Bounce Times Research Articles

New aspects on nonlinear Landau damping

Recently a new description of nonlinear Landau damping, applicable to wave propagation in a weakly collisional as well as collisionless plasma, has been presented. The results in that work are extended in order to give a more detailed picture of the long term evolution. It is concluded that collisions cannot be negligible more than 10–20 bounce times, even for a very low collision frequency.

The role of wave-particle decorrelation mechanisms in ICRF heating of toroidal plasmas

Wave-particle decorrelation mechanisms affect the ICRF heating efficiency. Depending on the relative magnitude of the bounce and decorrelation times, three regimes are distinguished. When the decorrelation is due to collisions, these three regimes roughly correspond to thermal, α and RF induced tail particles, respectively. Heating efficiencies may be significantly lower than predicted by models assuming uncorrelated resonance crossings; this has an immediate bearing on superadiabatic α particles which will then absorb less ICRH power.

Magnetospheric interchange instability in anisotropic plasma

We study magnetospheric interchange instability under the assumption that the plasma pressure distribution is anisotropic. Previous studies of magnetospheric interchange instability have only considered the case of isotropic pressure. We also argue that, under certain circumstances, substantial particle energization can accompany outward interchange motions in rapidly rotating magnetic fields. Our studies of instability treat the plasma as an MHD fluid and deal with two special cases in which the plasma pressure evolves anisotropically as the interchange motion proceeds. The first case is that of “fast” interchange motions, where interchange motions can take place rapidly compared with particle bounce times. Our analysis uses a small perturbation approach and takes into account the curved magnetic field, and external forces such as gravity or an effective gravity arising from rotation of the system. We contrast this with a second case in which the plasma motion conserves the adiabatic invariants μ and J, and in both cases consider the implications for a plasma generated by a satellite source in the equatorial plane of a rapidly rotating, spin-aligned magnetic field. A consequence of fast interchange motions in a corotation-dominated magnetosphere is that the rapid motions will be accompanied by motion of ionized material away from (toward) the equatorial plane as the material moves outward (inward). If an outward (inward) interchange motion should be slowed such that it is no longer rapid compared with particle bounce times, particles will resume bounce motion, but with increased (reduced) parallel energy. In practice, it is likely that lower energy particles in a distribution will violate the longitudinal invariant, J, during interchange motion, whereas particles of higher energy will conserve J. Thus our work implies that the lower the energy of a plasma, the less likely it is to remain equatorially confined during outward interchange motion, whether it is a diffusive or steady process. We discuss our results in the context of the Jovian magnetosphere.

Controlled experiments in the earth's magnetosphere with artifical electron beams

This article describes the Electron Echo project, which used artificial electron beams to determine how natural particles are accelerated and lost from the trapping region in the earth's magnetosphere. The problems of injecting electron beams into the ionosphere, including vehicle charging and beam-plasma instabilities, are discussed, and images of the Echo beams both in space and in the laboratory are shown. The beam pulses were detected and analyzed after reflection from the conjugate hemisphere mirror points. Although the injected beams contained a wide spread of energies, the echoes displayed a monoenergetic peak, which together with the exact drift displacement during one bounce permitted a separate evaluation of electric and magnetic components of the transverse drifts in the distant magnetosphere. Thus distant electric fields were measured and found to have large turbulent fluctuations compared to the local ionospheric fields, and to differ in average value from the local fields by about 50 mV/m, indicating the existence of parallel potential drops. The measured bounce times and field-line lengths were compared with model magnetic geometries. The best fit was with the Tsyganenko-Usmanov 1982 version. Pitch-angle diffusion out of the loss cone resulted in a large loss in beam intensity during one bounce, showing the presence of important beam perturbations near the electron gyrofrequency range. Thus the Echo experiments evaluated many effects on the natural trapped particles, but were limited to a moderately disturbed condition of the magnetosphere when the magnetic morphology was stable.

Comparison of Echo 7 field line length measurements to magnetospheric model predictions

The Echo 7 sounding rocket experiment injected electron beams on central tail field lines near L = 6.5. Numerous injections returned to the payload as “conjugate echoes” after mirroring in the southern hemisphere. We compare field line lengths calculated from measured conjugate echo bounce times and energies to predictions made by integrating electron trajectories through various magnetospheric models: the Olson‐Pfitzer Quiet and Dynamic models and the Tsyganenko‐Usmanov model. Although Kp at launch was 3−, quiet time magnetic models best fit the echo measurements. Geosynchronous satellite magnetometer measurements near the Echo 7 field lines during the flight were best modelled by the Olson‐Pfitzer Dynamic Model and the Tsyganenko‐Usmanov model for Kp = 3. The discrepancy between the models that best fit the Echo 7 data and those that fit the satellite data was most likely due to uncertainties in the small‐scale configuration of the magnetospheric models. The field line length measured by the conjugate echoes showed some temporal variation in the magnetic field, also indicated by the satellite magnetometers. This demonstrates the utility an Echo‐style experiment could have in substorm studies.

