Acceleration of charged particles in the magnetosphere of a collapsing star and their nonthermal electromagnetic radiation

We investigate a transformation of a magnetic field and plasma in nonhomogeneous magnetospheres of collapsing stars with a dipole initial magnetic field and certain initial energy distributions of particles in the magnetosphere as the power low, relativistic Maxwell and Boltzmann. The betatron mechanism of the charged particles acceleration in a collapsing star’s magnetosphere is considered. When a magnetized star is compressed in the stage of the gravitational collapse, the magnetic field increases strongly. This variable magnetic field generates a vortical electric field. Our calculations show that this electric field will accelerate charged particles up to relativistic velocities. Thus, collapsing stars may be sources of high energy cosmic rays in our galaxy as in others. The acceleration of particles during the collapse happens mostly in polar regions of the magnetosphere that leads to polar relativistic streams (jets) formation. When moving in a magnetic field, these particles will generate nonthermal electromagnetic radiation in a broad electromagnetic wavelength band from radioto gamma rays. Thus, in the stage of the gravitational collapse, relativistic jets are formed in stellar magnetospheres. These jets are powerful sources of the nonthermal electromagnetic radiation.     

Stochastic Acceleration of Energetic Particles in the Magnetosphere of Saturn

Voyager's plasma probe observations suggest that there are at least three fundamentally different plasma regimes in Saturn: the hot outer magnetosphere, the extended plasma sheet, and the inner plasma torus. At the outer regions of the inner torus some ions have been accelerated to reach energies of the order of 43 keV. We develop a model that calculates the acceleration of charged particles in the Saturn's magnetosphere. We propose that the stochastic electric field associated to the observed magnetic field fluctuations is responsible of such acceleration. A random electric field is derived from the fluctuating magnetic field – via a Monte Carlo simulation – which then is applied to the momentum equation of charged particles seeded in the magnetosphere. Taking different initial conditions, like the source of charged particles and the distribution function of their velocities, we find that particles injected with very low energies ranging from 0.129 eV to 5.659 keV can be strongly accelerated to reach much higher energies ranging from 22.220 eV to 9.711 keV as a result of 125,000 hitting events (the latter are used in the numerical code to produce the particle acceleration over a predetermined distance).     

Numerical simulation of energetic electron microsignature drifts at Saturn: Methods and applications

Many recent studies show that energetic electron microsignatures are a powerful tool for characterizing key aspects of Saturn’s magnetospheric configuration and dynamics. In all previous investigations, however, analysis of these features was performed through the use of a series of simplifying assumptions (e.g. dipole field model). Furthermore, typical observable parameters of microsignatures (e.g. energy dependent location) have only been discussed qualitatively and a clear understanding about how microsignatures evolve in the magnetosphere is currently lacking. In this study we present a numerical simulation that we developed in order to describe the apparent motion of microsignatures in Saturn’s magnetosphere, under the influence of arbitrary magnetic and electric field models. Our simulations reproduce successfully some typical microsignature properties (energy–time dispersion, high/low lifetime at low/high electron energies). They also indicate how simplifying assumptions used in analytical methods introduce several systematic errors. We demonstrate that, depending on the application and under certain conditions these errors can be neglected, like for instance for small pitch angles and at regions that the dipole approximation is sufficient (inside the orbit of Dione) or for electron energies below few hundred keV. For higher electron energies, systematic errors amplify significantly and existing analytical methods cannot be used. Our model can reconstruct the energy dependent position of microsignatures observed by the MIMI/LEMMS detector with high accuracy, allowing the inference of non-corotational flows (or electric fields) that can be as low as few tens of m s⁻¹. Since, however the calculation of such flows is indirect, the accuracy of such a determination can be reduced by more than an order of magnitude, if some of these free parameters involved in the simulation cannot be sufficiently constrained. One way to provide such constraints is through inputs (e.g. instantaneous plasma moments) from various Cassini instruments and updated magnetospheric field models. In that case, microsignature analysis may prove to be one of the best methods for attempting to measure or to at least constrain the magnitude of the very slow and global plasma outflow in Saturn’s magnetosphere that is driven by mass loading at Enceladus.     

