Magnetic Field Topology Reconstruction Using Machine Learning Algorithm

Ramiz A. Qudsi, Mike Richardson, Haley DeWeese, Bennett A. Maruca, Alexandro Chasapis, Bill Matthaeus, Jefferson Rueda

Dept. of Phys. and Astronomy, University of Delaware, DE, USA

19 January, 2021

MMS SWT Tag-up-2021

ahmadr@udel.edu

https://slides.com/qudsi/mmsswt2021/

What We Still Don’t Know About Solar-Wind Structure

Over 50 years of
single-spacecraft
magnetic-field measurements

Power spectra of
in-situ magnetic field
Clear indications of multi-scale structure
What is the actual, 3D magnetic structure of the solar wind?

Mariner 2

Parker Solar Probe

Coleman (ApJ, 1968)

Bale et al. (Nature, 2019)

What we Propose

What we propose

1. Launch a large number of small spacecraft with magnetometer

2. Arrange them in specific configuration

3. Record magnetic field at each spacecraft position

4. Carry out interpolation on the recorded data

5. Generate a full 3-D image of interplanetary magnetic field

Spacecraft

How we do it/Methodology

Methodology

1. Identify the most suitable algorithm for interpolation between data points

Methodology

2. Select the most appropriate kernel/combination of kernels

Constant

Linear

RBF

Matern

Methodology

3. Identify the least number of spacecraft needed to reproduce relevant structure

Methodology

3. Identify the least number of spacecraft needed to reproduce relevant structure

1. Identify the most suitable algorithm for extrapolation between data points

2. Select the most appropriate kernel/combination of kernels

Proof of Concept

Some relevant scales:

d_i \mathrm{(1AU)} \sim 100 ~\mathrm{km} \\ V_{sw} \sim 500 ~\mathrm{km/sec} \\ X_{sim} \mathrm{(box size)} \sim 40 d_i\\ \hspace{3.1cm}\sim 4\times 10^3 \mathrm{km}\\ d_{spc} \sim [1, 10]~d_i\\ \hspace{1.2cm}\sim \mathrm{ [10^2, 10^3]~ km} \\ f[min,max] \sim V_{sw}/(2\times d_{spc, max, min}) \\ \hspace{0.8cm}\sim [0.25, 2.5]~\mathrm{Hz}\\ \nu (\mathrm{sampling~rate}) \sim 13 \mathrm{Hz}\\ \mathrm{(just~because~of~box~size~and~stuff)}\\ \mathrm{time~to~move~across~the~simulation~box} \sim 10 ~\mathrm{sec}