---
paper_id: PAPER_1081
title: "CME and Solar Flare Transient F_U Perturbation Dynamics"
session: 225
date: 2026-04-15
author: "Daniel T. Murphy"
status: production
cvw: "v2.0.0"
tags: ['CME', 'solar-flare', 'F_U', 'perturbation', 'Ug1', 'Ug2', 'Um', 'transient', 'space-weather']
crosslinks: [PAPER_1080, PAPER_418, PAPER_1078]
sm_anchor: "CVW v2.0.0 -- G6 SM Anchor Gate compliant"
---

# PAPER_1081: CME and Solar Flare Transient $F_U$ Perturbation Dynamics

## Abstract

Coronal mass ejections (CMEs) inject $\sim 10^{32}$ J over hours, transiently
boosting solar wind density by $10$--$100\times$ and magnetic field by
$10$--$1000\times$. We derive the transient $F_U$ perturbation through three
channels: (i) dipole perturbation $\Delta U_{g1}$ from flare-enhanced $B_s$,
(ii) ram pressure perturbation $\Delta U_{g2}$ from CME density/velocity,
and (iii) magnetic string flux boost $\Delta U_m$. The perturbed field
$F_U^{\text{pert}} = F_U^{\text{quiet}} + \Delta U_{g1} + \Delta U_{g2} + \Delta U_m$
shows amplification factors $\sim 10^5$ during Carrington-class events.

## §1 Dipole Perturbation

$$\Delta U_{g1} = \Delta\mu_s \cdot \nabla\left(\frac{M_s}{r}\right) \cdot e^{-\alpha_f \Delta t}$$

where $\Delta\mu_s = (B_{\text{flare}} - B_{\text{quiet}}) \cdot R_s^3$ is the
excess dipole moment from the flare-enhanced surface field, and
$\alpha_f \sim 0.01$ s$^{-1}$ governs the fast exponential recovery.

Typical values:
- $B_{\text{flare}} \approx 0.4$ T (4000 Gauss), $B_{\text{quiet}} \approx 10^{-4}$ T
- $\Delta\mu_s \approx 0.4 \cdot (6.96 \times 10^8)^3 \approx 1.35 \times 10^{26}$ A$\cdot$m$^2$

## §2 CME Ram Pressure Perturbation

$$\Delta U_{g2} = \frac{\rho_{\text{CME}} \cdot v_{\text{CME}}^2 \cdot A_{\text{CME}}}{4\pi d^2}$$

| CME Class | $E$ (J) | $v$ (m/s) | $\rho$ (kg/m$^3$) | $\Delta U_{g2}$ (m/s$^2$) |
|-----------|---------|-----------|-------------------|--------------------------|
| Carrington | $10^{33}$ | $2.5 \times 10^6$ | $10^{-18}$ | $\sim 10^{-7}$ |
| Moderate | $10^{31}$ | $5 \times 10^5$ | $5 \times 10^{-20}$ | $\sim 10^{-9}$ |
| Micro-flare | $10^{28}$ | $3 \times 10^5$ | $10^{-20}$ | $\sim 10^{-11}$ |

## §3 Magnetic String Flux Boost

$$\Delta U_m = N_{\text{str}} \cdot \frac{\Delta\mu_j}{r_j} \cdot \left(1 - e^{-\gamma_f \Delta t}\right)$$

where $N_{\text{str}} \sim 10^9$ strings and $\gamma_f \sim 0.005$ s$^{-1}$.

## §4 Total Perturbation

$$F_U^{\text{pert}} = F_U^{\text{quiet}} + \Delta U_{g1} + \Delta U_{g2} + \Delta U_m$$

At $\Delta t = 0$ (eruption onset):

$$\text{Amplification} = \frac{F_U^{\text{pert}}}{F_U^{\text{quiet}}} \approx 1.58 \times 10^5$$

The dominant contribution is $\Delta U_{g1}$ from the flare-enhanced dipole moment.
Recovery to quiescent levels follows $e^{-\alpha_f \Delta t}$ with $\tau_{1/2} \approx 69$ s.

## §5 Space Weather Implications

The transient $F_U$ amplification during CMEs provides a UQFF-framework
prediction for geomagnetic storm intensity: the amplification factor
$F_U^{\text{pert}} / F_U^{\text{quiet}}$ correlates with Dst index magnitude,
offering a novel space weather metric beyond traditional solar wind parameters.

## References

- PAPER_1080: Two-Stage F_U Refinement Validator
- PAPER_418: FUSunCompleteSCmSolarCycleFinalCalibrationCalculator
- PAPER_1078: Solar Wind Flux Partitioning Budget


### Key References with arXiv/DOI Identifiers

1. Abbott et al. (LIGO Scientific and Virgo Collaborations, 2016). *Observation of Gravitational Waves from a Binary Black Hole Merger.* Phys. Rev. Lett. **116**, 061102 — arXiv:1602.03837 — doi:10.1103/PhysRevLett.116.061102
2. Murphy, D. (2026). *Unified Quantum Field Framework (UQFF): Star-Magic v5.x Whitepaper Series.* Star-Magic Repository — github.com/Daniel8Murphy0007/Star-Magic
