Radiation Reaction Plan

Note

This is a development-branch planning document. It can be committed on the development branch, but should not be promoted to main or release documentation until the implementation and validation tasks below are complete.

This plan tracks the remaining work needed to make radiation reaction in the integrator physically auditable. The current code should be treated as having three separate concepts:

  • passive Lienard radiated-power diagnostics,

  • an optional power-matched damping approximation, and

  • explicit candidate self-force models that act on mechanical momentum before recomposing canonical momentum.

The legacy bdot correction has been removed. It was a post-step edit to a stored acceleration field rather than a real force contribution, and it was not a reliable radiation-reaction implementation.

Reference Model From The Paper

The foundational paper discusses a Medina-style radiation-reaction force based on the Lorentz-Abraham-Dirac equation:

\[F^{RAD} = {2 \over 3}{e^2 \over mc^3} \left[ {d\gamma \over dt}F_{ext} - {\gamma^3 \over c^2}(F_{ext}\cdot a)v \right].\]

This remains a reasonable candidate model, but it should not be added directly to the existing canonical momentum accumulator until the variable mapping is explicit:

  • F_ext is a mechanical external force, not the canonical delta_Px/Py/Pz/Pt accumulator.

  • v and a are coordinate-time mechanical quantities.

  • the integrator evolves proper-time steps and canonical momentum, so the model needs a conversion layer: compute the mechanical impulse, update mechanical momentum, then recompose canonical momentum from the potentials.

  • the paper notes a dressed mass caveat. The first implementation should use rest mass only, document that choice, and leave dressed-mass handling behind an explicit option.

Medina Native-Units Derivation Draft

A standalone TeX supplement with the same derivation is available as Radiation Reaction Model Supplement.

The maintained solver uses the historical native system:

  • length: mm,

  • time: ns,

  • velocity: mm / ns,

  • mass: amu,

  • mechanical momentum: amu mm / ns,

  • mechanical force: amu mm / ns^2, and

  • mechanical energy: amu mm^2 / ns^2.

Charge uses the solver-native value ELEMENTARY_CHARGE = 1.178734e-5. A native electric field is a force-per-charge quantity, so q E has units of amu mm / ns^2. The current prescribed-field implementation converts SI V/m values by matching the SI force on one elementary charge to one native force unit.

The integrator step variable h is a proper-time increment d tau. The coordinate-time increment for a particle is therefore

\[dt = \gamma h.\]

The mechanical momentum is

\[p = \gamma m v = \gamma m c \beta,\]

with units amu mm / ns. The current prescribed external-field impulse is

\[\Delta p_{ext} = h q \gamma (E + \beta \times B) = dt\, F_{ext},\]

where

\[F_{ext} = q (E + \beta \times B).\]

For a general Medina implementation, the first required helper should expose the mechanical non-radiation force represented by a step:

\[F_{ext} \approx {\Delta p_{mech, nonrad} \over dt}.\]

For prescribed fields this can be computed directly from q(E + beta x B). For retarded image/source forces it must be derived from the mechanical momentum increment after subtracting the vector-potential contribution, not from the canonical delta_P accumulator alone.

The Medina force can be written in native variables as

\[F^{RAD} = \tau_0 \left[ {d\gamma \over dt}F_{ext} - {\gamma^3 \over c^2}(F_{ext}\cdot a)v \right],\]

where

\[\tau_0 = {2 \over 3}{q^2 \over m c^3}.\]

This is the same characteristic time already stored on particle states as char_time when native charge and rest mass are used. Here v = c beta and a = dv/dt = c d beta/dt are coordinate-time mechanical quantities. Both bracketed terms have units of force per time:

  • (d gamma / dt) F_ext gives amu mm / ns^3;

  • (gamma^3 / c^2)(F_ext dot a)v also gives amu mm / ns^3.

