# DREAM3D simulations of inner-belt dynamics

## Abstract

A 1973 paper by Lyons and Thorne explains the two-belt structure for electrons in the inner magnetosphere as a balance between inward radial diffusion and loss to the atmosphere, where the loss to the atmosphere is enabled by pitch-angle scattering from Coulomb and wave-particle interactions. In the 1973 paper, equilibrium solutions to a decoupled set of 1D radial diffusion equations, one for each value of the first invariant of motion, μ, were computed to produce the equilibrium two-belt structure. Each 1D radial diffusion equation incorporated an L-and μ-dependent `lifetime' due to the Coulomb and wave-particle interactions. This decoupling of the problem is appropriate under the assumption that radial diffusion is slow in comparison to pitch-angle scattering. However, for some values of μ and L the lifetime associated with pitch-angle scattering is comparable to the timescale associated with radial diffusion, suggesting that the true equilibrium solutions might reflect `coupled modes' involving pitch-angle scattering and radial diffusion and thus requiring a 3D diffusion model. In the work we show here, we have computed the equilibrium solutions using our 3D diffusion model, DREAM3D, that allows for such coupling. We find that the 3D equilibrium solutions are quite similar to the solutions shown inmore »

- 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:
- 1182626

- Report Number(s):
- LA-UR-15-23878

- 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, equilibrium distribution

### Citation Formats

```
Cunningham, Gregory Scott.
```*DREAM3D simulations of inner-belt dynamics*. United States: N. p., 2015.
Web. doi:10.2172/1182626.

```
Cunningham, Gregory Scott.
```*DREAM3D simulations of inner-belt dynamics*. United States. doi:10.2172/1182626.

```
Cunningham, Gregory Scott. Tue .
"DREAM3D simulations of inner-belt dynamics". United States. doi:10.2172/1182626. https://www.osti.gov/servlets/purl/1182626.
```

```
@article{osti_1182626,
```

title = {DREAM3D simulations of inner-belt dynamics},

author = {Cunningham, Gregory Scott},

abstractNote = {A 1973 paper by Lyons and Thorne explains the two-belt structure for electrons in the inner magnetosphere as a balance between inward radial diffusion and loss to the atmosphere, where the loss to the atmosphere is enabled by pitch-angle scattering from Coulomb and wave-particle interactions. In the 1973 paper, equilibrium solutions to a decoupled set of 1D radial diffusion equations, one for each value of the first invariant of motion, μ, were computed to produce the equilibrium two-belt structure. Each 1D radial diffusion equation incorporated an L-and μ-dependent `lifetime' due to the Coulomb and wave-particle interactions. This decoupling of the problem is appropriate under the assumption that radial diffusion is slow in comparison to pitch-angle scattering. However, for some values of μ and L the lifetime associated with pitch-angle scattering is comparable to the timescale associated with radial diffusion, suggesting that the true equilibrium solutions might reflect `coupled modes' involving pitch-angle scattering and radial diffusion and thus requiring a 3D diffusion model. In the work we show here, we have computed the equilibrium solutions using our 3D diffusion model, DREAM3D, that allows for such coupling. We find that the 3D equilibrium solutions are quite similar to the solutions shown in the 1973 paper when we use the same physical models for radial diffusion and pitch-angle scattering from hiss. However, we show that the equilibrium solutions are quite sensitive to various aspects of the physics model employed in the 1973 paper that can be improved, suggesting that additional work needs to be done to understand the two-belt structure.},

doi = {10.2172/1182626},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2015},

month = {5}

}