desc.objectives.ForceBalanceAnisotropic

class desc.objectives.ForceBalanceAnisotropic(eq, target=None, bounds=None, weight=1, normalize=True, normalize_target=True, loss_function=None, deriv_mode='auto', 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) – 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.

• loss_function ({None, 'mean', 'min', 'max'}, optional) – Loss function to apply to the objective values once computed. This loss function is called on the raw compute value, before any shifting, scaling, or normalization.

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

• deriv_mode ({"auto", "fwd", "rev"}) – Specify how to compute jacobian matrix, either forward mode or reverse mode AD. “auto” selects forward or reverse mode based on the size of the input and output of the objective. Has no effect on self.grad or self.hess which always use reverse mode and forward over reverse mode respectively.

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

Methods

build([use_jit, verbose])	Build constant arrays.
compute(params[, constants])	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.
equiv(other)	Compare equivalence between DESC objects.
grad(*args, **kwargs)	Compute gradient vector of self.compute_scalar wrt x.
hess(*args, **kwargs)	Compute Hessian matrix of self.compute_scalar wrt x.
jac_scaled(*args, **kwargs)	Compute Jacobian matrix of self.compute_scaled wrt x.
jac_scaled_error(*args, **kwargs)	Compute Jacobian matrix of self.compute_scaled_error wrt x.
jac_unscaled(*args, **kwargs)	Compute Jacobian matrix of self.compute_unscaled wrt x.
jit()	Apply JIT to compute methods, or re-apply after updating self.
jvp_scaled(v, x[, constants])	Compute Jacobian-vector product of self.compute_scaled.
jvp_scaled_error(v, x[, constants])	Compute Jacobian-vector product of self.compute_scaled_error.
jvp_unscaled(v, x[, constants])	Compute Jacobian-vector product of self.compute_unscaled.
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(*things)	Return a tuple of args required by this objective from optimizable things.

Attributes

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.
dim_f	Number of objective equations.
fixed	Whether the objective fixes individual parameters (or linear combo).
linear	Whether the objective is a linear function (or nonlinear).
name	Name of objective (str).
normalization	normalizing scale factor.
scalar	Whether default "compute" method is a scalar or vector.
target	Target value(s) of the objective.
things	Optimizable things that this objective is tied to.
weight	Weighting to apply to the Objective, relative to other Objectives.