Radial Couplings Research Articles

FEM-based optimal design and testing of synchronous magnetic coupling for aerospace Starter/Generator applications

Improvements in high energy density rare-earth permanent magnets make it innovative to develop magnetic couplings for Starter/Generator applications in the light of more electric aircraft to ensure magnetically insulated contactless power transmission between decoupled shafts for safe operation. Although there are essential studies on magnetic couplings in the literature, especially those for aerospace Starter/Generator structures are rarely encountered. However, methodologies considering system constraints and examining design parameters of couplings are in demand. In response to such a need, this paper proposes the novel design of highly reliable synchronous radial magnetic couplings with torque requirements of 6 and 12 N·m to isolate Starter/Generator and piston engine shafts in model aircraft. The preliminary volume is obtained analytically. Simulations are executed by optimetric approaches in Ansys Maxwell 2D. Optimisation techniques are compared in Maxwell 3D to get the final shape. The retaining sleeve of 0.5 mm is suggested. Loss of synchronisation in the event of the piston shaft failure or exceeding the maximum torque of the coupling is also examined. The torque fluctuation at load changes is 0.1%. Performance tests are conducted on the direct dynamic test bench. Absolute error margin is 37% for the Virtual Work method, 13% for 2D FEM and 6% for 3D FEM. The coupling efficiency is 93.8% at the maximum operating speed and the critical angle, and 96.9% at the minimum torque angle and the minimum operating speed.

Mutual neutralization in H++H− collisions: An improved theoretical model

The total and differential cross sections of mutual neutralization in ${\mathrm{H}}^{+}+{\mathrm{H}}^{\ensuremath{-}}$ collisions are calculated ab initio and fully quantum mechanically for energies between 0.001 and 600 eV. Effects which have not previously been considered in studies on mutual neutralization (MN) for this system, such as inclusion of rotational couplings and autoionization, are investigated. Adiabatic potential curves corresponding to the relevant states of $^{1}\mathrm{\ensuremath{\Sigma}}_{g}^{+}$, $^{1}\mathrm{\ensuremath{\Sigma}}_{u}^{+}$, $^{1}\mathrm{\ensuremath{\Pi}}_{g}$ and $^{1}\mathrm{\ensuremath{\Pi}}_{u}$ symmetries as well as radial and rotational nonadiabatic couplings are computed ab initio. A quasidiabatic model is developed and applied in order to investigate the importance of higher excited states as well as the inclusion of autoionization. Molecular data for the lowest electronic resonant state in each symmetry are obtained by performing electron scattering calculations. It is shown that rotational couplings cause a significant increase of the total MN cross section while autoionization plays a minor role as a loss mechanism. Additionally, a differential cross section is obtained that is symmetric around $\ensuremath{\theta}={90}^{\ensuremath{\circ}}$. This result is in disagreement with a previous theoretical calculation where it was found that the differential cross section is dominated by backwards scattering.

Notes on Fission Dynamics

The dynamics of the nuclear fission is a complex phenomenon, being not yet described adequately from the theoretical point of view. At present, they are not models giving a complete description of the richness of the features which characterizes this phenomenon. It is the mean reason for which I called this paper Notes on Fission Dynamics, being certain that I will not be able to make a global description, but only a picture underlining some particularities. So, this mini-overview should be considered only a part of the collection of articles treating the nuclear physics, published as a special number in the review of the Academy of Romanian Scientists, without an exhaustive character. A theory treating the nuclear fission is by excellence based on quantum mechanics. That is, a theory concerning the interactions between the smallest pieces that constitute a many-body nucleus. But, at present it is not possible to perform ab-initio calculations to describe the many-body structure of heavy nuclei which undergo fission by starting from fundamental interactions. To make the problem tractable, the nucleus as a whole are constrained by some collective parameters, associated to some collective degree of freedom. The collective variables are forced to vary, leading to a scission of the nuclear system. The response of the nuclear system to the external forces is given by the nuclear inertia. The mean field potential between the nucleons is obtained after a proper average, and then used to solve the Schrodinger equation. The treatments presented in this article are based on these simplifying concepts. I will give some examples of calculations that include the dissipation and the configuration mixing due to radial and angular couplings. The importance of the subject is also briefly reviewed.

