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We investigate the beaming of 11 Io-Jupiter decametric (Io-DAM) emissions observed by Juno/Waves, the Nan\c cay Decameter Array and NenuFAR. Using an up-to-date magnetic field model and three methods to position the active Io Flux Tube (IFT), we accurately locate the radiosources and determine their emission angle $\theta$ from the local magnetic field vector. These methods use (i) updated models of the IFT equatorial lead angle, (ii) ultraviolet (UV) images of Jupiter's aurorae and (iii) multi-point radio measurements. The kinetic energy $E_{e-}$ of source electrons is then inferred from $\theta$ in the framework of the Cyclotron Maser Instability. The precise position of the active IFT achieved from methods (ii,iii) can be used to test the effective torus plasma density. Simultaneous radio/UV observations reveal that multiple Io-DAM arcs are associated with multiple UV spots and provide the first direct evidence of an Io-DAM arc associated with a trans-hemispheric beam UV spot. Multi-point radio observations probe the Io-DAM sources at various altitudes, times and hemispheres. Overall, $\theta$ varies a function of frequency (altitude), by decreasing from $75^\circ-80^\circ$ to $70^\circ-75^\circ$ over $10-40$ MHz with slightly larger values in the northern hemisphere, and independently varies as a function of time (or longitude of Io). Its uncertainty of a few degrees is dominated by the error on the longitude of the active IFT. The inferred values of $E_{e-}$ also vary as a function of altitude and time. For the 11 investigated cases, they range from 3 to 16 keV, with a $6.6\pm2.7$ keV average.

On 6 Sept. 2017, an exceptional coronal mass ejection departed from the Sun toward the Earth and Uranus, whose magnetospheres are sensitive to the solar wind. The resulting interplanetary shock triggered geomagnetic storm and intense aurora at Earth the next day and was predicted by MHD models to reach Uranus around 10-11 Nov. This event provided a unique opportunity to investigate the auroral response of the asymmetric Uranian magnetosphere in its intermediate equinox-to-solstice configuration. Coordinated multi-spectral observations were acquired with the Hubble Space Telescope (HST) in the far-UV (FUV), with the Very Large Telescope (VLT) and Gemini North in the near-IR (NIR) and with Chandra in the X-ray domain. In this study, we focus on the analysis of NIR images obtained between 9 and 17 Nov. 2017 which are compared to one FUV image acquired on 11 Nov. The latter reveals a bright southern auroral spot in the H2 bands, which we use as a reference to locate auroral precipitations. The NIR images were aimed at mapping H3+ emission from the Uranian ionosphere and at updating the results built from a couple of pioneer images taken 25 years ago. These new high resolution images reveal H3+ from the whole disc although brighter near the southern pole, but show no evidence of localized auroral emission.

Throughout 2017, the Hubble Space Telescope (HST) observed the northern far-ultraviolet aurorae of Saturn at northern solstice, during the Cassini Grand Finale. These conditions provided a complete viewing of the northern auroral region from Earth and a maximal solar illumination, expected to maximize the ionosphere-magnetosphere coupling. In this study, we analyze 24 HST images concurrently with Cassini measurements of Saturn's Kilometric Radiation and solar wind parameters predicted by two MHD models. The aurorae reveal highly variable components, down to timescales of minutes, radiating 7 to 124 +/-11 GW. They include a nightside-shifted main oval, unexpectedly frequent and bright cusp emissions and a dayside low latitude oval. On average, these emissions display a strong Local Time dependence with two maxima at dawn and pre-midnight, the latter being newly observed and attributed to nightside injections possibly associated with solstice conditions. These results provide a reference frame to analyze Cassini in situ measurements, whether simultaneous or not.

