Pitch-Angle Spectra In The dHT Frame

sopran.experimental.kaguya.dht moves each KAGUYA ESA look velocity into the de Hoffmann–Teller (dHT) frame, in which the motional electric field of the solar-wind flow vanishes, and recomputes pitch angle and energy from there. It is meant for reading the electron distribution under the condition that the loss-cone boundary is fixed to the lunar surface. Records whose field is nearly tangent to the surface have no dHT velocity, so the usable sample is much smaller than the plain distribution. Keep the plain pitch-angle spectrum as the reference and use the dHT version as a comparison.

Velocity convention

The order fixed by the September 2026 lunarsat validation (20-minute interval, 59 records) is implemented as is.

Step	Content
1	Take \(\boldsymbol V_\mathrm{GSE}\) from the OMNI HRO 5-minute sample whose lunar arrival time is nearest the record (within omni_tolerance_seconds)
2	Restore the Earth orbital aberration that NASA removed, once, as +29.8 km/s in \(V_y\) (restore_omni_aberration)
3	Rotate GSE→J2000 with the Sun direction at the OMNI epoch, then J2000→MOON_ME at the record time
4	Subtract the Moon's geocentric velocity and build the HT velocity \(\boldsymbol H_M=\boldsymbol u_M-\frac{\boldsymbol u_M\cdot\boldsymbol n}{\boldsymbol B\cdot\boldsymbol n}\boldsymbol B\) with the local radial as the normal
5	Subtract the spacecraft's selenocentric velocity and rotate into the look frame (default SELENE_M_SPACECRAFT)
6	Subtract this boost from every look velocity and recompute the pitch angle \(\alpha'\) and energy \(E'\)

The lunar arrival time is \(t_\mathrm{arrival}=t_\mathrm{OMNI}+(R_E\,\mathrm{BSN}_x-x_\mathrm{Moon,GSE})/V_\mathrm{sw}\); arrival_shift="none" disables it. Moon and spacecraft velocities come from SPICE spkezr (DE421 and the SELENE SPK) in inertial axes, and only 3×3 pxform rotations are applied.

Records with \(|\boldsymbol B\cdot\boldsymbol n|/|\boldsymbol B|\) below min_abs_b_normal_fraction (default 0.15) are dropped as field_tangent. In the April 2026 lunarsat full-period runs the dHT branch kept about 27% of the non-dHT fits.

Usage

import numpy as np
import sopran as spn
from sopran.experimental.kaguya.dht import DhtSettings, dht_pitch_angle_spectrum
from sopran.frames import FrameContext
from sopran.missions.kaguya.geometry import lmag_position, lmag_position_gse
from sopran.missions.kaguya.spice import selene_spice_kernels

kg = spn.Kaguya()
time = spn.period("2008-04-02T08:20", "2008-04-02T08:50")
calibration = kg.esa1.load_calibration()
esa1 = kg.esa1.load(time, calibration=calibration)
lmag = kg.lmag.load(time)
omni = spn.omni.hro.load(spn.period("2008-04-02T07:00", "2008-04-02T09:00"))
frames = FrameContext(spice_kernels=selene_spice_kernels(kg.store, time), default_backend="spiceypy")

result = dht_pitch_angle_spectrum(
    pace=esa1.pace,
    time=time,
    calibration=calibration,
    magnetic_field=lmag.magnetic_field,
    position=lmag_position(lmag),
    position_gse=lmag_position_gse(lmag),
    omni=omni,
    frame_context=frames,
    energy_edges_eV=np.geomspace(20.0, 1500.0, 10),
    pitch_bins=16,
    settings=DhtSettings(),
)
result.spectrum            # counts on time x energy band x pitch_angle (SopranArray)
result.frame.coverage()    # {"records": ..., "ok": ..., "field_tangent": ..., "omni_missing": ...}
result.frame.to_pandas()   # per-record boost, |B.n|/|B|, OMNI time offset

Shifted energies fall into the energy_edges_eV bands, so every record shares one grid. The exposure coordinate is the look response summed with the factor \((E/E')^2\), so counts / exposure approximates the differential energy flux in the dHT frame (Liouville's theorem). exposure_unshifted is the plain sum, look_samples the number of looks per cell, and shifted_energy_mean_eV and unshifted_pitch_mean_deg the cell means.

The parts are available on their own: frame_velocity() gives the boost and diagnostics per record, shift_looks() the per-look shift, dht_tangential_velocity() the HT velocity and lunar_arrival_times() the arrival times.

Limits

• Only the motional electric field is removed; electrostatic potentials are not treated. DhtSettings.look_sign treats the look direction as the particle velocity direction (+1).
• Reasons for dropped records stay in frame.status (ok, omni_missing, geometry_missing, field_tangent, spice_failed). Report coverage() before plotting or fitting.
• The SPICE kernels must cover Earth, Moon and Sun (DE421), the spacecraft (SELENE SPK), the lunar orientation (MOON_ME) and the attitude (CK); selene_spice_kernels provides them.
• Sources: OMNI HRO documentation Appendix 4 (aberration), NAIF spkezr/pxform, lunarsat working/kgy-er/notes/er-dht-velocity-convention-2026-09-27.md.