Time-dependent quantum wave packet dynamics to study charge transfer in heavy particle collisions.

The method of time-dependent quantum wave packet dynamics has been successfully extended to study the charge transfer/exchange process in low energy two-body heavy particle collisions. The collision process is described by coupled-channel equations with diabatic potentials and (radial and rotational) couplings. The time-dependent coupled equations are propagated with the multiconfiguration time-dependent Hartree method and the modulo squares of S-matrix is extracted from the wave packet by the flux operator with complex absorbing potential (FCAP) method. The calculations of the charge transfer process 12Σ+ H-(1s2)+Li(1s22s)→22Σ+/32Σ+/12Π H(1s)+Li-(1s22s2l)(l=s,p) at the incident energy of about [0.3, 1.3] eV are illustrated as an example. It shows that the calculated reaction probabilities by the present FCAP reproduce that of quantum-mechanical molecular-orbital close-coupling very well, including the peak structures contributed by the resonances. Since time-dependent external interactions can be directly included in the present FCAP calculations, the successful implementation of FCAP provides us a powerful potential tool to study the quantum control of heavy particle collisions by lasers in the near future.

Excitation and charge transfer in low-energy hydrogen-atom collisions with neutral atoms: Theory, comparisons, and application to Ca

A theoretical method for the estimation of cross sections and rates for excitation and charge transfer processes in low-energy hydrogen atom collisions with neutral atoms, based on an asymptotic two-electron model of ionic-covalent interactions in the neutral atom-hydrogen atom system, is presented. The calculation of potentials and non-adiabatic radial couplings using the method is demonstrated. The potentials are used together with the multi-channel Landau-Zener model to calculate cross sections and rate coefficients. The main feature of the method is that it employs asymptotically exact atomic wavefunctions, which can be determined from known atomic parameters. The method is applied to Li+H, Na+H, and Mg+H collisions, and the results compare well with existing detailed full-quantum calculations. The method is applied to the astrophysically important problem of Ca+H collisions, and rate coefficients are calculated for temperatures in the range 1000-20000 K.

Ab-initio molecular treatment of the symmetric Mg2+–Mg charge transfer process

Potential energy curves of the MgMg2+ molecular system in the lowest electronic states as well as radial and rotational couplings between these states are obtained from ab-initio calculations at the CASSCF/MRCI level of theory using large basis sets. These data are used to investigate, via the semi-classical molecular close coupling method, the single symmetric charge transfer processes of Mg2+–Mg collisions in the [1.0–650]keV laboratory energy range. Total and partial cross sections for the expected capture channels are calculated and compared with the available experimental and theoretical results.

Photodissociation of the carbon monoxide dication in the (3)Σ(-) manifold: Quantum control simulation towards the C(2+) + O channel.

The photodissociation and laser assisted dissociation of the carbon monoxide dication X(3)Π CO(2+) into the (3)Σ(-) states are investigated. Ab initio electronic structure calculations of the adiabatic potential energy curves, radial nonadiabatic couplings, and dipole moments for the X (3)Π state are performed for 13 excited (3)Σ(-) states of CO(2+). The photodissociation cross section, calculated by time-dependent methods, shows that the C(+) + O(+) channels dominate the process in the studied energy range. The carbon monoxide dication CO(2+) is an interesting candidate for control because it can be produced in a single, long lived, v = 0 vibrational state due to the instability of all the other excited vibrational states of the ground (3)Π electronic state. In a spectral range of about 25 eV, perpendicular transition dipoles couple this (3)Π state to a manifold of (3)Σ(-) excited states leading to numerous C(+) + O(+) channels and a single C(2+) + O channel. This unique channel is used as target for control calculations using local control theory. We illustrate the efficiency of this method in order to find a tailored electric field driving the photodissociation in a manifold of strongly interacting electronic states. The selected local pulses are then concatenated in a sequence inspired by the "laser distillation" strategy. Finally, the local pulse is compared with optimal control theory.