Multiplying by tau_0 gives a mechanical force in amu mm / ns^2. The mechanical radiation-reaction impulse for one integrator step is therefore

\[\Delta p_{RAD} = F^{RAD} dt = F^{RAD} \gamma h.\]

The candidate implementation should apply this impulse to mechanical momentum, then recompose canonical momentum from the same potentials used by the normal step:

\[p_{new} = p_{nonrad} + \Delta p_{RAD},\]
\[\gamma_{new} = \sqrt{1 + {|p_{new}|^2 \over (m c)^2}},\]
\[P_{i,new} = p_{i,new} + m A_{i,solver},\]
\[P_{t,new} = \gamma_{new} m c + q \Phi.\]

The first Medina mode should use rest mass in tau_0 and explicitly state that the paper’s dressed-mass caveat is not yet modeled. It should also start with prescribed-field benchmarks before being applied to retarded image-charge collision cases.

Ordered Tasks

  1. Finish terminology cleanup. Status: complete.

    Rename diagnostics that historically referred to “radiation reaction activation” when they only detect large changes in stored acceleration. Keep compatibility aliases until downstream scripts are updated.

    Current implementation:

    • find_large_bdot_changes is the maintained diagnostic name.

    • find_radiation_reaction_activations remains as a compatibility alias.

    • legacy bdot radiation-reaction mode names are rejected.

  2. Lock down passive radiation bookkeeping. Status: in progress.

    Add regression tests for radiation_power, radiation_energy, and radiation_energy_applied in off and power_matched_damping modes. Verify that diagnostic-only radiation never changes trajectory state. These tests should cover both legacy list trajectories and TrajectoryArrays so the bookkeeping remains compatible with the current SoA optimization path.

    Current coverage:

    • off and diagnostic_only produce identical trajectory state.

    • power_matched_damping records applied radiated energy separately.

    • startup and SoA paths zero-fill radiation bookkeeping fields.

  3. Validate the Lienard power helper in isolation. Status: in progress.

    Required checks:

    • zero power for unaccelerated motion,

    • parallel and transverse acceleration terms,

    • circular-motion/synchrotron scaling,

    • coordinate-time bdot conversion from stored integrator values, and

    • timestep convergence of integrated radiated energy.

    Current coverage:

    • zero acceleration,

    • coordinate-time d beta / dt input,

    • parallel and transverse acceleration scaling,

    • synchrotron-like gamma scaling for transverse acceleration, and

    • prescribed magnetic-bend timestep convergence.

    Remaining coverage gap:

    • timestep convergence of active medina_lad energy/momentum changes, separately from passive Lienard power integration.

  4. Make the provisional damping model deliberately narrow. Status: in progress.

    The existing power_matched_damping mode should remain labeled as an energy-bookkeeping approximation. It should have tests showing that it removes at most the requested radiated energy, never crosses rest energy, and preserves momentum direction by construction. It should not be presented as a LAD, Landau-Lifshitz, or Medina self-force model.

    Current coverage:

    • isolated damping helper preserves momentum direction by scaling mechanical momentum magnitude,

    • the helper cannot remove more than kinetic energy above rest energy, and

    • the magnetic-bend integration test checks that applied damping energy matches the observed gamma reduction.

  5. Derive the Medina implementation in native units. Status: first draft complete; needs continued review.

    Produce a short derivation note before coding. It should define native units for charge, mass, force, acceleration, time, and energy; state whether the force is integrated over coordinate time or proper time; and include a dimension check for the final impulse.

  6. Implement the Medina candidate behind an explicit mode. Status: experimental first pass complete.

    The first code path should be opt-in, probably radiation_reaction_mode="medina_lad". It should:

    • compute the external mechanical force represented by the current step,

    • compute dgamma/dt from coordinate-time quantities,

    • compute coordinate-time acceleration from beta-dot,

    • apply the radiation-reaction impulse to mechanical momentum,

    • cap the impulse only as a numerical guard with diagnostics, and

    • recompose canonical momentum using the current potentials.

    Current implementation:

    • radiation_reaction_mode="medina_lad" is accepted as an explicit mode,

    • the non-radiation mechanical force is estimated from the mass-shell projected mechanical momentum increment over coordinate time,

    • d beta/dt and dgamma/dt are derived from the mechanical force estimate, keeping longitudinal Medina terms self-consistent and preserving the expected near-cancellation for one-dimensional acceleration,

    • the impulse is applied to mechanical momentum and canonical momentum is recomposed with the existing vector/scalar potential terms, and

    • the impulse has a small numerical cap with a verbosity-gated diagnostic.

