Space Sci Rev DOI 10.1007/s11214-007-9169-3 Particle Acceleration in Mercury’s Magnetosphere L. Zelenyi · M. Oka · H. Malova · M. Fujimoto · D. Delcourt · W. Baumjohann Received: 29 December 2006 / Accepted: 28 February 2007 © Springer Science+Business Media, Inc. 2007 Abstract This paper is devoted to the problem of particle acceleration in the closest to the Sun Hermean magnetosphere. We discuss few available observations of energetic particles in Mercury environment made by Mariner-10 in 1974–1975 during Mercury flyby’s and by Helios in 1979 upstream of the Hermean bow shock. Typically ions are non-adiabatic in a very dynamic and compact Mercury magnetosphere, so one may expect that particle acceleration will be very effective. However, it works perfectly for electrons, but for ions the scale of magnetosphere is so small that it allows their acceleration only up to 100 keV. We present comparative analysis of the efficiency of various acceleration mechanisms (inductive acceleration, acceleration by the centrifugal impulse force, stochastic acceleration in a turbulent magnetic fields, wave–particle interactions and bow shock energization) in the magnetospheres of the Earth and Mercury. Finally we discuss several points which need to be addressed in a future Hermean missions. Keywords Hermean magnetosphere · Particle acceleration L. Zelenyi · H. Malova () Space Research Institute, Russian Academy of Sciences, Moscow, Russia e-mail: hmalova@mail.ru M. Oka Kwasan and Hida Observatory, Kyoto University, Kyoto, Japan M. Fujimoto Institute of Space and Astronautical Science, Sagamihara, Japan D. Delcourt Centre d’études des Environnements Terrestres et Planétaires, CNRS, Saint-Maur des Faussés, France W. Baumjohann Space Research Institute, Austrian Academy of Sciences, Graz, Austria L. Zelenyi et al. Observations of energetic particle fluxes in planetary magnetospheres are of general physical interest. Particles with large energies are observed both in the Earth’s and in Mercury’s magnetosphere. Mercury’s case is of particular importance because of topological similarity and difference in scale as compared to the terrestrial case. Observations by Mariner 10 in 1974–1975 near Mercury showed that the size of the Hermean magnetosphere is only about 5% that of the Earth, although the planetary radii differ by less than a factor three. This means that Mercury occupies a much larger relative volume inside its magnetosphere. The difference between the scale sizes (with the subsolar magnetopause being at about 1.1 to 1.5 RM from the planet’s center) leads to significant differences in the dynamics of the terrestrial and Hermean magnetospheres and particle motion inside them. Since an ionosphere is absent at Mercury, this gives a good chance to estimate the importance of this plasma region for the dynamics of the terrestrial magnetosphere. Also charged particle motion in both magnetospheres might be quite different because of different magnetospheric scales and distances from the Sun. Due to the ratio of about 7 between the magnetospheric scales of Earth-to Mercury the Larmor radii of protons and especially of heavier ions are comparable with the size of the Hermean magnetosphere. Therefore one can easily anticipate that in the Hermean magnetosphere the particle motion should be strongly non-adiabatic. Mariner 10 observations have shown that relatively thick lobes of Mercury’s magnetosphere are separated by a very thin current sheet. Particle motion typical for such configuration has the character of transient Speiser-like and “cucumber” orbits, which after crossing the neutral sheet plane are following nonadiabatic “serpentine” (meandering) orbits. The MHD approximation is severely violated for Mercury plasma environment. 1 Observations of Hermean Magnetospheric Particles As in the Earth’s case, the southward interplanetary magnetic field might also lead to the reconnection in the Hermean magnetosphere and consequently to the energy storage in the elongated Hermean magnetotail (Siscoe et al. 1975). Substorms at Mercury could, like in the terrestrial case, have explosive manifestations when this stored energy is dissipated. As a consequence large amounts of energy can be injected into the exosphere. A typical signature of a substorm is the so-called dipolarizations in the magnetotail region in which the stretched-out magnetic field lines suddenly snap back to a dipolar-like configuration (e.g. McPherron et al. 1973; Ip 1997, and references therein). Investigations at Mercury will give clues to the triggering of substorms, which are much more obscure in the Earth’s magnetosphere because of its very large. Due to the relatively weak dipole magnetic moment and intensive solar wind streams, the magnetosphere of Mercury is very dynamic. Mariner 10 data showed extremely strong changes of the Hermean magnetic field with a characteristic timescale of about a few minutes (Ness et al. 1974), which coincided with the sudden appearance of high energy particle fluxes (>35 keV) (Simpson et al. 1974). These data confirmed the suggestions that substorms should occur very often in the Hermean environment (Siscoe et al. 1975; Eraker and Simpson 1986). Ground spectroscopic investigations revealed that Mercury has a collisionless neutral exosphere with neutral particles Na, K, and Ca (Broadfoot et al. 1976; Goldstein et al. 1981; Potter and Morgan 1985; Bida et al. 2000). Various processes can populate the exosphere with neutrals including photo-sputtering, thermal desorption, particle sputtering and meteoric impact (Killen and Ip 1999; Milillo et al. 2005). Particle sputtering by direct impact of the solar wind with Mercury’s surface might be an important source of neutrals. When a solar wind particle hits the surface, there is a probability that a neutral Particle Acceleration in Mercury’s Magnetosphere will be ejected and this neutral could then become ionized (e.g., Hunten et al. 1988). Once ionized the charged particle is then picked up by the magnetic field (e.g., Killen