1,101 research outputs found
Theory of flux anisotropies in a guiding center plasma
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
Nonzero electron temperature effects in nonlinear mirror modes
The nonlinear theory of the magnetic mirror instability (MI) accounting for nonzero electron temperature effects is developed. Based on our previous low-frequency approach to the analysis of this instability and including nonzero electron temperature effects a set of equations describing nonlinear dynamics of mirror modes is derived. In the linear limit a Fourier transform of these equations recovers the linear MI growth rate in which the finite ion Larmor radius and nonzero electron temperature effects are taken into account. When the electron temperature T-e becomes of the same order as the parallel ion temperature T the growth rate of the MI is reduced by the presence of a parallel electric field. The latter arises because the electrons are dragged by nonresonant ions which are mirror accelerated from regions of high to low parallel magnetic flux. The nonzero electron temperature effect also substantially modifies the mirror mode nonlinear dynamics. When T-e similar or equal to T the transition from the linear to nonlinear regime occurred for wave amplitudes that are only half that which was inherent to the cold electron temperature limit. Further nonlinear dynamics developed with the explosive formation of magnetic holes, ending with a saturated state in the form of solitary structures or cnoidal waves. This shows that the incorporation of nonzero temperature results in a weak decrease in their spatial dimensions of the holes and increase in their depth
Applications of numerical codes to space plasma problems
Solar wind, earth's bowshock, and magnetospheric convection and substorms were investigated. Topics discussed include computational physics, multifluid codes, ionospheric irregularities, and modeling laser plasmas
A study of waves in the earth's bow shock
The perturbation vectors of waves up and downstream from the region of maximum compression in the bow shock were examined on OGO-5 under particularly steady solar wind conditions. The polarization of the upstream waves was RH, circular and of the downstream waves LH, elliptical in the spacecraft frame. By observing that the polarization of the waves remained unchanged as the shock motion swept the wave structure back and forth across the satellite three times in eight minutes, it was found that the waves were not stationary in the shock frame. A study of the methods of determining the shock normal indicates that the normal estimated from a shock model should be superior to one based upon magnetic coplanarity. The propagation vectors of the waves examined did not coincide with the shock model normal, the average magnetic field, or the plasma flow velocity. However, the major axis of the polarization ellipse of the downstream wave was nearly parallel to the upstream propagation vector
Hamiltonian Theory of Adiabatic Motion of Relativistic Charged Particles
A general Hamiltonian theory for the adiabatic motion of relativistic charged
particles confined by slowly-varying background electromagnetic fields is
presented based on a unified Lie-transform perturbation analysis in extended
phase space (which includes energy and time as independent coordinates) for all
three adiabatic invariants. First, the guiding-center equations of motion for a
relativistic particle are derived from the particle Lagrangian. Covariant
aspects of the resulting relativistic guiding-center equations of motion are
discussed and contrasted with previous works. Next, the second and third
invariants for the bounce motion and drift motion, respectively, are obtained
by successively removing the bounce phase and the drift phase from the
guiding-center Lagrangian. First-order corrections to the second and third
adiabatic invariants for a relativistic particle are derived. These results
simplify and generalize previous works to all three adiabatic motions of
relativistic magnetically-trapped particles.Comment: 20 pages, LaTeX, to appear in Physics of Plasmas (Aug, 2007
Gyrokinetic Equations for Strong-Gradient Regions
A gyrokinetic theory is developed under a set of orderings applicable to the
edge region of tokamaks and other magnetic confinement devices, as well as to
internal transport barriers. The result is a practical set equations that is
valid for large perturbation amplitudes [q{\delta}{\psi}/T = O(1), where
{\delta}{\psi} = {\delta}{\phi} - v_par {\delta}A_par/c], which is
straightforward to implement numerically, and which has straightforward
expressions for its conservation properties. Here, q is the particle charge,
{\delta}{\phi} and {\delta}A_par are the perturbed electrostatic and parallel
magnetic potentials, v_par is the parallel velocity, c is the speed of light,
and T is the temperature. The derivation is based on the quantity
{\epsilon}:=({\rho}/{\lambda})q{\delta}{\psi}/T << 1 as the small expansion
parameter, where {\rho} is the gyroradius and {\lambda} is the perpendicular
wavelength. Physically, this ordering requires that the E\times B velocity and
the component of the parallel velocity perpendicular to the equilibrium
magnetic field are small compared to the thermal velocity. For nonlinear
fluctuations saturated at "mixing-length" levels (i.e., at a level such that
driving gradients in profile quantities are locally flattened), {\epsilon} is
of order {\rho}/L, where L is the equilibrium profile scale length, for all
scales {\lambda} ranging from {\rho} to L. This is true even though
q{\delta}{\psi}/T = O(1) for {\lambda} ~ L. Significant additional
simplifications result from ordering L/R =O({\epsilon}), where R is the spatial
scale of variation of the magnetic field. We argue that these orderings are
well satisfied in strong-gradient regions, such as edge and screapeoff layer
regions and internal transport barriers in tokamaks, and anticipate that our
equations will be useful as a basis for simulation models for these regions.Comment: Accepted for publication in the Physics of Plasmas, 12/30/201
Perturbation analysis of trapped-particle dynamics in axisymmetric dipole geometry
The perturbation analysis of the bounce action-angle coordinates
for charged particles trapped in an axisymmetric dipole magnetic field is
presented. First, the lowest-order bounce action-angle coordinates are derived
for deeply-trapped particles in the harmonic-oscillator approximation. Next,
the Lie-transform perturbation method is used to derive higher-order anharmonic
action-angle corrections. Explicit expressions (with anharmonic corrections)
for the canonical parallel coordinates and are
presented, which satisfy the canonical identity . Lastly, analytical expressions for the bounce and drift frequencies
(which include anharmonic corrections) yield excellent agreement with exact
numerical results.Comment: 16 pages, 3 figure
Bulletin No. 97 - Report on the Southern Utah Experiment Station
When, in the early part of the year 1905 , the management of the Southern Utah Experiment Farm was turned over to the officials of the Utah Agricultural Experiment Station, in compliance with an act of the legislature of that year a number of experiments were under way, principally variety tests with orchard and small fruit. The State Board of Horticulture had been in charge of this farm since its establishment in 1899, and had succeeded in making out of it not only a place that will indicate the varieties of fruits adapted to that climate and soil , but also a farm that in neatness and careful arrangement can be an instructive model to anyone contemplating engaging in that industry. The new management decided not to make any radical change in the tests that were under way , but to continue them to such a conclusion a will yield the valuable results that were to come out of them. New tests or investigations are to be started with the same crop without interfering with them as variety tests, and upon the ground still available or which has not yet been set out into orchard, vineyard, or other permanent crops. Such it is planned to do as the problems suggest themselves, and as means are available
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