Particle propagator

PushGuidingCenterParallel

Advances ions.

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What it solves

For each marker

p

, solves

⎩ ⎨ ⎧ \frac{d X _{p} ( t )}{d t} \frac{d v _{∥, p} ( t )}{d t} = v_{∥, p} (t) \frac{B ^{*}}{B _{∥}^{*}} (X_{p} (t)), = \frac{1}{ε} \frac{B ^{*}}{B _{∥}^{*}} \cdot E^{*} (X_{p} (t)),

where

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

where $B = B_{0} + B ~$ can be the full magnetic field (equilibrium + perturbation). The electric potential phi and/or the magnetic perturbation b_tilde can be ignored by passing None. In logical space this is given by $X = F (η)$ :

⎩ ⎨ ⎧ \frac{d η _{p} ( t )}{d t} \frac{d v _{∥, p} ( t )}{d t} = v_{∥, p} (t) \frac{B ^ ^{* 2}}{B ^ _{∥}^{* 3}} (η_{p} (t)), = \frac{1}{ε} \frac{B ^ ^{* 2}}{B ^ _{∥}^{* 3}} \cdot E^^{* 1} (η_{p} (t)) .

Available algorithms:

Explicit from struphy.ode.utils.ButcherTableau struphy.pic.pushing.pusher_kernels_gc.push_gc_Bstar_discrete_gradient_1st_order struphy.pic.pushing.pusher_kernels_gc.push_gc_Bstar_discrete_gradient_1st_order_newton struphy.pic.pushing.pusher_kernels_gc.push_gc_Bstar_discrete_gradient_2nd_order

Variables it advances

The variables this step updates over a time step dt, and the discrete spaces each one accepts.

Name	Kind	Accepted spaces
`ions`	PICVariable	—

Options

Set these on the propagator in a parameter file, for example PushGuidingCenterParallel.Options(evaluate_e_field=...).

Option	Default	Choices	Description
`evaluate_e_field`	`False`	bool	If `True`, evaluate and include electric-field contributions in drift-kinetic kernels.
`algo`	`discrete_gradient_1st_order`	`discrete_gradient_2nd_orderdiscrete_gradient_1st_orderdiscrete_gradient_1st_order_newtonexplicit`	Guiding-center pushing algorithm.
`butcher`	`None`	ButcherTableau	Butcher tableau used in explicit mode. If `None` and `algo="explicit"`, defaults to `ButcherTableau()`.
`maxiter`	`20`	int	Maximum number of fixed-point or Newton iterations in discrete-gradient modes.
`tol`	`1e-07`	float	Convergence tolerance for iterative discrete-gradient updates.
`mpi_sort`	`each`	`eachlastNone`	MPI sorting policy for particle exchange.

Used by

Each model splits its time step into a sequence of propagators. This one appears in 3 models, at the position shown.