Energetic Ion Population Research Articles

Energetic ion population formed in close collision with fusion alpha-particles

Close collisions of fusion alpha-particles with thermal plasma ions (both of impurities and of main component) give rise to formation of high energy "halo" in the ion velocity space, extending to the energies of MeV-range even for rather heavy ions, like iron. The implications of this process for the diagnostics of the burning plasmas have been discussed. There seem to be possible two versions of the diagnostics: (i) measurement of Doppler contours of the lines radiated by noncompletely stripped impurity ions; (ii) detection of prompt losses of light impurities. In both versions the spatial resolution can be attained by injecting into the plasma the pellets containing the desired impurities. Another option is to detect the prompt losses of 7MeV alpha-particles formed by collisions between 3.5 MeV alpha-particles.

Combined energy and pitch angle diffusion of pickup ions at comet Halley

It is well known that cometary pickup ions (e.g., H2O+, OH+, O+, CO+, H+) initially form a ring‐beam distribution in the solar wind reference frame, which is highly unstable to the growth of MHD waves (such as ion‐cyclotron waves). The low‐frequency magnetic fluctuations (or waves), which were observed upstream of comet Halley, cannot only pitch angle scatter the pickup ions so that the distribution becomes at least partially isotropized, but also stochastically accelerate the ions, resulting in the energetic ion populations observed in the vicinity of comet Halley. We have used numerical solutions of the quasi‐linear diffusion equation to investigate the cometary ion pickup process at comet Halley. Both pitch angle and energy diffusion are taken into account. Many quasi‐linear models of cometary pickup ions exist which involve one type of diffusion or the other but not both types at once. We find that the pitch angle scattering occurs faster than the energy diffusion, as expected. Moreover, our results demonstrate that the distribution of accelerated energetic ions is more isotropic than that of ions which have just been picked up. In fact, the ion distribution function on the initial pickup shell is quite anisotropic, even close to the comet Halley bow shock.

Suppression of magnetic islands by energetic ions in toroidal plasmas

This is a study of the effect of an energetic ion population injected from a neutral beam source on the nonlinear stability of magnetic islands. A kinetic theory is used to obtain the island current, which includes previously known modifications resulting from bootstrap currents and resistive interchanges. The island current thus obtained is used in an asymptotic treatment of the perturbed Ampère’s law, which yields an evolution equation for the island width. It is shown that the island width saturates at a very small amplitude in tokamaks (with Δ′>0) when the energetic ion density profile peaks just outside the rational surface. Energetic ions can also be used to modify the island width in three-dimensional equilibria. It is found that in stellarator equilibria with large vacuum islands, energetic ions can be injected to reduce the widths of equilibrium islands.

Pitch angle distributions of energetic ions in the lobes of the distant geomagnetic tail

Analysis of energetic ( > 35 keV) ion data from the ISEE-3 spacecraft obtained during 1982–1983, when the spacecraft made a series of traversais of the distant geomagnetic tail ( X GSE > −230 R E), indicates that the pitch angle distribution of energetic ions in the distant tail lobes is usually highly anisotropic, being peaked closely perpendicular to the magnetic field direction, but with a small net flow in the antisunward direction. In this paper we present a model, based on the motion of single particles into and within the tail lobes, which accounts for these observed distributions. This model assumes that the lobe ions originate in the magnetosheath, where the energetic ion population consists of two components; a spatially uniform “solar” population, and a population of “terrestrial” origin, which decreases in strength with downtail distance. The density of energetic ions in the magnetosheath is therefore high close to the Earth, and falls with increasing distance down the tail. The ions are assumed to enter the lobes across the open magnetopause boundary, and the speed and point of entry as a function of pitch angle are determined from consideration of the subsequent motion of the ions within the lobe, including mirroring close to the Earth. The pitch angle distribution at any point within the lobe may then be constructed, assuming that the value of the distribution function along the particle trajectory is conserved. In general, those ions with a large field-aligned component to their motion enter the lobes in the deep tail, where the “terrestrial” source is weak, whilst those moving closely perpendicular to the field enter the lobes at positions much closer to the Earth, where the source is strong. The fluxes of these latter ions are therefore much enhanced above the rest of the pitch angle distribution, and are shown to account for the form of the observed distributions. It is further shown that at a given point in the tail, the degree to which the ion distribution function is localized to large pitch angles depends on the spatial scale with which the magnetosheath source population decreases away from the Earth. The distributions broaden as the spatial scale gets larger, and show only modest variations with pitch angle in the limit that the source is uniform. The model thus also accounts for the more isotropic ion population observed in the lobe during solar particle events, when the “terrestrial” component of the magnetosheath source may be considered negligible in comparison to the enhanced “solar” component.

