Science Seminars
### 5/25/2017 – Eugene Romashets; Comparative study of a constant-alpha force-free ﬁeld and its approximations in an ideal toroid.

Speaker: *Eugene Romashets (Lonestar College, Houston, TX)*

Date: *Monday, May 25, 2020*

Time: *4:00 PM*

Location: *SPSC W120*

**Seminar Abstract:**Magnetic clouds in the solar wind are large, loop-like interplanetary ﬂux ropes and may be locally approximated by a toroidal ﬂux rope. We compare approximate constant-alpha force-free ﬁelds in an ideal toroid, used in magnetic cloud analysis, with the exact solution, and examine their validity for low aspect ratios, which can be found in magnetic clouds. The approximate toroidal solutions were originally derived under the assumption of large aspect ratios. Three analytic simple approximate constant-alpha force-free solutions and the exact analytic solution are compared with respect to magnetic ﬁeld proﬁles, magnetic ﬁeld magnitude distributions,and magnetic helicity, with moderate (2–3) and very low (<2) aspect ratios.
The Miller & Turner (1981, Phys. Fluids, 24, 363) ﬁeld and its modiﬁcation (to satisfy exact solenoidality) match the position of the magnetic axis in the toroidal ﬂux rope well even for very low aspect ratios. The same can be said for the modiﬁed ﬁeld and the position of the magnetic ﬁeld maximum. When calculating helicity of the toroidal ﬂux rope, the Miller & Turner solution yields better results. A simple formula for magnetic helicity derived from the Miller & Turner solution is valid with a good accuracy even for very low aspect ratios. The Miller & Turner solution is a reasonable substitute for the exact solution even for low aspect ratios (≈2).