Envelopes with Strong Magnetic Fields

Abstract

Magnetic fields B ≳ 10¹² G, typical for isolated neutron stars (§1.3.8), drastically modify many physical properties of the matter. Motion of free electrons and ions perpendicular to the field lines is quantized into Landau orbitals with a characteristic transverse scale equal to the magnetic length a_m = (ħc/eB)^1/2. This brings to the scene an atomic field-strength parameter γ = (a₀/a_m)², where a⁰ is the Bohr radius. If this parameter is large, the Lorentz force acting on valence electrons in atoms exceeds the Coulomb force. The Landau energy levels of electrons are modified by relativistic effects if the field strength in the relativistic units,

$$ b = h--\omega _c /(m_e c^2 ) = B/B_r , $$

((4.1))

becomes b ≳ 1. Here, ω_c = eB/(mec) is the electron cyclotron frequency and Br = m ²_e }c^{3}/(eħ) = 4.414 × 10¹³ G is often called the relativistic magnetic field.