Influence of an energetic ion population on tokamak plasma stability

The stability of a tokamak plasma to ideal and resistive internal kink modes in the presence of an energetic trapped-particle population is analyzed. Domains of stability are found for both slowing-down and Maxwellian particle distributions. The stable domains are at moderately high plasma beta and involve a significant, but easily obtainable high-energy trapped-particle density.

Alfvén-ion-cyclotron instability and absence of sawteeth in tokamaks

Linear stability of the anisotropic energetic ion population, observed in recent experiments at the Joint European Torus [Phys. Rev. Lett. 60, 2148 (1988)], to Alfvén-ion cyclotron wave excitations is analyzed and the saturation mechanism is discussed. In the absence of external heating the anisotropic distribution lifetime is found comparable to the observed delay time in the monster sawtooth crash after the turn-off of the heating. It is suggested that the ponderomotive force of unstable waves is responsible for this delay. Saturated wave fields are found sufficiently large to stabilize the internal kink mode.

A model of the energetic ion environment of Mars

Because Mars has a weak intrinsic magnetic field and a substantial atmosphere, instruments on orbiting spacecraft should detect a population of energetic heavy planetary ions which result from comet‐like ion pickup in the solar wind and magnetosheath convection electric fields, in addition to those that might result from processes internal to a Martian “magnetosphere.” Although this ion exosphere has been previously discussed in the literature, detailed predictions that might be directly applied to the interpretation of data are not available. Here a test particle model is used to construct a global picture of Martian pickup ions in the Mars environment. The model makes use of the recent Nagy and Cravens [1988] model of the Martian exosphere and Spreiter and Stahara's [1980] gas dynamic model of the magnetosheath. The pickup of ions originating at Phobos is also considered. Notable properties of the resulting ion distributions include their near‐monoenergetic spectra, pancake pitch angle distributions, and large gyroradii compared to the planetary scale.

Suppression of the tearing mode by energetic ions.

The effect of an energetic ion population on the nonlinear stability of a tearing mode of single helicity is determined using kinetic theory. A dynamical equation is derived for the magnetic-island width. It is shown that the island growth can be suppressed in a tokamak when the energetic ion-density profile peaks just outside the rational surface. Effects due to resistive interchanges and bootstrap currents are included in the model.

A precursor to the Venus bow shock

Electron and ion current measurements made by the Langmuir probe on the Pioneer Venus Orbiter exhibit significant enhancements just upstream from the Venus bow shock where one might have expected only solar wind plasma to be present. The region of enhancement, which we call the Venus precursor, is approximately centered on the subsolar point but extends in latitude up to solar zenith angles of about 80°; i.e., ahead of nearly the entire dayside shock. At higher latitudes, where its radial profile can be measured, the precursor extends about 1000 km ahead of the shock. The electron current is enhanced by a factor of about 1.6 at the nose, while the net ion current is enhanced by only a few percent because it is dominated by a large, but fixed, photoelectron emission current. There is little change in the amplitude and latitude of the precursor from orbit to orbit, a stability that suggests that this phenomenon is not very sensitive to the often variable solar wind and interplanetary magnetic field conditions. We suspect that the precursor signatures represent the effects of a small population of energetic ions in this region. Several possible planetary sources for these ions are discussed.

Low-energy ions at low equatorial altitudes

Williams and Frank (1984, J. geophys. Res. 89, 3903) have reported the observation of intense low-energy ion populations in the low-altitude, equatorial magnetosphere. They reported observing two narrow energy peaks in the total ion flux that increased in energy from ∼ 8 keV to > 24 keV as the altitude decreased from ≈ 4 R E to 2.1 R E. They analyzed one pass (29 November 1977) in detail and described the difficulties caused by the fact that the analysis had to use data from the limits of the response functions of the plasma and energetic particle instruments. Because of these difficulties, we have analyzed additional data and incorporated ion mass composition data from the Lockheed mass spectrometer. The new data agree in general with the earlier results and show that complex spectral features occur in the total ion observations. The observed ions are now identified as primarily H +, O +, and He +, whose spectra also show complex structures. Observed peak energies increase with decreasing altitude and can vary by at least 30% over time. An acceleration mechanism appears to be continuously present throughout the plasmasphere. As discussed earlier by Williams and Frank (1984), the most likely mechanism for the energization of the observed ions is a resonant wave-particle interaction, probably with ion cyclotron waves generated by an anisotropic energetic ion population. It has been estimated that such a mechanism may act in a two-phase mode resulting in the energization of minor ions up to the local Alfvén energy of the ambient plasma, E A = B 2 8πN total . Although this energy (~ 10 keV at L ∼ 2.5) is similar to the peak energies observed, the radial dependence of the peak energy is not consistent with that expected for E A.

