desc.objectives.ForceBalanceAnisotropic

class desc.objectives.ForceBalanceAnisotropic(eq=None, target=None, bounds=None, weight=1, normalize=True, normalize_target=True, grid=None, name='force-anisotropic')Source

Force balance for anisotropic pressure equilibria.

Solves for F = J × B − ∇ ⋅ Π = 0

Where Π is the anisotropic pressure tensor of the form Π = (p_∥ - p_⊥)𝐛𝐛 + p_⊥𝕀

Expanded out, this gives:

F = (1−βₐ)J × B − 1/μ₀ (B ⋅ ∇ βₐ)B − βₐ ∇(B²/2μ₀) − ∇(p_⊥)

where βₐ is the anisotropy term: βₐ = μ₀ (p_∥ − p_⊥)/B²

For this objective, the standard Equilibrium.pressure profile is used for p_⊥, and Equilibrium.anisotropy is used for βₐ. To get fully 3D anisotropy, these should be FourierZernikeProfile, not the standard PowerSeriesProfile (which is only a function of rho).

Parameters:

• eq (Equilibrium, optional) – Equilibrium that will be optimized to satisfy the Objective.

• target (float, ndarray, optional) – Target value(s) of the objective. len(target) must be equal to Objective.dim_f

• bounds (tuple, optional) – Lower and upper bounds on the objective. Overrides target. len(bounds[0]) and len(bounds[1]) must be equal to Objective.dim_f

• weight (float, ndarray, optional) – Weighting to apply to the Objective, relative to other Objectives. len(weight) must be equal to Objective.dim_f

• normalize (bool) – Whether to compute the error in physical units or non-dimensionalize.

• normalize_target (bool) – Whether target should be normalized before comparing to computed values. if normalize is True and the target is in physical units, this should also be set to True. grid : Grid, ndarray, optional Collocation grid containing the nodes to evaluate at.

• grid (Grid, ndarray, optional) – Collocation grid containing the nodes to evaluate at.

• name (str) – Name of the objective function.

Methods

build([eq, use_jit, verbose])	Build constant arrays.
compute(*args, **kwargs)	Compute MHD force balance errors.
compute_scalar(*args, **kwargs)	Compute the scalar form of the objective.
compute_scaled(*args, **kwargs)	Compute and apply weighting and normalization.
compute_scaled_error(*args, **kwargs)	Compute and apply the target/bounds, weighting, and normalization.
compute_unscaled(*args, **kwargs)	Compute the raw value of the objective.
copy([deepcopy])	Return a (deep)copy of this object.
eq(other)	Compare equivalence between DESC objects.
jit()	Apply JIT to compute methods, or re-apply after updating self.
load(load_from[, file_format])	Initialize from file.
print_value(*args, **kwargs)	Print the value of the objective.
save(file_name[, file_format, file_mode])	Save the object.
xs(eq)	Return a tuple of args required by this objective from the Equilibrium eq.

Attributes

args	Names (str) of arguments to the compute functions.
bounds	Lower and upper bounds of the objective.
built	Whether the transforms have been precomputed (or not).
constants	Constant parameters such as transforms and profiles.
derivatives	Derivatives of the function wrt the argument given by the dict keys.
dim_f	Number of objective equations.
dimensions	Dimensions of the argument given by the dict keys.
fixed	Whether the objective fixes individual parameters (or linear combo).
linear	Whether the objective is a linear function (or nonlinear).
name	Name of objective function (str).
normalization	normalizing scale factor.
scalar	Whether default "compute" method is a scalar or vector.
target	Target value(s) of the objective.
weight	Weighting to apply to the Objective, relative to other Objectives.