Conjugate echoes of artificially injected electron beams detected optically by means of new image processing

Following two upward injections of energetic electrons (38 keV and 26 keV) from the Echo 4 rocket‐borne electron accelerator (January 31, 1976, Poker Flat, Alaska), artificial auroral streaks were detected by ground‐based low‐light‐level television. The streaks were recognized recently by using newly developed image‐processing techniques. They were delayed relative to the injections by 2.06 s and 2.42 s, respectively. These measurements of the bounce times of electrons of known energy constitute two accurate determinations of a high‐latitude field line length (106±1×106 m). The delays are only 4–5% longer than calculated using a dynamic model of the geomagnetic field (Olson and Pfitzer, 1982). Other field models yielded shorter bounce times. Since the delays were in the inverse ratio of the relativistic velocities calculated for the nominal beam energies, it is concluded that the potential of the payload remained below 1 kV during 45 mA injections at an altitude of 210 km. The echo streaks showed little dispersion in either time or space, indicating that the portion of the beam returning to the northern hemisphere loss cone remained collimated and nearly monoenergetic. But there was a 70% loss in the return flux. A diligent search failed to locate similar echoes from the more powerful injections employed in the Echo 5 and Echo 7 rocket experiments, suggesting flux losses of at least 98% and 92%, respectively. The losses are thought to be due to pitch angle scattering out of the loss cone as the electrons traverse the equatorial region but could also be due to collective beam plasma interactions. The lower loss rate in Echo 4 is likely related to the presence of only weak diffuse aurora during that flight.

AUREOL-3 Results on Ion Precipitation

This paper attempts to summarize recent experimental studies on suprathermal (<14 keV) ion precipitation in the morning side auroral zone from ion composition data provided by the low-altitude (400-2000 km) AUREOL-3 polar orbiting satellite. Plasma measurements show that on auroral and polar cap field-lines upflowing ionospheric ions, mostly O+ and H+, are commonly observed. Imbedded in the discrete auroral region different narrow bands of ion precipitation are observed with a clear energy-lattitude dispersion. These structures can be interpreted as H+ ion beams which have experienced velocity filter effects after ejection either from the conjugate ionosphere or from reconnection regions in the magnetotail. Finally the low energy (< 200 eV) ion precipitation (H+, O+, He+) found equatoward of the precipitation region of more energetic and adiabatically accelerated ions can be satisfactorily explained by the drift of ionospheric ions, ejected with conical distributions and then convected earthward and eastward in a few bounce times.

Design Optimization of Rocker-Switch Dynamics to Reduce Pivot Bounce and the Effect of Load Current in Modifying Bounce Characteristics

A previously developed computer model of the dynamics of hand-operated rocker switches is used with the aim of reducing pivot bounce and erosion. The method used is to study the kinetic energy at the instant of main contact impact, showing how the energy is affected by the force applied to the switch and how it relates to the switch dimensions. Some possible modifications are suggested. These are compared in experiments using a low-current source. In the experiments the pivot bounce times are measured and compared to the computer-predicted values of kinetic energy, demonstrating the relationship between energy and pivot bounce and showing how a reduction in energy reduces bounce. When a load current flows, a reduction in the bounce time duration is observed. The results are presented of the reduction at 12-A dc for various mechanical bounce times.

A relativistic multiregion bounce-averaged Fokker-Planck code for mirror plasmas

We have developed a unique Fokker--Planck code to study the physics of plasmas that are trapped in magnetic and potential wells of general shape on a collisional time scale. The code was designed primarily to apply to mirror machines, either a simple mirror or a tandem mirror. A plasma confined in a mirror machine generally consists of various groups of particles trapped magnetically and/or electrostatically depending on their energy, magnetic moment, and axial position. Characteristic features of such a plasma are: first, that the bounce times of trapped particles are much shorter than the collision times; and second, that particles trapped in different axial locations can have the same energy and magnetic moment. The former feature allows us to perform bounce-orbit averaging of the kinetic equation, and the latter feature indicates that the distribution function can be multivalued. The code solves a relativistic Fokker--Planck equation averaged over bounce orbits for all the trapped-particle groups. In addition to the Coulomb collision operator, the code includes a synchrotron radiation term, a quasilinear rf diffusion operator, and source and loss terms. The numerical method consists of a mapping technique and a Galerkin finite-element method. Example results using the code for electron-cyclotron resonant heatingmore » and neutral beam injection in a tandem mirror are also presented.« less