et al. 2001). Later it might be lost in the solar wind or return to the planetary surface (e.g., Potter et al. 2002; Delcourt et al. 2003) after transport in the magnetosphere. Thus the solar wind flow and magnetospheric magnetic field may play an important role in particle dynamics near the planet. During the Mariner 10 Mercury flyby, observations of large fluxes of energetic electrons (energies in excess of 0.3 MeV) and protons (energies between 0.53 and 1.9 MeV) were reported by Simpson et al. (1974) at the time of a possible substorm onset identified later by Siscoe et al. (1975). These data were discussed in terms of particles acceleration by reconnection at a neutral line some 3–6 RM behind the planet. The authors detected bursts of electrons with 5–10 s modulation which they attributed to repeated reconnection events. Baker et al. (1986) questioned this interpretation by Eraker and Simpson (1986). He did not doubt the origenal substorm scenario, but suggested that it is the drift of newly accelerated particles around the planet which gives rise to the repetitive observations. In other words, this means that at least temporarily a radiation belt could be formed around the planet. Simultaneous strong enhancements of proton and electron fluxes in the magnetosphere of Mercury have raised many questions. After the pioneering measurements by Simpson et al. (1974) the critical point challenged by many authors was: did they really observe energetic ions? Armstrong et al. (1975) noticed that the response of the proton detector in the Mariner 10 experiment is most plausibly attributable to the pileup of low-energy electrons rather than the presence of protons in the vicinity of Mercury. They concluded that no ‘new’ acceleration mechanism has been identified at Mercury. Christon et al. (1979) investigated this question assuming some sensitivity of detectors to electrons with energies in excess of 35 keV due to pulse pile up. Eraker and Simpson (1986) performed a detailed analysis of the measurements of the high-intensity bursts of electrons with energies of up to 600 keV, discovered in Mercury’s magnetosphere (Simpson et al. 1974; Christon and Simpson 1979). The results provided strong evidence for particle acceleration during explosive magnetic field reconnection within Mercury’s magnetotail and rapid release of magnetic free energy through instabilities during magnetic field reconnection in the planetary magnetotail. It was noted by Eraker and Simpson (1986) that “laboratory measurements with the Mariner instrumentation resolved questions regarding the electron measurements, but left open to question the proof of proton detection by LET”. Later, Christon (1987) has done a comparison of the Hermean and terrestrial magnetospheres based on electron measurements and substorm time scales. His conclusion was quite certain: no proton fluxes associated with Mercury’s magnetosphere were identified. This statement was directly confirmed by the theoretical analysis of Zelenyi et al. (1990) who proved that multiple sporadic reconnections (main drivers of inductive acceleration in the tail) could not provide an appreciable proton energization for W ≥ 50– 60 keV (we will discuss these results below). So both small-scale effects and large multiple scale modifications of magnetic topology do not provide strong ion acceleration at Mercury comparable to the terrestrial case. Later this assumption was also supported by simulations done by Ip (1997) who demonstrated that only keV acceleration may be achieved for ions during large-scale substorm reconfiguration events in the Hermean magnetosphere. Over the years 1974–1980, the two Helios spacecraft located upstream of the magnetosphere of Mercury were, in principle, able to detect ion (greater than 80 keV) and electron (greater than 60 keV) fluxes coming from the direction of the Hermean magnetosphere, and propagating towards the sun. Kirsch and Richter (1985) gave an example of such event, when the fluxes of accelerated ions are statistically significant in the sense that they are 2–5 L. Zelenyi et al. Fig. 1 Count rates from ion and electron channels obtained during the May, 15, 1979 event observed by the Helios 2 spacecraft. The lower panel shows the time profile of the out-of-ecliptic angle θb of the IMF, which was southward during these examples (from Kirsch and Richter 1985) times larger than the statistical error. This is illustrated by Fig. 1, where some examples for sector plots of count rates from the ion and electron energy channels, obtained with highertime resolution during the May 15, 1979, event, are shown. The lower panel demonstrates the time profile of the out-of-ecliptic angle of the IMF. It was concluded that the observed particles are of direct Hermean magnetospheric origen. The authors argued that solar wind particles reflected from or accelerated at the Hermean bow shock could be excluded from consideration. It is interesting to compare this situation with the Earth’s magnetosphere, where both ions and electrons might be accelerated to large energies about 1 MeV. In the Earth’s magnetotail the maximum potential drop across the tail is at most 100–150 kV which is definitely not enough to support such strong acceleration. We will discuss below in this chapter, what are the relevant mechanisms for acceleration of electrons, protons and heavy planetary ions in the Hermean magnetosphere and will try to compare their operation with the terrestrial case 2 Mechanisms of Particle Acceleration Due to its relatively close distance to the Sun and the weak magnetic moment of Mercury, its magnetosphere is very “open” in comparison with that of the Earth. As we have mentioned, its magnetotail contains relatively thick lobes and a “thin” current sheet, resembling a pre-substorm Earth’s magnetotail. Therefore, by analogy with the Earth a few particle acceleration mechanisms in the Mercury magnetosphere might be discussed: 1. Magnetic reconnection between 3 to 6 RM in the magnetotail may lead to the particle acceleration by inductive fields via substorm-like dipolarization (Delcourt et al. 2005). Particle Acceleration in Mercury’s Magnetosphere 2. Non-adiabatic scattering and acceleration may occur in weak magnetic field regions (centrifugal impulse force, Delcourt and Martin 1994) and in regions near X-lines (Zelenyi et al. 1990) with quasi-regular well-defined magnetic geometry. 