The growth of the longitudinal beam–plasma instability in the presence of an inhomogeneous background

We study the longitudinal stability of beam–plasma systems in the presence of a density inhomogeneity in the background plasma. Previous works have focused on the non-relativistic regime where hydrodynamical models are used to evolve pre-existing Langmuir waves within inhomogeneous background plasmas. Here, for the first time we study the problem with kinetic equations in a fully relativistic way. We do not assume the existence of Langmuir waves, and we focus on the rate and the mechanism by which waves are excited in such systems from an initial perturbation. We derive the structure of the unstable modes and compute an analytical approximation for their growth rates. Our computation is limited to dilute and cold beams, and shows an excellent agreement with particle-in-cell simulations performed using the SHARP code. We show that, due to such an inhomogeneity, the virulent beam–plasma instabilities in the intergalactic medium are not suppressed but their counterparts in the solar wind can be suppressed as evidenced by propagating type-III solar radio bursts.

[1]  A. Lamberts,et al.  Constraints on the Intergalactic Magnetic Field from Bow Ties in the Gamma-Ray Sky , 2017, The Astrophysical Journal.

[2]  M. Pohl,et al.  Revisit of Nonlinear Landau Damping for Electrostatic Instability Driven by Blazar-induced Pair Beams , 2019, Proceedings of 36th International Cosmic Ray Conference — PoS(ICRC2019).

[3]  A. Lamberts,et al.  Missing Gamma-Ray Halos and the Need for New Physics in the Gamma-Ray Sky , 2018, The Astrophysical Journal.

[4]  D. Costantin,et al.  The Search for Spatial Extension in High-latitude Sources Detected by the Fermi Large Area Telescope , 2018, The Astrophysical Journal Supplement Series.

[5]  A. Lamberts,et al.  Growth of Beam–Plasma Instabilities in the Presence of Background Inhomogeneity , 2018, 1804.05071.

[6]  M. Pohl,et al.  The Electrostatic Instability for Realistic Pair Distributions in Blazar/EBL Cascades , 2018, 1803.02990.

[7]  Cosmological beam plasma instabilities , 2017 .

[8]  A. Lamberts,et al.  Importance of Resolving the Spectral Support of Beam-plasma Instabilities in Simulations , 2017, 1704.00014.

[9]  A. Lamberts,et al.  SHARP: A Spatially Higher-order, Relativistic Particle-in-cell Code , 2017, 1702.04732.

[10]  A. Lamberts,et al.  Bow Ties in the Sky. II. Searching for Gamma-Ray Halos in the Fermi Sky Using Anisotropy , 2017, 1702.02585.

[11]  A. V. B. Roderick,et al.  SHARP: A SPATIALLY HIGHER-ORDER, RELATIVISTIC PARTICLE-IN-CELL CODE , 2017 .

[12]  A. Lamberts,et al.  THE LINEAR INSTABILITY OF DILUTE ULTRARELATIVISTIC e± PAIR BEAMS , 2016, 1610.02040.

[13]  A. Lamberts,et al.  BOW TIES IN THE SKY. I. THE ANGULAR STRUCTURE OF INVERSE COMPTON GAMMA-RAY HALOS IN THE FERMI SKY , 2016, 1609.00387.

[14]  Kazem Ardaneh,et al.  COLLISIONLESS ELECTRON–ION SHOCKS IN RELATIVISTIC UNMAGNETIZED JET–AMBIENT INTERACTIONS: NON-THERMAL ELECTRON INJECTION BY DOUBLE LAYER , 2016, 1604.04388.

[15]  E. Quataert,et al.  PIC SIMULATIONS OF THE EFFECT OF VELOCITY SPACE INSTABILITIES ON ELECTRON VISCOSITY AND THERMAL CONDUCTION , 2016, 1602.03126.

[16]  F. Spanier,et al.  Energy loss in intergalactic pair beams: Particle-in-cell simulation , 2015, 1512.00662.

[17]  M. Pohl,et al.  EVOLUTION OF GLOBAL RELATIVISTIC JETS: COLLIMATIONS AND EXPANSION WITH kKHI AND THE WEIBEL INSTABILITY , 2015, 1511.03581.

[18]  K. Nishikawa,et al.  COLLISIONLESS WEIBEL SHOCKS AND ELECTRON ACCELERATION IN GAMMA-RAY BURSTS , 2015, 1507.05374.

[19]  A. Lamberts,et al.  THE EFFECT OF NONLINEAR LANDAU DAMPING ON ULTRARELATIVISTIC BEAM PLASMA INSTABILITIES , 2014, 1410.3797.