Positive ion distributions in the morning auroral zone: Local acceleration and drift effects

We report on the typical structure of the large scale ion precipitation in the morning sector of the auroral zone and associated low frequency electromagnetic waves. Data obtained during near radial passes of the AUREOL-3 satellite point to a distinction between two main precipitation regions: 1) In the poleward part of the auroral zone the latitudinal variation of the average energy (or temperature) of the precipitated ions (mainly H +) indicate that they are adiabatically accelerated in the outer magnetosphere. This “high energy” (⋍ 3 to > 20 keV) precipitation is usually associated with a low energy (E < 110 eV) upward flowing 0 + and H + component, and 2) near the boundary between discrete and diffuse electron aurorae a drastic change in the ion characteristics is observed. The flux of energetic precipitated H + ions is sharply reduced, which suggests the formation of an Alfvén layer. However, intense fluxes of precipitated H +, O +, and He + ions with energies < 3 keV are observed equatorward of the Alfvén layer, in coincidence with the diffuse aurora and in association with quasi-monochromatic electromagnetic waves with frequencies around the proton gyrofrequency. As the characteristic convection and bounce times of the low energy upward flowing ion component are comparable (τ > 3 hours) we suggest that the precipitation of ionospheric ions inside the diffuse aurora results from convection and corotation of the ions accelerated to suprathermal energies at higher latitudes.

The application of artificial electron beams to magnetospheric research

In the last decade, more than 25 large research rockets have injected electron beams into the ionosphere and magnetosphere to probe the magnetosphere or to investigate various basic problems in space plasma physics. The problem of vehicle neutralization has been studied in the altitude region 100–300 km, and it is now known that the beam injection produces a hot plasma extending possibly as much as 100 m from the vehicle. Vehicle neutralization is enhanced by a discharge associated with the beam or with the return current. The neutralization current may be locally enhanced by neutral gas. Beams have been projected for long distances and appear to be stable in many cases. However, certain beam‐plasma discharges similar to those observed in laboratory experiments may have also occurred in space, tending to thermalize high‐energy beams. Several types of experiments search for beam echoes from field‐aligned potential differences thought to cause auroras. Others have made observations at conjugate regions in the opposite hemisphere for magnetic geometry studies. In the Minnesota ‘Echo’ technique, conjugate hemisphere beam echoes are detected on board the source rocket. From the Echo experiments it was found that ionospheric electric fields map along auroral zone field lines as equipotentials through the equatorial plane. Echo bounce times can be fitted in some cases to model fields, but in other cases the field may be distorted or extended in the night region. Examples from the Echo program at Minnesota are used to illustrate electron beams as magnetospheric ‘probes.’ The injection of such beams creates rich sources of plasma and electromagnetic waves, which have been detected by ejected subsystems near the mother rocket or at ground level. The frequency range extends from a few kilohertz to at least 50 MHz and includes lower hybrid, whistler mode, electron cyclotron harmonics, upper hybrid, and plasma frequency emission. Electron beams have been used to produce artificial auroras that were observed by sensitive television techniques, by other optical methods, and by radar reflections. The scattering, energy loss, and magnetic reflection of beams in the 100‐km atmosphere region have also received detailed study. Future programs including Space Shuttle are discussed. Summaries of the current experimental programs and complete literature references are included.

Adiabatic particle motion in a nearly drift‐free magnetic field: Application to the geomagnetic tail

The guiding center motion of particles in a ‘nearly’ drift‐free magnetic field is analyzed in order to investigate the dependence of the mean drift velocity on equatorial pitch angle, the variation of the local drift velocity along the trajectory, and other properties. The fields considered here are two‐dimensional and depart slightly from a class of drift‐free fields, resembling the field of the geomagnetic tail, with the following properties: (1) no y component and no y dependence, (2) Bx = 0 in the equatorial plane and z = 0, and (3) Bz = B0 = const. In such a field, it has been shown, particles may be trapped, but they exhibit no net drift in the y direction: their instantaneous drifts at any time may be large, but when they are averaged over a sufficiently long time (or, for adiabatic particles, over a bounce period), the result is zero. Here a slight modification of this mode is explored, motion in a field in which Bz slowly varies in the x direction, as is indeed observed in the geomagnetic tail. The mean drift 〈υy〉 for adiabatic particles can now be expressed by means of elliptic integrals: it no longer vanishes but is merely small; if υ0 is the drift velocity for equatorial particles (which is easily derived), 〈υy〉 is typically between υ0 and υ0/3. By contrast, instantaneous guiding center drift velocities at z = 0 may be 50 times larger. Explicit approximations to the twice‐averaged Hamiltonian W(α, μ, J) near z = 0 are also derived, permitting simple representation of drift paths if an electric potential ϕ(α, β) also exists. In addition, the use of W or expressions for the longitudinal invariant allows the derivation of the twice‐averaged Liouville equation and the corresponding Vlasov equation. Bounce times are calculated (by using the drift‐free approximation), as are instantaneous guiding center drift velocities, which are then used to provide a numerical check on the formulas for 〈υy〉.