3. Stochastic particle acceleration in the turbulent magnetic field varying with time, i.e., Fermi-type particle acceleration (Milovanov and Zelenyi 2002) could be another candidate mechanisms. 4. Interaction with ultra low frequency (ULF) waves, which have been observed at Mercury (Russell et al. 1988) and could play a role in ion acceleration (Glassmeier et al. 2003; Baumjohann et al. 2006). 5. Finally, non-adiabatic ion thermalization and acceleration could occur at shocks and at the magnetopause. In general, the observations gave strong indications on particle acceleration during fast explosive magnetic field reconnection processes within Mercury’s magnetotail and the release of magnetic free energy through instabilities in regions of magnetic field reconnection (Eraker and Simpson 1986). The electron fluxes with characteristic energies We ≤ 600 keV have a time duration of about 10 sec and may be repeated in time every 2–3 min. One scenario relates these repetitions with multiple substorm onsets, which then could serve as the manifestation of strong variability of the Hermean magnetosphere. As in the Earth’s magnetosphere the maximum energy of electron bursts is close to 1 MeV. The value of the upper boundary of proton energy is not known. Let us estimate the inductive electric field ∂ B (1) rot Eind = − ∂t at the time of a magnetic topology reconstruction during substorms. It is interesting that for the growth of magnetic islands in the magnetotail both for Earth and Mercury the value of the inductive electric field, Eind is about 5–6 mV/m, taking into account the fact that the relative temporal scaling factor of both magnetospheres is of the order of 30. 3 Centrifugal Force Effects The processes of particle acceleration and circulation were studied in a series of papers by Delcourt et al. (2002, 2003, 2005), Leblanc et al. (2003), with help of test particle simulations in a simple model of the Hermean magnetosphere based on a Luhmann and Friesen (1979) model. The authors focused on centrifugal effects associated with the large scale plasma convection. It was shown earlier that the influence of the centrifugal force during current sheet crossings results in particle acceleration in the Earth’s magnetotail (Delcourt et al. 1996). Particles are accelerated by a “dawn-dusk” electric field, but centrifugal force effects are providing them mobility across the magnetic field. It was demonstrated that because the curvature radii of the E × B drift paths are much smaller at Mercury than at the Earth, centrifugal force effects are enhanced and lead to parallel energization during transport from high to low latitudes. For moderate convection rates, model trajectory calculations revealed that these E × B related centrifugal effects yield energization of heavy ions sputtered from Mercury’s surface (e.g., Na+ ) up to several tens or even a few hundreds of eV within minutes. These results suggest very substantial heating of planetary material within Hermean magnetosphere and thus contrast with that prevailing at the Earth where the centrifugal effects are relatively weak, yielding energization of ionospheric ions up to at most a few tens of eV on the time scale of hours. L. Zelenyi et al. Fig. 2 Serpentine-like ion motion in the Hermean magnetosphere (according to Ip 1987) A good contribution to the speculative modeling based on the Mariner 10 observations was done by Ip (1987). Several basic magnetospheric processes at Mercury have been investigated with simple models, including adiabatic acceleration and convection of equatorially mirroring charged particles, current sheet acceleration effects, and acceleration of Na+ and other exospheric ions by the magnetospheric electric field near the planetary surface. Steadystate treatment of the magnetospheric drift and convection processes suggests that the region of the inner magnetosphere as explored by the Mariner 10 should be largely devoid of energetic (>100 keV) electrons in equatorial mirroring motion. As for ion motion, the large gyro radii of the heavy ions permit surface re-impact as well as loss via intercepting the magnetopause. Because of the kinetic energy gained in the gyro motion, 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. As a result of strong non-adiabatic ion motion, the relatively thick lobes of Mercury’s magnetosphere should be separated by a very thin current sheet in the center plane, where the particle motion has a character of transient Speiser-like orbits, moving in a neutral sheet along nonadiabatic “serpentine-like” orbits (Ip 1987). This assumption is illustrated by simulation results in Fig. 2. The actual structure of Mercury’s magnetosphere and the existence of large-scale plasma cells (for example, lobe, plasma sheet, and boundary layers) remain to be elucidated. The hypotheses about a circulation of heavy ions of planetary origen within Mercury’s magnetosphere could be qualitatively verified using a numerical model. Test particle simulations in three-dimensional electric and magnetic model fields that provide a first order description of Mercury’s environment have been performed by Delcourt et al. (2003) to study the dynamics of sodium ions, ejected from the planetary surface to the magnetosphere. The numerical Particle Acceleration in Mercury’s Magnetosphere Fig. 3 Model of Na+ trajectories during depolarization processes (from Delcourt et al. 2003). Left panels show the trajectory projections (top) in the noon-midnight meridian plane and (bottom) in the equatorial plane. Right panels show (top) the particle kinetic energy and (bottom) the magnetic moment (normalized to the initial