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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Putting quasilinear theory to the test: A comparison of analytical theory with results from a trajectory code

Parallel and perpendicular diffusion coefficients were computed numerically by following particle orbits in a simulated magnetic field. The simulated field was chosen to have delta B/B(sub o) small, so as to provide a test of quasilinear theory in a regime where the theory should be most accurate. The simulation space is large enough to contain many magnetic field correlation lengths, so that effects of field line random walk can be studied. After presenting results for parallel diffusion, we will focus on two controversial issues relating to perpendicular diffusion: (1) Do quasilinear descriptions of perpendicular diffusion retain any validity for particles whose Larmor radius is smaller than a correlation length? (2) Does field line random walk lead to particle diffusion in the usual sense, or does it produce 'compound' diffusion for which particles spread out proportionally to t(exp 1/4) instead of t(exp 1/2)?

Bieber, J. W.↗
NASA NTRS1972

Electrothermal oscillations and the quasilinear theory of electron enthalpy fluctuations in magnetohydrodynamic generators and magnetoplasmadynamic arc thrusters

Flucturations in electron density and temperature coupled through OHM's Law are studied for MHD power generator and MPD arc thruster applications. The dispersion relation based on linear theory is derived, and the two limiting cases of infinite ionization rate and frozen flow are examined. The nonlinear effects of the frozen flow case are then studied in the quasilinear limit. Equations are derived for the amplitude of the fluctuation and its effect upon Ohm's Law and the electron temperature equation. Conditions under which a steady state can exist in the presence of the fluctuation are examined, and effective transport properties are determined.

Smith, J. M.↗
NASA NTRS1976

The partially averaged field approach to cosmic ray diffusion

The kinetic equation for particles interacting with turbulent fluctuations is derived by a new nonlinear technique which successfully corrects the difficulties associated with quasilinear theory. In this new method the effects of the fluctuations are evaluated along particle orbits which themselves include the effects of a statistically averaged subset of the possible configurations of the turbulence. The new method is illustrated by calculating the pitch angle diffusion coefficient D sub Mu Mu for particles interacting with slab model magnetic turbulence, i.e., magnetic fluctuations linearly polarized transverse to a mean magnetic field. Results are compared with those of quasilinear theory and also with those of Monte Carlo calculations. The major effect of the nonlinear treatment in this illustration is the determination of D sub Mu Mu in the vicinity of 90 deg pitch angles where quasilinear theory breaks down. The spatial diffusion coefficient parallel to a mean magnetic field is evaluated using D sub Mu Mu as calculated by this technique. It is argued that the partially averaged field method is not limited to small amplitude fluctuating fields and is hence not a perturbation theory.

Jones, F. C.↗
NASA NTRS1992

Ion radial diffusion in an electrostatic impulse model for stormtime ring current formation

Guiding-center simulations of stormtime transport of ring-current and radiation-belt ions having first adiabatic invariants mu is approximately greater than 15 MeV/G (E is approximately greater than 165 keV at L is approximately 3) are surprisingly well described (typically within a factor of approximately less than 4) by the quasilinear theory of radial diffusion. This holds even for the case of an individual model storm characterized by substorm-associated impulses in the convection electric field, provided that the actual spectrum of the electric field is incorporated in the quasilinear theory. Correction of the quasilinear diffusion coefficient D(sub LL)(sup ql) for drift-resonance broadening (so as to define D(sub LL)(sup ql)) reduced the typical discrepancy with the diffusion coefficients D(sub LL)(sup sim) deduced from guiding-center simulations of representative-particle trajectories to a factor of approximately 3. The typical discrepancy was reduced to a factor of approximately 1.4 by averaging D(sub LL)(sup sim), D(sub LL)(sup ql), and D(sub LL)(sup rb) over an ensemble of model storms characterized by different (but statistically equivalent) sets of substorm-onset times.

Chen, Margaret W.↗
NASA NTRS1995

Stormtime ring current and radiation belt ion transport: Simulations and interpretations

