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Analyze charged particle trajectories moving in plasma. Post processing tool: use pre-calculated plasma and magnetic field. Import of the plasma flow simulations into AMPS. Time-dependent results of the plasma modeling is saved in files. Output: 1) Individual particle trajectories, 2) Samples of the distribution functions. Particle trajectory integration in AMPS. Trajectory affected by the Lorentz force. Particle tracking along a magnetic field line.
Plasma kinetic theory application to particle distribution function for diffusion effects
A model of the quiet time middle magnetotail is developed using a consistent orbit tracing technique. The momentum equation is used to calculate geocentric solar magnetospheric components of the particle and electromagnetic forces throughout the current sheet. Ions generate the dominant x and z force components. Electron and ion forces almost cancel in the y direction because the two species drift earthward at comparable speeds. The force viewpoint is applied to a study of some substorm processes. Generation of the rapid flows seen during substorm injection and bursty bulk flow events implies substantial force imbalances. The formation of a substorm diversion loop is one cause of changes in the magnetic field and therefore in the electromagnetic force. It is found that larger forces are produced when the cross-tail current is diverted to the ionosphere than would be produced if the entire tail current system simply decreased. Plasma is accelerated while the forces are unbalanced resulting in field lines within a diversion loop becoming more dipolar. Field lines become more stretched and the plasma sheet becomes thinner outside a diversion loop. Mechanisms that require thin current sheets to produce current disruption then can create additional diversion loops in the newly thinned regions. This process may be important during multiple expansion substorms and in differentiating pseudoexpansions from full substorms. It is found that the tail field model used here can be generated by a variety of particle distribution functions. However, for a given energy distribution the mixture of particle mirror or reflection points is constrained by the consistency requirement. The study of uniqueness also leads to the development of a technique to select guiding center electrons that will produce charge neutrality all along a flux tube containing nonguiding center ions without the imposition of a parallel electric field.
The one particle distribution function f on the scale of the bounce motion of particles in a magnetic field B is considered. The Vlasov equation is expanded through O(epsilon) in the adiabatic parameter which is the ratio of particle gyroradius to scale length of the magnetic field. Because f is directly proportional to particle flux differential in kinetic energy and solid angle, f is in principle measurable in space experiments, and the analysis is tailored to be explicitly applicable to space problems. To O(1), f is gyrotropic; its first velocity moment is (if non-vanishing) parallel to B, and hence macroscopic parallel flow is included in this term. The O(epsilon) contribution is non-gyrotropic and macroscopic flow parallel to B plus additional parallel flow results from these terms. The degree of non-gyrotropy and the amount of cross-field macroscopic flow depend on the perpendicular component of the electric field, on curvature and shear in the magnetic field, and on the spatial gradient, pitch angle derivative, and speed derivative of the lowest order distribution function.
Assuming time stationarity of the one-particle distribution function f on the scale of the bounce motion of particles in a magnetic field, the paper expands the Vlasov equation through O(epsilon) in the adiabatic parameter epsilon, which is the ratio of particle gyroradius to scale length of the magnetic field. Since f is directly proportional to particle flux differential in kinetic energy and solid angle, f is in principle measurable in space experiments, and the present analysis is tailored to be explicitly applicable to space problems. It is shown that the usual expression for the electric field which produces plasma corotation in an axisymmetric system such as a dipole also holds for any nonaxisymmetric but rigidly rotating magnetic field pattern, provided the observed magnetic field is used in place of the dipole field. The analysis is applied to the electric field in a rigidly corotating magnetosphere.
The diffusion equation which describes the evolution of the average one particle distribution function for an ensemble of strongly turbulent plasmas is derived. The diffusion tensor is a time integral of the autocorrelation tensor of the fluctuations as observed by particles moving along statistically distributed orbits. These orbits contain the effects of fluctuations and thus differ from those encountered in weak turbulence theory. The plasma trajectory equations are used to relate each to the diffusion tensor itself when the turbulence is electrostatic. The diffusion tensor is explicity evaluated for a strongly turbulent unmagnetized plasma.
The diffusion equation which describes the evolution of the average one-particle distribution function for an ensemble of strongly turbulent plasmas is derived. The diffusion tensor is a time integral of the autocorrelation tensor of the fluctuations as observed by particles moving along statistically distributed orbits. These orbits contain the effects of fluctuations and thus differ from those encountered in weak turbulence theory. Two statistical orbit effects quadratic in the strength of the fluctuations affect the magnitude of the diffusion: (a) modification of the ensemble average orbits by the fluctuations, and (b) statistical dispersion in particle orbits about the average. The plasma trajectory equations are used to relate each to the diffusion tensor itself when the turbulence is electrostatic. The diffusion tensor is explicitly evaluated for a strongly turbulent unmagnetized plasma.