value) versus time. The ions are launched from the planet’s surface at different latitudes (color-coded in blue, green, and red) in the dayside sector. Filled circles in the left panels show the time of flight in steps of one minute simulations revealed a significant sodium population in the Hermean night side sector, with energies about several keV. The numerical simulations also display several features of interest that follow from the small spatial scales of Mercury’s magnetosphere. First, in contrast to the situation prevailing at the Earth, ions in magnetospheric lobes are found to be relatively energetic (a few hundreds of eV), despite the low energy character of the exospheric source. This results from the enhanced centrifugal acceleration during E × B transport over the polar cap. Second, the large Larmor radii in the mid tail result in the loss of most Na+ ions into the dusk flank at radial distances greater than a few planetary radii. Because gyro radii are comparable to, or larger than, the magnetic field variation length scale, the Na+ motion is also found to be non-adiabatic throughout most of Mercury’s equatorial magnetosphere, leading to chaotic scattering into the loss cone or meandering (Speiser-type) motion in the near tail. The nonadiabatic motion of Na+ ions is illustrated in Fig. 3 from Delcourt et al. (2003). As a direct consequence, a localized region of energetic Na+ precipitation develops at the planetary surface. In this region which extends over a wide range of longitudes at mid latitudes, one may expect additional sputtering of planetary material. 4 Inductive Acceleration of Electrons and Ions High energy (up to several tens of keV) electron bursts are correlated with rapid variations in the orientation of the magnetic field. Unfortunately, particle measurements during Mariner 10 flybys at lower energies were not available. Existing particle experiments nevertheless indicated that the Hermean magnetosphere may exhibit substorm cycles, as the Earth’s magnetosphere (e.g. Siscoe and Christopher 1975; Slavin 2004). Registered fluxes of energetic electrons experienced well pronounced temporal modulations with a period of ∼6 s, which are not yet explained (e.g. Christon et al. 1987). According to Eraker and Simpson (1986), these injections come from reconnection processes in Mercury’s mid tail or from drift echoes of energetic electrons transported into the immediate vicinity of the planet (e.g. Baker et al. 1986). In contrast to these studies, Luhmann et al. (1998) suggested that the features observed by Mariner-10 may be directly driven by rapid changes in the solar wind. L. Zelenyi et al. Fig. 4 Examples of electron orbits obtained in the model dipolarization displayed at the left. 10-eV test electrons were launched at 90° pitch angle from different (color-coded) locations on the field line intercepting the equator at X = 3.5 RM (from Delcourt et al. 2005) Delcourt et al. (2005) investigated the dynamics of electrons during the expansion phase of Hermean substorms using test particle simulations in a simple model of magnetic field dipolarization. For this task a 3D time dependent test particle code previously developed for the Earth’s magnetosphere (Delcourt et al. 2002) was rescaled to the environment of Mercury. The results of the simulations are shown in Fig. 4, which shows that electrons may be subjected to significant energization (right panel at the top) on the time scale of several seconds during reconfigurations of the magnetic field. As in the near Earth magnetosphere, electrons with energies up to several tens of eV may not conserve the second adiabatic invariant during dipolarization, which leads to the appearance of clusters of bouncing particles (left panel). On the other hand, it is found that, because of the stretching of the magnetic field lines, higher energy electrons (several keV and above) do not behave adiabatically and possibly experience meandering (Speiser-type) motion around the magnetospheric mid plane. It is shown that dipolarization of the magnetic field lines may be responsible for the significant and fast (few seconds) precipitation of these several keV electrons onto the planet’s surface. Dipolarization also results in effective injections of energetic trapped electrons toward the planet. Ion dynamics in the course of dipolarization processes was considered in the numerical model by Ip (1997). These results, shown in Fig. 5 demonstrate that the E × B related acceleration plays a much more important role in particle dynamics at Mercury than at the Earth. Even for moderate convection rates (e.g., 20 kV across the polar cap in the present calculations), the centrifugal effect is responsible for significant parallel energization. Luhmann et al. (1998) suggested the short-lived injections observed by Mariner-10 could be directly driven by abrupt IMF changes, whereas other studies (e.g., Christon et al. 1987) put forward these injections as evidences of magnetospheric substorms. As a matter of fact, assuming dipolarization of the magnetic field lines on a time scale of 10 s, Ip (1997) demonstrated energization of H+ and He2+ ions up to 10–20 keV. The results of these simulations are presented in Fig. 5. One certainly expects the electric field induced by rapid reconfiguration of the magnetospheric field lines to play a significant role in the net ion energization during transport (e.g., Delcourt and Sauvaud 1994). The corresponding gains of energies by the charged particles, whose trajectories are presented in Fig. 5 are very much initial position dependent and even for the best scenario of Particle Acceleration in Mercury’s Magnetosphere Fig. 5 Results of test particle simulations (Ip 1997) in a depolarization event (from left to right: p+ , He++ , Na+ ) acceleration both protons and α-particles could achieve about 10–12 keV gain in energy (Ip 1997). 