# Extending the radial diffusion model of Falthammar to non-dipole background field

## Abstract

A model for radial diffusion caused by electromagnetic disturbances was published by Falthammar (1965) using a two-parameter model of the disturbance perturbing a background dipole magnetic field. Schulz and Lanzerotti (1974) extended this model by recognizing the two parameter perturbation as the leading (non--dipole) terms of the Mead Williams magnetic field model. They emphasized that the magnetic perturbation in such a model induces an electric ield that can be calculated from the motion of field lines on which the particles are ‘frozen’. Roederer and Zhang (2014) describe how the field lines on which the particles are frozen can be calculated by tracing the unperturbed field lines from the minimum-B location to the ionospheric footpoint, and then tracing the perturbed field (which shares the same ionospheric footpoint due to the frozen -in condition) from the ionospheric footpoint back to a perturbed minimum B location. The instantaneous change n Roederer L*, dL*/dt, can then be computed as the product (dL*/dphi)*(dphi/dt). dL*/Dphi is linearly dependent on the perturbation parameters (to first order) and is obtained by computing the drift across L*-labeled perturbed field lines, while dphi/dt is related to the bounce-averaged gradient-curvature drift velocity. The advantage of assuming a dipole background magnetic field,more »

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program

- OSTI Identifier:
- 1182627

- Report Number(s):
- LA-UR-15-23879

- DOE Contract Number:
- AC52-06NA25396

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 58 GEOSCIENCES; Heliospheric and Magnetospheric Physics; radiation belts, radial diffusion

### Citation Formats

```
Cunningham, Gregory Scott.
```*Extending the radial diffusion model of Falthammar to non-dipole background field*. United States: N. p., 2015.
Web. doi:10.2172/1182627.

```
Cunningham, Gregory Scott.
```*Extending the radial diffusion model of Falthammar to non-dipole background field*. United States. doi:10.2172/1182627.

```
Cunningham, Gregory Scott. Tue .
"Extending the radial diffusion model of Falthammar to non-dipole background field". United States. doi:10.2172/1182627. https://www.osti.gov/servlets/purl/1182627.
```

```
@article{osti_1182627,
```

title = {Extending the radial diffusion model of Falthammar to non-dipole background field},

author = {Cunningham, Gregory Scott},

abstractNote = {A model for radial diffusion caused by electromagnetic disturbances was published by Falthammar (1965) using a two-parameter model of the disturbance perturbing a background dipole magnetic field. Schulz and Lanzerotti (1974) extended this model by recognizing the two parameter perturbation as the leading (non--dipole) terms of the Mead Williams magnetic field model. They emphasized that the magnetic perturbation in such a model induces an electric ield that can be calculated from the motion of field lines on which the particles are ‘frozen’. Roederer and Zhang (2014) describe how the field lines on which the particles are frozen can be calculated by tracing the unperturbed field lines from the minimum-B location to the ionospheric footpoint, and then tracing the perturbed field (which shares the same ionospheric footpoint due to the frozen -in condition) from the ionospheric footpoint back to a perturbed minimum B location. The instantaneous change n Roederer L*, dL*/dt, can then be computed as the product (dL*/dphi)*(dphi/dt). dL*/Dphi is linearly dependent on the perturbation parameters (to first order) and is obtained by computing the drift across L*-labeled perturbed field lines, while dphi/dt is related to the bounce-averaged gradient-curvature drift velocity. The advantage of assuming a dipole background magnetic field, as in these previous studies, is that the instantaneous dL*/dt can be computed analytically (with some approximations), as can the DLL that results from integrating dL*/dt over time and computing the expected value of (dL*)^2. The approach can also be applied to complex background magnetic field models like T89 or TS04, on top of which the small perturbations are added, but an analytical solution is not possible and so a numerical solution must be implemented. In this talk, I discuss our progress in implementing a numerical solution to the calculation of DL*L* using arbitrary background field models with simple electromagnetic perturbations.},

doi = {10.2172/1182627},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2015},

month = {5}

}