Kinetic model

GuidingCenter

Guiding-center equation for a single species in a static background magnetic field.

Overview

GuidingCenter is the reduced kinetic model used when fast gyromotion is

averaged out and only guiding-center motion needs to be resolved. It evolves particles in a fixed magnetic background without any self-consistent field solve.

Use cases

This model is appropriate for:

test-particle guiding-center orbit calculations
strongly magnetized plasmas with scale separation from gyromotion
verification of 5D guiding-center pushers and diagnostics

Governing equations

PDEs solved by model:

Guiding-center Vlasov equation:

\frac{\partial f}{\partial t} + [v_{∥} \frac{B ^{*}}{B _{∥}^{*}} + \frac{E ^{*} \times b _{0}}{B _{∥}^{*}}] \cdot \frac{\partial f}{\partial X} + [\frac{1}{ϵ} \frac{B ^{*}}{B _{∥}^{*}} \cdot E^{*}] \cdot \frac{\partial f}{\partial v _{∥}} = 0

where $f (X, v_{∥}, μ, t)$ is the guiding center distribution and

E^{*} = - ϵ μ \nabla∣ B_{0} ∣, B^{*} = B_{0} + ϵ v_{∥} \nabla \times b_{0}, B_{∥}^{*} = B^{*} \cdot b_{0}

Normalization

The reference speed is Alfvénic and the key small parameter is the

normalized cyclotron time:

v^= v^_{A}, ε = 1/ (Ω^_{c} t^) .

Discretization

Time integration is performed by the following propagators (in sequence):

struphy.propagators.push_guiding_center_bx_estar.PushGuidingCenterBxEstar
struphy.propagators.push_guiding_center_parallel.PushGuidingCenterParallel

Diagnostics

The following scalars are tracked during simulation:

Parallel kinetic energy: en_fv
Magnetic-moment energy contribution: en_fB
Total particle energy: en_tot
Lost markers: n_lost_particles

Example

Create and initialize a guiding-center model:

from struphy.models import GuidingCenter

model = GuidingCenter()

model.kinetic_ions.var