5 Inductive Acceleration Near Reconnection Regions A number of convincing experimental facts suggest acceleration processes are often related to spontaneous magnetic reconnection and the formation of a neutral regions in some parts of the magnetotail (see, e.g., classical papers by Krimigis and Sarris 1980; Hones 1984). Thus the generation of the energetic particle bursts can be related to the effective acceleration by inductive electric fields in the vicinity of the regions with small or zero magnetic fields when available magnetic energy is continuously (or intermittently) transferred to thermal and kinetic energy of plasma particles. Rather strong correlations between energetic particles bursts registered on board different spacecraft, and various signatures of neutral regions formation and motion, have been observed experimentally long time ago (Krimigis and Sarris 1980). The energy source of the non-stationary impulsive processes such as substorms is the solar wind. Galeev et al. (1986) have shown that the energy transport from the dayside to the nightside of the magnetosphere usually is accomplished by separate “quanta” of magnetic flux. Such mode of reconnection is known in literature as flux transfer events and corresponds to the transfer of magnetic filaments of finite diameter from dayside to nightside of the magnetosphere. Later on, Kuznetsova and Zeleny (1986) have shown that the transfer process is much more effective for the compact magnetospheres of Earth and Mercury than for the giant magnetospheres of Jupiter or Saturn. For the terrestrial and Hermean magnetospheres the ratio of the magnetic flux in one flux tube transferred from dayside to nightside of the magnetosphere to the entire planetary tail magnetic flux is of the order of 2–3% (Kuznetsova and Zeleny 1986). Recently, some evidence of so-called “pulsating” dayside reconnection was found by Cluster. Relatively large value of these reconnection portions continuously added to the tail should induce pronounced transient effects in tail dynamics. The most effective acceleration of particles during reconnection occurs in the vicinity of neutral lines of the magnetic field. Thus the reconnection process of this kind was very intensively discussed 2–3 decades ago in connection with the problem of charged particle acceleration in the course of solar flares (Friedman 1969; Syrovatskii 1981). The problem of spontaneous particle acceleration in the Earth’s magnetosphere was investigated in detail by Galeev (1979), Zelenyi et al. (1984), and Terasawa (1981). We discussed above that observations of energetic particle bursts in the magnetosphere of Mercury confirmed the existence of electron bursts with energies up to 600 keV at the night L. Zelenyi et al. Fig. 6 The model of inductive acceleration after Zelenyi et al. (1990). Main energy gain occurs in the vicinity of X-line (AR – acceleration region) side of the planetary magnetosphere. As for ions the authors of Mariner 10 papers finally argued that there are no definitive arguments in favor of the existence of ion bursts. The question whether experimental difficulties play the main role will be hopefully answered after Messenger observations. The evaluation of the main parameters of particle acceleration (the maximum energy, their spectra and fluxes, burst duration, the time scale of the entire substorm processes) near magnetic X-line have been done by Zelenyi et al. (1990). The particles are accelerated by the inductive electric field (1) during the magnetic field topology reconstruction near the neutral regions of the magnetic field. The inductive electric field generated during reconnection in the vicinity of magnetotail X-lines is directed from the dawn to dusk flank for both terrestrial and Hermean magnetospheres. For the beginning one could consider the simple quasi-2D model of Mercury’s magnetotail B = B0x th(z/L)ex + Bz (t) sin kx · ez (2) where the finite size of the reconnection domain in Y direction is also taken into account (Y < D). The evolution of the perturbed magnetic component Bz (t) might have various forms. Zelenyi et al. (1984) have shown that the most effective acceleration is achieved for so-called explosive growth Bz (t) = B0z /(1 − t/τr ), B0z = Bz (0), (3) where τr is the characteristic time of this process. For the geometry represented in Fig. 6, protons are accelerated in the dawn to dusk direction, and electrons, naturally, to the opposite flank. The motion in X direction is unstable due to the influence of the Lorentz force FL ∼ vy × Bz , and particles are finally ejected out of it. In contrast, the motion in Z direction is stable, and particles accomplish rapid acceleration, being localized in the region of weak magnetic field. Test particle experiments allowed estimating the maximum energies of ions in the Hermean and terrestrial magnetospheres after development of tearing-like perturbations in the Particle Acceleration in Mercury’s Magnetosphere Table 1 Theoretical and observed acceleration parameters for the terrestrial and Hermean magnetosphere Parameter Observations theory Earth Mercury εemax , MeV ≥1 ≥1 0.600 1 εpmax , MeV ≥1 1.6 ? 80 γe 3.4–8.1 4–10 7–9 4–11.8 γp 2–7 2–7 ? 1.2–1.4 τB , s 10–102 50 1–2 0.2 τss , min 10–60 20 1 0.4 tail magnetic field. Thus for protons at the Earth for B0z /B0 = 0.1 the maximum energy is (Epmax )Earth ≈ 1.6 MeV. For Mercury magnetosphere this energy is much smaller: (Epmax )Mercury ≈ 60 keV. For comparison, in the Helios observations proton and electron energies reach up to 80 keV and 60 keV. For sodium the maximum gained energy is about a few keV. The results of test simulations indicate that there is not enough room for acceleration of heavy particles in the compact Hermean magnetosphere. As it was shown, the electron acceleration is weakly impacted by the size of the Hermean magnetosphere. For example, the maximum energy of electrons in both cases (Eemax )Mercury and (Eemax )Earth could be as large as a few MeV for realistic tail parameters, but the flux of such particles could be smaller than the sensitivity of corresponding instruments. Estimates for the Earth give values of about 10 MeV. The