# Force on proton vortices in superfluid neutron stars

## TL;DR

This paper calculates the force on proton vortices in superfluid neutron star matter, clarifying the form of the Lorentz-type component and providing essential data for neutron star magnetic field modeling.

## Contribution

It provides a coherent derivation of both dissipative and Lorentz-type forces on proton vortices, resolving previous controversies and aiding neutron star magnetohydrodynamics.

## Key findings

- Derived both longitudinal and transverse force components.
- Resolved controversy on Lorentz-type force form.
- Key input for neutron star magnetic field evolution models.

## Abstract

Force on proton vortices in superfluid and superconducting matter of neutron stars is calculated at vanishing stellar temperature. Both longitudinal (dissipative) and transverse (Lorentz-type) components of the force are derived in a coherent way and compared in detail with the corresponding expressions available in the literature. This allows us to resolve a controversy about the form of the Lorentz-type force component acting on proton vortices. The calculated force is a key ingredient in magnetohydrodynamics of superconducting neutron stars and is important for modeling the evolution of stellar magnetic field.