# Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence

## Abstract

In the literature, one can find various analytical theories for perpendicular diffusion of energetic particles interacting with magnetic turbulence. Besides quasi-linear theory, there are different versions of the nonlinear guiding center (NLGC) theory and the unified nonlinear transport (UNLT) theory. For turbulence with high Kubo numbers, such as two-dimensional turbulence or noisy reduced magnetohydrodynamic turbulence, the aforementioned nonlinear theories provide similar results. For slab and small Kubo number turbulence, however, this is not the case. In the current paper, we compare different linear and nonlinear theories with each other and test-particle simulations for a noisy slab model corresponding to small Kubo number turbulence. We show that UNLT theory agrees very well with all performed test-particle simulations. In the limit of long parallel mean free paths, the perpendicular mean free path approaches asymptotically the quasi-linear limit as predicted by the UNLT theory. For short parallel mean free paths we find a Rechester and Rosenbluth type of scaling as predicted by UNLT theory as well. The original NLGC theory disagrees with all performed simulations regardless what the parallel mean free path is. The random ballistic interpretation of the NLGC theory agrees much better with the simulations, but compared to UNLT theory themore »

- Authors:

- Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2 (Canada)

- Publication Date:

- OSTI Identifier:
- 22663676

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal; Journal Volume: 839; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COMPARATIVE EVALUATIONS; COSMIC RADIATION; DIFFUSION; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; MEAN FREE PATH; NONLINEAR PROBLEMS; RANDOMNESS; SIMULATION; SLABS; TURBULENCE; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Heusen, M., and Shalchi, A., E-mail: husseinm@myumanitoba.ca, E-mail: andreasm4@yahoo.com.
```*Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence*. United States: N. p., 2017.
Web. doi:10.3847/1538-4357/AA6A55.

```
Heusen, M., & Shalchi, A., E-mail: husseinm@myumanitoba.ca, E-mail: andreasm4@yahoo.com.
```*Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence*. United States. doi:10.3847/1538-4357/AA6A55.

```
Heusen, M., and Shalchi, A., E-mail: husseinm@myumanitoba.ca, E-mail: andreasm4@yahoo.com. Thu .
"Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence". United States.
doi:10.3847/1538-4357/AA6A55.
```

```
@article{osti_22663676,
```

title = {Numerical Test of Analytical Theories for Perpendicular Diffusion in Small Kubo Number Turbulence},

author = {Heusen, M. and Shalchi, A., E-mail: husseinm@myumanitoba.ca, E-mail: andreasm4@yahoo.com},

abstractNote = {In the literature, one can find various analytical theories for perpendicular diffusion of energetic particles interacting with magnetic turbulence. Besides quasi-linear theory, there are different versions of the nonlinear guiding center (NLGC) theory and the unified nonlinear transport (UNLT) theory. For turbulence with high Kubo numbers, such as two-dimensional turbulence or noisy reduced magnetohydrodynamic turbulence, the aforementioned nonlinear theories provide similar results. For slab and small Kubo number turbulence, however, this is not the case. In the current paper, we compare different linear and nonlinear theories with each other and test-particle simulations for a noisy slab model corresponding to small Kubo number turbulence. We show that UNLT theory agrees very well with all performed test-particle simulations. In the limit of long parallel mean free paths, the perpendicular mean free path approaches asymptotically the quasi-linear limit as predicted by the UNLT theory. For short parallel mean free paths we find a Rechester and Rosenbluth type of scaling as predicted by UNLT theory as well. The original NLGC theory disagrees with all performed simulations regardless what the parallel mean free path is. The random ballistic interpretation of the NLGC theory agrees much better with the simulations, but compared to UNLT theory the agreement is inferior. We conclude that for this type of small Kubo number turbulence, only the latter theory allows for an accurate description of perpendicular diffusion.},

doi = {10.3847/1538-4357/AA6A55},

journal = {Astrophysical Journal},

number = 2,

volume = 839,

place = {United States},

year = {Thu Apr 20 00:00:00 EDT 2017},

month = {Thu Apr 20 00:00:00 EDT 2017}

}