From June 11 to September 16, 1974, the NOAA low-energy proton detector on board the ATS 6 satellite observed 71 cases of ultralow-frequency oscillations of proton flux intensities. The oscillation periods varied from 40 s to 6 min, and the events were observed most frequently during moderate geomagnetic conditions. The flux oscillations occurred at various local times, yet almost two thirds of the events were detected in the near-dusk region of the magnetosphere. For a majority of the events in this set a substantial phase shift in flux oscillation was detected between different energy channels and/or between two oppositely oriented detector telescopes. The phase shift is mainly due to the finite gyroradius effect of the protons gyrating in the geomagnetic field. By examining this finite gyroradius effect on the perturbed particle distribution function associated with the wave in a nonuniform magnetic field, the propagation direction of the wave from particle observations made by a single spacecraft is determined
This paper considers the energetic particle populations in the downstream region of three quasi-parallel interplanetary shock events, which was explored using the ISEE 3 Ultra Low Energy Charge Analyzer sensor, which unambiguously identifies protons and alpha particles using the electrostatic deflection versus residual energy technique. The downstream particles were found to exhibit anisotropies due largely to convection in the solar wind. The spectral indices of the proton and the alpha-particle distribution functions were found to be remarkably constant during the downstream period, being generally insensitive to changes in particle flux levels, magnetic field direction, and solar wind densities. In two of the three events, the proton and the alpha spectra were the same throughout the entire downstream period, supporting the prediction of diffusive shock acceleration theory.
A one-dimensional, hybrid simulation code is used to study current sheets with a nonzero normal magnetic field B(sub z) and a dawn-to-dusk electric field E(sub y). Such configurations are dependent upon only two parameters: we use the normalized normal magnetic field B-normalized (sub z) = B(sub z)/(4(pi)(n(sub b)) (v(exp 2 sub T))(exp 1/2) and normalized electric field V-normalized (sub D) = (1/V(sub T)(cE(sub y)/B(sub z)), where V(sub T) is the thermal velocity of ions prior to their interaction with the current sheet and n(sub b) is the number density outside the current sheet (at the simulation boundary). A third parameter that is relevant to the motion of particles in current sheets is kappa(sub A), the value of kappa = (R(sub min)/rho(sub max))(exp 1/2) for particles of average energy. We find that if either B-normalized (sub z) is close to or greater than 1, or if kappa(sub A) is close to 1, a rotational mode develops in which the z = 0 current rotates with the ion sense about the normal magnetic field, while for small values of both B-normalized (sub z) or kappa(sub A), the configuration is quasi-steady. To achieve values of kappa(sub A) of the order of or larger than 1, we decrease the value of V-normalized (sub D) uniformly. We find that the magnetic field fluctuations and particle distribution functions are similar in many respects to what was observed in the day 240, 1986, Active Magnetospheric Particle Tracer Explorer (AMPTE)/CCE current disruption event, an event that appears to be located at the site of initiation of current disruption and related particle energization.
A recently extended test particle computer model of the gyroresonance wave-particle interaction in the magnetosphere is applied to previously reported cases of observed correlations between whistler mode waves and ionospheric responses to particle precipitation. Three different ionospheric effects, namely, X-ray bursts, photoemissions, and D region perturbations, all correlated with VLF waves and believed to be caused by precipitated particles, are considered. The precipitation flux level, the pulse shape, and the associated time delays are computed for the parameters relevant to each case and are compared with values deduced from the data. The results demonstrate that the existing theoretical model can be useful for interpreting experimental results of this kind. Furthermore, the model results and observations, used together, provide a basis for additional diagnostics of the various parameters of the cold and energetic particle distributions in the magnetosphere. For example, when applied to the observed photoemission case (Helliwell et al., 1980) the model results imply that the trapped energetic particle distribution function at the time could be modeled as proportional to E exp -n/2 with n about 3.5 to 6, where E is the particle energy.
A theory of medium-energy (about keV) electrons and heavy ions in Jupiter's magnetosphere is presented. Lower hybrid waves are generated by the combined effects of a ring instability of neutral wind pickup ions and the modified two-stream instability associated with transport of cool Iogenic plasma. The quasi-linear energy diffusion coefficient for lower hybrid wave-particle interactions is evaluated, and several solutions to the diffusion equation are given. Calculations based on measured wave properties show that the noise substantially modifies the particle distribution functions. The effects are to accelerate superthermal ions and electrons to keV energies and to thermalize the pickup ions on time scales comparable to the particle residence time. The S(2+)/S(+) ratio at medium energies is a measure of the relative contribution from Iogenic thermal plasma and neutral wind ions, and this important quantity should be determined from future measurements. The theory also predicts a preferential acceleration of heavy ions with an accleration time that scales inversely with the root of the ion mass. Electrons accelerated by the process contribute to further reionization of the neutral wind by electron impact, thus providing a possible confirmation of Alfven's critical velocity effect in the Jovian magnetosphere.
