essos.objective_functions¶

Functions¶

`near_axis_field_quantities`(field_nearaxis)
`loss_B_difference_coils_near_axis`(field, field_nearaxis)
`loss_gradB_difference_coils_near_axis`(field, ...)
`loss_iota_near_axis`(field_nearaxis[, iota_target])
`loss_r0_near_axis`(field_nearaxis[, r0_target])
`loss_particle_radial_drift_fullorbit`(field, particles)
`loss_particle_radial_drift`(field, particles[, ...])
`loss_particle_alpha_drift`(field, particles[, ...])
`loss_particle_gammac`(field, particles[, timestep, ...])
`loss_particle_rcross_final`(field, particles[, ...])
`loss_particle_Br`(field, particles[, timestep, ...])
`loss_particle_iota`(field, particles[, timestep, ...])
`normB_axis`(field[, npoints])
`loss_normB_axis_average`(field[, npoints, target_B])
`loss_BdotN`(field, surface)
`loss_BdotN_constraint`(field, surface[, target_tol])
`copy_coils_from_field`(field)
`perturbed_field_from_field`(field, key, sampler)
`loss_bdotn_stochastic`(field, surface, sampler, keys)
`constraint_bdotn_stochastic`(field, surface, sampler, keys)
`loss_coil_length`(coils[, max_coil_length])
`loss_coil_curvature`(coils[, max_coil_curvature])
`compute_candidates`(coils, min_separation)
`loss_coil_separation`(coils, min_separation[, ...])	Memory-efficient coil separation loss using blockwise vmap.
`loss_coil_surface_distance`(coils, surface, min_distance)	Memory-efficient coil-surface distance loss using blockwise vmap and symmetry reduction.
`loss_linkingnumber`(coils[, candidates, block_size])
`loss_lorentz_force_coils`(coils[, p, threshold, ...])	Loss function penalizing Lorentz force on coils using Landreman-Hurwitz method.
`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.near_axis_field_quantities(field_nearaxis)¶

essos.objective_functions.loss_B_difference_coils_near_axis(field, field_nearaxis)¶

essos.objective_functions.loss_gradB_difference_coils_near_axis(field, field_nearaxis)¶

essos.objective_functions.loss_iota_near_axis(field_nearaxis, iota_target=0.41)¶

essos.objective_functions.loss_r0_near_axis(field_nearaxis, r0_target=1.0)¶

essos.objective_functions.loss_particle_radial_drift_fullorbit(field, particles, timestep=1e-08, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, model='GuidingCenterAdaptative', boundary=None)¶

essos.objective_functions.loss_particle_radial_drift(field, particles, timestep=1e-08, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, model='GuidingCenterAdaptative', boundary=None)¶

essos.objective_functions.loss_particle_alpha_drift(field, particles, timestep=1e-08, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, model='GuidingCenterAdaptative', boundary=None)¶

essos.objective_functions.loss_particle_gammac(field, particles, timestep=1e-08, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, model='GuidingCenterAdaptative', boundary=None)¶

essos.objective_functions.loss_particle_rcross_final(field, particles, timestep=1e-08, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, model='GuidingCenterAdaptative', boundary=None)¶

essos.objective_functions.loss_particle_Br(field, particles, timestep=1e-08, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, model='GuidingCenterAdaptative', boundary=None)¶

essos.objective_functions.loss_particle_iota(field, particles, timestep=1e-08, maxtime=1e-05, num_steps=300, trace_tolerance=1e-05, model='GuidingCenterAdaptative', boundary=None, target_iota=0.41)¶

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

essos.objective_functions.loss_normB_axis_average(field, npoints=15, target_B=5.7)¶

essos.objective_functions.loss_BdotN(field, surface)¶

essos.objective_functions.loss_BdotN_constraint(field, surface, target_tol=1e-06)¶

essos.objective_functions.copy_coils_from_field(field)¶

essos.objective_functions.perturbed_field_from_field(field, key, sampler)¶

essos.objective_functions.loss_bdotn_stochastic(field, surface, sampler, keys)¶

essos.objective_functions.constraint_bdotn_stochastic(field, surface, sampler, keys, target_tol=1e-06)¶

essos.objective_functions.loss_coil_length(coils, max_coil_length=0)¶

essos.objective_functions.loss_coil_curvature(coils, max_coil_curvature=0)¶

essos.objective_functions.compute_candidates(coils, min_separation)¶

essos.objective_functions.loss_coil_separation(coils, min_separation, candidates=None, block_size=None)¶

Memory-efficient coil separation loss using blockwise vmap. :param coils: Coils object :param min_separation: Minimum allowed separation :param candidates: Optional tuple of (i, j) coil index arrays :param block_size: Block size for memory efficiency. If None, uses full vmap (no chunking)

Returns:: Scalar loss (sum over all coil pairs)

essos.objective_functions.loss_coil_surface_distance(coils, surface, min_distance, block_size=None)¶

Memory-efficient coil-surface distance loss using blockwise vmap and symmetry reduction. :param coils: Coils object :param surface: Surface object (with gamma, unitnormal) :param min_distance: Minimum allowed coil-surface distance :param block_size: Block size for memory efficiency. If None, uses full vmap (no chunking) :param nfp: Number of field periods :param stellsym: Whether stellarator symmetry is present

Returns:: Scalar loss (sum over all relevant coil-surface pairs)

essos.objective_functions.loss_linkingnumber(coils, candidates=None, block_size=None)¶

essos.objective_functions.loss_lorentz_force_coils(coils, p=1, threshold=500000.0, block_size=None, conductor_radius=None)¶

Loss function penalizing Lorentz force on coils using Landreman-Hurwitz method.

Matches SIMSOPT’s LpCurveForce:

J = (1/p) sum_i (1/L_i) int max(|dF_i/dl| - F_0, 0)^p dl_i

so it is independent of the quadrature resolution. The self-force uses the regularized self field of a circular conductor of radius a (delta = a**2 / sqrt(e); Hurwitz, Landreman & Antonsen, arXiv:2310.09313).

Parameters:

coils – Coils object (with gamma, gamma_dash, gamma_dashdash, currents, quadpoints)
p – Power for penalty (default 1)
threshold – Force threshold F_0 in N/m (default 0.5e6)
block_size – Block size for memory efficiency. If None, uses full vmap (no chunking)
conductor_radius – Radius of the conductor cross-section in meters (required: the self-force depends logarithmically on it).

Returns:

Scalar loss (sum over all coils)

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