Energy spectra of plasma sheet ions and electrons from ∼50 eV/e to ∼1 MeV during plasma temperature transitions

Measurements of charged particles in the plasma sheet by the low energy proton and electron differential energy analyzer (LEPEDEA) and medium energy particle instrument (MEPI) on ISEE 1 are combined to obtain ion and electron differential energy spectra for use in studying eight plasma sheet temperature transitions, periods of low plasma bulk velocity typically ∼1 hour in length during which the plasma thermal energy either increases or decreases steadily. Over the entire kinetic energy range sampled (50 eV/e ≲ E ≲ 1 MeV), the plasma and energetic ion and electron populations respond collectively as a single unified particle population during these temperature transitions. In order to test the hypothesis that the energy spectra of plasma sheet ions and electrons can be represented by a single functional form, the observed particle energy spectra have been visually compared to three model distribution functions: the Maxwellian (, where ET is the thermal energy), the kappa (ƒ ∼ [1 + E/κET]−κ −1, where κ is a constant), and the velocity exponential (ƒ ∼ e−( E/ε)1/2, where ε is constant). The kappa and velocity exponential distributions both provide reasonable fits above ∼200 eV, with the kappa distribution being more successful at the highest energies but less successful at the lowest energies. The Maxwellian does not provide an adequate fit for the overall distributions observed in the temperature transitions. At high energies (E ≫ κET) the observed spectra are more often similar to the kappa than to the velocity exponential; that is, a roughly power law form (E−κ) is in evidence. Although the value of the index varies from event to event, the particle distributions maintain their overall shape throughout a transition, during which the spectral index at high energies stays roughly constant. This could indicate either that the relaxation time of the plasma is short with respect to the time scale of the temperature transitions or that the spatial regions being sampled were all maintaining a stationary state plasma population, or both. Both temporal and spatial effects are evident in the temperature transitions studied. An indication of temporal dependence during the transitions is that on the average, ET increases with geomagnetic activity as indicated by the AE index at low to moderate levels (∼30 to 600 nT). However, a spatial effect is evident as well, since temperature increases (decreases) occurred as ISEE 1 was traveling toward (away from) the geocentric solar magnetospheric equator.

The role of ring current O+ in the formation of stable auroral red arcs

Coulomb collisions between ring current protons and thermal electrons were first proposed by Cole (1965) as the energy source for stable auroral red (SAR) arcs. Recent observations have shown that the ring current and magnetospheric plasma contain significant amounts of heavy ions (Johnson et al., 1977; Young et al., 1977; Geiss et al., 1978; and others). In fact, the ring current is often dominated by heavy ions at those energies (E ≤ 17 keV) important for Coulomb collisions on SAR arc field lines (Kozyra et al., 1986a). Observations (during four SAR arcs in 1981) of thermal and energetic ion populations by the Dynamics Explorer 1 satellite in the magnetospheric energy source region and nearly simultaneous Langmuir probe measurements of enhanced electron temperatures by Dynamics Explorer 2 within the SAR arc at F region heights have allowed us to examine the role of heavy ions in the formation of SAR arcs. We find that (1) sufficient energy is transferred to the electron gas at high altitudes via Coulomb collisions between the observed ring current ions and thermal electrons to support the enhanced (SAR arc) F region electron temperatures measured on these field lines, (2) the latitudinal variation in the electron heating rates calculated using observed ion populations is consistent with the observed variation in electron temperature across the SAR arc, and (3) in all cases, ring current O+ is the major source of energy for the SAR arcs. This implies a relationship between the heavy ion content of the magnetospheric plasma and the occurrence frequency and intensity of SAR arcs.

