A (quick?) Primer on Magnetic Reconnection
Presented by: M. Hasan Barbhuiya and Chen Shi (on behalf of the RX-FG)
Hands-on Tutorial @ GEM 2025
Outline
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Very Simplified Picture of Magnetic Reconnection in 2D
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(Hesse and Cassak, JGR, 2020)
Oppositely directed magnetic field over a small length-scales gives rise to a thin and strong current sheet
1. Dissipation breaks field lines which reconnect – creates an “X” line
2. Bent newly reconnected field straighten out
3. On large scales, plasma moves outward with the straightening field:
Magnetic energy 🡪 particle energy + internal energy
4. Plasma moving into the low-pressure region takes field with it
Collisionless Antiparallel Symmetric Reconnection
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Downstream region: ions again recouple to the reconnected field
Hall current carried by mostly electrons at small lengths scales
Quadrupolar Hall B field
Inflow
Outflow
2D reconnection – Reconnection rate
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Phase-Space Density
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Boltzmann-Maxwell Equations
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Gauss’ law
No divergence of B
Maxwell-Faraday’s law of induction
Ampere’s law
Boltzmann Equation
Fluid Equations from Boltzmann
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Integrate over v-space, i.e., 0th moment
Boltzmann Equation
Electron Momentum equation – Generalized Ohm’s Law
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Rewrite this as
Background for Simulations
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PIC – basic idea
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Terms in the Electron Momentum Equation
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EDR
MHD equations
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Manipulate fluid equations
Mass continuity equation
Momentum equation
Pressure equation
No divergence of B
Maxwell-Faraday’s law of induction
Ampere’s law
MHD equation set in conservation form
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Mass continuity equation
Momentum equation
Pressure equation
Pseudo-spectral method
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Link to the code: https://github.com/chenshihelio/MHD2DSpectral
Source files
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makefile: Compilation procedure
mhd.f90: Main program of the code.
mhd.input: Input parameters
mhdinit.f90: Initial setup
You only need to modify these two files.
mhdinit.f90�
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Initialize fluctuations
Example:
Initialize background fields
mhd.input��
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Maximum simulation time
Output the fields every time
Output RMS(fields) every time
Method for “de-aliasing”
Number of grid points
Size of simulation domain
mhd.input��
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Case # of background fields
Other parameters for background fields
Case # of fluctuations
Other parameters for fluctuations
Adiabatic index
If turn on resistivity. T: True. F: False.
Resistivity
If turn on viscosity.
Viscosity
Test: tearing-unstable current sheet��
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Maintain equilibrium
Seed perturbations
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Plasma is Ubiquitous in Space!
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Our Sun
Heliospheric Current Sheet
Earth’s Magnetosphere
Lagoon Nebula
Black Hole Accretion Disk and Plasma Jets
Mars’ (induced) Magnetosphere
Phase Space Density and Local Thermodynamic Equilibrium
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We need Kinetic Theory for Non-LTE Systems
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Non-LTE systems inside Earth’s Magnetosphere
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upstream
downstream
Dayside reconnection
Tailside reconnection
�Magnetosphere (Burch+, 2016, Science)
Bow Shock (Wang+, 2018, GRL)
Solar Wind (Marsch, 2018, Ann. Geophys.)
PHASMA @ WVU (Shi+, 2022, PRL)
Visualizing Energy Conversion
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Collisionless Shock
1. Solar wind comes in with relatively high bulk flow energy, and relatively low thermal energy
Pressure-Strain Interaction in Simulations and Observations
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MMS measurements (Bandyopadhyay+ 2021)
Simulation Results (Pezzi+ 2021)
Changes to Higher Moments – A Cartoon
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Start with a Maxwellian distribution
(Cassak+, PRL, 2023)
Quantifying Energy Conversion
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is called pressure-strain interaction and it describes the channel for
Plasma Criteria
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Energy Equations
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Rewrite and use continuity equation
From Maxwell’s equations
2D reconnection – Reconnection rate and Aspect ratio
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Curvature force causes plasma to flow out of the diffusion region into the downstream
Integrate over diffusion region volume, use Gauss’ volume integral
Considering upstream and downstream sides’ surfaces for scaling
Integrate over diffusion region volume, use Gauss’ volume integral
Ideal MHD at large scales has
2D reconnection – Electron Frozen in Condition for two-scale reconnection structure
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At scales when pressure and inertia terms aren’t important
Describes the change in magnetic flux due to change in local field
Thus, we end up with frozen in condition but for electrons instead and so to break this condition, pressure tensor elements and/or inertia are needed!
2D reconnection – EDR and IDR aspect ratio
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Rewrite the RHS
Extrapolating fields on the grid to macroparticles
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Advancing macroparticles using Boris Stepper
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Calculating charge and current densities
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Other than “Jacobi relaxation”, Gauss-Seidel, Red-Black, Successive Overrelaxation, Multigrid
Multigrid approach
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Jacobi pre-smoother, for “relaxation”, 4
Jacobi post-smoother, for “relaxation”, 4
For “Successive Overrelaxation”, 20
2000 (tried 1000, convergence failed)
8 (tried 3, convergence failed)
Used in our simulations
Set to 10
We used periodic boundaries but didn’t use it
Used in our simulations
Used in our simulations
Didn’t use since JACOBI was used
PIC simulations: Normalizations
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Energy conservation in the PIC simulation
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Total energy density
Change in total energy density
PIC simulations: Initial set-up
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Optimizing the velocity-space grid
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Within -3% error
Within -1 % error
Figure for electrons from PPG = 25600 simulation
Particle Weight Calculation
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Installation of the code (Linux/MacOS)
Installation of the code (Linux/MacOS)
Time advancement