The wave energy density and growth rate for the resonant instability in relativistic plasmas
Open Access
- 30 March 2023
- journal article
- research article
- Published by Oxford University Press (OUP) in Monthly Notices of the Royal Astronomical Society
- Vol. 521 (4), 6170-6179
- https://doi.org/10.1093/mnras/stad934
Abstract
The wave instability acts in astrophysical plasmas to redistribute energy and momentum in the absence of frequent collisions. There are many different types of waves, and it is important to quantify the wave energy density and growth rate for understanding what type of wave instabilities are possible in different plasma regimes. There are many situations throughout the universe where plasmas contain a significant fraction of relativistic particles. Theoretical estimates for the wave energy density and growth rate are constrained to either field-aligned propagation angles, or non-relativistic considerations. Based on linear theory, we derive the analytic expressions for the energy density and growth rate of an arbitrary resonant wave with an arbitrary propagation angle in relativistic plasmas. For this derivation, we calculate the Hermitian and anti-Hermitian parts of the relativistic-plasma dielectric tensor. We demonstrate that our analytic expression for the wave energy density presents an explicit energy increase of resonant waves in the wavenumber range where the analytic expression for the growth rate is positive (i.e., where a wave instability is driven). For this demonstration, we numerically analyse the loss-cone driven instability, as a specific example, in which the whistler-mode waves scatter relativistic electrons into the loss cone in the radiation belt. Our analytic results further develop the basis for linear theory to better understand the wave instability, and have the potential to combine with quasi-linear theory, which allows to study the time evolution of not only the particle momentum distribution function but also resonant wave properties through an instability.Funding Information
- Science and Technology Facilities Council (ST/W000369/1)
This publication has 50 references indexed in Scilit:
- Statistics of whistler mode waves in the outer radiation belt: Cluster STAFF‐SA measurementsJournal of Geophysical Research: Space Physics, 2013
- TWO-STREAM-LIKE INSTABILITY IN DILUTE HOT RELATIVISTIC BEAMS AND ASTROPHYSICAL RELATIVISTIC SHOCKSThe Astrophysical Journal, 2011
- The Weibel instability in relativistic plasmasAstronomy & Astrophysics, 2007
- Whistler wave excitation by relativistic electrons in coronal loops during solar flaresAstronomy & Astrophysics, 2006
- Resonant cyclotron scattering and Comptonization in neutron star magnetospheresMonthly Notices of the Royal Astronomical Society, 2006
- Generation of Suprathermal Electrons by Resonant Wave‐Particle Interaction in the Solar Corona and WindThe Astrophysical Journal, 2003
- Instability of electromagnetic R-mode waves in a relativistic plasmaPhysics of Plasmas, 1998
- The role of negative energy waves in some instabilities of parallel flowsJournal of Fluid Mechanics, 1979
- Collisionless Damping of Hydromagnetic Waves in Relativistic Plasma. Weak Landau DampingThe Astrophysical Journal, 1973
- Resonant particle instabilities in a uniform magnetic fieldJournal of Plasma Physics, 1967