# On the Sweet-Parker model for incompressible visco-resistive magnetic reconnection in two dimensions associated to ideal magnetohydrodynamic instabilities

@inproceedings{Baty2022OnTS, title={On the Sweet-Parker model for incompressible visco-resistive magnetic reconnection in two dimensions associated to ideal magnetohydrodynamic instabilities}, author={Hubert Baty}, year={2022} }

We revisit the well known Sweet-Parker (SP) model for magnetic reconnection in the framework of two dimensional incompressible magnetohydrodynamics. The steady-state solution is re-derived by considering a non zero viscosity via the magnetic Prandtl number Pm. Moreover, contrary to the original SP model, a particular attention is paid to the possibility that the inflowing magnetic field Be and the length of the current layer L are not necessarily fixed and may depend on the dissipation…

## One Citation

### New Invariant Quantity To Measure The Entanglement In The Braids

- MathematicsJournal of the Nigerian Society of Physical Sciences
- 2022

In this work, we demonstrate that the integral formula for a generalised Sato-Levine invariant is consistent in certain situations with Evans and Berger's formula for the fourth-order winding…

## References

SHOWING 1-10 OF 24 REFERENCES

### Reconnection rates of magnetic fields including the effects of viscosity

- Physics
- 1984

The Sweet–Parker and Petschek scalings of the magnetic reconnection rate are modified to include the effect of the viscosity. The modified scalings show that the viscous effect can be important in…

### Magnetic reconnection in incompressible fluids

- Physics
- 1992

The paper investigates the dynamical relaxation of a disturbed X-type magnetic neutral point in a periodic geometry, with an ignorable coordinate, for an incompressible fluid. It is found that the…

### Formation of plasmoid chains and fast magnetic reconnection during nonlinear evolution of the tilt instability

- Physics
- 2020

We investigate, by means of two-dimensional incompressible magnetohydrodynamic (MHD) numerical simulations, the fast collisional magnetic reconnection regime that is supported by the formation of…

### Magnetic reconnection and plasmoid formation driven by the two-dimensional resistive kink instability in a current hole configuration

- Physics
- 2020

We investigate the nonlinear evolution of the $m = 1$ resistive internal kink mode in a two-dimensional (2D) configuration containing a central region of negative current density, also known as the…

### On the growth rate of plasmoid chains during nonlinear viscoresistive evolution of the tilt instability

- Physics
- 2020

We investigate by means of two-dimensional incompressible magnetohydrodynamic (MHD) numerical simulations, the onset phase of the fast collisional magnetic reconnection regime that is supported by…

### FINMHD: An Adaptive Finite-element Code for Magnetic Reconnection and Formation of Plasmoid Chains in Magnetohydrodynamics

- PhysicsThe Astrophysical Journal Supplement Series
- 2019

Solving the problem of fast eruptive events in magnetically dominated astrophysical plasmas requires the use of particularly well adapted numerical tools. Indeed, the central mechanism based on…

### Reconnection and particle acceleration in interacting flux ropes - I. Magnetohydrodynamics and test particles in 2.5D

- Physics
- 2017

Magnetic reconnection and non-thermal particle distributions associated with current-driven instabilities are investigated by means of resistive magnetohydrodynamics (MHD) simulations combined with…

### Visco-resistive plasmoid instability

- Physics
- 2016

The plasmoid instability in visco-resistive current sheets is analyzed in both the linear and nonlinear regimes. The linear growth rate and the wavenumber are found to scale as S1/4(1+Pm)−5/8 and…

### Magnetic reconnection driven by current repulsion

- Physics
- 1990

The evolution of an equilibrium consisting of two magnetic islands with oppositely directed currents embedded in a strong magnetic field is investigated, using numerical simulation methods. The rapid…

### Nonlinear Magnetohydrodynamics

- Physics
- 1998

Nonlinear magnetohydrodynamics by Dieter Biskamp is a thorough introduction to the physics of the most impressive non-linear phenomena that occur in conducting magnetoplasmas. The basic systems, in…