Characterization of the MgO2+dication in the gas phase: electronic states, spectroscopy and atmospheric implications

Franzreb and Williams at Arizona State University detected recently the MgO(2+) molecular species in the gas phase. Here we report a very detailed theoretical investigation of the low-lying electronic states of this dication including their potentials, spin-orbit, rotational and radial couplings. Our results show that the potential energy curves of the dicationic electronic states have deep potential wells. This confirms that this dication does exist in the gas phase; it is a thermodynamically stable molecule in its ground state, and it has several excited long-lived metastable states. The potential energy curves are used then to predict a set of spectroscopic parameters for the bound states of MgO(2+). We have also incorporated these potentials, rotational and radial couplings in dynamical calculations to derive the cross sections for the charge transfer Mg(2+) + O → Mg(+) + O(+) reaction in the 1-10(3) eV collision energy domain via formation-decomposition of the MgO(2+) dication. Our work shows the role of MgO(2+) in the Earth ionosphere and more generally in atmospheric processes in solar planets, where this reaction efficiently participates in the predominance of Mg(+) cations in these media compared to Mg and Mg(2+).

Ab Initio Cross Sections for Low-Energy Inelastic Mg+H Collisions

Full quantum scattering calculations of cross sections for low-energy near-threshold inelastic Mg + H collisions are reported, such processes being of interest for modelling of Mg spectral lines in stellar atmospheres. Nonadiabatic transions associated with radial couplings at avoided ionic crossings in the 2Σ+ molecular states are found to be the main mechanism for excitation and ion-pair production processes.

Potential energy curves crossing and low-energy charge transfer dynamics in (BeH2O)2+ complex

The singlet rigid Be—O dissociation potential energy curves correlating to the first four molecular limits of (BeH2O)2+ complex were calculated using the multi-reference single and double excitation configuration interaction theory. The radial couplings of three low-lying 1A1 states were calculated and combined with adiabatic potential energy curves to investigate and charge-transfer collision dynamics by using quantum-mechanical molecular orbital close-coupling methods. It is found that the total charge-transfer cross sections are dominated by the Be+(2S)+H2O+(A2A1) channel. The rate coefficients in the range of 10−17–10−12 cm3/s are very sensitive to temperature below 1000 K. The complexation energy without charge-transfer was determined to be 143.6 kcal/mol, including zero-point vibration energy corrections. This is in good agreement with the previous results.

Ab initio many-electron study for the low-lying states of the alkali hydride cations in the adiabatic representation

An ab initio multireference single- and double-excitation configuration interaction (CI) study is carried out for the ground and excited electronic states of alkali-hydride cations (LiH(+), NaH(+), KH(+), RbH(+), and CsH(+)). For all alkali-metal atoms, the first inner-shell and valence electrons (nine active electrons, three for Li) are considered explicitly in the ab initio self-consistent-field and CI calculations. The adiabatic potential energy curves, radial and rotational couplings are calculated and presented. Short-range (∼3 a.u.) potential wells produced by the excitation of the inner-shell electrons are found. The depths of the inner potential wells are much greater than those of the outer wells for the CsH(+) system. The computed spectroscopic constants for the long-range potential well of the 2 (2)Σ(+) state are very close to the available theoretical and experimental data. The electronic states of alkali-hydrogen cations are also compared with each other, it is found that the positions of the potential wells shift to larger internuclear distances gradually, and the depths of these potential wells become greater with increasing alkali-metal atomic number. The relationships between structures of the radial coupling matrix elements and the avoiding crossings of the potential curves are analyzed. From NaH(+) to CsH(+), radial coupling matrix elements display more and more complex structures due to the gradual decrease of energy separations for avoided crossings. Finally, the behavior of some rotational couplings is also shown.

