A self-consistent marginally stable state for parallel ion cyclotron waves

We derive an equation whose solutions describe self-consistent states of marginal stability for a proton-electron plasma interacting with parallel-propagating ion cyclotron (IC) waves. Ion cyclotron waves propagating through this marginally stable plasma will neither grow nor damp. The dispersion relation of these waves, ω(k), smoothly rises from the usual MHD behavior at small |k| to reach ω = Ωp as k → ± ∞. The proton distribution function has constant phase-space density along the characteristic resonant surfaces defined by this dispersion relation. Our equation contains a free function describing the variation of the proton phase-space density across these surfaces. Taking this free function to be a simple “box function”, we obtain specific solutions of the marginally stable state for a range of proton parallel betas. The phase speeds of these waves are larger than those given by the cold plasma dispersion relation, and the characteristic surfaces are more sharply peaked in the υ⊥ direction. The thres...

[1]  Jiansen He,et al.  POSSIBLE EVIDENCE OF ALFVÉN-CYCLOTRON WAVES IN THE ANGLE DISTRIBUTION OF MAGNETIC HELICITY OF SOLAR WIND TURBULENCE , 2011 .

[2]  D. Summers,et al.  Finite‐beta effects on quasi‐linear diffusion coefficients , 2011 .

[3]  Petr Hellinger,et al.  Evolution of the solar wind proton temperature anisotropy from 0.3 to 2.5 AU , 2007 .

[4]  P. Isenberg,et al.  RESONANT INTERACTIONS BETWEEN PROTONS AND OBLIQUE ALFVEN/ION-CYCLOTRON WAVES IN THE SOLAR CORONA AND SOLAR FLARES , 2010 .

[5]  P. Yoon,et al.  Analytic model of electromagnetic ion-cyclotron anisotropy instability , 2010 .

[6]  S. Gary,et al.  Proton temperature anisotropy in the magnetosheath: Hybrid simulations , 1996 .

[7]  Charles F. Kennel,et al.  Velocity Space Diffusion from Weak Plasma Turbulence in a Magnetic Field , 1966 .

[8]  S. Gary,et al.  MAGNETIC HELICITY SPECTRUM OF SOLAR WIND FLUCTUATIONS AS A FUNCTION OF THE ANGLE WITH RESPECT TO THE LOCAL MEAN MAGNETIC FIELD , 2011 .

[9]  P. Isenberg,et al.  Preferential Perpendicular Heating of Coronal Hole Minor Ions by the Fermi Mechanism , 2005 .

[10]  S. Gary,et al.  Mirror and ion cyclotron anisotropy instabilities in the magnetosheath , 1992 .

[11]  Dan Winske,et al.  The proton cyclotron instability and the anisotropy/β inverse correlation , 1994 .

[12]  R. Gendrin.  PITCH ANGLE DIFFUSION OF LOW-ENERGY PROTONS DUE TO GYRORESONANT INTERACTION WITH HYDROMAGNETIC WAVES. , 1968 .

[13]  N. A. Krall,et al.  Principles of Plasma Physics , 1973 .

[14]  J. Bortnik,et al.  Nonlinear evolution of EMIC waves in a uniform magnetic field: 1. Hybrid simulations , 2010 .

[15]  S. Gary,et al.  Simulations of ion cyclotron anisotropy instabilities in the terrestrial magnetosheath , 1993 .

[16]  Joseph Wang,et al.  Proton temperature anisotropy upper bound , 1997 .

[17]  J. Albert.  Using quasi‐linear diffusion to model acceleration and loss from wave‐particle interactions , 2004 .

[18]  S. Gary,et al.  The ion cyclotron anisotropy instability and the inverse correlation between proton anisotropy and proton beta , 1994 .

[19]  Danny Summers,et al.  Quasi‐linear diffusion coefficients for field‐aligned electromagnetic waves with applications to the magnetosphere , 2005 .

[20]  J. Steinberg,et al.  Proton temperature anisotropy constraint in the solar wind: ACE observations , 2001 .

[21]  P. Isenberg.  Turbulence-driven Solar Wind Heating and Energization of Pickup Protons in the Outer Heliosphere , 2005 .

[22]  S. Gary,et al.  Electromagnetic proton cyclotron instability: Proton velocity distributions , 1996 .

[23]  D. Mccomas,et al.  Hot proton anisotropies and cool proton temperatures in the outer magnetosphere , 1994 .

[24]  B. Anderson,et al.  Proton and helium cyclotron anisotropy instability thresholds in the magnetosheath , 1994 .

[25]  B. Anderson,et al.  A limited closure relation for anisotropic plasmas from the Earth’s magnetosheath* , 1994 .

[26]  C. Kennel,et al.  Resonantly unstable off-angle hydromagnetic waves , 1967, Journal of Plasma Physics.

[27]  J. Richardson,et al.  Turbulent Heating of the Solar Wind by Newborn Interstellar Pickup Protons , 2006 .

[28]  P. Isenberg,et al.  A KINETIC MODEL OF SOLAR WIND GENERATION BY OBLIQUE ION-CYCLOTRON WAVES , 2011 .

[29]  Brian J. Anderson,et al.  Bounded anisotropy fluid model for ion temperatures , 1994 .

[30]  S. Gary,et al.  Ion cyclotron anisotropy instabilities in the magnetosheath: Theory and simulations , 1993 .

[31]  Philip A. Isenberg,et al.  A dispersive analysis of bispherical pickup ion distributions , 1996 .

[32]  A. Lazarus,et al.  Solar wind proton temperature anisotropy: Linear theory and WIND/SWE observations , 2006 .

[33]  S. Peter Gary,et al.  Proton temperature anisotropy instabilities in the solar wind , 1976 .

[34]  P. Isenberg.  The kinetic shell model of coronal heating and acceleration by ion cyclotron waves: 3. The proton halo and dispersive waves , 2004 .

[35]  P. Isenberg,et al.  PREFERENTIAL ACCELERATION AND PERPENDICULAR HEATING OF MINOR IONS IN A COLLISIONLESS CORONAL HOLE , 2009 .

[36]  E. Quataert,et al.  Magnetic fluctuation power near proton temperature anisotropy instability thresholds in the solar wind. , 2009, Physical review letters.

[37]  J. Ogden,et al.  Electromagnetic ion cyclotron instability driven by ion energy anisotropy in high‐beta plasmas , 1975 .

[38]  C. Kennel,et al.  Resonant particle instabilities in a uniform magnetic field , 1967, Journal of Plasma Physics.

[39]  E. Marsch,et al.  On the temperature anisotropy of the core part of the proton velocity distribution function in the solar wind , 2004 .

[40]  S. Brecht,et al.  A simulation study of the Alfvén ion‐cyclotron instability in high‐beta plasmas , 1987 .

[41]  S. Cuperman.  Electromagnetic kinetic instabilities in multicomponent space plasmas: theoretical predictions and computer simulation experiments , 1981 .

[42]  E. Marsch,et al.  Anisotropy regulation and plateau formation through pitch angle diffusion of solar wind protons in resonance with , 2002 .

[43]  E. Marsch,et al.  Diffusion plateaus in the velocity distributions of fast solar wind protons , 2007 .

[44]  L. Yin,et al.  Electromagnetic proton cyclotron anisotropy instability: Wave‐particle scattering rate , 2000 .