Simons Hour Talk

On the Distribution of Heat in Integrable and Non-Integrable Magnetic Fields
Jan 5, 2023, 10:00 am – 11:00 am



Event Description

Title: Anisotropic Diffusion in Irregular Magnetic Fields
We study the equilibrium temperature distribution in a model for strongly magnetized plasmas in dimension two and higher. Provided the magnetic field is sufficiently structured (integrable in the sense that it is fibered by co-dimension one invariant tori, on most of which the field lines ergodically wander) and the effective thermal diffusivity transverse to the tori is small, it is proved that the temperature distribution is well approximated by a function that only varies across the invariant surfaces. The same result holds for "nearly integrable" magnetic fields up to a "critical" size. In this case, a volume of non-integrability is defined in terms of the temperature defect distribution and related to the non-integrable structure of the magnetic field, confirming a physical conjecture of Paul-Hudson-Helander. Our proof crucially uses a certain quantitative ergodicity condition for the magnetic field lines on full measure set of invariant tori, which is automatic in two dimensions for magnetic fields without null points and, in higher dimensions, is guaranteed by a Diophantine condition on the rotational transform of the magnetic field.

Talk time in other timezones:
AEDT  2:00 AM Fri 06 Jan,
JST  12:00 AM Fri 06 Jan,
CET  16:00    Thu 05 Jan,
GMT  15:00    Thu 05 Jan,
UTC  15:00    Thu 05 Jan,
EST  10:00 AM Thu 05 Jan,
CST   9:00 AM Thu 05 Jan,
MST   8:00 AM Thu 05 Jan
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