Isotope effect in charge-transfer collisions of H with He+

We present a theoretical study of the isotope effect arising from the replacement of H by T in the charge-transfer collision H(n=2) + He{sup +}(1s) at low energy. Using a quasimolecular approach and a time-dependent wave-packet method, we compute the cross sections for the reaction including the effects of the nonadiabatic radial and rotational couplings. For H(2s) + He{sup +}(1s) collisions, we find a strong isotope effect at energies below 1 eV/amu for both singlet and triplet states. We find a much smaller isotopic dependence of the cross section for H(2p) + He{sup +}(1s) collisions in triplet states, and no isotope effect in singlet states. We explain the isotope effect on the basis of the potential energy curves and the nonadiabatic couplings, and we evaluate the importance of the isotope effect on the charge-transfer rate coefficients.

Inelastic Mg+H collision processes at low energies

Full quantum scattering calculations of cross sections for low-energy near-threshold inelastic Mg + H collisions are reported, such processes being of interest for modelling of Mg spectral lines in stellar atmospheres. The calculations are made for three transitions between the ground and two lowest excited Mg states, Mg(3s2 1S0), Mg(3s3p 3P) and Mg(3s3p 1P). The calculations are based on adiabatic potentials and nonadiabatic couplings for the three low-lying 2Σ+ and the first two 2Π states, calculated using large active spaces and basis sets. Non-adiabatic regions associated with radial couplings at avoided ionic crossings in the 2Σ+ molecular potentials are found to be the main mechanism for excitation. Cross sections of similar order of magnitude to those obtained in Li + H and Na + H collisions are found. This, together with the fact that the same mechanism is important, suggests that as has been found earlier for Li and Na, processes such as ion pair production may be important in astrophysical modelling of Mg, and motivates continued study of this system including all states up to and including the ionic limit.

Stabilization of ion temperature gradient driven instability by a vortex flow

Stabilization of ion temperature gradient (ITG) driven mode by a large-scale vortex flow is investigated using a gyrofluid model in slab geometry. Extending a recent work [Z. X. Wang et al., Phys. Rev. Lett. 103, 015004 (2009)], the focus in this work is put on the effect of magnetic shear. It is shown that the vortex flow can effectively stabilize the ITG mode by inducing both radial and poloidal mode couplings. Furthermore, decreasing magnetic shear is identified to weaken the stabilizing role of the vortex flow. The effects of the magnetic shear on the ITG mode structure and on the growth rate in the presence of various shear flows are obtained and the relevant mechanisms are discussed in detail.

Analytical Design of Permanent Magnet Radial Couplings

This paper presents a three-dimensional analytical approach for computing the torque transmitted by synchronous radial couplings with radially polarized tile permanent magnets. An expression is given as a finite sum of elliptic functions, which has no underlying simplificating assumptions. Such an expression allows parametric studies and optimizations of coupling structures. It is applied first to the study of conventional radial couplings. Then, structures with “short pitch” magnets are considered and compared with conventional ones. Eventually, special designs are presented, as the ones dedicated to screwing applications, for instance, which require creating an asymmetrical torque.

Isotope effects on the charge transfer into then=1, 2, and 3 shells ofHe2+in collisions with H, D, and T

Processes for charge transfer into ${\mathrm{He}}^{2+}$ colliding with the atomic isotopes hydrogen (H), deuterium (D), and tritium (T) are theoretically studied at collision energies as low as 30 eV/amu. Probabilities and cross sections for electron capture into different shells of the projectile are calculated using an ab initio approach which solves the time-dependent Schr\"odinger equation. The results are interpreted in terms of radial and rotational couplings between molecular orbitals. The probabilities exhibit strong Stueckelberg oscillations for charge transfer into shells with the principal quantum numbers $n=2$ and 3 due to radial coupling mechanisms in specific ranges of the impact parameter. The total cross sections for charge transfer, evaluated for a given shell, differ by orders of magnitude, as different isotopes are used in the collisions. The isotope effect increases significantly for decreasing $n=3$, 2, and 1. This finding is attributed to the influence of the rotational coupling mechanism, which is strongly affected by the distance of closest approach between the collision partners.

