Documentation

Aristotle.Landau.main.VelocityDecayInstance

Lorentz Force Component Bound #

Proves lorentz_component_bound: each component of the Lorentz force (E + v x B) is bounded by C * (1 + ||v||). Used by CoulombSpatialTransport for bounding spatial transport integrands.

theorem VML.lorentz_component_bound (E₀ B₀ : Fin 3) :
∃ (CL : ), 0 CL ∀ (v : Fin 3) (i : Fin 3), |(E₀ + cross v B₀) i| CL * (1 + v)

Bound on a Lorentz force component: |(E₀ + v × B₀)ᵢ| ≤ C·(1 + ‖v‖). Each cross product component is bilinear in v, B₀, hence linear in ‖v‖. Proved by Aristotle.