desc.objectives.BootstrapRedlConsistency

class desc.objectives.BootstrapRedlConsistency(eq, target=None, bounds=None, weight=1, normalize=True, normalize_target=True, loss_function=None, deriv_mode='auto', grid=None, helicity=(1, 0), degree=None, name='Bootstrap current self-consistency (Redl)', jac_chunk_size=None)Source 

Promote consistency of the bootstrap current for axisymmetry or quasi-symmetry.

This objective function penalizes the difference between the MHD and neoclassical profiles of parallel current, using the Redl formula for the bootstrap current. The scalar objective is defined as

f = ½ ∫dρ [(⟨J⋅B⟩_MHD - ⟨J⋅B⟩_Redl) / (J_ref B_ref)]²

where J_ref and B_ref are the reference magnitudes of current density and magnetic field strength. This objective is treated as a sum of Nρ least-squares terms, where Nρ is the number of rho grid points.

Parameters:

eq (Equilibrium) – Equilibrium that will be optimized to satisfy the Objective.
grid (Grid, optional) – Collocation grid containing the nodes to evaluate at. Requires poloidal and toroidal resolution as the objective must compute flux surface averages. Defaults to grid = LinearGrid(M=eq.M_grid,N=eq.N_grid,NFP=eq.NFP, sym=eq.sym,rho=np.linspace(1 / eq.L, 1, eq.L) - 1 / (2 * eq.L),)
helicity (tuple, optional) – Type of quasi-symmetry (M, N). Default = quasi-axisymmetry (1, 0). First entry must be M=1. Second entry is the toroidal mode number N, used for evaluating the Redl bootstrap current formula. Set to 0 for axisymmetry or quasi-axisymmetry; set to +/-NFP for quasi-helical symmetry.
degree (int, optional) – The degree kwarg to pass to the <J*B>_Redl compute call, which controls the degree of polynomial fit to the Redl current derivative before it is integrated.
target ({float, ndarray}, optional) – Target value(s) of the objective. Only used if bounds is None. Must be broadcastable to Objective.dim_f. Defaults to target=0.
bounds (tuple of {float, ndarray}, optional) – Lower and upper bounds on the objective. Overrides target. Both bounds must be broadcastable to Objective.dim_f. Defaults to target=0.
weight ({float, ndarray}, optional) – Weighting to apply to the Objective, relative to other Objectives. Must be broadcastable to Objective.dim_f.
normalize (bool, optional) – Whether to compute the error in physical units or non-dimensionalize.
normalize_target (bool, optional) – Whether target and bounds 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.
loss_function ({None, 'mean', 'min', 'max','sum'}, 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.
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, optional) – Name of the objective.
jac_chunk_size (int or auto, optional) – Will calculate the Jacobian jac_chunk_size columns at a time, instead of all at once. The memory usage of the Jacobian calculation is roughly memory usage = m0+m1*jac_chunk_size: the smaller the chunk size, the less memory the Jacobian calculation will require (with some baseline memory usage). The time it takes to compute the Jacobian is roughly t = t0+t1/jac_chunk_size so the larger the jac_chunk_size, the faster the calculation takes, at the cost of requiring more memory. If None, it will use the largest size i.e obj.dim_x. Can also help with Hessian computation memory, as Hessian is essentially jacfwd(jacrev(f)), and each of these operations may be chunked. Defaults to chunk_size=None. Note: When running on a CPU (not a GPU) on a HPC cluster, DESC is unable to accurately estimate the available device memory, so the auto chunk_size option will yield a larger chunk size than may be needed. It is recommended to manually choose a chunk_size if an OOM error is experienced in this case.

Methods

`build`([use_jit, verbose])	Build constant arrays.
`compute`(params[, constants])	Compute the bootstrap current self-consistency objective.
`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.
`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[, args0])	Print the value of the objective and return a dict of values.
`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).
`helicity`	Type of quasi-symmetry (M, N).
`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.