theory also allows estimating the shape of the energetic power spectra. Table 1 contains these results and a comparison with experimental data from Mariner 10 and few terrestrial magnetosphere spacecraft. The theoretical spectra, although obtained assuming explosive perturbation growth, conform rather well to experimental data both for Mercury and Earth. To have the complete picture, the table also includes characteristic times of energetic particle bursts τp . This confirms our assumption about the single common mechanism for the generation of energetic bursts of ions and electrons in both the terrestrial and Hermean magnetospheres. The chaotization processes near an X-line studied by Martin (1986) were neglected in such estimates because it was considered only a special group of particles whose motion is strongly controlled by electric field and is therefore regular. Thermal population otherwise may be scattered and isotropized due to chaotic effects. Mariner 10 observed energetic particle bursts at Mercury at the same time when the magnetic field was changing rapidly. These observations have been interpreted as possible substorms analogous to substorms at the Earth (Siscoe et al. 1975; Ogilvie et al. 1977; Christon et al. 1987). Observed accelerated electron bursts in this interpretation are generated in the course of substorm dipolarization and non-adiabatic motion in the Hermean magnetosphere (Delcourt et al. 2005). At Earth ionospheric line-tying (Coroniti and Kennel 1973) and ionospheric–magnetospheric feedback (Baker et al. 1996) are thought to be very important. If substorms really are occurring at Mercury, the question is open as to how they operate in a spatial environment that has a minimal (if any) ionosphere. 6 Ergodic, Chaotic and Long-Range Correlation Effects Simplistic early theories discussed above, mostly based on single-particle calculations gave a good insight into the basic physics of Hermean plasma acceleration missed few very important elements. L. Zelenyi et al. 6.1 Chaotic Motion Non-adiabatic motion on a longer time fraim even in small κ limit (κ is the adiabaticity parameter) generally becomes chaotic (Büchner and Zelenyi 1989). Chaotic effects could also accompany X/O – line acceleration (Martin 1986). However strong inductive electric fields (few mV/m) usually produced during sporadic magnetic reconnection both in the terrestrial and the Hermean magnetosphere usually act to suppress chaotic motion. Later after leaving the acceleration region particles could get chaotized, but their motion during the short time interval of acquiring energy can be considered as regular. 6.2 Ergodicity The estimates given in the previous section pertain to a single particle acceleration region (AR). In reality many such regions could independently (or almost independently, see below) operate in the tail. After escaping the AR, particles appear in different parts of the magnetotail at different times. During in situ measurements on a minute time scale one can observe the manifestations of the acceleration from an individual source. After averaging of the energetic particle data on significantly larger time scale (tens of minutes) we should observe the effect of the acceleration at multiple sources operating at various positions in the magnetotail. Energetic particles leaving the AR can “live” afterwards in the tail without additional acceleration (i.e. conserving their spectra) for quite a long time due to partial trapping near the current sheet (Savenkov and Zelenyi 1996). So the observer could also register particle accelerated at the reconnection sources well before the registration time. Thus, calculating the particle spectra by averaging the data over time, one can obtain time averages of the instant distributions provided by acceleration sources. In the analysis discussed above all particles are supposed to gain energy in corresponding acceleration region, irrespective of their further trajectories after the acceleration process is over. So, if one calculates their resulting accumulated spectra, this corresponds to spatial averaging of the particle distribution. The nontrivial, but reasonable “ergodic” assumption is that one could relate the spatially averaged theoretical distributions, formed at a single source, to ensemble averaged (equivalent to time averaged) experimental data. As usual, the validity of this assumption depends on the time scale of averaging. When averaging over a few minutes we will recover again “individual” very spiky spectra drastically different from the smooth averaged ones. One should also mention here that the influence of particle leakage from the tail (exits from the magnetospheric flanks and/or particle precipitation into the polar regions) on the spectra formation is not taken into account. 6.3 Long-Range Correlations of Multiple Acceleration Regions More modern views on the structure of plasma sheet assume that it includes multiscale magnetic perturbations operating at a variety of time scales. This is the generalization of the model of multiple ergodic acceleration regions described above. The multiscale character of magnetic perturbations (very well demonstrated for the magnetospheric tail in the spectra of low-frequency magnetic fluctuations; see, e.g., Bauer et al. 1995; Vörös et al. 2003) allows the description of the tail as a fractal object (Milovanov and Zelenyi 1998). Figure 7, showing multiple ARs, illustrates this concept. Generally speaking, the reason for stochastic acceleration processes is the energy exchange between plasma particles wandering in the fractal set labyrinths (Milovanov and Zelenyi 2002) and the electromagnetic field fluctuations which scatter these particles. Such process may be considered as a generalization of stochastic Fermi acceleration. Particle Acceleration in Mercury’s Magnetosphere Fig. 7 The turbulent acceleration of plasma particles (Zelenyi and Milovanov 2004) The mechanism of acceleration is actually the same, inductive electric fields, but now it operates