The aurorae of Uranus were recently detected in the far ultraviolet with the Hubble Space Telescope (HST) providing a new, so far unique, means to remotely study the asymmetric Uranian magnetosphere from Earth. We analyze here two new HST Uranus campaigns executed in Sept. 2012 and Nov. 2014 with different temporal coverage and under variable solar wind conditions numerically predicted by three different MHD codes. Overall, HST images taken with the Space Telescope Imaging Spectrograph reveal auroral emissions in three pairs of successive images (one pair acquired in 2012 and two in 2014), hence six additional auroral detections in total, including the most intense Uranian aurorae ever seen with HST. The detected emissions occur close the expected arrival of interplanetary shocks. They appear as extended spots at southern latitudes, rotating with the planet. They radiate 5-24 kR and 1.3-8.8 GW of ultraviolet emission from H$_2$, last for tens of minutes and vary on timescales down to a few seconds. Fitting the 2014 observations with model auroral ovals constrains the longitude of the southern (northern) magnetic pole to 104+\-26{\deg} (284-\-26{\deg}) in the Uranian Longitude System. We suggest that the Uranian near-equinoctial aurorae are pulsed cusp emissions possibly triggered by large-scale magnetospheric compressions., Comment: 10 pages, 5 Figures

Ultraviolet (UV) planetary astronomy is a unique tool to probe planetary environments of the solar system and beyond. But despite a rising interest for new generation giant UV telescopes regularly proposed to international agencies, none has been selected yet, leaving the Hubble Space Telescope (HST) as the most powerful UV observatory in activity. HST regularly observed the auroral emissions of the Jupiter, Saturn and Uranus systems, leading to significant discoveries and achievements. This rich legacy remains of high interest for further statistical and long-term studies, but new observations are necessary to comparatively tackle pending questions, under varying solar or seasonal cycles., Comment: White paper submitted in response to the HST 2020 vision call

From the 27th to the 28th January 2009, the Cassini spacecraft remotely acquired combined observations of Saturns southern aurorae at radio, ultraviolet and infrared wavelengths, while monitoring ion injections in the middle magnetosphere from energetic neutral atoms. Simultaneous measurements included the sampling of a full planetary rotation, a relevant timescale to investigate auroral emissions driven by processes internal to the magnetosphere. In addition, this interval coincidently matched a powerful substorm-like event in the magnetotail, which induced an overall dawnside intensification of the magnetospheric and auroral activity. We comparatively analyze this unique set of measurements to reach a comprehensive view of kronian auroral processes over the investigated timescale. We identify three source regions in atmospheric aurorae, including a main oval associated with the bulk of Saturn Kilometric Radiation (SKR), together with polar and equatorward emissions. These observations reveal the co-existence of corotational and sub-corototational dynamics of emissions associated with the main auroral oval. Precisely, we show that the atmospheric main oval hosts short-lived sub-corotating isolated features together with a bright, longitudinally extended, corotating region locked at the southern SKR phase. We assign the susbtorm-like event to a regular, internally driven, nightside ion injection possibly triggerred by a plasmoid ejection. We also investigate the total auroral energy budget, from the power input to the atmosphere, characterized by precipitating electrons up to 20 keV, to its dissipation through the various radiating processes. Finally, through simulations, we confirm the search-light nature of the SKR rotational modulation and we show that SKR arcs relate to isolated auroral spots. The resulting findings are discussed in the frame of pending questions.

We discuss several problems in quasiclassical physics for which approximate solutions were recently obtained by a new method, and which can also be solved by novel versions of the Born-Oppenheimer approximation. These cases include the so-called bouncing ball modes, low angular momentum states in perturbed circular billiards, resonant states in perturbed rectangular billiards, and whispering gallery modes. Some rare, special eigenstates, concentrated close to the edge or along a diagonal of a nearly rectangular billiard are found. This kind of state has apparently previously escaped notice., Comment: 9 pages, 7 eps figures

