essos.objective_functions¶

Functions¶

`pertubred_field_from_dofs`(x, key, sampler, ...[, ...])
`perturbed_coils_from_dofs`(x, key, sampler, ...[, ...])
`field_from_dofs`(x, dofs_curves, currents_scale, nfp[, ...])
`coils_from_dofs`(x, dofs_curves, currents_scale, nfp[, ...])
`curves_from_dofs`(x, dofs_curves, nfp[, n_segments, ...])
`loss_coils_for_nearaxis`(x, field_nearaxis, ...[, ...])
`difference_B_gradB_onaxis`(nearaxis_field, coils_field)
`loss_coils_and_nearaxis`(x, field_nearaxis, ...[, ...])
`loss_particle_radial_drift`(x, particles, dofs_curves, ...)
`loss_particle_alpha_drift`(x, particles, dofs_curves, ...)
`loss_particle_gamma_c`(x, particles, dofs_curves, ...)
`loss_particle_r_cross_final`(x, particles, dofs_curves, ...)
`loss_particle_r_cross_max_constraint`(x, particles, ...)
`loss_Br`(x, particles, dofs_curves, currents_scale, nfp)
`loss_iota`(x, particles, dofs_curves, currents_scale, nfp)
`loss_lost_fraction`(x, particles, dofs_curves, ...[, ...])
`loss_lost_fraction_times`(x, particles, dofs_curves, ...)
`normB_axis`(field[, npoints, target_B_on_axis])
`loss_coil_length`(x, dofs_curves, currents_scale, nfp)
`loss_coil_curvature`(x, dofs_curves, currents_scale, nfp)
`loss_normB_axis`(x, dofs_curves, currents_scale, nfp[, ...])
`loss_normB_axis_average`(x, dofs_curves, ...[, ...])
`loss_coil_curvature_new`(x, dofs_curves, ...[, ...])
`loss_coil_length_new`(x, dofs_curves, currents_scale, nfp)
`loss_optimize_coils_for_particle_confinement`(x, ...[, ...])
`loss_bdotn_over_b`(x, vmec, dofs_curves, ...[, ...])
`loss_BdotN`(x, vmec, dofs_curves, currents_scale, nfp)
`loss_BdotN_only`(x, vmec, dofs_curves, currents_scale, nfp)
`loss_BdotN_only_constraint`(x, vmec, dofs_curves, ...)
`loss_BdotN_only_stochastic`(x, sampler, N_samples, ...)
`loss_BdotN_only_constraint_stochastic`(x, sampler, ...)
`loss_cs_distance`(x, surface, dofs_curves, ...[, ...])
`loss_cs_distance_array`(x, surface, dofs_curves, ...[, ...])
`loss_cc_distance`(x, dofs_curves, currents_scale, nfp)
`loss_cc_distance_array`(x, dofs_curves, currents_scale, nfp)
`cc_distance_pure`(gamma1, l1, gamma2, l2, minimum_distance)	Compute the curve-curve distance penalty between two curves.
`cs_distance_pure`(gammac, lc, gammas, ns, minimum_distance)	Compute the curve-surface distance penalty between a curve and a surface.
`loss_linking_mnumber`(x, dofs_curves, currents_scale, nfp)
`loss_linking_mnumber_constarint`(x, dofs_curves, ...[, ...])
`linking_number_pure`(gamma1, lc1, gamma2, lc2, dphi)
`integrand_linking_number`(r1, dr1, r2, dr2, dphi1, dphi2)	Compute the integrand for the linking number between two curves.
`loss_lorentz_force_coils`(x, dofs_curves, ...[, ...])
`lp_force_pure`(index, gamma, gamma_dash, ...)	Pure function for minimizing the Lorentz force on a coil.
`B_regularized_singularity_term`(rc_prime, ...)	The term in the regularized Biot-Savart law in which the near-singularity
`B_regularized_pure`(gamma, gammadash, gammadashdash, ...)
`regularization_circ`(a)	Regularization for a circular conductor
`regularization_rect`(a, b)	Regularization for a rectangular conductor
`rectangular_xsection_k`(a, b)	Auxiliary function for field in rectangular conductor
`rectangular_xsection_delta`(a, b)	Auxiliary function for field in rectangular conductor

