# On the bounce-averaging of scattering rates and the calculation of bounce period

## Abstract

For many applications to planetary magnetospheres and elsewhere in the Universe, it is desirable to average physical quantities such as particle and plasma transport coefficients over a charged particle's bounce motion between magnetic mirror points along field lines. In this paper, we perform such bounce-averaging in a way that avoids singularities in the integrands of expressions that arise in calculations of this sort. Our method applies in principle to an almost arbitrary magnetic field model. We illustrate the advantage of using our method for removing the integrand's singularity through a change of variables (rather than by truncating the integral over latitude at points progressively nearer to the mirror point) by computing the component of the bounce-averaged momentum-space diffusion tensor in a dipolar magnetic field both ways for resonance interaction of geomagnetically trapped relativistic (1 MeV) electrons with field-aligned whistler-mode plasma waves at L = 6 (a field line that passes near synchronous altitude). Moreover, we develop improved analytical approximations for particle bounce periods in a dipolar magnetic field by minimizing mean square errors with respect to expansion coefficients in algebraic representations of the bounce period.

- Authors:

- Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California 90095 (United States)
- Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095 (United States)
- (United States)

- Publication Date:

- OSTI Identifier:
- 22043513

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 18; Journal Issue: 9; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; APPROXIMATIONS; CHARGED PARTICLES; DIFFUSION; EXPANSION; INTERACTIONS; MAGNETIC FIELDS; MAGNETIC MIRRORS; MEV RANGE 01-10; MIRRORS; PLANETARY MAGNETOSPHERES; PLASMA WAVES; RELATIVISTIC PLASMA; RELATIVISTIC RANGE; RESONANCE; SCATTERING; TRAPPING; UNIVERSE; WHISTLER INSTABILITY; WHISTLERS

### Citation Formats

```
Orlova, K. G., Shprits, Y. Y., and Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California 90095.
```*On the bounce-averaging of scattering rates and the calculation of bounce period*. United States: N. p., 2011.
Web. doi:10.1063/1.3638137.

```
Orlova, K. G., Shprits, Y. Y., & Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California 90095.
```*On the bounce-averaging of scattering rates and the calculation of bounce period*. United States. doi:10.1063/1.3638137.

```
Orlova, K. G., Shprits, Y. Y., and Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California 90095. Thu .
"On the bounce-averaging of scattering rates and the calculation of bounce period". United States. doi:10.1063/1.3638137.
```

```
@article{osti_22043513,
```

title = {On the bounce-averaging of scattering rates and the calculation of bounce period},

author = {Orlova, K. G. and Shprits, Y. Y. and Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California 90095},

abstractNote = {For many applications to planetary magnetospheres and elsewhere in the Universe, it is desirable to average physical quantities such as particle and plasma transport coefficients over a charged particle's bounce motion between magnetic mirror points along field lines. In this paper, we perform such bounce-averaging in a way that avoids singularities in the integrands of expressions that arise in calculations of this sort. Our method applies in principle to an almost arbitrary magnetic field model. We illustrate the advantage of using our method for removing the integrand's singularity through a change of variables (rather than by truncating the integral over latitude at points progressively nearer to the mirror point) by computing the component of the bounce-averaged momentum-space diffusion tensor in a dipolar magnetic field both ways for resonance interaction of geomagnetically trapped relativistic (1 MeV) electrons with field-aligned whistler-mode plasma waves at L = 6 (a field line that passes near synchronous altitude). Moreover, we develop improved analytical approximations for particle bounce periods in a dipolar magnetic field by minimizing mean square errors with respect to expansion coefficients in algebraic representations of the bounce period.},

doi = {10.1063/1.3638137},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 9,

volume = 18,

place = {United States},

year = {2011},

month = {9}

}