    Remaining work before treating this as physics evidence:

    • add timestep convergence tests for medina_lad itself,

    • record when the numerical impulse cap activates in controlled tests, and

    • evaluate whether the mechanical-force estimator is adequate for retarded image/source forces or whether those contributions need a more explicit force-decomposition API.

  7. Add prescribed external-field support for controlled benchmarks. Status: complete for uniform fields.

    Radiation-reaction validation needs clean external accelerators that do not depend on image-charge or point-source artifacts. Start with uniform fields in native solver units, including the static longitudinal E_z case discussed around Eq. 21 of the foundational paper. Required guardrails:

    • provide explicit SI-to-native conversion helpers for electric fields,

    • keep field configs compatible with the canonical SoA/Numba integrator path,

    • support simple spatial and temporal windows, and

    • document that the first implementation is a mechanical Lorentz-force impulse, not yet a full external potential/map system.

    Later extensions can add field maps, callable fields, and explicit vector/scalar-potential providers for fully covariant canonical updates.

    Time-dependent fields need their own model boundary. The static Eq. 21 longitudinal field used in the paper can be written as E_z = partial^z A^0 - partial^0 A^z with the time derivative set to zero. For any time-dependent extension, do not implement this as a scalar field amplitude toggle alone. Add a potential-provider interface that can evaluate A^0, A^i, and their derivatives at (x, y, z, t) so the -partial^0 A^i contribution is represented explicitly and canonical momentum can be recomposed from the same potentials used to compute the mechanical Lorentz-force impulse.

    Current implementation:

    • uniform electric and magnetic fields in native solver units,

    • SI-to-native conversion helper for electric fields,

    • spatial and temporal field windows,

    • canonical integrator, SoA/Numba, CLI, GUI, and config plumbing, and

    • explicit documentation that this is not yet a full external-potential or time-dependent field-map system.

  8. Benchmark self-force candidates against controlled systems. Status: in progress.

    Start with tests that do not require wall images or retarded multi-particle edge cases:

    • prescribed straight-line acceleration,

    • uniform circular motion in an imposed magnetic field,

    • ultra-relativistic transverse acceleration,

    • a low-energy case where reaction is negligible, and

    • a high-gamma case where the reaction term is visible but stable.

    Current coverage:

    • direct Medina helper test for longitudinal cancellation,

    • direct Medina helper test for transverse/synchrotron-style damping,

    • prescribed longitudinal electric acceleration with nonzero dgamma/dt, verifying diagnostic-only neutrality and small Medina longitudinal applied energy,

    • short high-gamma prescribed magnetic bend, and

    • several-hundred-mm prescribed transverse magnetic bend.

    Remaining coverage gap:

    • active-mode timestep convergence for medina_lad,

    • mixed longitudinal/transverse prescribed fields, and

    • low-energy negligible-reaction and ultra-relativistic visible-reaction brackets with explicit acceptance thresholds.

  9. Revisit conducting-surface collision cases. Status: not started.

    The paper motivates radiation reaction mostly as a way to prevent runaway behavior near image-charge collisions. After isolated benchmarks pass, compare off, power_matched_damping, and medina_lad on the original aperture/image-charge scenarios. The acceptance criterion should be energy bookkeeping and timestep convergence, not just smoother trajectories.

  10. Evaluate alternatives only after the Medina track is measurable. Status: not started.

Alternative reduced-order formalisms should remain literature cross-checks, not the production target. In particular, Landau-Lifshitz is less aligned with the maintained solver because it is normally written in terms of local field-solution quantities, while this code’s primary representation is covariant Lienard-Wiechert potentials and canonical momentum. Keep any LL or Eliezer-Ford-O’Connell work behind explicit comparison modes and use them only if they clarify Medina stability, convergence, or near-surface behavior.

Next Best Steps

The immediate low-risk work is now validation rather than new physics:

  • keep the Medina/native-units derivation under review as the primary implementation target,

  • add active-mode timestep convergence tests for medina_lad under known prescribed external forces,

  • add mixed-field and low/high-energy benchmark brackets with explicit tolerances, and

  • refine the mechanical-force extraction API before using medina_lad as evidence in conducting-wall collision cases.