[Paper Review] Photon-Axion conversions in transversely inhomogeneous magnetic fields

Javier Redondo|arXiv (Cornell University)|Mar 1, 2010

Dark Matter and Cosmic Phenomena6 references3 citations

TL;DR

This paper investigates photon-axion conversions in transversely inhomogeneous magnetic fields using the eikonal approximation, finding that field gradients do not enhance conversion probabilities as previously speculated. Contrary to expectations, the conversion rate in quadrupole-like fields is typically lower than in uniform dipoles due to reduced effective field strength, ruling out a significant advantage for laboratory axion searches using such geometries.

ABSTRACT

We compute the photon-axion conversion probability in an external magnetic field with a strong transverse gradient in the eikonal approximation for plane waves. We find it typically smaller than a comparable uniform case. Some insights into the phenomenon of photon-axion splitting are given.

Motivation & Objective

• To assess whether transverse magnetic field gradients enhance photon-axion conversion probabilities, particularly in the context of solar X-ray emission models.
• To evaluate the feasibility of using quadrupole magnets instead of dipoles in laboratory axion experiments like CAST and OSQAR.
• To determine whether the phenomenon of 'photon-axion splitting' in inhomogeneous fields leads to measurable enhancements in conversion efficiency.
• To analyze the role of diffraction and wavefront curvature in 2D inhomogeneous fields using the eikonal approximation.
• To provide a quantitative comparison between 1D uniform field models and 2D transversely varying field configurations.

Proposed method

• Formulates the photon-axion mixing equations in a magnetic field with transverse gradient, using the effective mass matrix approach.
• Applies the eikonal approximation to solve the wave equation, neglecting diffraction and amplitude variations for initial estimates.
• Solves the Hamilton-Jacobi equations for ray trajectories via the method of characteristics, tracking phase evolution in 2D.
• Derives the eikonal function S(x,z) for A+ and A- fields, accounting for field gradient B1 and frequency ω.
• Computes the conversion probability per unit transverse length as a function of phase difference ΔS between A+ and A- waves.
• Normalizes the 2D probability to the 1D uniform field case to assess enhancement or suppression effects.

Experimental results

Research questions

• RQ1 Does a transverse magnetic field gradient significantly enhance photon-axion conversion probabilities compared to a uniform field?
• RQ2 Can quadrupole magnets provide a measurable advantage over dipoles in light-shining-through-walls experiments for axion detection?
• RQ3 To what extent do diffraction effects or wavefront curvature in 2D fields alter the 1D approximation of conversion probabilities?
• RQ4 Is the phenomenon of 'photon-axion splitting' in inhomogeneous fields physically realizable with observable enhancements?
• RQ5 What is the quantitative impact of field gradient on the effective coupling strength in axion-photon conversion?

Key findings

• The conversion probability in a transversely inhomogeneous magnetic field is typically smaller than in a comparable uniform field due to reduced effective field strength.
• The ratio of 2D (gradient) to 1D (uniform) conversion probabilities scales as (B₁X / B₀)² / 3 in the weak-coupling limit, indicating suppression rather than enhancement.
• For realistic parameters, the characteristic deflection length scale is ~5×10¹⁷ m, implying negligible ray curvature under typical laboratory or solar conditions.
• The eikonal approximation shows that phase differences in A+ and A- waves remain small unless extreme field gradients are present, with no significant deviation from 1D estimates.
• Diffraction effects are unlikely to reverse the suppression, as the typical divergence angle from diffraction exceeds the splitting angle only under extreme conditions.
• No measurable enhancement is expected in helioscope experiments using quadrupole magnets, and such configurations do not outperform standard dipole magnets for axion detection.