Ab initio calculation of the 66 low-lying electronic states of HeH+: adiabatic and diabatic representations

Using the quantum chemistry package MOLPRO and an adapted basis set, we have calculated the adiabatic potential energy curves of the first 20 1Σ+, 19 3Σ+, 12 1Π, 9 3Π, 4 1Δ and 2 3Δ electronic states of the HeH+ molecular ion in CASSCF and CI approaches. The results are compared with previous works. The radial and rotational non-adiabatic coupling matrix elements as well as the dipole moments are also calculated. The asymptotic behaviour of the potential energy curves and of the various couplings between the states is also studied. Using the radial couplings, the diabatic representation is defined and we present an example of our diabatization procedure on the 1Σ+ states.

Accurate potential energy functions and non-adiabatic couplings in the Mg+H system

Potential energy functions of the MgH molecule are investigated by the MRCI method using large active space and basis sets. The calculations are performed up to the Mg(3s3d, 1D) + H dissociation limit. The molecular constants compare well with the available data. The dipole moment functions exhibit a series of crossings due to the strong interactions between the states. Radial and rotational couplings among these states are also calculated, with a state-averaged MCSCF approach. This work will enable calculations of collisional cross sections and rate coefficients, important for the modelling of stellar spectra when collisions compete with radiative processes in non-LTE conditions. (C) 2010 Elsevier B. V. All rights reserved.

Nonadiabatic couplings in the collisional removal of O2(b Σ1g+,v) by O2

The effect of nonadiabatic couplings on the collisional removal of O(2)(b (1)Sigma(g) (+),v) by O(2)(X (3)Sigma(g) (-), v=0) is investigated. Two-dimensional adiabatic and quasidiabatic potential energy surfaces for the excited dimer states and the corresponding nonadiabatic radial couplings have been computed by means of ab initio calculations. Alternately, a two-state theoretical model, based on the Landau-Zener and Rosen-Zener-Demkov assumptions, has been employed to derive analytical forms for the nonadiabatic couplings and an adiabatic-to-diabatic transformation only depending on a reduced set of adiabatic energy terms. Compared to the ab initio results, the predictions of the model are found to be highly accurate. Quantum dynamics calculations for the removal of the first ten vibrational states of O(2)(b (1)Sigma(g) (+),v) indicate a clear dominant contribution of the vibration-electronic relaxation mechanism relative to the vibration-translation energy transfer. Although the present reduced-dimensionality model precludes any quantitative comparison with experiments, it is found that the removal probabilities for v=1-3 are qualitatively consistent with the experimental observations, once the vibrational structure of the fragments is corrected with spectroscopical terms. Besides, the model served to show how the computation of the adiabatic PESs just at the crossing seam was sufficient to describe the nonadiabatic dynamics related to a given geometrical arrangement. This implies considerable savings in the calculations which will eventually allow for larger accuracy in the ab initio calculations as well as higher dimensional treatments.

Photodissociation of theHeH+ion into excited fragments(n=2,3)by time-dependent methods

The total and partial photodissociation cross sections of the molecular ion ${\text{HeH}}^{+}$ are computed by time-dependent methods for fragmentation into the excited shells $n=1,2,3$ up to a photon energy of 40 eV. ${^{1}\ensuremath{\Sigma}}^{+}$ and $^{1}\ensuremath{\Pi}$ states are considered for parallel and perpendicular transitions for different initial rotational or vibrational excitations. Nonadiabatic radial and rotational couplings are taken into account. The results from coupled-channel equations are compared with the Born-Oppenheimer approximation. A time-dependent calculation with a femtosecond laser pulse is carried out to simulate a recent crossed beam photodissociation imaging experiment with vacuum ultraviolet free-electron laser [H. B. Pedersen et al., Phys. Rev. Lett. 98, 223202 (2007)]. The dominance of photodissociation perpendicular to the photon polarization is confirmed.