Special quantum states exist which are quasiclassical quantizations of regions of phase space that are weakly chaotic. In a weakly chaotic region, the orbits are quite regular and remain in the region for some time before escaping and manifesting possible chaotic behavior. Such phase space regions are characterized as being close to periodic orbits of an integrable reference system. The states are often rather striking, and can be concentrated in spatial regions. This leads to possible phenomena. We review some methods we have introduced to characterize such regions and find analytic formulas for the special states and their energies., Comment: 9 pages, 8 eps figures

Eigenstates and energy levels of a square quantum billiard in a magnetic field, or with an Aharonov-Bohm flux line, are found in quasiclassical approximation, that is, for high enough energy. Explicit formulas for the energy levels and wavefunctions are found. A number of interesting states are shown, together with their wavefunctions. Some states are diamagnetic, others paramagnetic, still others both dia- and paramagnetic. Some states are strongly localized. Related systems and possible experiments are briefly mentioned., Comment: 15 pages, 14 eps figures; added the following comment about the availability of figures: the higher quality figures are available in postscript from the authors at ozaitsev@physics.umd.edu

Eigenstates and energy levels of a square quantum billiard in a magnetic field, or with an Aharonov-Bohm flux line, are found in quasiclassical approximation, that is, for high enough energy. Explicit formulas for the energy levels and wavefunctions are found. There are localized states, never before noticed in this well studied problem, whose localization is due to phase interference, even though there is no or negligible classical effect of the magnetic field. These and related states account almost entirely for the magnetic response in certain temperature ranges, and thus have a bearing on the experiments of Levy et al., Comment: 5 pages, 3 figures

The trace formulas commonly used in discussing spectral properties of quantum or wave systems are derived simply and directly from the Bogomolny transfer operator. Special cases are the Gutzwiller formula, the Berry-Tabor formula, and the perturbed Berry-Tabor formula. A comment is made about interpolation formulas proposed in the latter case., Comment: 6 pages, 3 eps figures

Perturbation theory, the quasiclassical approximation and the quantum surface of section method are combined for the first time. This gives a new solution of the the long standing problem of quantizing the resonances generically appearing in classical perturbation theory. Our method is restricted to two dimensions. In that case, however, the results are simpler, more explicit and more easily expressed visually than the results of earlier techniques. The method involves expanding the `phase' of the wavefunction in powers of the square root of the small parameter. It gives explicit WKB-like wavefunctions and energies even for certain systems which classically show hard chaos., Comment: 19 pages, LaTeX, 10 figures, 2 tables

The spectral form factor, k(t), is the Fourier transform of the two level correlation function C(x), which is the averaged probability for finding two energy levels spaced x mean level spacings apart. The average is over a piece of the spectrum of width W in the neighborhood of energy E0. An additional ensemble average is traditionally carried out, as in random matrix theory. Recently a theoretical calculation of k(t) for a single system, with an energy average only, found interesting nonuniversal semiclassical effects at times t approximately unity in units of {Planck's constant) /(mean level spacing). This is of great interest if k(t) is self-averaging, i.e, if the properties of a typical member of the ensemble are the same as the ensemble average properties. We here argue that this is not always the case, and that for many important systems an ensemble average is essential to see detailed properties of k(t). In other systems, notably the Riemann zeta function, it is likely possible to see the properties by an analysis of the spectrum., Comment: 4 pages, RevTex, no figures, submitted to Phys. Rev. Lett., permanent e-mail address, prange@quantum.umd.edu

We directly combine ideas of the quasiclassical approximation with random matrix theory and apply them to the study of the spectrum, in particular to the two-level correlator. Bogomolny's transfer operator T, quasiclassically an NxN unitary matrix, is considered to be a random matrix. Rather than rejecting all knowledge of the system, except for its symmetry, [as with Dyson's circular unitary ensemble], we choose an ensemble which incorporates the knowledge of the shortest periodic orbits, the prime quasiclassical information bearing on the spectrum. The results largely agree with expectations but contain novel features differing from other recent theories., Comment: 4 pages, RevTex, submitted to Phys. Rev. Lett., permanent e-mail prange@quantum.umd.edu