Long-term perturbations due to a disturbing body in elliptic inclined orbit

In the current study, a double-averaged analytical model including the action of the perturbing body's inclination is developed to study third-body perturbations. The disturbing function is expanded in the form of Legendre polynomials truncated up to the second-order term, and then is averaged over the periods of the spacecraft and the perturbing body. The efficiency of the double-averaged algorithm is verified with the full elliptic restricted three-body model. Comparisons with the previous study for a lunar satellite perturbed by Earth are presented to measure the effect of the perturbing body's inclination, and illustrate that the lunar obliquity with the value 6.68\degree is important for the mean motion of a lunar satellite. The application to the Mars-Sun system is shown to prove the validity of the double-averaged model. It can be seen that the algorithm is effective to predict the long-term behavior of a high-altitude Martian spacecraft perturbed by Sun. The double-averaged model presented in this paper is also applicable to other celestial systems.Comment: 28 pages, 6 figure

On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection

A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)

A semi-analytical approach using the single and double averaged methods and the Lidov–Kozai mechanism

An analysis of the orbital motion of artificial satellites around Mercury is presented taking into account its non-sphericity (J2, J3, C22) and the perturbation of the third body. The disturbing potential due to the third body is developed in circular and inclined orbit. The double-averaged method should be used with caution in some situations where the averaging is applied at different timescales. In this work, a study is presented considering this observation for orbits around Mercury. When the mean anomaly of the Sun is eliminated, the idea is that all effects whose periods below 88 days are neglected. As the rotation of Mercury is about 58.6 days, this means that the perturbation due to the C22 term must also be neglected. However, since the C22 term is important and should be taken into account, then terms longer than 58.6 days should also be preserved. In other words, keeping the C22 term with a period of 58.6 days means that the solar terms with the longest period (88 days) will be maintained here. The single-averaged method is applied to eliminate only the mean anomaly of the spacecraft. A comparison between the single and double averaged models is presented. We found that for the case of Mercury the two models are in agreement, but the single-averaged model is more realistic because it keeps more terms in the disturbing potential. Several types of resonances can be analyzed starting of the single-averaged potential. Considering our single-averaged disturbing potential, the terms due to Lidov–Kozai resonance were isolated to make a qualitative analysis considering the libration and circulation regions in the diagram, eccentricity versus argument of the pericenter

An optimization approach to search for quasi-critical inclinations for direct and retrograde orbits

When only the secular terms due to the central body oblateness are considered in the gravitational potential, the critical inclination classical values are about 63.43° and 116.56° for the direct and retrograde orbits, respectively. If sectoral terms are included into disturbing function, the equations of motion become coupled, then searching for critical inclinations is not a trivial problem. Thus, for the purpose of overcoming this difficulty and to shed light on the effect of inserting the C22 sectoral hamornic in the Hamiltonian function, the quasi-critical inclinations concept is revised and its solution is proposed as an optimization problem. In this sense, the present article makes the following contributions to the quasi-critical inclination problem: (i) applying the nonlinear optimization tools to solve this problem; (ii) through this technique, obtaining quasi-critical inclinations for the retrograde case for the first time; (iii) using this technique to find direct and retrograde orbits around Io, a very important body to be studied in the future