# HarrisSheet

class plasmapy.plasma.equilibria1d.HarrisSheet(B0, delta, P0=<Quantity 0. Pa>)[source]

Bases: object

Define a Harris Sheet Equilibrium.

Magnetic field will be in the $$±x$$ direction and the current density will be in the $$±z$$ direction in a $$\hat{x} × \hat{y} = \hat{z}$$ coordinate system.

Parameters:
• B0 (Quantity) – Magnitude of magnetic field in the limit of $$y → ∞$$ in units convertible to teslas.

• delta (Quantity) – The thickness of the current sheet in units convertible to meters.

• P0 (Quantity) – The plasma pressure in the limit of $$y → ∞$$ in units convertible to pascals.

Notes

A current sheet is current limited to a surface.

A Harris sheet is a 1D ideal MHD equilibrium. In resistive MHD if there is any resistivity, it won’t be a true equilibrium since the resistivity will gradually smooth the profile out over time.

A Harris sheet is often used as the initial condition for simulations of magnetic reconnection.

Examples

>>> import astropy.units as u
>>> harris_sheet = HarrisSheet(delta=3 * u.m, B0=2 * u.T)
>>> harris_sheet.magnetic_field(y=5 * u.m)
<Quantity 1.8622... T>


Methods Summary

 Compute the current density. Compute the magnetic field. Compute plasma pressure.

Methods Documentation

current_density(y: Quantity) [source]

Compute the current density.

$J_z(y) = - \frac{B_0}{δ μ_0) \mathrm{sech}^2 \left( \frac{y}{δ} \right)$
Parameters:

y (Quantity) – Orthogonal distance from the current sheet center.

magnetic_field(y: Quantity) [source]

Compute the magnetic field.

In this equation, $$B_0$$ is the asymptotic magnitude of the magnetic field for $$y → ±∞$$ and $$δ$$ is the thickness of the sheet.

$B_x(y) = B_0 \tanh \left( \frac{y}{δ} \right)$
Parameters:

y (Quantity) – Orthogonal distance from the current sheet center.

plasma_pressure(y: Quantity) [source]

Compute plasma pressure.

$p(y) = \frac{B_0^2}{2 μ_0} \mathrm{sech}^2 \left( \frac{y}{δ} \right) + p_0$
Parameters:

y (Quantity) – Orthogonal distance from the current sheet center.