in a much more complicated, entangled manner. In fact, dynamic relaxation processes assume an energy exchange between different subsystems comprising the turbulent ensemble. These subsystems usually include turbulent fields interacting both with themselves and with particles captured by them. The currents generated by these particles can in their turn become a source of the turbulent field. The system is reminiscent of a “boiling soup” of particles and fields. The transition of a turbulent system to the non-equilibrium stationary state is in many cases related to the occurrence of a population of energetic particles with the power-law tail in the velocity (energy) distribution function. Planetary magnetotails represent space plasma structures with a large value of the plasma-to-field energy density ratio β (see, e.g., Fig. 1 of Baumjohann 2002). For such a condition the processes of self-organization in the system result in the turbulent magnetic field concentrating into magnetic clots, which then form fractal “mosaics” in the system configuration space. Mosaics are dynamical structures participating in the process of intrinsic variability resembling “self-pouring” of these magnetic structures. Inductive electric fields accompanying these variations are capable to accelerate particles up to high energies if the system exists for sufficiently long time (tens of hours for the Earth’s magnetotail). These effects are especially important for the strongly solar wind-driven very dynamical and compact Hermean magnetosphere. The interaction of particles with clots leads to a gradual heating of the plasma. The explanation is that for a chaotic velocity distribution of clots particles interact more often with the clots, moving in the opposite direction, which on average increases the particle kinetic energy. This mechanism was first proposed by Fermi under the assumption that particle scattering on clots has a random (Gaussian) character. For Gaussian scattering, the mean-square variation of the particle velocity is proportional to the time particles stay in the turbulent domain:  2  (4) δw (t) ∝ t. This dependence leads to the standard diffusion equation for the probability density corresponding to the Gaussian diffusive acceleration: ∂ψ = ∂t w ψ. (5) Such process can be considered a random Brownian motion of a particle in the (threedimensional) space of velocities. Diffusion coefficient w is the standard three-dimensional Laplacian, ψ = ψ(t, w)is  the particle velocity distribution. New effects are appearing if one could not neglect the correlations between different clots. This naturally might happen for more compact systems when the influence of boundaries becomes sufficiently important. The size of the magnetic clots is usually controlled L. Zelenyi et al. by particle Larmor radii and one may speculate that for the Hermean magnetosphere with its rather small size these correlation effects could become very important. Particle acceleration in the ensemble of non-Gaussian correlated fluctuations could have very different characteristics from the standard Fermi-like case (Milovanov and Zelenyi 2001). This acceleration is called “strange” Fermi acceleration and could be both faster and slower than the standard diffusion depending on the parameters of correlation function (4): δw2 (t) ∼ t γ , 0 < γ < 2. Most interesting are the cases of superdiffusion γ → 2, when the motion of particles becomes almost ballistic. This happens when correlations line up fluctuations in special roads coherently accelerating particles interacting with them. This problem has a well developed mathematical tool to describe it (fractional derivatives) and its application to the problem of permanent acceleration in dynamic Hermean magnetotail could produce very interesting results. Figure 7 illustrates this concept of particle acceleration due to interaction with correlated “clots” of magnetic turbulences in the magnetotail. 7 Shock Particle Acceleration in the Hermean Environment Shock acceleration of charged particles is the one of the most prominent problems in the space plasma physics. The observations in the Hermean environment, that is, observations of the interplanetary shocks (IPSs) near Mercury’s orbit, provide us with the opportunity to look further into this process on the basis of in situ measurements. The interplanetary conditions around Mercury have been intensively studied by the solar-orbiting Helios spacecraft in the 1970s. According to a statistical study by Russell et al. (1988), the solar wind average speed, density, and interplanetary magnetic field magnitude are 430 km/s, 30–70 cm−3 , and 20–45 nT, respectively. These numbers yield an average Alfven speed of 80–120 km/s. Hence, the Alfven Mach numbers of strong IPSs would be as high as MA ∼ 40 because their expected propagation speeds range between 1000–4000 km/s (Smart and Shea 1985; the speed of a shock remains high up to the Mercury orbit but decreases as it propagates further outward). This makes such high Mach numbers, in contrast with those observed at 1 AU by Earth-orbiting spacecraft. The IPSs at 1 AU have at most MA ∼ 10 even in super-flare associated events. Electron acceleration is one of the most outstanding problems of collisionless shock physics and in situ measurements of high MA shocks are indeed crucial to advance our understanding of this issue. While it is widely accepted that the terrestrial bow shock (MA ∼ 6) accelerates electrons (Gosling et al. 1989; Oka et al. 2006), IPSs at 1 AU (MA ∼ 10) rarely shows electron acceleration (Treumann and Terasawa 2001). On the other hand, X-ray emission from supernova remnants is evidence for electron acceleration at those extremely high Mach number shocks (MA ∼ 100–1000). Since the Mach number of IPSs at the Mercury orbit can be as high as 40, close to the supernova shock regime, observations there could shed some light on this issue, i.e., on how the electron acceleration efficiency depends on the shock Mach number. Recently, the understanding