---
title: Dispersion and Response
status: partial
doc_kind: reference
audience: user
owner: fullmag-public-docs
---

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# Dispersion and Response

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## Contract
This page records the dispersion-curve and frequency-response observables attached to eigenmode
and frequency-response studies.

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## Governing equations
Response and dispersion definitions belong to {doc}`../../numerical-methods/frequency-domain/index`
and {doc}`../../numerical-methods/eigensolvers/index`.

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## Symbols and SI units
Eigenfrequency values are in hertz; response observables carry the units of their definition.

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## Assumptions and validity
Response observable identifiers and dispersion names are validated immediately.

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## Python API
| Python | Type | Default | SI unit | Validation | Meaning | Backend support | ProblemIR |
| --- | --- | --- | --- | --- | --- | --- | --- |
| --- | --- | --- | $1$ | --- | --- | FEM/FDM CPU/GPU; planner and runtime capability checks remain authoritative | --- |
| `SaveDispersion.name` | `str` | `"dispersion"` | $1$ | Non-empty | Curve name | FEM/FDM CPU/GPU; planner and runtime capability checks remain authoritative | `dispersion_curve.name` |
| `SaveDispersion.include_branch_table` | `bool` | `True` | $1$ | Boolean | Include branch table | FEM/FDM CPU/GPU; planner and runtime capability checks remain authoritative | `dispersion_curve.include_branch_table` |
| `SaveResponse.observable` | `str` | `required` | $1$ | One of the supported response observables | Response output | FEM/FDM CPU/GPU; planner and runtime capability checks remain authoritative | `frequency_response_output.observable` |

Supported response observables include `susceptibility_tensor`, `m_complex`, `u_complex`,
`strain_complex`, `stress_complex`, `absorbed_power_density`, `response_amplitude`,
`response_phase`, and `mode_hybridization_index`.

### Complete stage-first example

```python
# %% Frequency response with a susceptibility observable
import fullmag as fm

nm = 1.0e-9

study = fm.study("dispersion_response_api_example")
study.engine("fdm")
study.device("cpu", precision="double")
study.mode("strict")

study.objects.mesh.defaults(cell_size=(2 * nm, 2 * nm, 5 * nm))
film = study.geometry(fm.Box(100 * nm, 20 * nm, 5 * nm), name="film")
film.Ms = 800.0e3
film.Aex = 13.0e-12
film.alpha = 0.02
film.m = fm.init.UniformMagnetization((1.0, 0.0, 0.0))
study.exchange()
study.stages.add_relax(stage_id="relax", algorithm="projected_gradient_bb", max_steps=1000, tolT=1e-8)
study.save_response("susceptibility_tensor")
study.stages.add_frequency_response(
    frequencies_hz=[1.0e9, 2.0e9],
    excitation_field_au_per_m=(0.0, 1.0, 0.0),
    equilibrium_source="relax",
)
```

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## ProblemIR
`SaveDispersion.to_ir()` emits `dispersion_curve`; `SaveResponse.to_ir()` emits
`frequency_response_output`. Both are carried in the study's `sampling.outputs`.

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## Round-trip and failure semantics

Requested intent is the value authored by Python and preserved in ProblemIR; resolved execution is the planner or realization result. Validation errors identify the violated domain rule, and unsupported combinations are rejected explicitly rather than silently substituted.

Unknown response observables fail immediately; dispersion names are preserved without
interpretation.

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## Discrete realization
Response materialization follows the frequency-domain solvers; dispersion follows the eigensolver.

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## Implementation mapping
Anchor: `packages/fullmag-py/src/fullmag/model/outputs.py` (`SaveDispersion`, `SaveResponse`).

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## Validation
Ownership tests compare this inventory with live signatures.

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## Limitations
Requesting an output does not guarantee the solver materializes it; planner and solver capability
resolution are authoritative.

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## Scientific bibliography
Definitions belong to the frequency-domain and eigensolver pages.

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## Control Room crosswalk

Status: Table/field autosave and result inspection are partial; unsupported output formats remain not implemented.

| Python/API surface | Control Room path | Status | Transaction |
|---|---|---|---|
| Parameters documented on this page | `Model Explorer -> Stages -> <stage> -> Autosave` | `partial` | Submit autosave draft; output resources are revised after execution |
| Parameters without a named UI field | `Model Explorer -> Stages -> <stage> -> Autosave` | `not implemented` | Python-only until implemented |

not implemented: frontend support for output parameters not rendered by the autosave/result inspectors.
See [Control Room capability register](/frontend/capability-register) for the support matrix and not implemented policy.
Frontend source owner: `apps/control-room/src/modules/inspector/panels/stages/AutosaveStageInspector.tsx (AutosaveStageInspector)`.

## Source-code index
| Claim | Path | Stable symbol | Responsibility | Evidence |
|---|---|---|---|---|
| Dispersion/response outputs | `packages/fullmag-py/src/fullmag/model/outputs.py` | `SaveDispersion`, `SaveResponse` | Output lowering | Ownership test |

### Source-map coverage

| Claim | Path | Stable symbol | Responsibility | Evidence |
|---|---|---|---|---|
| Dispersion output request validation and lowering. | `packages/fullmag-py/src/fullmag/model/outputs.py` | `class SaveDispersion` | Dispersion output request validation and lowering. | Source-map validator and focused API tests |
| Response output request validation and lowering. | `packages/fullmag-py/src/fullmag/model/outputs.py` | `class SaveResponse` | Response output request validation and lowering. | Source-map validator and focused API tests |