7 | 2.98E9 |

High S & G activities (see | ||||

n_{O} | n_{N2} | n_{O2} | n_{N} | n_{TOT} |

1.13E10 | 1.02E10 | 4.82E8 | 1.21E8 | 2.21E10 |

7.61E9 | 5.27E9 | 1.98E8 | 1.29E8 | 1.32E10 |

5.37E9 | 2.93E9 | 1.00E8 | 1.15E8 | 8.52E9 |

3.94E9 | 1.73E9 | 4.94E7 | 9.49E7 | 5.81E9 |

Very high S & G activities (see | ||||

n_{O} | n_{N2} | n_{O2} | n_{N} | n_{TOT} |

1.98E10 | 1.44E10 | 1.54E9 | 1.51E9 | 3.73E10 |

1.44E10 | 8.44E9 | 8.21E8 | 1.12E9 | 2.48E10 |

1.10E10 | 5.23E9 | 4.60E8 | 8.56E8 | 1.76E10 |

8.47E9 | 3.38E9 | 2.74E8 | 6.76E8 | 1.28E10 |

altitudes represented, except that for 180 km, where O density is the same than this of N_{2}. The O_{2} density is between 1.5 and 2 orders of magnitude lower that this of O, illustrating the important O_{2} dissociation. Atomic N, the fourth component, shows a quite low density. According to results from the literature, presence of He, Ar and H is also observed. In a general way, we see that heavier components (N_{2}, O_{2} and Ar) are decreasing quickly with the altitude. Atomic oxygen and nitrogen (O, N) having lighter masses are decreasing in a slower way. Finally, densities of the lighter components (H, He) diminish very slowly with altitude. It is also to be noted that decrease rate of N is quite lower than this of O, because N components are fed from N_{2} dissociation. The latter increase with altitude, leading to a somehow flat density curve for N. Results from the two MSISE codes compare quite well, except for N_{2}, N and H, where substantial differences are observed. Our results from 4CGM, obtained when ρ and T_{GAS} are used as input, are also included in _{2} and O_{2} species. However, we obtain a slightly smoother N density variation. Indeed, 4CGM calculations result to a N density slightly higher than this of NRL-MSISE-00 for 180 km altitude. Note that although input data used in the 4CGM calculations were in fact taken from NRL-MSISE-00, our results are in agreement with MSISE-90 results for 180 km altitude.

For mean S & G activity variations, density as a function of the altitude for the same seven species addressed previously, are illustrated in _{2} (which are the prevailing species) and for He and Ar, while for those for O_{2}, N and H species, densities present important differences. Especially, the O_{2} density is about 30% lower with the new code version NRL-MSISE-00 in comparison with MSISE-90. It is to be noted that our 4 CGM results give O_{2} densities located between those of NRL-MSISE-00, and those of MSISE-90. Moreover, the N density we calculate for 180 km altitude is slightly higher than this of NRL-MSISE-00, as was also the case in the previous

Variations of the density of species as a function of the altitude for high S & G activity are illustrated in

Lighter species have almost constant densities within 180 km and 240 km altitude, as was the case in the two previous figures. Note that N density is quite constant, as atomic N is substantially formed by N_{2} dissociation. The latter increases with altitude and becomes important for high S&G activities. Our 4CGM results are in good agreement with NRL-MSISE-00 for O, N_{2} and N densities, but give bigger O_{2} density. This may be due to data pertaining to O_{2} dissociation and has to be further investigated.

Finally,

the altitudes. Moreover, N_{2} density is quite big, followed by N and O_{2} densities. The He density constitutes about 0.1% of the total density and it remains quite constant with the altitude. Ar density, although higher than this of He for 180 km, decreases steadily with increasing altitude. Moreover, the H density is so low, that it was necessary to be multiplied by a factor of 100, in order to be contained in the figure.

For extremely high S & G activity, data from MSISE-90 have been used as input for the 4CGM calculations. We see that our 4CGM results are in good agreement with MSISE-90 for O, N_{2} and N densities, as was somehow expected. However, as previously, the O_{2} density calculated with 4 CGM is quite higher than this of MSISE-90.

As was illustrated in the provided figures, the 4CGM considering the four main components present is able to characterize the main variations of the atmosphere composition. This includes only O, N_{2}, N and O_{2} species as main components. It is also possible to add H, He and Ar species, to obtain a 7 CGM code. Comparison of results of 7CGM versus 4CGM will be made elsewhere. By adding Ar species to the four original ones, we developed the 5CArGM code, which is of interest for O beam and electric thrusters characterization in LEO conditions laboratory simulations [

It is important to point out that for the very low total pressures (from 9.1 × 10^{−5} mTorr to 5.1 × 10^{−3} mTorr) expected in the 180 km to 240 km altitudes region, when the absorbed power is sufficiently low (say 10 W), our results are consistent with those given by [_{2}O, air and N_{2} discharges.

Detailed structure of each of the main initial compounds of atmospheric mixtures in altitudes of about 200 km, which is taken into consideration in the present GM, allows for evaluation of the mixture radiative properties. The latter strongly depend on the absorbed power. Their calculation is necessary for diagnostics based on Optical Emission Spectroscopy (OES). In so doing, comparison of theoretical spectra with experimental ones is mandatory [

In fact, GM constitutes a multi-physics code, which was used here for the atmosphere assessment. It can also be used for studying the propellant containment vessel and the thruster functioning and as a support of the necessary diagnostics of it.

We provide four figures illustrating a summary description of AtR in about 200 km altitude. Differences observed within available data sources become occasionally considerable. For LEO technology needs, we recommend to use results from JB2008 for total mass density. These have not been included in ECSS-04C probably because they were not made available in time. For temperature of neutrals and density of species, we propose to use results of NRL-MSISE-00 whenever exist, represented by plain lines in Figures 1-3 and results of MSISE-90 when no other data are available. Results obtained by our 4 CGM code, simplifying the situation by taking into consideration only the main four species present, are shown to be very satisfactory. In view of the obtained very satisfactory comparison of 4CGM code results to those provided by the literature we consider this code as validated for LEO applications. This allows using of our model in any case of atmospheric studies, notably within the 180 km - 240 km altitude. 4CGM code results pertaining to these altitudes will be presented and commented elsewhere [

Ch. Berenguer and K. Katsonis thank ESA/ESTEC/TEC-MPE for its support.

Konstantinos Katsonis,Chloe Berenguer,José Gonzalez del Amo,Constantinos Stavrinidis, (2015) Atmospheric Remnants in the Low Earth Orbit Region around 200 km Altitude. World Journal of Engineering and Technology,03,26-32. doi: 10.4236/wjet.2015.33C004