# Radio Pulsars Resonantly Accelerating Electrons

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Brief Outline of Theory

- (1)
- The rate of energy gain stems from a quantum effect;
- (2)
- It requires the perpendicular momentum ${K}_{\perp}$ to be nonzero;
- (3)
- It is resonantly enhanced.

## 3. Theory in the Pulsar Context

^{−1}Hz

^{−1}with $\alpha \simeq 0.98$ [31]. Therefore, it is clear that the resonant mechanism of particle energization is extremely efficient providing relativistic factors of the order of ${10}^{16}$ on the LC area for the emission frequency 100 MHz.

^{−1}), it reaches the value $6.5\times {10}^{6}$ on the LC zone. Here, ${n}_{{}_{GJ}}=\Omega \xb7B/\left(2\pi ec\right)$ is the so-called Goldreich–Julian number density (or the number density of pulsar’s magentospheric particles) [33], and $\Omega =2\pi /P$ represents the angular velocity of the pulsar. Thus, for very-high-energy particles ($\gamma >>{\gamma}_{co-rot}$), curvature losses will not be relevant.

^{−1}, $T\simeq 7\times {10}^{4}K\equiv {T}_{1}$. The accelerated electrons will, inevitably, encounter the thermal photons and lose energy via inverse Compton (IC) scattering. We will consider the IC cooling rates in two different domains, the Compton and the Klein–Nishina regimes. The maximum $\gamma $ acquired by the particle is, as before, attained when the energization rate is balanced by the cooling rate. In the Compton regime, the cooling rate is given by [28]

^{−3}(for $P=0.001$ s) to $4.4\times {10}^{-4}$ cm

^{−3}(for $P=1$ s). Realistic number densities will be, surely, much less because pulsars slow down via the magneto-dipole radiation. Therefore, the flux of ultra-high-energy particles will be much less than the theoretical limit, $F\simeq {L}_{sd}/\left(4\pi {r}^{2}\right)\sim 4\times {10}^{-13}$ erg cm

^{−2}s

^{−1}.

## 4. Summary

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AGN | Active galactic nuclei |

EM | Electromagnetic |

IC | Inverse Compton |

KG | Klein–Gordon |

KN | Klein–Nishina |

LC | Light cylinder |

MA | Magneto-centrifugal acceleration |

VHE | Very high energy |

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**Figure 1.**Here, we show the plots of the maximum energy E(P) for different emission frequencies, $f=(1;10;100)\times {10}^{8}$ Hz on the LC zone $r={R}_{lc}$.

**Figure 2.**For $P=1$ s, we show the maximum energy E(r) versus the radial coordinate for the same set of frequencies, $f=(1;10;100)\times {10}^{9}$ Hz.

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**MDPI and ACS Style**

Osmanov, Z.N.; Mahajan, S.M.
Radio Pulsars Resonantly Accelerating Electrons. *Astronomy* **2023**, *2*, 226-234.
https://doi.org/10.3390/astronomy2040016

**AMA Style**

Osmanov ZN, Mahajan SM.
Radio Pulsars Resonantly Accelerating Electrons. *Astronomy*. 2023; 2(4):226-234.
https://doi.org/10.3390/astronomy2040016

**Chicago/Turabian Style**

Osmanov, Zaza N., and Swadesh M. Mahajan.
2023. "Radio Pulsars Resonantly Accelerating Electrons" *Astronomy* 2, no. 4: 226-234.
https://doi.org/10.3390/astronomy2040016