ForceFreeFluxRope

class plasmapy.plasma.cylindrical_equilibria.ForceFreeFluxRope(B0, alpha: float)[source]

Bases: object

Representation of the analytical Lundquist solution for force-free magnetic flux ropes [Lundquist, 1950].

Parameters:

B0 (Quantity) – Magnetic field strength in units convertible to tesla.
alpha (Quantity) – Eigenvalue to make \(\mathbf{J} × \mathbf{B} = 0\), in units convertible to inverse length.

Notes

The Lundquist solution [also known as the Bessel Function Model (BFM)] is a cylindrically symmetric force-free equilibrium which is often used to approximate the magnetic structure of interplanetary coronal mass ejections (ICMEs).

Methods Summary

`B_magnitude`(r)	Compute the total magnetic field.
`B_theta`(r)	Compute the component of the magnetic field in the azimuthal direction.
`B_z`(r)	Compute the axial component of the magnetic field.

Methods Documentation

B_magnitude(r)[source]

Compute the total magnetic field.

The magnitude of the magnetic field is given by

\[B(r) = \sqrt{B_z(r)^2 + B_θ(r)^2}.\]

Parameters:: r (Quantity) – Radial distance from flux rope axis in units convertible to meters.
Return type:: Quantity

B_theta(r)[source]

Compute the component of the magnetic field in the azimuthal direction.

\[B_θ(r) = B_0 J_1(α r)\]

where \(α\) is the eigenvalue and \(J_1\) is the Bessel function of the first kind of order 1.

Parameters:: r (Quantity) – Radial distance from flux rope axis in units convertible to meters.
Return type:: Quantity

B_z(r)[source]

Compute the axial component of the magnetic field.

\[B_z(r) = B_0 J_0(α r)\]

where \(α\) is the eigenvalue and \(J_0\) is the Bessel function of the first kind of order 0.

Parameters:: r (Quantity) – Radial distance from flux rope axis in units convertible to meters.
Return type:: Quantity