Module Contents¶

essos.objective_functions.pertubred_field_from_dofs(x, key, sampler, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True)¶

essos.objective_functions.perturbed_coils_from_dofs(x, key, sampler, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True)¶

essos.objective_functions.field_from_dofs(x, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True)¶

essos.objective_functions.coils_from_dofs(x, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True)¶

essos.objective_functions.curves_from_dofs(x, dofs_curves, nfp, n_segments=60, stellsym=True)¶

essos.objective_functions.loss_coils_for_nearaxis(x, field_nearaxis, dofs_curves, currents_scale, nfp, max_coil_length=42, n_segments=60, stellsym=True, max_coil_curvature=0.1)¶

essos.objective_functions.difference_B_gradB_onaxis(nearaxis_field, coils_field)¶

essos.objective_functions.loss_coils_and_nearaxis(x, field_nearaxis, dofs_curves, currents_scale, nfp, max_coil_length=42, n_segments=60, stellsym=True, max_coil_curvature=0.1)¶

essos.objective_functions.loss_particle_radial_drift(x, particles, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, model='GuidingCenterAdaptative', boundary=None)¶

essos.objective_functions.loss_particle_alpha_drift(x, particles, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, model='GuidingCenterAdaptative', target=-1000.0, boundary=None)¶

essos.objective_functions.loss_particle_gamma_c(x, particles, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, model='GuidingCenterAdaptative', boundary=None)¶

essos.objective_functions.loss_particle_r_cross_final(x, particles, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, model='GuidingCenterAdaptative', boundary=None)¶

essos.objective_functions.loss_particle_r_cross_max_constraint(x, particles, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, target_r=0.4, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, model='GuidingCenterAdaptative', boundary=None)¶

essos.objective_functions.loss_Br(x, particles, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, model='GuidingCenterAdaptative', boundary=None)¶

essos.objective_functions.loss_iota(x, particles, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, target_iota=0.5, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, model='GuidingCenterAdaptative', boundary=None)¶

essos.objective_functions.loss_lost_fraction(x, particles, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, timestep=1e-07, model='GuidingCenterAdaptative', boundary=None)¶

essos.objective_functions.loss_lost_fraction_times(x, particles, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, timestep=1e-07, model='GuidingCenterAdaptative', boundary=None)¶

essos.objective_functions.normB_axis(field, npoints=15, target_B_on_axis=5.7)¶

essos.objective_functions.loss_coil_length(x, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, max_coil_length=31)¶

essos.objective_functions.loss_coil_curvature(x, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, max_coil_curvature=0.4)¶

essos.objective_functions.loss_normB_axis(x, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, npoints=15, target_B_on_axis=5.7)¶

essos.objective_functions.loss_normB_axis_average(x, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, npoints=15, target_B_on_axis=5.7)¶

essos.objective_functions.loss_coil_curvature_new(x, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, max_coil_curvature=0.4)¶

essos.objective_functions.loss_coil_length_new(x, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, max_coil_length=31)¶

essos.objective_functions.loss_optimize_coils_for_particle_confinement(x, particles, dofs_curves, currents_scale, nfp, max_coil_curvature=0.5, n_segments=60, stellsym=True, target_B_on_axis=5.7, maxtime=1e-05, max_coil_length=22, num_steps=30, trace_tolerance=1e-05, model='GuidingCenterAdaptative', boundary=None)¶

essos.objective_functions.loss_bdotn_over_b(x, vmec, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True)¶

essos.objective_functions.loss_BdotN(x, vmec, dofs_curves, currents_scale, nfp, max_coil_length=42, n_segments=60, stellsym=True, max_coil_curvature=0.1)¶

essos.objective_functions.loss_BdotN_only(x, vmec, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True)¶

essos.objective_functions.loss_BdotN_only_constraint(x, vmec, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, target_tol=1e-06)¶

essos.objective_functions.loss_BdotN_only_stochastic(x, sampler, N_samples, vmec, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True)¶

essos.objective_functions.loss_BdotN_only_constraint_stochastic(x, sampler, N_samples, vmec, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, target_tol=1e-06)¶

essos.objective_functions.loss_cs_distance(x, surface, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, min_distance_cs=1.3)¶

essos.objective_functions.loss_cs_distance_array(x, surface, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, min_distance_cs=1.3)¶

essos.objective_functions.loss_cc_distance(x, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, min_distance_cc=0.7, downsample=1)¶

essos.objective_functions.loss_cc_distance_array(x, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, min_distance_cc=0.7, downsample=1)¶

essos.objective_functions.cc_distance_pure(gamma1, l1, gamma2, l2, minimum_distance, downsample=1)¶

Compute the curve-curve distance penalty between two curves.