We perform a parameter study of the temporal evolution of a test particle distribution function in MHD turbulence. The turbulent fields are calculated using a pseudo-spectral method and periodic boundary conditions on a regular grid of 180(exp 3) points, appropriate for incompressible, homogeneous and isotropic turbulence. Initially, the kinetic and the magnetic energy are equal on the average. Both, deterministic and random initial conditions are used, in the former case with zeros of the magnetic field located at grid points, in the latter case located by interpolation between grid points. The evolution of the minor ion distribution function is studied in detail as these turbulent fields evolve, developing strong current and vorticity sheets. Using the full collisionless equation of motion for the test particles, the efficiency of nonlinear interactions can be studied. The results are compared to theoretical predictions and are then discussed in connection with the observations of the dynamical properties of solar wind minor ions derived from in situ observations.
Using the field-particle correlation technique, we examine the particle energization in a 1D-2V continuum Vlasov-Maxwell simulation of a perpendicular magnetized collisionless shock. The combination of the field-particle correlation technique with the high fidelity representation of the particle distribution function provided by a direct discretization of the Vlasov equation allows us to ascertain the details of the exchange of energy between the electromagnetic fields and the particles in phase space. We identify the velocity-space signatures of shock-drift acceleration of the ions and adiabatic heating of the electrons due to the perpendicular collisionless shock by constructing a simplified model with the minimum ingredients necessary to produce the observed energization signatures in the self-consistent Vlasov-Maxwell simulation. We are thus able to completely characterize the energy transfer in the perpendicular collisionless shock considered here and provide predictions for the application of the field-particle correlation technique to spacecraft measurements of collisionless shocks.
When charged particles spiral along a large constant magnetic field, their trajectories are scattered by random components that are superposed on the guiding field. In the simplest analysis of this situation, scattering causes the particles to diffuse parallel to the guiding field. At the next level of approximation, moving pulses that correspond to a coherent mode of propagation are present, but they are represented by delta-functions whose infinitely narrow width makes no sense physically and is inconsistent with the finite duration of coherent pulses observed in solar energetic particle events. To derive a more realistic description, the transport problem is formulated in terms of 4 x 4 matrices, which derive from a representation of the particle distribution function in terms of eigenfunctions of the scattering operator, and which lead to useful approximations that give explicit predictions of the detailed evolution not only of the coherent pulses, but also of the diffusive wake. More specifically, the new description embodies a simple convolution of a narrow Gaussian with the solutions above that involve delta-functions, but with a slightly reduced coherent velocity. The validity of these approximations, which can easily be calculated on a desktop computer, has been exhaustively confirmed by comparison with results of Monte Carlo simulations which kept track of 50 million particles and which were carried out on the Maspar computer at Goddard Space Flight Center.
Spectra of importance for the analysis of relativistic thermal plasmas are numerically calculated assuming a thermal form for the particle distribution functions. Complete sets of optically thin thermal electron-proton, electron-electron, and electron-positron bremsstrahlung spectra are calculated throughout the transrelativistic regime of electron temperatures and compared with approximate expressions for the spectra in the nonrelativistic and extreme relativistic regimes of temperature. A method for calculating accurate secondary particle production spectra in proton-proton collisions from threshold to the highest energies is presented based on an isobaric model near threshold and scaling representations at high energies. The production spectra of charged and neutral pions resulting from proton-proton collisions in relativistic proton plasmas are calculated, and the resultant electron, positron, and gamma-ray spectra from the decay of secondary pions are presented.
The shift from wave-generated anomalous resistivity toward the more large-scale effects of magnetic confinement of current carrying plasmas was inspired by the more extensive data on auroral particle distribution functions that were made available, data that may often seem consistent with a dissipation-free acceleration of auroral electrons over an extended altitude range. Efforts to interpret these data have brought new vigor to the concept that a smooth and static electric field can be self-consistently generated by suitable pitch angle anisotropies among the high altitude particle populations, different for electrons and ions, and that such an electric field is both necessary and sufficient to maintain the plasma in a quasi-neutral steady state. Certain aspects of this concept are reviewed and criticized, both from a general theoretical standpoint and from the standpoint of what is known about the magnetospheric environment. It is argued that this concept has flaws and that the actual physical problem is considerably more complicated, requiring a more complex electric field, possibly including double layer structures.
An important region of the earth's magnetosphere is the nightside magnetotail, which is believed to play a significant role in energy storage and release associated with substorms. The magnetotail contains a current sheet which separates regions of oppositely directed magnetic field. Particle motion in the collisionless magnetotail has been a long-standing problem. Recent research from the dynamical point of view has yielded considerable new insights into the fundamental properties of orbits and of particle distribution functions. A new framework of understanding magnetospheric plasma properties is emerging. Some novel predictions based directly on nonlinear dynamics have proved to be robust and in apparent good agreement with observation. The earth's magnetotail may serve as a paradigm, one accessible by in situ observation, of a broad class of boundary regions with embedded current sheets. This article reviews the nonlinear dynamics of charged particles in the magnetotail configuration. The emphasis is on the relationships between the dynamics and physical observables. At the end of the introduction, sections containing basic material are indicated.