Ring torque on janus and the melting of Enceladus

Voyager 2 images show parts of Enceladus' surface to be very smooth, lacking craters down to the resolution limit of 4 km. This absence of craters indicates geologically recent resurfacing, probably due to internal melting. However, calculations of current heating mechanisms, including radioactive decay and tidal heating due to Enceladus' resonance with Dione, yield heating rates too small to cause melting. The orbital mean motion of Janus (1980S1) is slightly less than twice that of Enceladus and, according to theoretical calculations, is currently decreasing as Janus' orbit evolves outward due to resonant torques from Saturn's rings. If Janus were ever locked into a stable 2:1 orbital commensurability with Enceladus, the resulting angular momentum transfer could have sufficiently enhanced the eccentricity of Enceladus' orbit for the ensuing tidal heating to have melted Enceladus' interior. The existence of a Laplace-like three-body resonance including Dione, although unlikely, would have increased heating. If Janus were indeed held in resonance with Enceladus until recently (10⁷–10⁸ years B.P.) when the lock was disrupted by an unspecified event (possibly a catastrophic collision which simultaneously created the coorbital pair, or by the influence of Dione) both the recent internal activity of Enceladus and the proximity of Janus to Saturn's rings may be explained. However, the predicted rapid time scale for ring evolution due to resonant torques from Saturn's inner moons remains a major problem.     

Electric fields within the martian magnetosphere and ion extraction: ASPERA-3 observations

Observations made by the ASPERA-3 experiment onboard the Mars Express spacecraft found within the martian magnetosphere beams of planetary ions. In the energy (E/q)-time spectrograms these beams are often displayed as dispersive-like, ascending or descending (whether the spacecraft moves away or approach the planet) structures. A linear dependence between energy gained by the beam ions and the altitude from the planet suggests their acceleration in the electric field. The values of the electric field evaluated from ion energization occur close to the typical values of the interplanetary motional electric field. This suggests an effective penetration of the solar wind electric field deep into the martian magnetosphere or generation of large fields within the magnetosphere. Two different classes of events are found. At the nominal solar wind conditions, a ‘penetration’ occurs near the terminator. At the extreme solar wind conditions, the boundary of the induced magnetosphere moves to a more dense upper atmosphere that leads to a strong scavenging of planetary ions from the dayside regions.     

Dynamics of electrons and heavy ions in Mercury's magnetosphere

Several basic magnetospheric processes at Mercury have been investigated with simple models. These include the adiabatic acceleration and convection of equatorially mirroring charged particles, the current sheet acceleration effect, and the acceleration of Na⁺ and other exospheric ions by the magnetospheric electric and magnetic fields near the planetary surface. The current steady-state treatment of the magnetospheric drift and convection processes suggests that the region of the inner magnetosphere as explored by the Mariner 10 spacecraft during its encounter with Mercury should be largely devoid of energetic (>100 keV) electrons in equatorial mirroring motion. As for ion motion, the large gyroradii of the heavy ions permit surface reimpact as well as loss via intercepting the magnetopause. Because of the kinetic energy gained in the gyromotion, the first effect could lead to sputtering processes and hence generation of secondary ions and neutrals. The second effect could account for the loss of about 50% of Mercury's exospheric ions.     

Acceleration of energetic particles of the outer regions of planetary magnetospheres: Inferences from laboratory and space experiments

High energy particles, with energies above those attainable by adiabatic or steady-state electric field acceleration, have been observed in and around the outer regions of planetary magnetospheres. Acceleration by large amplitude sporadic cross-tail electric fields over an order of magnitude greater than steady-state convection fields is proposed as a source of these particles. It is suggested that such explosive electric fields will occur intermittently in the vicinity of the tail neutral line in the expansive phases of substorms. We use laboratory Double Inverse Pinch Device (DIPD) and satellite evidence to estimate this electric potential for substorms at Earth; values of 500 kV to 2 MV are calculated, in agreement with particle observations. It is further suggested that these particles, which have been accelerated in the night side magnetosphere, drift to the dayside on closed field lines, and under certain interplanetary conditions can escape to regions upstream of the bow shock.     

