PLUTO Test Problems  4.4-patch2
Functions
init.c File Reference

Reconnection test (Harris sheet) in 2D. More...

Functions

void InitDomain (Data *d, Grid *grid)
 

Detailed Description

In this setup - see also Section 5.3 of Mignone et al., ApJS (2012) 198:7 - we reproduce a 2D Harris current sheet with magnetic field profile given by

\[ B_x(y) = B_0 \tanh(y/l) \]

where l is the half thickness of the layer. The density profile is given by

\[ \rho(y) = \rho_0 \cosh^{-2}(y/l) + \rho_{\infty} \]

We use $ \rho_0=1 $ and $ \rho_{\infty} = 0.2 $, following the guidelines of Birn et al., 2001, while l is user supplied.
In order to achieve equilibrium with the magnetic pressure, the thermal pressure is chosen to be $ p = c_s^2 \rho $, where $ c_s^2 = \frac{B_0^2}{2\rho_0} $. The initial equilibrium is pertubed by an additional magnetic field defined as

\[ \begin{array}{lcl} B_x(x,y) &=& \DS -\Psi_0\frac{\pi}{L_y}\cos\left(\frac{2\pi x}{L_x}\right) \sin\left(\frac{\pi y}{L_y}\right), \\ \noalign{\medskip} B_y(x,y) &=& \DS +\Psi_0 \frac{2\pi}{L_x}\sin\left(\frac{2\pi x}{L_x}\right) \cos\left(\frac{\pi y}{L_y}\right). \end{array} \]

The Lundquist number $ S $ of a plasma is defined as

\[ S = \frac{v_A L}{\eta} \]

where $ v_A $ is the Alfvén velocity, $ v_A = \DS \frac{B}{\sqrt{\rho}}$, $ L $ is a typical lenght scale, and $ \eta $ the plasma resistivity. The reconnection rate $\mathcal{E} = \DS \frac{v_{in}}{v_{out}}$, with $ v_{in} $ and $ v_{out}$ the plasma inflow and outflow velocities, follows the Sweet-Parker scaling law $\mathcal{E} \sim \frac{\delta}{L} \sim \frac{1}{\sqrt{S}}$. In this example several values of the resitivity $ \eta $, that correspond to different values of the Lundquist number $ S $, are provided. The reconnection rate, calculated as the ratio $ \frac{\delta}{L} $ (see Mignone et al., 2012) verifies the Sweet-Parker scaling in the range $ \eta = 10^{-2} - 10^{-4} $ (see the first figure below).

The input parameters (read from pluto.ini) for this test problem are:

Note
  • Configuration #02 employs a small width (l -> 0, current-sheet) large resistivity (test passes only with the new implementation of the resistive-CT module in PLUTO 4.1. Crash with PLUTO 4.0).
  • Configuratation #09 employs adaptive mesh refinement as in the original PLUTO-Chombo paper (ApJS 2012).
fig1.png
Computed Sweet-Parker scaling for different values of eta with a resolution of 512x256.
vx_rho_plot__137.png
Density map and magnetic field lines for eta = 2.e-3 at t = 137.
Authors
E. Striani (edoar.nosp@m.do.s.nosp@m.trian.nosp@m.i@ia.nosp@m.ps.in.nosp@m.af.i.nosp@m.t)
A. Mignone (migno.nosp@m.ne@p.nosp@m.h.uni.nosp@m.to.i.nosp@m.t)
Date
March 02, 2017

Reference

Function Documentation

◆ InitDomain()

void InitDomain ( Data *  d,
Grid *  grid 
)

Assign initial condition by looping over the computational domain. Called after the usual Init() function to assign initial conditions on primitive variables. Value assigned here will overwrite those prescribed during Init().