2594 lo l2 updates to cg code and bg variable names

[subagonsouth]

Change Summary

Overview

Updates included:

• Going through the CG code with Nathan, he wanted the equations I used to exactly match his Mapping document even though I was doing thing right just without a few negative signs.
• Update to the bg_rate and associated uncertainty variables in order to get them to output to the CDF.

Closes: #2594

[Copilot]

Pull request overview

This pull request updates the Compton-Getting (CG) transformation equations to match Nathan's mapping document and renames background rate variables from plural to singular form for consistency.

Changes:

• Updated CG correction equations with sign changes to match the mapping document exactly
• Renamed background rate variables from bg_rates to bg_rate and similar plural-to-singular changes for related uncertainty variables
• Updated CDF configuration files to reflect new variable names
• Added test to verify new background rate variables are present in L2 output

Reviewed changes

Copilot reviewed 6 out of 6 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
imap_processing/ena_maps/utils/corrections.py	Updated CG transformation equations with sign corrections and comment clarifications
imap_processing/lo/l2/lo_l2.py	Renamed bg_rates variables to bg_rate (singular) throughout the processing pipeline
imap_processing/cdf/config/imap_enamaps_l2-rectangular_variable_attrs.yaml	Added configuration for bg_rate_stat_uncert and bg_rate_sys_err variables
imap_processing/cdf/config/imap_enamaps_l2-healpix_variable_attrs.yaml	Added configuration for bg_rate_stat_uncert and bg_rate_sys_err variables
imap_processing/cdf/config/imap_enamaps_l2-common_variable_attrs.yaml	Updated variable names and descriptions from bg_rate_uncert to bg_rate_stat_uncert and added bg_rate_sys_err
imap_processing/tests/lo/test_lo_l2.py	Added test to verify bg_rate variables are present in integration test output

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[Copilot]

The comment states that "dot_product = look_hat dot usc_hat = (-êₛ · û_sc)" implying the dot product equals the negative of the look direction dot spacecraft direction. However, the actual calculation at lines 581-588 computes a positive dot product between pset["look_direction"] and sc_direction_vector without any negation. Either the comment or the code needs to be corrected for consistency.

Suggested change

	# x_k = (-êₛ · û_sc) + sqrt(y² + (êₛ · û_sc)² - 1)
	# dot_product = look_hat dot usc_hat = (-êₛ · û_sc)
	# x_k = (êₛ · û_sc) + sqrt(y² + (êₛ · û_sc)² - 1)
	# dot_product = look_hat · û_sc = (êₛ · û_sc)

[Copilot]

The comment states "Calculate the kinetic energy of the spacecraft" but this should be "Calculate the kinetic energy of the ENA in the spacecraft frame" to accurately reflect what is being calculated. The variable name "energy_sc" correctly indicates it's the ENA energy in spacecraft frame, not the spacecraft's own kinetic energy.

Suggested change

	# Calculate the kinetic energy of the spacecraft
	# Calculate the kinetic energy of the ENA in the spacecraft frame