Ionospheric plasma acceleration at Mars: ASPERA-3 results

The Analyzer of Space Plasma and Energetic Atoms (ASPERA) on-board the Mars Express spacecraft (MEX) measured penetrating solar wind plasma and escaping/accelerated ionospheric plasma at very low altitudes (250 km) in the dayside subsolar region. This implies a direct exposure of the martian topside atmosphere to solar wind plasma forcing leading to energization of ionospheric plasma. The ion and electron energization and the ion outflow from Mars is surprisingly similar to that over the magnetized Earth. Narrow “monoenergetic” cold ion beams, ion beams with broad energy distributions, sharply peaked electron energy spectra, and bidirectional streaming electrons are particle features also observed near Mars. Energized martian ionospheric ions (O⁺, O⁺₂, CO⁺₂, etc.) flow in essentially the same direction as the external sheath flow. This suggests that the planetary ion energization couples directly to processes in the magnetosheath/solar wind. On the other hand, the beam-like distribution of the energized plasma implies more indirect energization processes like those near the Earth, i.e., energization in a magnetized environment by waves and/or parallel (to B) electric fields. The general conditions for martian plasma energization are, however, different from those in the Earth's magnetosphere. Mars has a weak intrinsic magnetic field and solar wind plasma may therefore penetrate deep into the dense ionospheric plasma. Local crustal magnetization, discovered by Acuña et al. [Acuña, M.J., Connerey, J., Ness, N., Lin, R., Mitchell, D., Carlsson, C., McFadden, J., Anderson, K., Rème, H., Mazelle, C., Vignes, D., Wasilewski, P., Cloutier, P., 1999. Science 284, 790-793], provide some dayside shielding against the solar wind. On the other hand, multiple magnetic anomalies may also lead to “hot spots” facilitating ionospheric plasma energization. We discuss the ASPERA-3 findings of martian ionospheric ion energization and present evidences for two types of plasma energization processes responsible for the low- and mid-altitude plasma energization near Mars: magnetic field-aligned acceleration by parallel electric fields and plasma energization by low frequency waves.     

Electron transport and precipitation at Mercury during the MESSENGER flybys: Implications for electron-stimulated desorption

To examine electron transport, energization, and precipitation in Mercury's magnetosphere, a hybrid simulation study has been carried out that follows electron trajectories within the global magnetospheric electric and magnetic field configuration of Mercury. We report analysis for two solar-wind parameter conditions corresponding to the first two MESSENGER Mercury flybys on January 14, 2008, and October 6, 2008, which occurred for similar solar wind speed and density but contrasting interplanetary magnetic field (IMF) directions. During the first flyby the IMF had a northward component, while during the second flyby the IMF was southward. Electron trajectories are traced in the fields of global hybrid simulations for the two flybys. Some solar wind electrons follow complex trajectories at or near where dayside reconnection occurs and enter the magnetosphere at these locations. The entry locations depend on the IMF orientation (north or south). As the electrons move through the entry regions they can be energized as they execute non-adiabatic (demagnetized) motion. Some electrons become magnetically trapped and drift around the planet with energies on the order of 1–10 keV. The highest energy of electrons anywhere in the magnetosphere is about 25 keV, consistent with the absence of high-energy (>35 keV) electrons observed during either MESSENGER flyby. Once within the magnetosphere, a fraction of the electrons precipitates at the planetary surface with fluxes on the order of 10⁹ cm⁻² s⁻¹ and with energies of hundreds of eV. This finding has important implications for the viability of electron-stimulated desorption (ESD) as a mechanism for contributing to the formation of the exosphere and heavy ion cloud around Mercury. From laboratory estimates of ESD ion yields, a calculated ion production rate due to ESD at Mercury is found to be on par with ion sputtering yields.     

Kronos: exploring the depths of Saturn with probes and remote sensing through an international mission

Kronos is a mission aimed to measure in situ the chemical and isotopic compositions of the Saturnian atmosphere with two probes and also by remote sensing, in order to understand the origin, formation, and evolution of giant planets in general, including extrasolar planets. The abundances of noble gases, hydrogen, carbon, nitrogen, oxygen, sulfur and their compounds, as well as of the D/H, ⁴He/³He, ²²Ne/²¹Ne/²⁰Ne, ³⁶Ar/³⁸Ar, ¹³C/¹²C, ¹⁵N/¹⁴N, ¹⁸O/(¹⁷O)/¹⁶O, ¹³⁶Xe/¹³⁴Xe/¹³²Xe/¹³⁰Xe/¹²⁹Xe isotopic ratios will be measured by mass spectrometry on two probes entering the atmosphere of Saturn at two different locations near mid-latitudes, down to a pressure of 10 Bar. The global composition of Saturn will be investigated through these measurements, together with microwave radiometry determination of H₂O and NH₃ and their 3D variations. The dynamics of Saturn’s atmosphere will be investigated from: (1) measurements of pressure, temperature, vertical distribution of clouds and wind speed along the probes’ descent trajectories, and (2) determination of deep winds, differential rotation and convection with combined probe, gravity and radiometric measurements. Besides these primary goals, Kronos will also measure the intensities and characteristics of Saturn’s magnetic field inside the D ring as well as Saturn’s gravitational field, in order to constrain the abundance of heavy elements in Saturn’s interior and in its central core. Depending on the preferred architecture (flyby versus orbiter), Kronos will be in a position to measure the properties of Saturn’s innermost magnetosphere and to investigate the ring structure in order to understand how these tiny structures could have formed and survived up to the present times. An erratum to this article can be found at     