Parameters:

gamma1 (array-like) – Points along the first curve.
l1 (array-like) – Tangent vectors along the first curve.
gamma2 (array-like) – Points along the second curve.
l2 (array-like) – Tangent vectors along the second curve.
minimum_distance (float) – The minimum allowed distance between curves.
downsample (int, default=1) – Factor by which to downsample the quadrature points by skipping through the array by a factor of downsample, e.g. curve.gamma()[::downsample, :]. Setting this parameter to a value larger than 1 will speed up the calculation, which may be useful if the set of coils is large, though it may introduce inaccuracy if downsample is set too large, or not a multiple of the total number of quadrature points (since this will produce a nonuniform set of points). This parameter is used to speed up expensive calculations during optimization, while retaining higher accuracy for the other objectives.

Returns:

The curve-curve distance penalty value.

Return type:

float

essos.objective_functions.cs_distance_pure(gammac, lc, gammas, ns, minimum_distance)¶

Compute the curve-surface distance penalty between a curve and a surface.

Parameters:

gammac (array-like) – Points along the curve.
lc (array-like) – Tangent vectors along the curve.
gammas (array-like) – Points on the surface.
ns (array-like) – Surface normal vectors.
minimum_distance (float) – The minimum allowed distance between curve and surface.

Returns:

The curve-surface distance penalty value.

Return type:

float

essos.objective_functions.loss_linking_mnumber(x, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, downsample=1)¶

essos.objective_functions.loss_linking_mnumber_constarint(x, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, downsample=1)¶

essos.objective_functions.linking_number_pure(gamma1, lc1, gamma2, lc2, dphi)¶

essos.objective_functions.integrand_linking_number(r1, dr1, r2, dr2, dphi1, dphi2)¶

Compute the integrand for the linking number between two curves.

Parameters:

r1 (array-like) – Points along the first curve.
dr1 (array-like) – Tangent vectors along the first curve.
r2 (array-like) – Points along the second curve.
dr2 (array-like) – Tangent vectors along the second curve.
dphi1 (array-like) – increments of quadpoints 1
dphi2 (array-like) – increments of quadpoints 2

Returns:

The integrand value for the linking number.

Return type:

float

essos.objective_functions.loss_lorentz_force_coils(x, dofs_curves, currents_scale, nfp, n_segments=60, stellsym=True, p=1, threshold=500000.0)¶

essos.objective_functions.lp_force_pure(index, gamma, gamma_dash, gamma_dashdash, currents, quadpoints, p, threshold)¶: Pure function for minimizing the Lorentz force on a coil.

essos.objective_functions.B_regularized_singularity_term(rc_prime, rc_prime_prime, regularization)¶

The term in the regularized Biot-Savart law in which the near-singularity has been integrated analytically.

regularization corresponds to delta * a * b for rectangular x-section, or to a²/√e for circular x-section.

A prefactor of μ₀ I / (4π) is not included.

The derivatives rc_prime, rc_prime_prime refer to an angle that goes up to 2π, not up to 1.

essos.objective_functions.B_regularized_pure(gamma, gammadash, gammadashdash, quadpoints, current, regularization)¶

essos.objective_functions.regularization_circ(a)¶: Regularization for a circular conductor

essos.objective_functions.regularization_rect(a, b)¶: Regularization for a rectangular conductor

essos.objective_functions.rectangular_xsection_k(a, b)¶: Auxiliary function for field in rectangular conductor

essos.objective_functions.rectangular_xsection_delta(a, b)¶: Auxiliary function for field in rectangular conductor