Characteristics of the tail of comet Giacobini-Zinner

On September 11, 1985 the International Cometary Explorer (ICE) traversed the tail of Comet Giacobini-Zinner to provide the only in situ information on the physical structure and characteristics of a comet tail. ICE passed 7800 km behind the nucleus, where it clearly detected a draped two-lobe magnetic field configuration and a narrow central plasma sheet. Throughout the tail and inner sheath region, the ICE instruments gave complete information on variations in the vector B-field configuration, the electron distribution function, the energetic ion population, and the electromagnetic and electrostatic plasma wave spectrum. These direct observations supply a framework to test theoretical models of comet tail formation.

Numerical simulations of the magnetospheric convection including the effects of electron precipitation

We present a new self‐consistent model of the transport of hot electrons in the earth's magnetosphere and of their precipitation in the auroral ionosphere. In this model, the electron transport is described by the same fluid equations as in the work by Fontaine and Blanc (1983). But the electric field distribution which drives electron motions is computed from the equations of ionospheric currents, instead of being described by an empirical model as previously. The two basic equations to be solved, the hyperbolic equation governing electron transport and the elliptic equation governing the ionosphere current flow and the distribution of the electrostatic potential on the ionospheric conductor, are coupled via the ionospheric conductivities, which are functions of the electron precipitation flux at the top of the ionosphere. The numerical model is run to simulate the evolution of the system from an initial state in which there is no hot electron in the inner magnetosphere, to a steady state situation in which electrons penetrate into the inner magnetosphere from the tail and are transported onward until they precipitate into the ionosphere. To achieve this, the dawn‐to‐dusk electrostatic potential drop which is induced by the solar wind across the magnetosphere is turned on at t = 0 and maintained constant for the rest of the simulation. Using different values of this potential drop for each individual run, we simulate various levels of magnetic activity and compare our results with observations. The formation of a belt of electron precipitation in the auroral zones is very well reproduced by the model. Both its distribution in local time and the ionospheric location of its equatorward edge agree fairly well with statistical models derived from satellite observations of the auroral electron precipitation zones. On this latter point the agreement with observations is improved relative to our previous study. The formation of the electron precipitation belt modifies the convection pattern as it generates a localized enhancement of ionospheric conductivities in the auroral zone. This modification is essentially negligible on the sunlit side of the earth, where convection remains controlled by the distribution of conductivities due to the solar illumination. But it is very sensitive on the nightside, where the equipotentials are strongly distorted at the poleward and equatorward edges of the belt of enhanced conductivities, and where the evening vortex expands toward middle latitudes. In the equatorial plane of the magnetosphere, the shape of the plasmapause is also well reproduced; but its absolute size is underestimated for high levels of magnetic activity. A careful comparison of our computed electric fields with the fields measured at auroral and middle latitudes by several ionospheric incoherent scatter radars indicates that the shape of the local time variation of the fields is reproduced reasonably well, given the uncertainties inherent to the statistical averages derived from observations, and the intrinsic variability of the geophysical context. However, there is some indication that our model underestimates the magnitude of the meridional electric field at high latitudes, overestimates it at mid‐latitudes, and predicts a position in local time of the convection vortices which is two or three hours westward of the observed ones. These discrepancies can receive the same explanation: the lack of a trapped population of energetic ions in our model, which other studies have shown to be responsible for increasing the high‐latitude electric field and decreasing appreciably the mid‐latitude electric field. Our next step in magnetospheric convection modeling will be to develop a two‐fluid theory in which both electron and ion transport equations will be self‐consistently coupled to the equation of the ionospheric electrical circuit.

A simple model for the formation of “reflected,” “intermediate,” and “diffuse” ion distributions upstream of Earth's bow shock

We present a simple model unifying the distinct energetic ion populations and their associated low‐frequency hydromagnetic waves within earth's ion foreshock. Ions initially injected onto magnetic field lines at the shock excite hydromagnetic waves which pitch angle scatter the ions back toward the shock. The ions are represented by inhomogeneous inward (toward the shock) and outward traveling beams, and the transition rate between beams is determined by an effective quasi‐linear pitch angle diffusion coefficient for the transition. The intensities of waves resonant with the beams are calculated from wave kinetic equations utilizing linear wave growth rates which in turn are determined by the instantaneous, local beam densities. The coupled equations for the spatial and temporal evolution of the ion densities and wave intensities along a given magnetic field line are solved numerically assuming steady injection of ions at the shock following the initial magnetic connection of the field line to the bow shock. The initial interplanetary waves are assumed to be unpolarized on average and to propagate predominantly away from the sun relative to the solar wind. We find that (1) the ion anisotropy near the shock decreases slowly during the initial minutes of magnetic contact, but then makes a rapid transition to a steady, “diffuse” distribution; (2) the diffuse ion density declines steeply away from the shock with a scale length of ∼5 RE, forms a broad minimum, and then increases with increasing anisotropy to form an “intermediate” ion distribution; (3) upstream of the intermediate ions the density forms a broad “reflected” ion distribution with high anisotropy extending to the foreshock boundary; (4) the reflected and intermediate ion distributions are confined to spatial bands which are aligned with the foreshock boundary and have ∼5‐RE widths; and (5) the waves associated with intermediate ions are strongly right‐hand polarized in the solar wind frame whereas the waves associated with diffuse ions exhibit a net polarization within a range about zero.