Electron-positron plasma generation in a magnetar magnetosphere

We consider the electron—positron plasma generation processes in the magnetospheres of magnetars—neutron stars with strong surface magnetic fields, B ? 10¹⁴–10¹⁵ G. We show that the photon splitting in a magnetic field, which is effective at large field strengths, does not lead to the suppression of plasma multiplication, but manifests itself in a high polarization of γ-ray photons. A high magnetic field strength does not give rise to the second generation of particles produced by synchrotron photons. However, the density of the first-generation particles produced by curvature photons in the magnetospheres of magnetars can exceed the density of the same particles in the magnetospheres of ordinary radio pulsars. The plasma generation inefficiency can be attributed only to slow magnetar rotation, which causes the energy range of the produced particles to narrow. We have found a boundary in the \(P - \dot P\) diagram that defines the plasma generation threshold in a magnetar magnetosphere.     

Magnetar corona

Persistent high-energy emission of magnetars is produced by a plasma corona around the neutron star, with total energy output of ～10³⁶ erg/s. The corona forms as a result of sporadic starquakes that twist the external magnetic field of the star and induce electric currents in the closed magnetosphere. Once twisted, the magnetosphere cannot untwist immediately because of its self-induction. The self-induction electric field lifts particles from the stellar surface, accelerates them, and initiates avalanches of pair creation in the magnetosphere. The created plasma corona maintains the electric current demanded by curl B and regulates the self-induction e.m.f. by screening. This corona persists in dynamic equilibrium: it is continually lost to the stellar surface on the light-crossing time ～10^?4 s and replenished with new particles. In essence, the twisted magnetosphere acts as an accelerator that converts the toroidal field energy to particle kinetic energy. The voltage along the magnetic field lines is maintained near threshold for ignition of pair production, in the regime of self-organized criticality. The voltage is found to be about ～1 GeV which is in agreement with the observed dissipation rate ～10³⁶ erg/s. The coronal particles impact the solid crust, knock out protons, and regulate the column density of the hydrostatic atmosphere of the star. The transition layer between the atmosphere and the corona is the likely source of the observed 100 keV emission. The corona also emits curvature radiation up to 10¹⁴ Hz and can supply the observed IR-optical luminosity.     

Energy and pitch angle distributions for auroral ions using the current sheet acceleration model

Using a dipole plus tail magnetic field model, H⁺, He⁺⁺ and O ₁₆ ⁺⁶ ions are followed numerically, backward in time, from an output plane perpendicular to the axis of the geomagnetic tail, to their point of entrace to the magnetosphere as solar wind particles in the magnetosheath. An adiabatic or guiding center approximation is used in regions where the particles do not interact directly with the current sheet. A Maxwellian distribution with bulk flow is assumed for solar wind particles in the magnetosheath. Bulk velocity, density, and temperature along the magnetopause are taken from the fluid calculations of Spreiter. Using Liouville's theorem, and varying initial conditions at the output plane, the distribution function is found as a function of energy and pitch angle at the output plane. These results are then mapped to the auroral ionosphere using guiding center theory. Results show that the total precipitation rate is sufficient only for particles which enter the magnetosphere near the edges of the current sheet. Small pitch angles are favored at the output plane, but mappings to the auroral ionosphere indicate isotropic pitch angle distributions are favored with some peaking of the fluxes parallel or at other angles to the field lines. Perpendicular auroral pitch angle anisotropies are at times produced by the current sheet acceleration mechanism. Therefore, caution must be used in interpreting all such observations as ‘loss cone-trapping’ distributions. Energy spectra appear to be quite narrow for small cross-tail electric fields, and a little broader as the electric field increases. Comparisons of these results with experimental observations are presented.     