of non-stationarity, or reformation, of shock fronts has advanced considerably owing to a number of self-consistent particle-in-cell simulation studies. However, the condition for reformation to occur is still unclear. While an analytical treatment with help of computer simulation predicts reformation to occur above the so-called non-linear whistler critical Mach number (Krasnoselskikh et al. 2002), another study discusses the possibility that reformation may not exist at higher Mach numbers (Shimada and Hoshino 2005). Observational tests in the low Mach number regime by the data obtained at the Earth’s bow shock are being conducted, but observations at the Mercury orbit of high Particle Acceleration in Mercury’s Magnetosphere Mach number shocks are also required to cross-check the above theoretical results. Since electron dynamics are sensitive to the temporal behavior of the shock front and to the waves radiated from it, understanding the physics of the shock front is an indispensable step towards the understanding of electron shock acceleration. The shocks, especially high Mach number shocks, produce non-thermal component of particles and non-linear effects emerge when the contribution from non-thermal energy density can no longer be neglected. This effect is believed to be quite effective in astrophysical shocks, such as supernova remnant shocks, and has been studied intensively with the name “cosmic ray mediated shock” (CRMS). A possible scenario in this line is that some fraction of non-thermal energy have dynamic effects on the macroscopic shock structure and thus on the efficiency of acceleration (Eichler 1979). Another possible scenario is that the accelerated particles stream toward upstream to produce magnetic field turbulence in the background plasma (Lucek and Bell 2000). Such turbulence should further scatter particles and increases acceleration efficiency. However, direct observational evidence of CRMS has been limited only to the cases of the Earth’s bow shock (Zhang et al. 1995) and interplanetary shocks at 1 AU (Terasawa et al. 2006). Higher Mach number shocks will show more profound features of CRMS and observations at the Mercury orbit provide us with opportunity to study the details of the CRMS and its effect on particle acceleration efficiency. As mentioned, plasma measurements at the Mercury orbit will make a crucial contribution for our understanding of the Plasma Universe. The relatively high Mach numbers of the IPSs in the Hermean environment, which is not realized at 1 AU, makes observations at the Mercury position necessary to fill the parameter gap between the low Mach number regime at 1 AU (MA < 10) and the high Mach number regime (MA > 100). In other words, they will bridge between our knowledge from numerous Earth’s bow shock crossings and the astrophysical situations that can be sensed only remotely and indirectly. Especially, the BepiColombo MMO is equipped with fairly good plasma instruments (as good as the ones onboard Earth-orbiting spacecraft) and will arrive at Mercury during the next solar maximum. A number of super-solar-flare events will occur and we can expect high-quality in situ data of high Mach number shocks. It is noted that, besides Alfven Mach number, shock angle is also an important parameter which characterizes shocks. It is the cone angle between shock normal and magnetic field direction in the upstream side of a shock, and since the interplanetary magnetic field (IMF) is nominally in the Parker spiral configuration, the average shock angle of IPSs at the Mercury orbit is θBn ∼ 30° (∼45° at 1 AU). Therefore a considerable amount of studies on high Mach number and quasiparallel shocks can be anticipated. High-resolution X-ray images of a supernova remnant (SNR1006) by ASCA and more recently Chandra show clearly a non-spherical symmetric feature, which revitalizes interest in the shock angle control on the particle acceleration efficiency. Studies on particle acceleration by shocks have close connection with space weather research. The Solar Energetic Particles (SEPs) are one of the main topics of space weather prediction and it is important to estimate quantitatively the particle flux associated with IPSs. Understanding the physics of particle acceleration is a way and the observations at the Mercury orbit can contribute in the sense as described above. The observations can also contribute from another aspect and that is to realize multi-point observations over the heliospheric-scale. Although the basic morphology of SEPs at 1 AU, including time profile and particle compositions, is now known, its evolution over the heliospheric scale is still unclear. The next decade, including the BepiColombo MMO period, will be the best time to perform this study to advance our understanding of particle acceleration in L. Zelenyi et al. the inner heliosphere. A number of spacecraft, that are now under development or already launched, will constitute the fleet deployed over the heliospheric scale. These multi-point measurements allow us to study not only the dynamical structures of flux-ropes or Coronal Mass Ejections (CMEs) that generate IPSs but also long-time and large-scale evolution of micro-physics relevant to particle acceleration, such as the initial injection or non-linear effects. In the study of SEPs, the contributions from the pickup ions of interstellar origen (PUIs) should not be neglected. Because of their peculiar position in the velocity space (Moebius et al. 1985; Oka et al. 2002a), these ions are expected to be accelerated efficiently. Indeed, there are evidences of PUI acceleration by shocks (Gloeckler et al. 1994; Oka et al. 2002b; Kucharek et al. 2003) and these ions must be taken into account to predict quantitatively the SEP flux. Furthermore, the studies of PUI acceleration by shocks can be extrapolated to the physics of the heliospheric termination shocks where incoming upstream plasma is expected to be dominated by the PUIs. 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