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Quasi-equilibrium electron density along a magnetic field line
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View: Figures


Image of FIG. 1.
FIG. 1.

1-D test field for quasi-equilibrium analysis. Note that the distance between dipoles is 2L while the domain under consideration is 2D.

Image of FIG. 2.
FIG. 2.

Density profile that results from an isotropic distribution of particles injected at position . The velocity space overlays show the behavior of particles along various points of the magnetic field line.

Image of FIG. 3.
FIG. 3.

Graphic series depicting the thermalization process. (1) Particles within a differential element are isolated. (2) Differential population undergoes velocity space diffusion. Particles that enter the loss cone are lost to the domain boundaries. (3) Remaining particles are redistributed along the field line based on the original position of the differential element. (4) Differential profiles are integrated to find the post-collision profile. For clarity, profiles in (4) are not normalized.

Image of FIG. 4.
FIG. 4.

Insertion shape functions, , calculated for Eq. (1) yield the normalized distribution along x given an insertion point .

Image of FIG. 5.
FIG. 5.

Normalized density profile evolution for three separate initial condition profiles. The profiles converge after a few thermalization cycles regardless of the initial profile. The converged curve shows the invariance through 100 recursions. Markers are used for distinction and do not reflect the resolution.

Image of FIG. 6.
FIG. 6.

Reduction fraction between successive thermalization cycles. As seen in Eq. (8), the convergence of the normalized density profiles leads to a constant reduction fraction.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Quasi-equilibrium electron density along a magnetic field line