Tidal dissipation,orbital evolution,and the nature of Saturn's inner satellites

Estimates of tidal damping times of the orbital eccentricities of Saturn's inner satellites place constraints on some satellite rigidities and dissipation functions Q. These constraints favor rock-like rather than ice-like properties for Mimas and probably Dione. Photometric and other observational data are consistent with relatively higher densities for these two satellites, but require lower densities for Tethys, Enceladus, and Rhea. This leads to a nonmonotonic density distribution for Saturn's inner satellites, apparently determined by different mass fractions of rocky materials. In spite of the consequences of tidal dissipation for the orbital eccentricity decay and implications for satellite compositions, tidal heating is not an important contributor to the thermal history of any Saturnian satellite.     

The long term stability of coorbital moons of the satellites of Saturn: I. Conservative case

The aim of this work is to understand the absence of objects along the orbits of Mimas and Enceladus in contrast to their presence at the orbits of neighbouring Tethys and Dione from the point of view of dynamical stability. Large scale numerical simulations of 360 test particles within the coorbital regions of these four saturnian satellites were carried out for 4×¹⁰⁵ yr or 1.6×¹⁰⁸ revolutions of the innermost moon Mimas. The tidal forcing of the satellites' orbits was not taken into account in these simulations. We have quantitatively reproduced the Mimas-Tethys 4:2 and Enceladus-Dione 2:1 mean motion resonances in the system and devised a scheme by which the parameter space of the coorbital resonance is sampled uniformly by our test particles. We observe that 6 out of the 36 integrated horseshoe particles of Enceladus escaped the coorbital region. All 54 tadpole particles remained stable. The main cause of instability for Enceladus coorbitals appears to be the overlap between the coorbital resonance and the 2:1 mean motion resonance between the particle and Dione. This leads particles with starting semimajor axes near the horseshoe-tadpole separatrix to be ejected from the resonance, as proposed by Morais [Morais, M.H.M., 2000. The effect of secular perturbations and mean motion resonances on trojan dynamics. Ph.D. thesis, Univ. of London], over timescales of ∼8×¹⁰⁷ revolutions of Enceladus. For Mimas we observe a larger number of coorbital escapes overall, both of tadpole (7/54) and horseshoe (29/36) librators. An analysis of the observed dynamical evolution suggests a two-stage process at work: The semimajor axis of particles with starting conditions near the horseshoe-tadpole separatrix undergoes a slow random walk over timescales of ¹⁰⁵ yr through a mechanism similar to that at Enceladus but involving the 4:2 inclination resonance with Tethys. These particles are eventually injected into a region of short-term (?¹⁰⁴ yr) instability just inside the nominal boundary of stable, symmetric horseshoe motion. The presence of the 4:2 eccentricity triplet at that location is the most likely culprit for the instability. In both the cases of Mimas and Enceladus small-amplitude tadpoles remain stable until the end of the integration. The existence of fast escapers at Mimas provides a dynamical avenue for the short-term survival of impact ejecta in horseshoe orbits within Mimas' coorbital region.     

Energetic particles in space

Particles ranging in energy from just above solar wind, 1 keV, to galactic cosmic rays of many GeV or greater are observed to be always present in the interplanetary medium. These suprathermal particles appear to come from many different sources: among them the galaxy and nearby interstellar medium, the Sun, planetary magnetospheres and bow shock waves. Recent studies have shown that the interplanetary medium itself is a major source of low energy, 10² MeV ions, particularly during solar quiet times. Although the physical mechanisms by which various suprathermal particle populations are produced are not well understood, it appears that collisionless shock waves are often involved in the acceleration of these particles. Here we review previous observations of these suprathermal particles and present some preliminary new observations of low energy, <10² keV particles from experiments aboard the ISEE-1, 2, and 3 spacecraft.Review talk given at the meeting of Commission 10 of the International Astronomical Union General Assembly, Montreal, Canada, August 15, 1979.     

About Hypothesis of the Superconducting Origin of the Saturn’s Rings

Hypothesis of possible superconductivity of the iced matter of the rings of Saturn (based on the data of Voyager and Pioneer space missions) allow us to explain many phenomena which have not been adequately understood earlier. Introducing into planetary physics force of magnetic levitation of the superconducting iced particle of the rings, which interact with magnetosphere of the planet, becomes to be possible to explain origin, evolution, and dynamics of the rings; to show how the consequent precipitation of the rings’ matter upon the planet was concluded; how the rings began their rotation; how they were compressed by the magnetic field into the thin disc, and how this disc was fractured into hundreds of thousands of separated rings; why in the ring B do exist “spokes”; why magnetic field lines have distortion near by ring F; why there is a variable azimuth brightness of the ring A; why the rings reflected radio waves so efficiently; why exists strong electromagnetic radiation of the rings in the 20.4 kHz–40.2 MHz range and Saturnian kilometric radiation; why there is anomalous reflection of circularly polarized microwaves; why there are spectral anomalies of the thermal radiation of the rings; why the matter of the various rings does not mix but preserves its small-scale color differences; why there is an atmosphere of unknown origin nearby the rings of Saturn; why there are waves of density and bending waves within Saturn’s rings; why planetary rings in the solar system appear only after the Belt of Asteroids (and may be the Belt of Asteroids itself is a ring for the Sun); why our planet Earth has no rings of its own.     

