### Modulated heat pulse propagation and partial transport barriers in chaotic magnetic fields

Direct numerical simulations of the time dependent parallel heat transport equation modeling heat pulses driven by power modulation in 3-dimensional chaotic magnetic fields are presented. The numerical method is based on the Fourier formulation of a Lagrangian-Green's function method that provides an accurate and efficient technique for the solution of the parallel heat transport equation in the presence of harmonic power modulation. The numerical results presented provide conclusive evidence that even in the absence of magnetic flux surfaces, chaotic magnetic field configurations with intermediate levels of stochasticity exhibit transport barriers to modulated heat pulse propagation. In particular, high-order islands and remnants of destroyed flux surfaces (Cantori) act as partial barriers that slow down or even stop the propagation of heat waves at places where the magnetic field connection length exhibits a strong gradient. The key parameter is $$\gamma=\sqrt{\omega/2 \chi_\parallel}$$ that determines the length scale, $$1/\gamma$$, of the heat wave penetration along the magnetic field line. For large perturbation frequencies, $$\omega \gg 1$$, or small parallel thermal conductivities, $$\chi_\parallel \ll 1$$, parallel heat transport is strongly damped and the magnetic field partial barriers act as robust barriers where the heat wave amplitude vanishes and its phase speed slows down to a halt. On the other hand, in the limit of small $$\gamma$$, parallel heat transport is largely unimpeded, global transport is observed and the radial amplitude and phase speed of the heat wave remain finite. Results on modulated heat pulse propagation in fully stochastic fields and across magnetic islands are also presented. In qualitative agreement with recent experiments in LHD and DIII-D, it is shown that the elliptic (O) and hyperbolic (X) points of magnetic islands have a direct impact on the spatio-temporal dependence of the amplitude and the time delay of modulated heat pulses.

- Publication Date:

- Grant/Contract Number:
- AC05-00OR22725

- Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 23; Journal Issue: 4; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Research Org:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

- OSTI Identifier:
- 1248785

```
del-Castillo-Negrete, Diego, and Blazevski, Daniel.
```*Modulated heat pulse propagation and partial transport barriers in chaotic magnetic fields*. United States: N. p.,
Web. doi:10.1063/1.4946869.

```
del-Castillo-Negrete, Diego, & Blazevski, Daniel.
```*Modulated heat pulse propagation and partial transport barriers in chaotic magnetic fields*. United States. doi:10.1063/1.4946869.

```
del-Castillo-Negrete, Diego, and Blazevski, Daniel. 2016.
"Modulated heat pulse propagation and partial transport barriers in chaotic magnetic fields". United States.
doi:10.1063/1.4946869. https://www.osti.gov/servlets/purl/1248785.
```

```
@article{osti_1248785,
```

title = {Modulated heat pulse propagation and partial transport barriers in chaotic magnetic fields},

author = {del-Castillo-Negrete, Diego and Blazevski, Daniel},

abstractNote = {Direct numerical simulations of the time dependent parallel heat transport equation modeling heat pulses driven by power modulation in 3-dimensional chaotic magnetic fields are presented. The numerical method is based on the Fourier formulation of a Lagrangian-Green's function method that provides an accurate and efficient technique for the solution of the parallel heat transport equation in the presence of harmonic power modulation. The numerical results presented provide conclusive evidence that even in the absence of magnetic flux surfaces, chaotic magnetic field configurations with intermediate levels of stochasticity exhibit transport barriers to modulated heat pulse propagation. In particular, high-order islands and remnants of destroyed flux surfaces (Cantori) act as partial barriers that slow down or even stop the propagation of heat waves at places where the magnetic field connection length exhibits a strong gradient. The key parameter is $\gamma=\sqrt{\omega/2 \chi_\parallel}$ that determines the length scale, $1/\gamma$, of the heat wave penetration along the magnetic field line. For large perturbation frequencies, $\omega \gg 1$, or small parallel thermal conductivities, $\chi_\parallel \ll 1$, parallel heat transport is strongly damped and the magnetic field partial barriers act as robust barriers where the heat wave amplitude vanishes and its phase speed slows down to a halt. On the other hand, in the limit of small $\gamma$, parallel heat transport is largely unimpeded, global transport is observed and the radial amplitude and phase speed of the heat wave remain finite. Results on modulated heat pulse propagation in fully stochastic fields and across magnetic islands are also presented. In qualitative agreement with recent experiments in LHD and DIII-D, it is shown that the elliptic (O) and hyperbolic (X) points of magnetic islands have a direct impact on the spatio-temporal dependence of the amplitude and the time delay of modulated heat pulses.},

doi = {10.1063/1.4946869},

journal = {Physics of Plasmas},

number = 4,

volume = 23,

place = {United States},

year = {2016},

month = {4}

}