Particle acceleration parallel and perpendicular to the magnetic field observed by DE‐2

Observations by the instrument payload on DE‐2 have been used to study the plasma and electrodynamic properties of the ionosphere when field‐aligned currents approaching 100 µA m−2 flow at about 900‐km altitude. In such a situation it is found that the thermal ions may account for a substantial fraction of the current carriers and that the bulk of the energetic electron population has undergone a net acceleration of a few hundred electron volts. Large amplitude electrostatic waves that have a maximum near 100 Hz and an energetic ion population that shows evidence for both parallel and perpendicular acceleration to about 30 eV also accompany such events. The horizontal thermal ion drift (electric field) that accompanies these plasma phenomena has extremely large gradients over small spatial scales. Such a signature is consistent with a requirement for a large field‐aligned current and a limit to the available field‐aligned potential difference that may be applied to the plasma.

Numerical calculations relevant to the initial expansion of the polar wind

The collisionless expansion of an H+‐O+ electron plasma into a vacuum was studied because of the relevance to the polar wind. A systematic parameter study was conducted by varying the ion composition, the initial ion‐electron temperature ratio, and the scale length of the density gradient at the plasma‐vacuum interface. The effect of gravity on O+ was also simulated. The character of the expansion is different depending on whether H+ is the major or minor ion. When H+ is the major ion, the density profile in the expansion region is always concave. On the other hand, when H+ is a minor ion, a distinct plateau forms in the H+ density, H+ drift velocity, and electrostatic potential profiles. The longer the density‐gradient scale length at the plasma‐vacuum interface, the longer it took for plateau formation. However, after plateau formation, the expansion proceeds nearly in an identical fashion regardless of the initial density‐gradient scale length. When O+ was fixed to simulate gravity, the lower end of the plateau region remained fixed at the location of the initial plasma‐vacuum interface, whereas when O+ was allowed to expand the H+ plateau region moved along with the moving O+ density front. For all cases, energetic H+ and O+ ions were observed in the expansion region. This suggests that the energization of ionospheric ions through the process of plasma expansion could be one of the mechanisms for creating the energetic ion population of ionospheric origin in the magnetosphere. Such a process would operate over the entire high‐latitude region, not just on auroral field lines. Since the largest density‐gradient scale length at the plasma‐vacuum interface that was considered is much less than typical ionospheric scale lengths, the numerical results cannot be directly applied to the polar wind. However, they illustrate the basic physical processes occuring in the polar wind expansion.

Energetic ion composition in the Earth's magnetosphere

In the previous quadrennium, 1971–1974, energetic ion composition measurements provided the first compelling evidence that the ionosphere was contributing large quantities of ions to the energetic ion fluxes in the earth's magnetosphere. With an energetic ion mass spectrometer aboard a low altitude polar orbiting satellite (1971‐089A) relatively large fluxes of energetic (0.7–12 keV) O+ and He+ ions were discovered precipitating from the magnetosphere (Shelley et al., 1972; Sharp et al., 1974; and Johnson et al., 1974). Because of the instrumentation orientation and the low altitude of the satellite, it was difficult to obtain specific information on the important basic questions relating to these ions: What were the relative contributions of the solar wind and the ionosphere to the energetic ion populations? Where was the ionospheric source region located in latitude, altitude, and local time? What physical processes were responsible for the acceleration, transport, and loss of the ionospheric ions? The presence of large fluxes of heavy (O+ and He+) energetic ionospheric ions also made it appear likely that some of the energetic H+ ions in the magnetosphere were also of ionospheric origin. This further emphasized the need for ion mass and charge identification for investigations of the entry of solar wind ions into the magnetosphere and of their subsequent acceleration, transport, and loss processes since the solar wind H+ ions could no longer always be assumed to be dominant over other sources of H+ ions in the magnetosphere.