[20]  H. Reid,et al.  A review of solar type III radio bursts , 2014, 1404.6117.

[21]  L. Sironi,et al.  RELATIVISTIC PAIR BEAMS FROM TeV BLAZARS: A SOURCE OF REPROCESSED GeV EMISSION RATHER THAN INTERGALACTIC HEATING , 2013, 1312.4538.

[22]  A. Broderick,et al.  IMPLICATIONS OF PLASMA BEAM INSTABILITIES FOR THE STATISTICS OF THE FERMI HARD GAMMA-RAY BLAZARS AND THE ORIGIN OF THE EXTRAGALACTIC GAMMA-RAY BACKGROUND , 2013, 1308.0340.

[23]  V. Krasnoselskikh,et al.  INTERACTION OF ENERGETIC PARTICLES WITH WAVES IN STRONGLY INHOMOGENEOUS SOLAR WIND PLASMAS , 2013 .

[24]  F. Miniati,et al.  RELAXATION OF BLAZAR-INDUCED PAIR BEAMS IN COSMIC VOIDS , 2012, 1208.1761.

[25]  A. Broderick,et al.  THE COSMOLOGICAL IMPACT OF LUMINOUS TeV BLAZARS. I. IMPLICATIONS OF PLASMA INSTABILITIES FOR THE INTERGALACTIC MAGNETIC FIELD AND EXTRAGALACTIC GAMMA-RAY BACKGROUND , 2011, 1106.5494.

[26]  A. Broderick,et al.  THE COSMOLOGICAL IMPACT OF LUMINOUS TeV BLAZARS. III. IMPLICATIONS FOR GALAXY CLUSTERS AND THE FORMATION OF DWARF GALAXIES , 2011, 1106.5505.

[27]  A. Broderick,et al.  THE COSMOLOGICAL IMPACT OF LUMINOUS TeV BLAZARS. II. REWRITING THE THERMAL HISTORY OF THE INTERGALACTIC MEDIUM , 2011, 1106.5504.

[28]  V. Springel,et al.  The Lyman α forest in a blazar-heated Universe , 2011, 1107.3837.

[29]  L. Gremillet,et al.  Multidimensional electron beam-plasma instabilities in the relativistic regime , 2010 .

[30]  R. Shankar,et al.  Principles of Quantum Mechanics , 2010 .

[31]  D. Melrose.  Coherent emission , 2008, Proceedings of the International Astronomical Union.

[32]  P. Robinson,et al.  Eigenmode structure in solar-wind Langmuir waves. , 2008, Physical review letters.

[33]  E. Ramirez-Ruiz,et al.  e± Pair Loading and the Origin of the Upstream Magnetic Field in GRB Shocks , 2007, 0707.4381.

[34]  J. Sanderson,et al.  The Physics of Plasmas: Index , 2003 .

[35]  T. Sanderson,et al.  Wind Spacecraft Observations of Solar Impulsive Electron Events Associated with Solar Type III Radio Bursts , 1998 .

[36]  D. Gurnett,et al.  Energetic electrons and plasma waves associated with a solar type III radio burst , 1981 .

[37]  Charles K. Birdsall,et al.  Plasma self-heating and saturation due to numerical instabilities☆ , 1980 .

[38]  N. Panagia,et al.  Are Crab-type Supernova Remnants (Plerions) Short-lived? , 1978 .

[39]  D. Ryutov,et al.  Relaxation of Relativistic Electron Beam in a Plasma with Random Density Inhomogeneities , 1976 .

[40]  R. Sudan,et al.  Linear two-stream instability of warm relativistic electron beams , 1975 .

[41]  B. Breizman,et al.  Nonlinear Effects in the Interaction Between an Ultrarelativistic Electron Beam and a Plasma , 1972 .

[42]  V. Zakharov.  Collapse of Langmuir Waves , 1972 .

[43]  A. G. Greenhill,et al.  Handbook of Mathematical Functions with Formulas, Graphs, , 1971 .

[44]  B. Breizman,et al.  Quasilinear Relaxation of an Ultrarelativistic Electron Beam in a Plasma , 1971 .

[45]  A. Vedenov.  THEORY OF A WEAKLY TURBULENT PLASMA , 1967 .

[46]  David M. Miller,et al.  Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55) , 1965 .

[47]  D. Griffiths.  Introduction to Quantum Mechanics , 2016 .

[48]  V. Ginzburg,et al.  On the Possible Mechanisms of Sporadic Solar Radio Emission (Radiation in an Isotropic Plasma) , 1958 .