We use a dynamical guiding-center model to investigate the stormtime transport of ring current and radiation-belt ions. We trace the motion of representative ions' guiding centers in response to model substorm-associated impulses in the convection electric field for a range of ion energies. Our simple magnetospheric model allows us to compare our numerical results quantitatively with analytical descriptions of particle transport, (e.g., with the quasilinear theory of radial diffusion). We find that 10-145-keV ions gain access to L approximately 3, where they can form the stormtime ring current, mainly from outside the (trapping) region in which particles execute closed drift paths. Conversely, the transport of higher-energy ions (approximately greater than 145 keV at L approximately 3) turns out to resemble radial diffusion. The quasilinear diffusion coefficient calculated for our model storm does not vary smoothly with particle energy, since our impulses occur at specific (although randomly determined) times. Despite the spectral irregularity, quasilinear theory provides a surprisingly accurate description of the transport process for approximately greater than 145-keV ions, even for the case of an individual storm. For 4 different realizations of our model storm, the geometric mean discrepancies between diffusion coefficients D(sup sim, sub LL) obtained from the simulations and the quasilinear diffusion coefficient D(sup ql, sub LL) amount to factors of 2.3, 2.3, 1.5, and 3.0, respectively. We have found that these discrepancies between D(sup sim, sub LL) and D(sup ql, sub LL) can be reduced slightly by invoking drift-resonance broadening to smooth out the sharp minima and maxima in D(sup ql, sub LL). The mean of the remaining discrepancies between D(sup sim, sub LL) and D(sup ql, sub LL) for the 4 different storms then amount to factors of 1.9, 2.1, 1.5, and 2.7, respectively. We find even better agreement when we reduce the impulse amplitudes systematically in a given model storm (e.g., reduction of all the impulse amplitudes by half reduces the discrepancy factor by at least its square root) and also when we average our results over an ensemble of 20 model storms (agreement is within a factor of 1.2 without impulse-amplitude reduction). We use our simulation results also to map phase-space densities f in accordance with Liouville's theorem. We find that the stormtime transport of approximately greater than 145-keV ions produces little change in f-bar the drift-averaged phase-space density on any drift shell of interest. However, the stormtime transport produces a major enhancement from the pre-storm phase-space density at energies approximately 30-145 keV, which are representative of the stormtime ring current.

Lyons, Larry R.↗
NASA NTRS1975

Charged particle propagation in strong disordered magnetic fields

The use of quasilinear theory in calculating particle trajectories in strong random fields is beset by a basic difficulty concerning the breakdown of the basic assumption of the theory. This assumption is that the random force acting on the particle becomes self-incoherent before it has changed the particle's trajectory in phase space, ie., its position or velocity, by a significant amount. The various time scales involved in this problem are defined and compared to determine in which regions the basic assumptions of quasilinear theory are violated. It is shown how nonlinear theories in general and the Partially Averaged Field theory (Jones et al. 1973) can partly alleviate these difficulties.

Jones, F. C.↗
NASA NTRS1973

On the improper neglect of certain terms in random function theory

This paper presents some exact solutions of problems in random function theory for the purpose of testing the validity of an approximate method known variously in the many different fields of its application as first order smoothing theory, first order cumulant discard, quasilinear theory, or the adiabatic approximation. The hydromagnetic dynamo equations are used here, as particularly appropriate for such an investigation. The calculations show that in one case the exact and approximate solutions agree. In the other case the approximate solution is wrong. Hence, in the absence of a general criterion for validity, a result based on first order smoothing theory is a conjecture rather than a fact. This impacts strongly on much of the recent work on hydromagnetic dynamos.

Lerche, I.↗
NASA NTRS1986

Relativistic dispersion modifications to the cyclotron maser theory of planetary radio emissions

The effects of relativistic dispersion on the electron-cyclotron maser instability are investigated by linear theory, electromagnetic particle simulation, and quasilinear theory. When vsq/csq greater than or = omega pesq/Omega sq for the energetic electrons, the instability is localized just below k c/Omega e = 1, and the growth rate is strongly peaked for emission at 90 deg to the magnetic field. Saturation of the instability is due to perpendicular diffusion in momentum space, and the saturation level increases as omega pe/Omega e is decreased. Applications of the maser instability to the generation of the Earth's auroral kilometric radiation are discussed.

Pritchett, P. L.↗
NASA NTRS1986

Relativistic dispersion modifications to the cyclotron maser theory of planetary radio emissions

The effects of relativistic dispersion on the electron-cyclotron maser instability are investigated by means of linear theory, electromagnetic particle simulation, and quasilinear theory. Saturation of the instability is due to perpendicular diffusion in momentum space, and the saturation level increases as the plasma frequency/electron cyclotron ratio is decreased. Applications of the maser instability to the generation of the the earth's auroral kilometric radiation are discussed.

Pritchett, P. L.↗
NASA NTRS1974

Simulation of pitch angle diffusion of charged particles in a disordered magnetic field

Results are reported for computer simulation experiments in which a statistical ensemble of random magnetic field realizations is generated, orbits of charged particles in the random fields are followed, and a pitch-angle diffusion coefficient is derived from the temporal evolution of the orbits. Diffusion coefficients predicted by three nonlinear theories are compared with the derived coefficients for the standard quasilinear theory of velocity diffusion, and the goals of future simulations are outlined.

Kaiser, T. B.↗