[Paper Review] Acceleration and Particle Field Interactions of Cosmic Rays II: Calculations

Abdel Nasser Tawfik, A. Saleh+2 more|arXiv (Cornell University)|Oct 28, 2010

Astrophysics and Cosmic Phenomena1 references3 citations

TL;DR

This paper proposes a generic acceleration model for ultra-high-energy cosmic rays (UHECRs) based on plasma field interactions, excluding Fermi mechanisms. It calculates energy gains from four drift types—$\mathbf{E} \times \mathbf{B}$, polarization, curvature, and grad E drift—finding that the grad E drift in time-varying magnetic fields can accelerate protons to ~10^22 eV, exceeding the GZK cutoff and rivaling the Hillas mechanism.

ABSTRACT

Based on the generic acceleration model, which suggests different types of electromagnetic interactions between the cosmic charged particles and the different configurations of the electromagnetic (plasma) fields, the ultra high energy cosmic rays are studied. The plasma fields are assumed to vary, spatially and temporally. The well-known Fermi accelerations are excluded. Seeking for simplicity, it is assumed that the energy loss due to different physical processes is negligibly small. The energy available to the plasma sector is calculated in four types of electromagnetic fields. It has been found that the drift in a time--varying magnetic field is extremely energetic. The energy scale widely exceeds the Greisen-Zatsepin-Kuzmin (GZK) cutoff. The polarization drift in a time--varying electric field is also able to raise the energy of cosmic rays to an extreme value. It can be compared with the Hillas mechanism. The drift in a spatially--varying magnetic field is almost as strong as the polarization drift. The curvature drift in a non--uniform magnetic field and a vanishing electric field is very weak.

Motivation & Objective

• To investigate non-Fermi acceleration mechanisms for ultra-high-energy cosmic rays (UHECRs) using electromagnetic plasma field interactions.
• To evaluate the energy gain from different plasma drift mechanisms in varying electromagnetic field configurations.
• To assess whether plasma field interactions can produce energies exceeding the Greisen-Zatsepin-Kuzmin (GZK) cutoff.
• To compare the effectiveness of various drift mechanisms, including polarization and grad E drift, against the Hillas mechanism.

Proposed method

• The generic acceleration model from Tawfik:2010jh is applied, assuming spatial and temporal variations in electromagnetic fields.
• Four types of plasma drifts are analyzed: $\mathbf{E} \times \mathbf{B}$, polarization, curvature, and grad E drift.
• Energy gain is calculated using the generalized form $\mathcal{E} = 2q\mathbf{E} \cdot \mathbf{r}$, derived from field configurations and conservation laws.
• The model assumes negligible energy loss from radiation (e.g., synchrotron, Bremsstrahlung), focusing solely on field interaction contributions.
• Magnetohydrodynamic (MHD) constraints are applied, including $\mathbf{E} \cdot \mathbf{B} = 0$ and $\mathbf{E} = -\mathbf{V} \times \mathbf{B}$, to ensure physical consistency.
• Numerical calculations are performed for a particle of mass $m$ and charge $q$, with initial velocity assumed finite or zero.

Experimental results

Research questions

• RQ1 Can plasma field interactions, excluding Fermi mechanisms, produce ultra-high-energy cosmic rays exceeding the GZK cutoff?
• RQ2 Which of the four plasma drift mechanisms—$\mathbf{E} \times \mathbf{B}$, polarization, curvature, or grad E—contributes most significantly to cosmic ray energy gain?
• RQ3 How does the energy gain from time-varying magnetic fields compare to the Hillas mechanism in terms of achievable energy scales?
• RQ4 To what extent do spatial and temporal variations in electromagnetic fields enhance particle acceleration beyond standard models?
• RQ5 Can the grad E drift in time-varying magnetic fields produce energies on the order of 10^22 eV, as suggested by Faraday’s law and field dynamics?

Key findings

• The grad E drift in a time-varying magnetic field produces the highest energy gain, capable of accelerating protons to approximately 10^22 eV, far exceeding the GZK cutoff of ~10^19.7 eV.
• The polarization drift in a time-varying electric field is highly effective and can achieve energy scales comparable to the Hillas mechanism.
• The drift in a spatially varying magnetic field produces energy gains nearly as large as the polarization drift, indicating strong acceleration potential.
• The curvature drift in a non-uniform magnetic field with vanishing electric field is extremely weak, contributing only a few MeV, and is negligible in the relativistic regime.
• The $\mathbf{E} \times \mathbf{B}$ drift and other standard drifts are found to be less effective than the grad E and polarization drifts in achieving extreme energies.
• Despite neglecting energy losses, the model demonstrates that plasma field interactions alone can account for UHECR energies without invoking Fermi acceleration or exotic physics.