Echo III: The study of electric and magnetic fields with conjugate echoes from artificial electron beams injected into the auroral zone ionosphere

The third in a series of rocket flights carrying large electron guns for electron beam‐plasma analysis and magnetosphere probing has been carried out from the Poker Flat rocket range near Fairbanks, Alaska at L=6. Echoes from the injected electrons mirroring at the southern hemisphere conjugate point were observed on the rocket by particle detectors and in the nearby ionosphere by photometers on board the rocket. The bounce time and drift velocities of the echoes were measured using the known trajectory and aspect of the rocket. Ionospheric electric fields near the rocket were inferred from drift motion of the ambient ion population measured by two techniques, electrostatic analyzers on board the rocket and incoherent backscatter radar from the ground. Using model magnetic fields, gradient and curvature drift and bounce times have been computed under the conditions appropriate for this experiment. Assuming that field lines are equipotentials, the addition of the observed ionospheric electric field drift to the model‐dependent gradient and curvature drift predicts a net echo drift velocity that is in agreement with the observations, provided the Mead‐Fairfield 1972‐73 model is used. The observed bounce time constitutes an independent model check and is in better agreement with the Olson‐Pfitzer model. Echo spatial and temporal fluctuations reflected the turbulence associated with the diffuse aurora into which the rocket was launched.

Electron Echo Experiment 1: Comparison of observed and theoretical motion of artificially injected electrons in the magnetosphere

On August 13, 1970, a sounding rocket launched from Wallops Island, Virginia, was used to successfully inject a controlled beam of energetic electrons into the trapping region of the earth's magnetosphere. The Aerobee 350 rocket carried a high-voltage electron gun, electron detectors, receivers to measure the electric field of waves generated by the experiment, and other apparatus to a peak altitude of 350 km. During a 10-min flight, more than 3000 16-ms-long 70-mA pulses of 35- to 43-keV electrons were injected into the magnetosphere with pitch angles within 25° of the local 90° mirror angle. The electrons, trapped in the geomagnetic field, bounced between the mirror point near the rocket and the southern conjugate point (−66° latitude, −82° longitude) while they were drifting eastward across field lines on a drift shell of constant McIlwain L parameter (2.56) under the gradient and curvature forces. Since Wallops Island conjugate mirror altitudes are at least 300 km lower than the injection altitudes, all returning electrons were backscattered from the atmosphere in the southern hemisphere. The rocket was launched eastward in an attempt to intercept the returning electrons, and for a 90-s interval about L apogee, electrons were detected returning from one, two, and in one case, three complete bounces to the southern hemisphere. The analyzed electron data agree well with echo patterns predicted from theoretical particle motion in models of the geomagnetic field combined with Monte Carlo studies of energy loss and diffusion in the conjugate point atmosphere. Observed bounce times, drift displacements, and cross L diffusion were in substantial agreement with theory. However, the returning flux was lower than predicted, and discrepancies between theory and experiment were observed at large diffusion distances. This experiment, Electron Echo 1, verified the concept of using controlled particle beams as magnetospheric probes, showing that such beams are sufficiently stable to be intercepted after bounces to the conjugate point and back.

Recent Investigations of Hydromagnetic Emissions Part II. Theoretical Interpretation

Recent experimental and theoretical work suggests the hypothesis that hydromagnetic (hm) emissions are hydromagnetic wave packets guided by field lines as they bounce back and forth between hemispheres of the earth. As such they are analogous to whistlers, and one test of the hypothesis is the quantitative calculation of plasma densities in the outer magnetosphere and their comparison with whistler densities closer to the earth.Many hm emission exhibit measurable dispersion when displayed in the form of sonagrams (frequency vs time displays). In such cases, the measurement of group bounce times at two different emission frequencies can be combined with an accurate model of the magnetosphere to determine the zero-frequency (Alfvén) bounce period and the equatorial cyclotron frequency above which the wave cannot propagate. These two quantities uniquely define the field line along which the hm emission propagated and the integrated plasma density along that field line.Analysis of 9 events showed they occurred on field lines crossing the equatorial plane between 4 and 10 earth radii, and showed equatorial plasma densities in agreement with extrapolated whistler “knee” densities.