On the thermal history of Saturn’s satellites Titan and Enceladus

The thermal histories of two geologically active satellites of Saturn—Titan and Enceladus—are discussed. During the Cassini mission, it was found that there are both nitrogen-containing compounds—NH₃ and N₂-and CO₂ and CH₄ in the water plumes of Enceladus; at that, ammonia is the prevailing form. This may testify that during evolution, the material of the satellite was warmed up to T ∼ 500–600 K, when NH₃ (the form of nitrogen capable of being accreted) could only be partly converted into N₂. Contrary to Enceladus, the temperature inside Titan probably reached values higher than 800 K or even higher than 1000 K, since the process of the chemical dissociation of ammonia was completely finished on this satellite and its atmosphere contains only molecular nitrogen. While the internal heating of Titan up to high temperatures can be explained by its large mass, the heating source for Enceladus’ interior is far from evident. Such traditional heating sources as the energy of gravitational differentiation and the radiogenic heating due to shortliving ²⁶Al and ⁶⁰Fe could not be effective. The first one is because of the small size of Enceladus (RE ≈ 250 km), and the inefficiency of the second one is caused by the fact that the satellite was formed not earlier than 8–10 Myr after the formation of calcium and aluminum-enriched inclusions in carbonaceous chondrites (CAI), i.e., after ²⁶Al had completely decayed. In the present paper, we propose other heating mechanisms-the heat of long-living radioactive elements and tidal heat, which could provide the observed chemical composition of the water plumes of Enceladus rather than only the differentiation of its protomatter into the ironstone core and the ice mantle.     

Problems related to macroscopic electric fields in the magnetosphere

The macroscopic electric fields in the magnetosphere originate from internal as well as external sources. The fields are intimately coupled with the dynamics of magnetospheric plasma convection. They also depend on the complicated electrical properties of the hot, collisionless plasma. Macroscopic electric fields are responsible for some important kinds of energization of charged particles that take place in the magnetosphere and affect not only particles of auroral energy but also, by multistep processes, trapped high-energy particles.A particularly interesting feature of magnetospheric electric fields is the fact that they can have substantial components along the geomagnetic field. Several physical mechanisms have been identified by which such electric fields can be supported even when collisions between particles are negligible. Comments are made on the magnetic-mirror effect, anomalous resistivity, collisionless thermoelectric effect and electric double layers, emphasizing key features and differences and their significance in the light of recent observational data.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978.Reprinted, with due permission fromRev. Geophys. Space Phys. 15, (1977), 457     

A fast tour design method using non-tangent v-infinity leveraging transfer

The announced missions to the Saturn and Jupiter systems renewed the space community interest in simple design methods for gravity assist tours at planetary moons. A key element in such trajectories are the V-Infinity Leveraging Transfers (VILT) which link simple impulsive maneuvers with two consecutive gravity assists at the same moon. VILTs typically include a tangent impulsive maneuver close to an apse location, yielding to a desired change in the excess velocity relative to the moon. In this paper we study the VILT solution space and derive a linear approximation which greatly simplifies the computation of the transfers, and is amenable to broad global searches. Using this approximation, Tisserand graphs, and heuristic optimization procedure we introduce a fast design method for multiple-VILT tours. We use this method to design a trajectory from a highly eccentric orbit around Saturn to a 200-km science orbit at Enceladus. The trajectory is then recomputed removing the linear approximation, showing a Δv change of <4%. The trajectory is 2.7 years long and comprises 52 gravity assists at Titan, Rhea, Dione, Tethys, and Enceladus, and several deterministic maneuvers. Total Δv is only 445 m/s, including the Enceladus orbit insertion, almost 10 times better then the 3.9 km/s of the Enceladus orbit insertion from the Titan–Enceladus Hohmann transfer. The new method and demonstrated results enable a new class of missions that tour and ultimately orbit small mass moons. Such missions were previously considered infeasible due to flight time and Δv constraints.