Periodic Drift Motion and Conservation of the Third Adiabatic Invariant

Author(s):  
J. G. Roederer
2009 ◽  
Vol 27 (5) ◽  
pp. 2173-2181 ◽  
Author(s):  
A. Y. Ukhorskiy ◽  
M. I. Sitnov ◽  
K. Takahashi ◽  
B. J. Anderson

Abstract. During geomagnetic storms relativistic electron fluxes in the outer radiation belt exhibit dynamic variability over multiple orders of magnitude. This requires radial transport of electrons across their drift shells and implies violation of their third adiabatic invariant. Radial transport is induced by the interaction of the electron drift motion with electric and magnetic field fluctuations in the ULF frequency range. It was previously shown that solar-wind driven ULF waves have long azimuthal wave lengths and thus can violate the third invariant of trapped electrons in the process of resonant interaction with their gradient-curvature motion. However, the amplitude of solar-wind driven ULF waves rapidly decreases with decreasing L. It is therefore not clear what mechanisms are responsible for fast transport rates observed inside the geosynchronous orbit. In this paper we investigate wether stormtime Pc5 waves can contribute to this process. Stormtime Pc5s have short azimuthal wave lengths and therefore cannot exhibit resonance with the the electron drift motion. However we show that stormtime Pc5s can cause localized random scattering of electron drift motion that violates the third invariant. According to our results electron interaction with stormtime Pc5s can produce rapid radial transport even as low as L≃4. Numerical simulations show that electron transport can exhibit large deviations from radial diffusion. The diffusion approximation is not valid for individual storms but only applies to the statistically averaged response of the outer belt to stormtime Pc5 waves.


2010 ◽  
Vol 3 (2) ◽  
pp. 76-79
Author(s):  
Andrey V. Ivanov ◽  
Mikhail A. Tiunov

The technique of adiabatic invariant calculation in cross-section of magnetized intensive relativistic beam with consideration of drift motion of beam particles centers of rotation is suggested. Example of adiabatic invariant calculation of electrons of intensive beam in electrostatic accelerating system with longitudinal magnetic field is presented. It was shown that in strong enough magnetic field transverse energy of electrons preserves even at abrupt alteration of electric field.


1967 ◽  
Vol 31 ◽  
pp. 177-179
Author(s):  
W. W. Shane

In the course of several 21-cm observing programmes being carried out by the Leiden Observatory with the 25-meter telescope at Dwingeloo, a fairly complete, though inhomogeneous, survey of the regionl11= 0° to 66° at low galactic latitudes is becoming available. The essential data on this survey are presented in Table 1. Oort (1967) has given a preliminary report on the first and third investigations. The third is discussed briefly by Kerr in his introductory lecture on the galactic centre region (Paper 42). Burton (1966) has published provisional results of the fifth investigation, and I have discussed the sixth in Paper 19. All of the observations listed in the table have been completed, but we plan to extend investigation 3 to a much finer grid of positions.


1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.


1988 ◽  
Vol 102 ◽  
pp. 79-81
Author(s):  
A. Goldberg ◽  
S.D. Bloom

AbstractClosed expressions for the first, second, and (in some cases) the third moment of atomic transition arrays now exist. Recently a method has been developed for getting to very high moments (up to the 12th and beyond) in cases where a “collective” state-vector (i.e. a state-vector containing the entire electric dipole strength) can be created from each eigenstate in the parent configuration. Both of these approaches give exact results. Herein we describe astatistical(or Monte Carlo) approach which requires onlyonerepresentative state-vector |RV> for the entire parent manifold to get estimates of transition moments of high order. The representation is achieved through the random amplitudes associated with each basis vector making up |RV>. This also gives rise to the dispersion characterizing the method, which has been applied to a system (in the M shell) with≈250,000 lines where we have calculated up to the 5th moment. It turns out that the dispersion in the moments decreases with the size of the manifold, making its application to very big systems statistically advantageous. A discussion of the method and these dispersion characteristics will be presented.


Author(s):  
Zhifeng Shao

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.


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